Interactions of a Light Hypersonic Jet with a Non-Uniform Interstellar Medium
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超声速型面可控喷管设计方法赵一龙;赵玉新;王振国;易仕和【摘要】提出了基于B-Spline曲线和特征线方法的超声速型面可控喷管设计方法,通过设置喷管轴向马赫数分布可以灵活地调整喷管的型面形状.数值验证结果表明,该方法不仅可以设计出高品质的喷管出口流场,而且能够实现喷管型面的灵活调整,可以获得长度与最短长度喷管一致,但流场品质更优的喷管.%A designing method of supersonic nozzle with controllable contour based on B-Spline curve and characteristic line algorithm is proposed. The contour of the nozzle was adjusted by assigning the distribution of Mach number on the nozzle ' s axis. The reliability of the designing method was validated by numerical simulation, which shows that the outflow of the nozzle with high quality can be produced and the contour can be adjusted freely. The result also shows that the nozzle designed by the proposed method can produce better flow than the minimal length nozzle ( MLN) with the same length.【期刊名称】《国防科技大学学报》【年(卷),期】2012(034)005【总页数】4页(P1-4)【关键词】超声速;喷管设计;B-Spline曲线;特征线方法【作者】赵一龙;赵玉新;王振国;易仕和【作者单位】国防科技大学航天与材料工程学院,湖南长沙 410073;国防科技大学航天与材料工程学院,湖南长沙 410073;国防科技大学航天与材料工程学院,湖南长沙 410073;国防科技大学航天与材料工程学院,湖南长沙 410073【正文语种】中文【中图分类】V434.1喷管是超声速风洞的核心部件,一般为对称构型,由收敛段(亚声速段)和膨胀段(超声速段)组成。
Acta Astronautica59(2006)181–191/locate/actaastroX-43A Hypersonic vehicle technology developmentRandall T.V oland∗,Lawrence D.Huebner,Charles R.McClintonNASA Langley Research Center,Hampton,VA,USAAbstractNASA recently completed two major programs in hypersonics:Hyper-X,with the record-breakingflights of the X-43A,and the next generation launch technology(NGLT)program.The X-43Aflights,the culmination of the Hyper-X program,were the first-ever examples of a scramjet engine propelling a hypersonic vehicle and provided unique,convincing,detailedflight data required to validate the design tools needed for design and development of future operational hypersonic airbreathing vehicles. Concurrent with Hyper-X,NASA’s NGLT program focused on technologies needed for future revolutionary launch vehicles. The NGLT was“competed”by NASA in response to the President’s redirection of the agency to space exploration,after making significant progress towards maturing technologies required to enable airbreathing hypersonic launch vehicles.NGLT quantified the benefits,identified technology needs,developed airframe and propulsion technology,chartered a broad University base,and developed detailed plans to mature and validate hypersonic airbreathing technology for space access.NASA is currently in the process of defining plans for a new hypersonic technology program.Details of that plan are not currently available.This paper highlights results from the successful Mach7and10flights of the X-43A,and the current state of hypersonic technology.©2006Published by Elsevier Ltd.1.IntroductionJulian Allen made an important observation in the 195825th Wright Brothers Lecture:“Progress in aero-nautics has been brought about more by revolutionary than evolutionary changes in methods of propulsion”[1].Steam engines replaced sails and introduced mass transportation on the sea and lead to the railroads.The internal combustion engine replaced the horse for pri-vate transportation and lead to the airplane.The jet en-gine replaced the piston engine,and revolutionized the airliner,taking it routinely above the weather and be-yond the seas.Modern rockets opened the space age for the bold and wealthy.In the21st century,revolution-ary applications of airbreathing propulsion will make space travel routine and intercontinental travel as easy as ∗Corresponding author.0094-5765/$-see front matter©2006Published by Elsevier Ltd. doi:10.1016/j.actaastro.2006.02.021intercity travel today.One of NASA’s focuses today remains the application of revolutionary propulsion systems for space transportation.Fig.1represents thefirst application of this revo-lutionary propulsion technology to space access mis-sions with an airline-sized space vehicle that serves as a high-speed,high-altitude,first-stage launch platform for an expendable or reusable rocket-powered second stage[2].This modest approach significantly improves launch safety and reliability.In addition,it places the world on a new path to reduced cost for space access which cannot be achieved with evolutionary improve-ments of current systems.Benefits of airbreathing launch systems are safety, missionflexibility,robustness,and operating costs[2] as highlighted in Fig.2.Safety benefits result from char-acteristics such as abort capability and power density. Horizontal takeoff and powered landing allows ability to abort over most of theflight,both ascent and decent.182R.T.Voland et al./Acta Astronautica59(2006)181–191Fig.1.Revolutionary launch vehicle.High lift-to-drag ratio(L/D)allows longer-range glide for a large landing footprint.Power density,or the quan-tity of propellant pumped,is110that of a vertical take offrocket due to lower thrust loading(T/W),smaller vehi-cle weight and higher specific impulse(lsp),defined as thrust per pound of propellant—a measure of efficiency. Power density is a large factor in catastrophic failures. Recent analysis indicates that safety increases by sev-eral orders of magnitude are possible using airbreath-ing systems.Missionflexibility results from horizontal takeoff and landing,the large landing(unpowered)foot-print and high L/D.Utilization of aerodynamic forces rather than thrust allows efficient orbital plane changes during ascent,and a wider launch window.Robustness and reliability can be built into airbreathing systems be-cause of large margins and reduced weight-growth sen-sitivity,and the low thrust required for smaller,horizon-tal takeoff systems.Cost models under development for airbreathing launch systems indicate about one order-of-magnitude reduction in operating cost is possible. The development of reusable launch vehicles holds great promise as the key to unlocking the vast potential of space for business exploitation.Only when access to space is assured in a system that provides routine operation with airline-like safety and affordable cost will businesses be willing to take the risks and make the investments necessary to realize this great potential. Rocket-powered vehicles are approaching their limits in terms of these parameters[2],switching to a new approach is the only way to achieve significant im-provements.Airbreathing vehicles that are capable of hypersonic speeds can transform access to space,just like turbojets transformed the airline business.NASA has funded hypersonic vehicle and propul-sion technology for over40years,aiming at futuristic space launch capabilities[3].This work represents the next frontier in air vehicle design.Recent US industry focus has been on avionics,stealth,and methods of making the last generation of aircraft more effective. Evolutionary vehicle changes will give way to revo-lutionary changes when a new propulsion system is available.Studies by the next generation launch tech-nology(NGLT)program reconfirmed that hypersonic systems using turbine-based“low-speed”engines com-bined with scramjets for higher speed operation,up to at least Mach7and eventually to Mach13–15,are the preferred long-term approach for airbreathing space access vehicles.Clearly,these turbine-based systems are also needed for supersonic cruise/hypersonic dash or pure hypersonic cruise aircraft of the future(Fig.3). NASA funded scramjet technology development, focused mostly on the propulsion cycle efficiency with numerous ground tests in wind tunnels(Fig.4)over the past40years[3].Starting in the mid1960s,NASA built and tested a hydrogen-fueled and-cooled scramjet engine that verified scramjet cycle efficiency,struc-tural integrity,first-generation design tools,and engine system integration.Starting in the early1970s,NASA designed and demonstrated afixed-geometry,airframe-integrated scramjet“flowpath”capable of propelling a hypersonic vehicle from Mach4to7in wind tunnel tests.Starting in the mid1980s,NASA teamed with the Department of Defense in the National AeroSpace Plane(NASP)program to demonstrate hypersonic technologies required for a hypersonic,scramjet-based, combined-cycle powered,single-stage-to-orbit launch vehicle.Under the NASP program NASA focused on engine definition and testing for both the aerodynamicR.T.Voland et al./Acta Astronautica 59(2006)181–191183Fig.2.Benefits of hypersonic airbreathing vehicles.lines/cycle efficiency and hydrogen-cooled engine structure.NASA developed the concept for the Hyper-X (X-43A)program in 1995–1996as a result of several blue-ribbon panel recommendations that flight exper-iments of airframe-integrated scramjet-propulsion sys-tems be the next major step in hypersonic research.The experts agreed that,at a minimum and as a first step,a vehicle must fly with an airframe-integrated supersonic-combustion ramjet (scramjet)propulsion system.Con-sequently,NASA initiated the Hyper-X program [1]to provide the flight data to validate the design tools and methods to be used in the development of future hy-personic vehicles.The program goals were established to provide performance data to reduce development risks for subsequent,operational vehicles;to advance performance-prediction capabilities for airbreathing hy-personic vehicles;to flight-validate airframe-integrated scramjet performance and design methods;and to flight-validate other selected,key technologies.The Hyper-X team developed the X-43A as a small-scale research vehicle to provide flight data for a hydrogen-fueled,airframe-integrated scramjet engine [4].In addition,aerodynamic,thermal,structural,guid-Fig.3.Future hypersonic air vehicles.ance,flush-air-data-system,and other data were to be obtained.Test plans called for boosting each of three X-43A research vehicles to the required test condition by a drop-away booster.The resulting 12ft long vehicle is illustrated in Fig.5.The development of the X-43A and its systems are detailed in Refs.[5–13].The NASA Hyper-X program employed a low-cost approach to design,build,and flight test three small,184R.T.Voland et al./Acta Astronautica 59(2006)181–191Fig.4.Historicalperspective.Fig.5.X-43A vehicle geometry.airframe-integrated scramjet-powered research vehicles at Mach 7and 10.The research vehicles were dropped from the NASA Dryden B-52,rocket-boosted to test point by a modified Pegasus first stage,separated from the booster,and then operated in autonomous flight.Tests were conducted at approximately 100,000ft at a dynamic pressure of about 1000psf.2.Flight resultsThe first Mach 7flight was attempted June 2,2001.This flight failed when the launch vehicle went outofFig.6.Flight 2trajectory.control early in the flight.The second flight occurred March 27,2004.The flight was completely success-ful,and demonstrated acceleration of the X-43A vehicle during climbing flight at Mach 6.83.Preparations for the third flight started before the second flight was com-pleted.The third flight occurred November 16,2004.This final flight successfully demonstrated cruise thrust at Mach 9.68.Many technical results from these flights will be discussed herein.Details on the preparation and execution of these flights are addressed in Refs.[14–17].The second flight trajectory is illustrated in Fig.6.The launch vehicle was dropped from the B-52flying at Mach 0.8and 40,000ft.The booster ignited after 5s free fall to about 39,500ft.The launch vehicle executedR.T.Voland et al./Acta Astronautica 59(2006)181–191185a 1.9g pull-up,followed by a 0.7g pushover to achieve nearly level flight at 95,000ft.Following burnout and stage separation,the engine opened for about 30s:5s of fuel-off tare,11s of powered flight (at about Mach 6.83and dynamic pressure of 980psf),another 5s of unpowered steady tare,followed by 10s of parameter identification (PID)maneuvers [18].The engine cowl then closed,and the vehicle flew a controlled descent over 300NM to “splash-down”in the Pacific Ocean.The powered portion of this flight included 1.5s for ignition,followed by hydrogen fuel ramp up and ramp down [19]to generate a large database.The flight 3trajectory was somewhat different than flight 2.The B-52flight conditions were the same;how-ever,the launch vehicle executed a 2.5g pull-up to a flight path angle of over 30◦,followed by 0.5g push over to achieve nearly level flight at 110,000ft.Follow-ing burnout and stage separation,the engine opened for about 20s:3s of fuel-off tare,11s of powered flight (at about Mach 9.68and dynamic pressure of 930psf),and another 6s of unpowered steady tare.(No cowl-open PID maneuvers were performed due to cowl survival concerns.)The engine cowl closed,and the vehicle flew a controlled descent over 800NM to “splash-down”in the Pacific Ocean.During descent,PID maneuvers were successfully performed at each successively decreasing Mach number [18].The powered portion of flight in-cluded 5s of silane-piloted operation at two fuel equiv-alence ratio settings,followed by hydrogen-only fueled operation at two settings,then ramp down [19].This conservative approach assured good data before trying to operate the small engine without piloted fuel.The following discussion highlights flight 2and flight 3data and results from design tool validation studies.The flight results contain much commonality,sotheFig.7.Lower surface instrumentation.results are presented in terms of flight sequence and technology areas,including results from both successful flights.These are designated as F2for the successful second flight that targeted Mach 7,and F3for the third flight that targeted Mach 10.3.Experimental measurementsThe X-43A vehicles were well instrumented,with over 200measurements of surface pressure;over 100thermocouples (T/C)to measure surface,structure and environmental temperatures;and discrete local strain measurements on the hot wings and tail structure.The flight management unit included a highly accurate 3-axis measurement of acceleration and rates.In addition,over 500data words were extracted from the flight com-puter.Instrumentation density is illustrated in Fig.7by external and internal wall pressure and temperature on the lower body surface.Internal engine instrumentation on the body side is more dense in order to capture in-ternal flow details of the engine.All of the data from the X-43A flights were suc-cessfully telemetered and captured by multiple air and ground stations.The instrumentation health and performance were excellent:very few lost instru-ments/parameters,extremely low noise content,no significant calibration issues,no significant delay or time-lag issues,and extremely limited TM drop outs.Accuracy of these measurements benefited from day-of-flight atmospheric measurements by weather bal-loons.These measurements provide a small change in flight Mach number and dynamic pressure vis-à-vis atmospheric conditions and winds from historical atmospheric tables.Flight 2best estimated trajectory (BET)resulted in higher dynamic pressure and Mach186R.T.Voland et al./Acta Astronautica59(2006)181–191Fig.8.X-43A poweredflight video from army HALO aircraft. number,but only a trivial change in angle of attack (AOA).Flight3BET resulted in lower dynamic pressure and higher Mach number and AOA.Theflight trajectory reconstruction is discussed in Ref.[22].The data obtained from theseflights meets the pri-mary Hyper-X program objective:validation of design methods including experimental,analytical and compu-tational methods.The data was released to the US hy-personic community in the form of complete classified data packages[20,21]to more than20US Government and industrial entities and well over50classified and unclassified papers and presentations.3.1.X-43A freeflightFollowing stage separation from the rocket booster (boost and stage separation discussed in Refs.[23–27]), the X-43A F2research vehicle stabilized to2.5◦AOA, and the engine cowl was opened.After5s of tare force measurements,the engine was ignited with a pyrophoric silane-hydrogen fuel mixture(left side of Fig.8),then switched to pure hydrogen fuel for about10s of pow-eredflight.The contrail from the pure-hydrogen fuel was not visible in the raw image from the high-altitude observatory(HALO)aircraft(right side of Fig.8). Following poweredflight,with the engine cowl open, the vehicle performed pre-programmed PID maneuvers to quantify the X-43A aerodynamic stability and con-trol derivatives[18].These maneuvers lasted15s,after which the engine cowl was closed,the vehicle glided another300miles,and splashed into the Pacific Ocean. During the descent of bothflights,the vehicle contin-ued to perform a series of PID maneuvers at each de-creasing Mach number to Mach2.This segment of the flight provided a large,unique aerodynamic database for sharp leading edge lifting body configurations that will be used to validate wind tunnel data and computa-tional tools.3.1.1.Scramjet powered vehicle performanceFor Mach7,flight2the X-43A was commanded tofly at2.5◦AOA during the cowl-open portion of theflight.However,as the fuel is turned-on/off and thethrottle adjusted,the pitching moment changes signifi-cantly.Fig.9illustrates the measured AOA—from cowlopen to fuel off and the start of the Mach7PID maneu-vers.During the scramjet-powered segment,the AOAwas maintained to2.5◦±0.2◦,except duringflameout. Some efforts were made in theflight control systemto provide feed-forward control.For Mach10,flight3,the vehicle was commanded tofly at1.0◦AOA dur-ing the cowl open segment.The vehicle maintainedpitch control about the same as during the poweredsegment of F2.For both F2and F3the fuel sequencing for pow-eredflight starts with a silane/hydrogen mixture toassure ignition,then transitions to pure hydrogen fuel.The ignition sequence for F2requires about 1.5s.With transition to pure hydrogen fuel,the throttle isramped up to either a predetermined or controlledmaximum value,and then decreased as the fuel isdepleted from the tanks.The resulting vehicle per-formance is characterized by vehicle acceleration,asshown in Fig.9.The ignition sequence for F3wasdifferent—the silane remains on for thefirst two fueledconditions,requiring5s of piloted data.Then the sameequivalence ratio test conditions were run with onlyhydrogen.The green band in Fig.9illustrates pretest MonteCarlo predictions of acceleration(using an unclassifiedrepresentative propulsion database).The heavy blue linedepictsflight data trends.The vehicle deceleration isgreater than predicted,both with cowl closed and open[28]because of two factors:(1)actualflight conditionsvs.predicted(23of the error),and(2)vehicle drag ishigher than predicted(13of the error).However,the drag was within the uncertainty associated with the wind tun-nel database[30,p.831].The uncertainty was not re-solved/reduced beforeflight because it did not threaten the outcome of the engine tests.Flight data will be used to help resolve the wind tunnel uncertainty for future flights/missions.Under scramjet power the F2vehicle acceleration was positive,and varies with throttle position.The increment in acceleration is about as predicted,which confirms the predicted engine thrust to within less than2%[5]. It should be noted that the engine throttle was varied over a wide range without engine unstart orflame-out. Under scramjet power the F3vehicle cruised(thrust =drag)at the reference fuel equivalence ratio with2%R.T.Voland et al./Acta Astronautica 59(2006)181–191187Fig.9.X-43A axial acceleration and angle of attack during powered flight:(a)Flight 2,Mach 6.83;(b)Flight 3,Mach9.68.Fig.10.X-43flowpath pressure distribution:design throttle position:(a)F2,Mach 6.83;(b)F3,Mach 9.68.silane pilot,and engine thrust was in agreement with predictions [31].The predicted scramjet performance is also confirmed by the excellent comparison of pre-test predicted and flight scramjet flowpath wall pressure (Fig.10).Data is presented from vehicle nose to tail for F2(Fig.10(a)),and from cowl leading edge to cowl trailing edge for F3(Fig.10(b)).The Mach 7data is clearly operating in “dual mode,”with sonic flow in the isolator dissipating the inlet shocks.The Mach 10data exhibits classical pure supersonic combustion mode,and the combustor pressure is shock dominated.The pretest prediction for Mach 7was made using the SRGULL code,with com-bustion efficiency determined by analysis of multiple wind tunnel tests,most notably,the 8-foot high temper-ature tunnel (8-Ft.HTT)test of the Hyper-X flight en-gine (HXFE)on the vehicle flowpath simulator (VFS).The Mach 10pretest prediction was performed using a combination of CFD tools,with the SHIP code used for the combustor.The reaction efficiency used in the SHIP code was derived from analysis of data from the HYPULSE scramjet module test.Storch [5]and Ferle-mann [31]present a detailed discussion of these codes and the pretest predictions for F2and F3,respectively.3.1.2.Wind tunnel/flight scramjet comparisonComparison of the wall pressure measured in four wind tunnel tests with F2data is included in Refs.[6,32].Likewise,results from shock tunnel tests are compared with F3data in Ref.[33].Tests with nearly identical fuel equivalence ratio were selected for com-parison.Fig.11illustrates the resulting comparison of188R.T.Voland et al./Acta Astronautica 59(2006)181–191Fig.11.X-43A flowpath pressure distribution comparison with wind tunnel data:design throttle position.internal wall pressure for the 8-Ft HTT test of the HXFE on the VFS and is typical of results from other wind tunnel tests.These data show that the flowfield in the isolator was separated on the cowl side,and featured a supersonic stream,evidenced by shock structure on the body side through most of the combustor length.In other words,the isolator was not “pushed”very hard for this design condition.Storch discusses the implication of this agreement,and the impact on observed combus-tor performance in Ref.[5].Rogers reported a similar trend for the Mach 10,flight 3data [33].These results show that ground tests are representative of flight,if careful attention is paid to modeling the appropriate flow phenomena.3.1.3.Aerothermal/thermo-structural analysis and boundary layer transitionThe design of the X-43A research vehicle structure and thermal protection system depended greatly on accurate estimation of the aerothermal environment,which required understanding of the boundary layer state during the entire flight.For design purposes,the lower surface flowpath into the inlet was assumed tur-bulent due to the inclusion of boundary layer trips near the forebody leading edge.The trips were required to insure the forebody boundary layer was turbulent for mitigation of any flow separations along the engine flowpath due to adverse pressure gradients.A substan-tial research and design effort was executed to ensure proper sizing of the trips with minimum induced trip drag [30,p.853].The upper surface,however,was predicted to be laminar during the Mach 7test point,based on a pre-flight trajectory using a classical cor-relation methodology (momentum thickness Reynolds number over Mach number of 305).Fig.12provides upper surface temperature time his-tories during the entire flight 2trajectory from thepointFig.12.Flight 2X-43A upper surface temperatures from B-52drop tosplash.Fig.13.Flight 3nose LE temperature confirms thermal model.of release from the B-52.The three upper surface T/C were evenly spaced along the vehicle centerline start-ing about midpoint for T/C#19and ending nearR.T.Voland et al./Acta Astronautica 59(2006)181–191189Fig.14.Flight 2X-43A post test CFD solutions:(a)unpowered;cowl closed and open tare;(b)fueled;and (c)comparison with flight acceleration.the trailing edge for T/C#21.Note that by the time the cowl opens and the scramjet is ignited,the entire up-per surface appears to be laminar,as indicated by the dramatic temperature decrease that begins at about 70s for the farthest forward T/C and 85s for the farthest after T/C.Likewise,at about 240s the boundary layer transitions from laminar to turbulent as the vehicle de-celerates.These results are discussed relative to pre-test predictions in detail in Ref.[34]along with discussions of the trip effectiveness on the lower surface.3.1.4.Thermal loadsPreliminary and continuing assessment of thermal loads for the F2and F3,compared with design values,are documented in various sources [35–38].These doc-uments show that the engineering approach used in the design and development of the flight vehicles was gener-ally conservative.However,some temperature measure-ments were higher than anticipated in regions of steep gradients,particularly late in the boost.The effect of “actual boost trajectory”vs.“design trajectory”is con-tinuing to be studied.Results to date generally confirm prediction methods.Accuracy of the predictions ap-pears significantly better than the assumed uncertaintyfor both Mach 7and 10flights.For example,Fig.13illustrates heating to the leading edge of the vehicle pre-dicted using the “as flown”trajectory,with measured temperature within the C–C leading edge material.Ad-jacent nodes from the FEA model bracket the measured temperatures over the boost and scramjet-powered flight at Mach 10.3.2.Post test analysisPost test analysis of the flight data is underway at NASA Langley Research Center and elsewhere.This is required to model the “as flown”trajectory to properly assess thermal loads;to assess inlet mass capture at exactly the flight condition evaluated [39]using analyt-ical methods;to evaluate the boundary layer state for BLT assessment;and to assess the overall vehicle drag,engine force,and vehicle acceleration/deceleration at exact flight conditions and control surface plete nose-to-tail CFD solutions for the actual flight condition are discussed in Refs.[39,40].These solutions,for cowl closed,cowl open,and powered operation show excellent agreement (within a few percent)with measured acceleration/deceleration in flight (Fig.14).They also demonstrate the significant190R.T.Voland et al./Acta Astronautica59(2006)181–191Fig.15.X-43A lsp scaled to vision vehicle. increase in computational throughput,which permit full 3-D solutions for the entire X-43A vehicle,which were not possible at earlier stages of the Hyper-X program. Another post-test analysis was to determine the en-gine lsp as tested,and“scale”to a vision vehicle,remov-ing effects of small scale,cold fuel,fuel equivalence ratio,operating dynamic pressure,etc.This analysis is discussed in Ref.[41]and unclassified results shown in Fig.15.The effective impulse developed in this scal-ing study will certainly set the standard for follow-on vehicle configurations.4.Summary and conclusionsThe second and thirdflights of the X-43A were successfully completed on March27and November 16,2004.This was the world’sfirst scramjet-powered aircraft,and is recognized as the world’s fastest“jet-powered aircraft.”All phases of these twoflights were performed as planned.The booster delivered the stack to the stage separation point at slightly lower Mach number and dynamic pressure than expected.The stage separation system performed smoothly,accomplish-ing thefirst known successful non-symmetric,high-dynamic pressure,high Mach number stage separation. Vehicleflight controls held AOA commanded to within a few tenths of a degree.Both vehicle drag and lift were slightly higher than predicted,but within the design uncertainty.The F2vehicle accelerated under its own power for15miles in11s.The F3vehicle demonstrated powered cruise at Mach9.68,at110,000ft altitude, covering20miles in10.5s of poweredflight.Scramjet thrust measured matched prediction to within better than2%.A significant,excellent-quality database was generated,which is only now starting to be evaluated. Analysis and validation of design methods are con-tinuing,but the conclusion is clear:scramjet-powered vehicles can meet the performance claims and chal-lenges of the next generation of air vehicles! References[1]H.Julian Allen,Hypersonicflight and the reentry problem,Thetwenty-first Wright brothers lecture,Journal of the Aerospace Sciences25(4)(1958).[2]V.J.Bilardo,J.L.Hunt,N.T.Lovell,G.Maggio,A.W.Wilhite,L.E.McKinney,The benefits of hypersonic airbreathing launch systems for access to space,AIAA2003-5265,July2003, Huntsville,AL.[3]C.R.McClinton,E.H.Andrews,J.L.Hunt,Engine developmentfor space access:past,present and future,26th JANNAF Airbreathing Propulsion Subcommittee(APS)Meeting,April 8–12,2001,Destin,FL.[4]C.R.McClinton,V.L.Rausch,Hyper-X program status,26th JANNAF Airbreathing Propulsion Subcommittee(APS) Meeting,April8–12,2002,Destin,FL.[5]A.R.Storch,S.M.Ferlemann,R.D.Bittner,Hyper-X,Mach7scramjet preflight predictions versusflight results,28th JANNAF Airbreathing Propulsion Subcommittee Meeting,June 13–17,2005,Charleston,SC.[6]S.M.Ferlemann,R.T.V oland,K.Cabell,D.Whitte,E.Ruf,Hyper-X Mach7scramjet pretest predictions and ground toflight comparison,AIAA2005-3322,Presented at13th International Space Planes and Hypersonic Systems and Technology Conference,May2005,Capua,Italy.[7]P.Ferlemann,Hyper-X Mach10scramjet preflight predictionsvs.flight data,AIAA2005-3352,Presented at13th International Space Planes and Hypersonic Systems and Technology Conference,May2005,Capua,Italy.[8]M.E.Redifer,Y.Lin,J.Kelly,M.Hodge, C.Barklow,The Hyper-Xflight system validation program,Hyper-X Program Office Report:HX-849,2003(Also:Hyper-Xfluid/environmental systems:ground andflight operation and lessons learned,28th JANNAF Airbreathing Propulsion Subcommittee Meeting,June13–17,2005,Charleston,SC.)[9]P.T.Harsha,L.C.Keel, A.Castrogiovanni,R.T.Sherrill,X-43A vehicle design and manufacture,28th JANNAF Airbreathing Propulsion Subcommittee Meeting,June13–17, 2005,Charleston,SC.(See also:L.C.Keel,X-43A research vehicle design and manufacture,AIAA2005-3334;P.T.Harsha, L.C.Keel, A.Castrogiovanni,R.T.Sherrill,X-43A vehicle design and manufacture,Presented at13th International Space Planes and Hypersonic Systems and Technology Conference, May2005,Capua,Italy.)[10]L.C.Keel,X-43A design and manufacture(Mach7and10),28th JANNAF Airbreathing Propulsion Subcommittee Meeting, June13–17,2005,Charleston,SC.[11]P.J.Joyce,J.B.Pomroy,L.Grindle,The Hyper-X launchvehicle:challenges and design considerations for hypersonic flight testing,AIAA2005-3333,Presented at13th International Space Planes and Hypersonic Systems and Technology Conference,May2005,Capua,Italy.[12]P.J.Joyce,J.B.Pomroy,Launch vehicle design challengesfor hypersonicflight testing(Mach7and10),28th JANNAF Airbreathing Propulsion Subcommittee Meeting,June13–17, 2005,Charleston,SC.[13]X-43A Mishap Investigation Board,Report of Findings:X-43AMishap,NASA,Washington,DC,May8,2003.。
空气动力学家英语Aerodynamics: The Unsung Heroes of Modern EngineeringAerodynamics, a field of study that delves into the intricate interactions between objects and the air that surrounds them, has long been a crucial component of modern engineering. From the sleek designs of high-performance aircraft to the streamlined silhouettes of racing cars, the principles of aerodynamics have been instrumental in pushing the boundaries of technological innovation.At the heart of this field are the unsung heroes – the aerodynamicists, a dedicated group of scientists and engineers who have dedicated their careers to understanding the complexities of fluid dynamics and its application in the real world. These individuals, armed with a deep understanding of physics, mathematics, and computational analysis, work tirelessly to optimize the performance and efficiencyof a wide range of systems, from the smallest components to the largest structures.One of the primary responsibilities of an aerodynamicist is to analyze the flow of air around an object, whether it's a vehicle, a building, or even a simple household item. By using advanced computationalfluid dynamics (CFD) simulations and wind tunnel testing, they can identify areas of high pressure, low pressure, and turbulence, which can have a significant impact on the object's performance and stability.For example, in the design of a high-performance race car, aerodynamicists play a crucial role in ensuring that the vehicle's body and components are shaped in a way that minimizes drag and maximizes downforce. This delicate balance between these two forces can mean the difference between a car that dominates the track and one that struggles to keep up with the competition.Similarly, in the design of aircraft, aerodynamicists work closely with aerospace engineers to create airframes and wing configurations that maximize lift and minimize drag, allowing the aircraft to achieve greater speeds, higher altitudes, and improved fuel efficiency. This knowledge is not only critical for commercial and military aviation but also for the development of cutting-edge technologies, such as unmanned aerial vehicles (UAVs) and hypersonic aircraft.But the impact of aerodynamics extends far beyond the transportation industry. In the field of architecture, aerodynamicists collaborate with designers to create buildings and structures that are not only aesthetically pleasing but also energy-efficient and resilient to environmental forces, such as wind and rain. By understanding theway air flows around a building, they can optimize the placement of windows, doors, and other features to improve natural ventilation and reduce the need for energy-intensive cooling systems.Even in the world of sports, aerodynamics plays a crucial role. Sportswear manufacturers work closely with aerodynamicists to develop clothing and equipment that minimize air resistance and maximize the athlete's performance. From the dimpled surface of a golf ball to the streamlined designs of cycling helmets, the principles of aerodynamics are constantly being applied to push the boundaries of human athletic achievement.Despite the profound impact of their work, aerodynamicists often operate in the background, their contributions overshadowed by the more visible aspects of engineering and design. However, their dedication and expertise are essential to the ongoing progress of technology and the improvement of our daily lives.As we continue to push the boundaries of what is possible, the role of the aerodynamicist will only become more critical. From the development of sustainable energy solutions to the exploration of space, these unsung heroes will be at the forefront of the next generation of technological advancements, using their deep understanding of fluid dynamics to unlock new possibilities and transform the world around us.。
流体力学中英文术语Index 翻译(Fluid Mechanics)Absolute pressure,绝对压力(压强)Absolute temperature scales, 绝对温标Absolute viscosity, 绝对粘度Acceleration加速度centripetal, 向心的convective, 对流的Coriolis, 科氏的field of a fluid, 流场force and,作用力与……local, 局部的Uniform linear, 均一线性的Acceleration field加速度场Ackeret theory, 阿克莱特定理Active flow control, 主动流动控制Actuator disk, 促动盘Added mass, 附加质量Adiabatic flow绝热流with friction,考虑摩擦的isentropic,等熵的air, 气体with area changes, 伴有空间转换Bemoullii’s equation and, 伯努利方程Mach number relations,马赫数关系式,pressure and density relations, 压力-速度关系式sonic point,critical values, 音速点,临界值,stagnation enthalpy, 滞止焓Adiabatic processes, 绝热过程Adiabatic relations, 绝热关系Adverse pressure gradient, 逆压力梯度Aerodynamic forces, on road vehicles, 交通工具,空气动力Aerodynamics, 空气动力学Aeronautics, new trends in, 航空学,新趋势Air空气testing/modeling in, 对……实验/建模useful numbers for, 关于……的有用数字Airbus Industrie, 空中客车产业Aircraft航行器airfoils机翼new designs, 新型设计Airfoils, 翼型aspect ratio (AR), 展弦比cambered, 弧形的drag coefficient of , 阻力系数early, 早期的Kline-Fogleman, 克莱恩-佛莱曼lift coefficient, 升力系数NACA,(美国) 国家航空咨询委员会separation bubble, 分离泡stalls and, 失速stall speed, 失速速度starting vortex, 起动涡stopping vortex, 终止涡Airfoil theory, 翼型理论flat-plate vortex sheet theory, 平板面涡理论Kutta condition, 库塔条件Kutta-Joukowski theorem, 库塔-儒科夫斯基定理1thick cambered airfoils, 厚弧面翼型thin-airfoils, 薄翼型wings of finite span, 有限展宽的翼型A-380 jumbo jet, 大型喷气式客机Alternate states, 交替状态American multiblade farm HA WT, 美式农庄多叶水平轴风机Angle of attack, 攻角Angle valve, 角阀Angular momentum角动量differential equation of , 关于…的微分方程relation/theorem, 联系/理论Annular strips, 环形带Applied forces, linear momentum, 外加力,线性冲力Apron,of a dam, 大坝的护坦Arbitrarily moving/deformable control volume, 任意运动/可变形控制体Arbitrary fixed control volume, 任意固定控制体Arbitrary viscous motion, 随机粘性运动Archimedes, 阿基米德Area changes, isentropic flow. 域变换,等熵流Aspect ratio (AR), 展弦比Automobiles, aerodynamic forces on, 汽车,气动力A verage velocity, 平均速度Axial-flow pumps. 轴流泵Axisymmetric flow, stream function 轴对称流,流函数Axisymmetric Potential flow, 轴对称有势流hydrodynamic mass, 水力学质量Point doublet, 点偶极子point source or sink, 点源与点汇spherical Polar coordinates and, 球极坐标uniform stream in the x direction, x方向的均匀流uniform stream plus a point doublet, 均匀流附加点偶极子uniform stream plus a point source, 均匀流附加点源BBackward-curved impeller blades, 后向曲叶轮片,Backwater curves, 回水曲线Basic equations, non dimensional, 基本方程,无量纲的Bernoulli obstruction theory, 伯努利障碍理论Bernoulli's equation, 伯努利方程with adiabatic and isentropic steady flow, as绝热、等熵稳态流frictionless flow, 无摩擦流assumptions/restrictions for, 假想/约束HGLs and EGLs, 水力坡度线和能量梯度线steady flow energy and, 定常流动能量in rotating coordinates. 在旋转坐标下,Best efficiency point (BEP), pumps, 最佳效率点,Betz number, 贝兹数Bingham plastic idealization, 宾汉塑性理想化,Biological drag reduction, 生物学阻力衰减Blade angle effects, on pump head, 叶片安装角效率,泵头处Blasius equation, 布拉修斯方程Body drag, at high Mach numbers, 机体阻力,在高马赫数下Body forces, 体力Boeing Corp., 波音公司Boundaries, of systems, 边界,系统Boundary conditions. 边界条件,differential relations for fluid flow, 流体的微分关系nondimensionalizalion and, 无量纲化Boundary element method (BEM), 边界元方法2Boundary layer (BL) analysis, 边界层分析boundary layer flows, 边界层流动boundary layer separation on a half body, 边界层半体分离displacement thickness, 位移厚度drag force and, 阻力equations, 方程flat-plate. 平板,Karman's analysis, 卡门分析momentum integral estimates, 动量积分估计momentum integral relation. 动量积分关系momentum integral theory, 动量积分理论pressure gradient 压力梯度separation on a half body, 半模分离skin friction coefficient, 表面摩擦系数two-dimensional flow derivation, 二维流推导Boundary layers with Pressure gradient, 边界层压力梯度adverse gradient, 反梯度favorable gradient, 正梯度laminar integral theory, 层流积分理论,nozzle-diffuser example,喷口扩散算例Bourdon tube, 波登管Bow shock wave, 弓形激波Brake horsepower,制动马力Broad-crested weirs, 宽顶堰Buckingham Pi Theorem, 白金汉定理Bulb Protrusion, 球形突出物(船头)Bulk modulus. 体积模量Buoyancy, 浮力Buoyant particles, local velocity and, 悬浮颗粒,局部速度Buoyant rising light spheres, 浮力作用下自由上升的球体Butterfly valve, 蝶形阀CCambered airfoils, 弓型翼Cauchy-Riemann equations, 柯西-黎曼方程Cavitation/Cavitation number, 气穴/气蚀数Celsius temperature scales, 摄氏温标Center of buoyancy, 浮心Center of Pressure (CP),压力中心,压强中心Centrifugal pumps, 离心泵backward-curved impeller blades, 后曲叶轮片blade angle effects on pump head, 泵头处叶片安装角效率brake horsepower, 制动马力circulation losses, 环量损失closed blades, 闭叶片efficiency of, 效率的elementary pump theory. 基泵理论Euler turbomachine equations, 欧拉涡轮机方程eye of the casing, 泵体通风口friction losses, 摩擦损失hydraulic efficiency, 水力[液压]效率mechanical efficiency.机械效率open blades, 开放式叶片output parameters, 输出参数power, delivered, 功率,传递pump surge, 泵涌,scroll section of casing, 卷形截面,泵体,shock losses, 激波损失vaneless, 无叶片的3volumetric efficiency, 容积效率[系数]water horsepower, 水马力Centripetal acceleration, 向心加速度Channel control Point, 传送控制点Characteristic area. external flows, 特征区域,外流Chezy coefficient, 薛齐系数Chezy formula, 薛齐公式Chezy coefficient,薛齐系数flow in a Partly full circular pipe, 流体非充满的圆管流Manning roughness correlation. 曼宁粗糙度关系,normal depth estimates, 法向深度估计Choking, 壅塞;堵塞of compressors, 压缩机的due to friction, compressible duct and, 由于摩擦,可压缩管的isentropic flow with area changes, 变横截面积等熵流simple heating and, 单纯加热Circular cylinder, flow with circulation. 圆柱体,Circulation环量and flow past circular cylinder, 流体经过圆柱体losses, in centrifugal pumps, 损失,离心泵potential flow and, 有势流Circumferential pumps, 环型泵Classical venturi, 标准文氏管Closed blades, centrifugal pumps. 闭叶片,离心泵Closed-body shapes, 闭体外形,circular cylinder, with circulation, 圆柱体,环量Kelvin oval, 开尔文椭圆,Kutta-Joukowski lift theorem,库塔-儒科夫斯基升力定理,Potential flow analogs, 有势流模拟Rankine oval, 兰金椭圆rotating cylinders. lift and drag, 旋转柱体,升力与阻力Coanda effect, 柯恩达效应( 沿物体表面的高速气流在Cobra P-530 supersonic interceptor, 眼镜蛇超音速拦截机Coefficient matrix. 系数矩阵Coefficient of surface tension, 表面张力系数Coefficient of viscosity, 粘滞系数Commercial CFD codes, viscous flow, 商业的计算流体力学代码,粘流Commercial ducts, roughness values for, 商业管道Composite-flow, open channels, 合成流,开槽道Compressibility, non dimensional. 压缩性,无量纲Compressibility effects, 压缩效果Compressible duct flow with friction, 伴有摩擦的可压缩管流adiabatic, 绝热的, 隔热的choking and, 壅塞;堵塞isothermal flow in long pipelines, 管线中的等温流动,long pipelines, isothermal flow in, 管线,等温流动,mass flow for a given pressure drop, 给定压降下质量流动minor losses in, 最小损失subsonic inlet, choking due to friction, 亚音速进口,摩擦引发阻塞,supersonic inlet, choking due to friction, 超音速进口,摩擦引发阻塞,Compressible flow, 可压缩流flow with friction摩擦流choking and, 壅塞;堵塞converging-diverging nozzles, 拉瓦尔喷管converging nozzles, 收缩喷嘴Fanno flow, 法诺流动,gas flow correction factor, 气流校正参数hypersonic flow, 高超音速气流4incompressible flow, 不可压缩流isentropic.等熵的isentropic Process, 等熵过程,Mach number, 马赫数normal shock wave. 正激波the perfect gas, 理想气体Prandtl-Meyer waves. 普朗特-麦耶膨胀波shock waves. 激波specific-heat ratio, 比热比speed of sound and,声速subsonic, 亚音速的supersonic,超音速的transonic, 跨音速的two-dimensional supersonic, 二维超音速的Compressible gas flow correction factor, 可压缩气流校正因数Compressors, 压缩机Computational fluid dynamics (CFD), 计算流体力学pump simulations, 泵模拟viscous flow. 粘流Concentric annulus, viscous flows in, 同心环Cone flows, 锥体绕流Conformal mapping, 保角映射[变换] Conservation of energy, 能量守恒定律Conservation of mass. 质量守恒定律Consistent units, 相容单元Constants, 常量dimensional, 空间的pure, 纯粹的Constant velocity, fluid flow at, 常速度, 等速度Constructs, 结构Contact angle, 交会角Continuity, 连续性,equation of ,方程nondimensionalization and, 无量纲的Continuum, fluid as, 连续流体Contraction flow, 收缩流动Control Point, channel, 控制点,管道Control volume analysis,控制体分析angular momentum theorem. 角动量定理,arbitrarily moving/deformable CV,任意运动/可变形控制体arbitrarily fixed control volume, 任意固定控制体conservation of mass, 质量守恒定律control volume moving at constant velocity, 控制体以等速运动control volume of constant shape but variable velocity作变速运动的刚性控制体energy equation. 能量方程introductory definitions, 介绍性定义linear momentum equation. 线性动量方程,one-dimensional fixed control volume, 一维固定控制体,one-dimensional flux term approximations, 一维通量项近似Physical laws. 物理定律。
跨越千年飞天梦主要内容英文回答:Across Millennia, the Dream of Soaring Takes Flight.Humankind's fascination with the heavens has sparked an enduring dream of flight. The celestial expanse has always beckoned us to conquer its vastness. Across cultures and civilizations, the pursuit of aerial locomotion has persisted, fueled by a relentless drive to transcend our terrestrial limitations.Throughout history, the human imagination has soared on wings of ingenuity. From the ancient Greek myth of Icarus and Daedalus to the 15th-century sketches of Leonardo da Vinci, the concept of human flight has captivated our minds. In the early 19th century, the invention of the hot air balloon brought the dream closer to reality, offering a tantalizing glimpse of what was possible. But it was notuntil the advent of powered flight in the early 20thcentury that the dream of soaring through the skies truly took flight.The Wright brothers, Orville and Wilbur, made historyon December 17, 1903, when they achieved the first successful flight of a heavier-than-air aircraft. Their iconic "Flyer" airplane, powered by a gasoline engine, took off from Kitty Hawk, North Carolina, and flew for 12 seconds, covering a distance of 120 feet. This momentousfeat marked a pivotal moment in human history, forever altering our perception of the possibilities of air travel.In the decades that followed, aviation technology advanced at an astonishing pace. Airplanes became faster, more reliable, and more efficient. The invention of the jet engine in the 1940s ushered in the era of supersonic flight, enabling commercial airliners to cross oceans in a matterof hours. And in the late 20th century, the space shuttle program pushed the boundaries of human endeavor even further, allowing astronauts to travel beyond Earth's atmosphere and explore the vast expanse of space.Today, air travel has become an integral part of modern life. Commercial airplanes transport millions of passengers and cargo worldwide every day, connecting people, cultures, and economies. The dream of flight has been realized on an unprecedented scale, opening up new possibilities for exploration, trade, and communication.But the pursuit of flight continues to drive human innovation. The development of electric aircraft, autonomous drones, and hypersonic technology is pushing the limits of what is possible in the realm of aerial locomotion. As we look to the future, it is clear that the dream of soaring through the skies will continue to inspire and captivate generations to come.中文回答:跨越千年飞天梦。
On the Interactions of Light GravitinosT.E.Clark1,Taekoon Lee2,S.T.Love3,Guo-Hong Wu4Department of PhysicsPurdue UniversityWest Lafayette,IN47907-1396AbstractIn models of spontaneously broken supersymmetry,certain light gravitino processes are governed by the coupling of its Goldstino components.The rules for constructing SUSY and gauge invariant actions involving the Gold-stino couplings to matter and gaugefields are presented.The explicit oper-ator construction is found to be at variance with some previously reported claims.A phenomenological consequence arising from light gravitino inter-actions in supernova is reexamined and scrutinized.1e-mail address:clark@2e-mail address:tlee@3e-mail address:love@4e-mail address:wu@1In the supergravity theories obtained from gauging a spontaneously bro-ken global N=1supersymmetry(SUSY),the Nambu-Goldstone fermion, the Goldstino[1,2],provides the helicity±1degrees of freedom needed to render the spin3gravitino massive through the super-Higgs mechanism.For a light gravitino,the high energy(well above the gravitino mass)interactions of these helicity±1modes with matter will be enhanced according to the su-persymmetric version of the equivalence theorem[3].The effective action de-scribing such interactions can then be constructed using the properties of the Goldstinofields.Currently studied gauge mediated supersymmetry breaking models[4]provide a realization of this scenario as do certain no-scale super-gravity models[5].In the gauge mediated case,the SUSY is dynamically broken in a hidden sector of the theory by means of gauge interactions re-sulting in a hidden sector Goldstinofield.The spontaneous breaking is then mediated to the minimal supersymmetric standard model(MSSM)via radia-tive corrections in the standard model gauge interactions involving messenger fields which carry standard model vector representations.In such models,the supergravity contributions to the SUSY breaking mass splittings are small compared to these gauge mediated contributions.Being a gauge singlet,the gravitino mass arises only from the gravitational interaction and is thus farsmaller than the scale √,where F is the Goldstino decay constant.More-2over,since the gravitino is the lightest of all hidden and messenger sector degrees of freedom,the spontaneously broken SUSY can be accurately de-scribed via a non-linear realization.Such a non-linear realization of SUSY on the Goldstinofields was originally constructed by Volkov and Akulov[1].The leading term in a momentum expansion of the effective action de-scribing the Goldstino self-dynamics at energy scales below √4πF is uniquelyfixed by the Volkov-Akulov effective Lagrangian[1]which takes the formL AV=−F 22det A.(1)Here the Volkov-Akulov vierbein is defined as Aµν=δνµ+iF2λ↔∂µσν¯λ,withλ(¯λ)the Goldstino Weyl spinorfield.This effective Lagrangian pro-vides a valid description of the Goldstino self interactions independent of the particular(non-perturbative)mechanism by which the SUSY is dynam-ically broken.The supersymmetry transformations are nonlinearly realized on the Goldstinofields asδQ(ξ,¯ξ)λα=Fξα+Λρ∂ρλα;δQ(ξ,¯ξ)¯λ˙α= F¯ξ˙α+Λρ∂ρ¯λ˙α,whereξα,¯ξ˙αare Weyl spinor SUSY transformation param-eters andΛρ≡−i Fλσρ¯ξ−ξσρ¯λis a Goldstinofield dependent translationvector.Since the Volkov-Akulov Lagrangian transforms as the total diver-genceδQ(ξ,¯ξ)L AV=∂ρ(ΛρL AV),the associated action I AV= d4x L AV is SUSY invariant.The supersymmetry algebra can also be nonlinearly realized on the matter3(non-Goldstino)fields,generically denoted byφi,where i can represent any Lorentz or internal symmetry labels,asδQ(ξ,¯ξ)φi=Λρ∂ρφi.(2) This is referred to as the standard realization[6]-[9].It can be used,along with space-time translations,to readily establish the SUSY algebra.Under the non-linear SUSY standard realization,the derivative of a matterfield transforms asδQ(ξ,¯ξ)(∂νφi)=Λρ∂ρ(∂νφi)+(∂νΛρ)(∂ρφi).In order to elim-inate the second term on the right hand side and thus restore the standard SUSY realization,a SUSY covariant derivative is introduced and defined so as to transform analogously toφi.To achieve this,we use the transformation property of the Volkov-Akulov vierbein and define the non-linearly realized SUSY covariant derivative[9]Dµφi=(A−1)µν∂νφi,(3) which varies according to the standard realization of SUSY:δQ(ξ,¯ξ)(Dµφi)=Λρ∂ρ(Dµφi).Any realization of the SUSY transformations can be converted to the standard realization.In particular,consider the gauge covariant derivative,(Dµφ)i≡∂µφi+T a ij A aµφj,(4)4with a=1,2,...,Dim G.We seek a SUSY and gauge covariant deriva-tive(Dµφ)i,which transforms as the SUSY standard ing the Volkov-Akulov vierbein,we define(Dµφ)i≡(A−1)µν(Dνφ)i,(5) which has the desired transformation property,δQ(ξ,¯ξ)(Dµφ)i=Λρ∂ρ(Dµφ)i, provided the vector potential has the SUSY transformationδQ(ξ,¯ξ)Aµ≡Λρ∂ρAµ+∂µΛρAρ.Alternatively,we can introduce a redefined gaugefieldV aµ≡(A−1)µνA aν,(6) which itself transforms as the standard realization,δQ(ξ,¯ξ)V aµ=Λρ∂ρV aµ, and in terms of which the standard realization SUSY and gauge covariant derivative then takes the form(Dµφ)i≡(A−1)µν∂νφi+T a ij V aµφj.(7) Under gauge transformations parameterized byωa,the original gaugefield varies asδG(ω)A aµ=(Dµω)a=∂µωa+gf abc A bµωc,while the redefinedgaugefield V aµhas the Goldstino dependent transformation:δG(ω)V aµ= (A−1)µν(Dνω)a.For all realizations,the gauge transformation and SUSY transformation commutator yields a gauge variation with a SUSY trans-formed value of the gauge transformation parameter,δG(ω),δQ(ξ,¯ξ)=δG(Λρ∂ρω−δQ(ξ,¯ξ)ω).(8) 5If we further require the local gauge transformation parameter to also trans-form under the standard realization so thatδQ(ξ,¯ξ)ωa=Λρ∂ρωa,then the gauge and SUSY transformations commute.In order to construct an invariant kinetic energy term for the gaugefields, it is convenient for the gauge covariant anti-symmetric tensorfield strength to also be brought into the standard realization.The usualfield strengthF a αβ=∂αA aβ−∂βA aα+if abc A bαA cβvaries under SUSY transformations asδQ(ξ,¯ξ)F aµν=Λρ∂ρF aµν+∂µΛρF aρν+∂νΛρF aµρ.A standard realization of thegauge covariantfield strength tensor,F aµν,can be then defined asF aµν=(A−1)µα(A−1)νβF aαβ,(9) so thatδQ(ξ,¯ξ)F aµν=Λρ∂ρF aµν.These standard realization building blocks consisting of the gauge singlet Goldstino SUSY covariant derivatives,Dµλ,Dµ¯λ,the matterfields,φi,their SUSY-gauge covariant derivatives,Dµφi,and thefield strength tensor,F aµν, along with their higher covariant derivatives can be combined to make SUSY and gauge invariant actions.These invariant action terms then dictate the couplings of the Goldstino which,in general,carries the residual consequences of the spontaneously broken supersymmetry.A generic SUSY and gauge invariant action can be constructed[9]asI eff=d4x detA L eff(Dµλ,Dµ¯λ,φi,Dµφi,Fµν)(10)6where L effis any gauge invariant function of the standard realization basic building ing the nonlinear SUSY transformationsδQ(ξ,¯ξ)detA=∂ρ(ΛρdetA)andδQ(ξ,¯ξ)L eff=Λρ∂ρL eff,it follows thatδQ(ξ,¯ξ)I eff=0.It proves convenient to catalog the terms in the effective Lagranian,L eff, by an expansion in the number of Goldstinofields which appear when covari-ant derivatives are replaced by ordinary derivatives and the Volkov-Akulov vierbein appearing in the standard realizationfield strengths are set to unity. So doing,we expandL eff=L(0)+L(1)+L(2)+···,(11)where the subscript n on L(n)denotes that each independent SUSY invariant operator in that set begins with n Goldstinofields.L(0)consists of all gauge and SUSY invariant operators made only from light matterfields and their SUSY covariant derivatives.Any Goldstinofield appearing in L(0)arises only from higher dimension terms in the matter covariant derivatives and/or thefield strength tensor.Taking the light non-Goldstinofields to be those of the MSSM and retaining terms through mass dimension4,then L(0)is well approximated by the Lagrangian of the mini-mal supersymmetric standard model which includes the soft SUSY breaking terms,but in which all derivatives have been replaced by SUSY covariant ones and thefield strength tensor replaced by the standard realizationfield7strength:L(0)=L MSSM(φ,Dµφ,Fµν).(12) Note that the coefficients of these terms arefixed by the normalization of the gauge and matterfields,their masses and self-couplings;that is,the normalization of the Goldstino independent Lagrangian.The L(1)terms in the effective Lagrangian begin with direct coupling of one Goldstino covariant derivative to the non-Goldstinofields.The general form of these terms,retaining operators through mass dimension6,is given byL(1)=1[DµλαQµMSSMα+¯QµMSSM˙αDµ¯λ˙α],(13)Fwhere QµMSSMαand¯QµMSSM˙αcontain the pure MSSMfield contributions to the conserved gauge invariant supersymmetry currents with once again all field derivatives being replaced by SUSY covariant derivatives and the vector field strengths in the standard realization.That is,it is this term in the effective Lagrangian which,using the Noether construction,produces the Goldstino independent piece of the conserved supersymmetry current.The Lagrangian L(1)describes processes involving the emission or absorption of a single helicity±1gravitino.Finally the remaining terms in the effective Lagrangian all contain two or more Goldstinofields.In particular,L(2)begins with the coupling of two8Goldstinofields to matter or gaugefields.Retaining terms through mass dimension8and focusing only on theλ−¯λterms,we can writeL(2)=1F2DµλαDν¯λ˙αMµν1α˙α+1F2Dµλα↔DρDν¯λ˙αMµνρ2α˙α+1F2DρDµλαDν¯λ˙αMµνρ3α˙α,(14)where the standard realization composite operators that contain matter and gaugefields are denoted by the M i.They can be enumerated by their oper-ator dimension,Lorentz structure andfield content.In the gauge mediated models,these terms are all generated by radiative corrections involving the standard model gauge coupling constants.Let us now focus on the pieces of L(2)which contribute to a local operator containing two gravitinofields and is bilinear in a Standard Model fermion (f,¯f).Those lowest dimension operators(which involve no derivatives on f or¯f)are all contained in the M1piece.After application of the Goldstino field equation(neglecting the gravitino mass)and making prodigious use of Fierz rearrangement identities,this set reduces to just1independent on-shell interaction term.In addition to this operator,there is also an operator bilinear in f and¯f and containing2gravitinos which arises from the product of det A with L(0).Combining the two independent on-shell interaction terms involving2gravitinos and2fermions,results in the effective actionIf¯f˜G˜G =d4x−12F2λ↔∂µσν¯λf↔∂νσµ¯f9+C ffF2(f∂µλ)¯f∂µ¯λ,(15)where C ff is a model dependent real coefficient.Note that the coefficient of thefirst operator isfixed by the normaliztion of the MSSM Lagrangian. This result is in accord with a recent analysis[10]where it was found that the fermion-Goldstino scattering amplitudes depend on only one parameter which corresponds to the coefficient C ff in our notation.In a similar manner,the lowest mass dimension operator contributing to the effective action describing the coupling of two on-shell gravitinos to a single photon arises from the M1and M3pieces of L(2)and has the formIγ˜G˜G =d4xCγF2∂µλσρ∂ν¯λ∂µFρν+h.c.,(16)with Cγa model dependent real coefficient and Fµνis the electromagnetic field strength.Note that the operator in the square bracket is odd under both parity(P)and charge conjugation(C).In fact any operator arising from a gauge and SUSY invariant structure which is bilinear in two on-shell gravitinos and contains only a single photon is necessarily odd in both P and C.Thus the generation of any such operator requires a violation of both P and ing the Goldstino equation of motion,the analogous term containing˜Fµνreduces to Eq.(16)with Cγ→−iCγ.Recently,there has appeared in the literature[11]the claim that there is a lower dimensional operator of the form˜M2F2∂νλσµ¯λFµνwhich contributes to the single photon-102gravitino interaction.Here˜M is a model dependent SUSY breaking massparameter which is roughly an order(s)of magnitude less than √.¿Fromour analysis,we do notfind such a term to be part of a SUSY invariant action piece and thus it should not be included in the effective action.Such a term is also absent if one employs the equivalent formalism of Wess and Samuel [6].We have also checked that such a term does not appear via radiative corrections by an explicit graphical calculation using the correct non-linearly realized SUSY invariant action.This is also contrary to the previous claim.There have been several recent attempts to extract a lower bound on the SUSY breaking scale using the supernova cooling rate[11,12,13].Unfortu-nately,some of these estimates[11,13]rely on the existence of the non-SUSY invariant dimension6operator referred to ing the correct low en-ergy effective lagrangian of gravitino interactions,the leading term coupling 2gravitinos to a single photon contains an additional supression factor ofroughly Cγs˜M .Taking√s 0.1GeV for the processes of interest and using˜M∼100GeV,this introduces an additional supression of at least10−12in the rate and obviates the previous estimates of a bound on F.Assuming that the mass scales of gauginos and the superpartners of light fermions are above the core temperature of supernova,the gravitino cooling of supernova occurs mainly via gravitino pair production.It is interesting to11compare the gravitino pair production cross section to that of the neutrino pair production,which is the main supernova cooling channel.We have seen that for low energy gravitino interactions with matter,the amplitudes for gravitino pair production is proportional to1/F2.A simple dimensional analysis then suggests the ratio of the cross sections is:σχχσνν∼s2F4G2F(17)where GF is the Fermi coupling and√s is the typical energy scale of theparticles in a supernova.Even with the most optimistic values for F,thegravitino production is too small to be relevant.For example,taking √F=100GeV,√s=.1GeV,the ratio is of O(10−11).It seems,therefore,thatsuch an astrophysical bound on the SUSY breaking scale is untenable in mod-els where the gravitino is the only superparticle below the scale of supernova core temperature.We thank T.K.Kuo for useful conversations.This work was supported in part by the U.S.Department of Energy under grant DE-FG02-91ER40681 (Task B).12References[1]D.V.Volkov and V.P.Akulov,Pis’ma Zh.Eksp.Teor.Fiz.16(1972)621[JETP Lett.16(1972)438].[2]P.Fayet and J.Iliopoulos,Phys.Lett.B51(1974)461.[3]R.Casalbuoni,S.De Curtis,D.Dominici,F.Feruglio and R.Gatto,Phys.Lett.B215(1988)313.[4]M.Dine and A.E.Nelson,Phys.Rev.D48(1993)1277;M.Dine,A.E.Nelson and Y.Shirman,Phys.Rev.D51(1995)1362;M.Dine,A.E.Nelson,Y.Nir and Y.Shirman,Phys.Rev.D53,2658(1996).[5]J.Ellis,K.Enqvist and D.V.Nanopoulos,Phys.Lett.B147(1984)99.[6]S.Samuel and J.Wess,Nucl.Phys.B221(1983)153.[7]J.Wess and J.Bagger,Supersymmetry and Supergravity,second edition,(Princeton University Press,Princeton,1992).[8]T.E.Clark and S.T.Love,Phys.Rev.D39(1989)2391.[9]T.E.Clark and S.T.Love,Phys.Rev.D54(1996)5723.[10]A.Brignole,F.Feruglio and F.Zwirner,hep-th/9709111.[11]M.A.Luty and E.Ponton,hep-ph/9706268.13[12]J.A.Grifols,R.N.Mohapatra and A.Riotto,Phys.Lett.B400,124(1997);J.A.Grifols,R.N.Mohapatra and A.Riotto,Phys.Lett.B401, 283(1997).[13]J.A.Grifols,E.Masso and R.Toldra,hep-ph/970753.D.S.Dicus,R.N.Mohapatra and V.L.Teplitz,hep-ph/9708369.14。
七年级英语作文介绍歼二十全文共6篇示例,供读者参考篇1The J-20 Mighty Dragon: China's Amazing Stealth Fighter JetHi everyone! Today I want to tell you all about one of the coolest and most impressive fighter jets in the world - the Chengdu J-20 "Mighty Dragon" stealth fighter made in China. It looks just like something out of a sci-fi movie!The J-20 is a big deal because it's China's first ever stealth fighter jet. Stealth technology makes planes harder to detect on radar, meaning enemies can't easily see them coming. The J-20's shape and special coatings help make it stealthy and hard to spot.This fighter is massive - its wings stretch almost 13 meters across! It's over 20 meters long too. Despite being so huge, it can reach incredible speeds of over 2,500 km/h. That's over twice as fast as the fastest cars on Earth! The J-20 can fly higher than 60,000 feet as well, which is about 20 times higher than a commercial airliner flies.What makes the J-20 so special though is that it combines stealth capabilities with being a multi-role fighter. That means it's designed to do all sorts of different missions - not justair-to-air combat against other fighter jets, but also bombing targets on the ground, reconnaissance to collect intelligence, and more. Very versatile!The J-20 packs a serious punch with its weaponry too. It can be armed with a deadly assortment of air-to-air missiles to take down enemy planes, as well as laser-guided bombs and anti-ship missiles. There are even rumors it may one day be able to launch hypersonic weapons that fly at over 6 times the speed of sound! Those would be some of the fastest missiles ever.Probably the most amazing part of the J-20 though is the amazing technology inside its cockpit. While older jets have analog dials and displays, the J-20's cockpit is fully digital with wide panoramic screens giving the pilot a 360-degree view around the jet. It has the world's most advanced avionics for things like communications, navigation, and electronic warfare systems.One system I find especially cool is called the Electro-Optical Targeting System. It uses infrared and laser sensors to detect and track targets for the jet's weapons at extremely long ranges, inany weather conditions. Another rad piece of tech is the J-20's Active Electronically Scanned Array radar, which rapidly searches and tracks multiple targets simultaneously while being harder for enemies to detect.So how did China's "Mighty Dragon" come to be? Well, the J-20 program secretly began way back in the late 1990s. Engineers studied the latest stealth technology, including taking a close look at an American F-117 Nighthawk stealth fighter that crashed in Serbia in 1999. In the early 2000s, they began putting together designs for their own stealthy fighter.The J-20's first flight wasn't until 2011, when it took off from the Chengdu Aircraft Corporation's airfield. At first, it was just a technology demonstrator to test out stealth, engines, avionics and other systems. But over the years, the design was refined through multiple improved prototypes.Finally, in 2017 the J-20 entered operational service with the People's Liberation Army Air Force. The first combat-ready unit was the 9th Air Brigade based in Wuhu, Anhui province. Since then, over 150 J-20s have been produced for the Chinese military, with the fleet continuing to grow rapidly.China isn't just using the J-20 within its own borders though. The jets have been taking part in long-range exercises and drillsaround Taiwan, the South China Sea, and other potential future battlegrounds. They flex China's military muscle and work on tactics like penetrating advanced air defenses.So in the eyes of a kid like me, what's not to love about the J-20? It looks awesome, it goes supersonically fast, it has epic weapons, and its tech gives it incredible capabilities unseen in other jets. The J-20 really drives home how incredibly advanced China's aviation industry has become in a short period of time.While I'm just a student now, I can't wait to see what else China's aerospace engineers come up with in the years ahead. Maybe I'll even get to pilot one of these mighty dragons myself one day! Who knows what future fighter jets will be capable of - but I bet whatever comes next will be just as exciting as the J-20. Thanks for reading!篇2The J-20: China's Cutting-Edge Fighter JetHave you ever seen a fighter jet roaring through the skies, leaving behind a trail of vapor like a dragon breathing fire? That's how I imagine the J-20, China's most advanced fighter jet, to be like. It's a plane that's got some serious cool factor, and I'm going to tell you all about it!The J-20 is a stealth fighter jet, which means it's designed to be hard to spot on radar. It has a unique shape that helps it evade detection, with sleek curves and angles that make it look like something straight out of a sci-fi movie. The body is made of special materials that absorb or deflect radar waves, making it almost invisible to enemy radars. How awesome is that?But the J-20 isn't just about looking cool; it's also incredibly fast and maneuverable. It can reach speeds of up to Mach 2.5, which means it can fly at two and a half times the speed of sound! That's faster than most other fighter jets out there. And with its advanced thrust vectoring system, it can make sharp turns and execute complex maneuvers that would leave other planes in the dust.One of the most impressive features of the J-20 is its advanced avionics and sensor suite. It has a cutting-edge radar system that can detect targets from incredibly long distances, and it can track multiple targets simultaneously. It also has advanced electronic warfare capabilities that can jam enemy radar and communications systems, giving it a serious advantage in combat situations.But what really sets the J-20 apart is its weapons payload. This fighter jet can carry a wide variety of air-to-air andair-to-ground missiles, as well as precision-guided bombs and other munitions. It's like having a whole arsenal of destruction at your fingertips. And with its internal weapons bays, it can carry these weapons while still maintaining its stealthy profile.Now, you might be wondering, "Why does China need such an advanced fighter jet?" Well, the answer is pretty simple: to protect its airspace and defend its national interests. With tensions rising in the Asia-Pacific region and increasing military competition, having a state-of-the-art fighter jet like the J-20 is crucial for maintaining a strong defense capability.But the J-20 isn't just about military might; it's also a symbol of China's technological prowess and aerospace industry. Developing a cutting-edge fighter jet like this requires years of research, billions of dollars in investment, and some of the brightest minds in engineering and aerospace. The fact that China has been able to produce the J-20 is a testament to its growing technological capabilities and its ambition to become a global leader in advanced manufacturing.But regardless of these criticisms, there's no denying that the J-20 is a remarkable achievement for China's aerospace industry. It's a symbol of the country's technological ambitions and a clearindication that it's not content to play second fiddle to anyone when it comes to military hardware.So, the next time you see a sleek, stealthy fighter jet streaking across the sky, remember that it might just be the J-20 – China's cutting-edge answer to the world's most advanced fighter jets. And who knows, maybe one day I'll get the chance to pilot one of these bad boys myself! (Well, a kid can dream, right?)篇3The Mighty J-20: China's Cutting-Edge Stealth FighterHave you ever dreamed of soaring through the clouds at supersonic speeds in an incredibly advanced fighter jet? Well, get ready to be blown away by the amazing Chengdu J-20 –China's first-ever stealth fighter! This awesome plane is like something straight out of a futuristic movie.Let me tell you all about the mind-blowing capabilities of the J-20. First off, it's a 5th generation fighter which means it has the latest and greatest technology. One of its most incredible features is stealth. The J-20 is covered in special radar-absorbing materials and has a unique shape that makes it really hard to detect on radar. It's like a ninja in the sky!The engines on this jet are insanely powerful too. It can reach incredible speeds of over 1,500 mph! That's almost double the speed of sound. Just imagine how fast you'd have to go to keep up with the J-20. You'd get soaked by a tsunami of sonic booms! The engines also allow for super maneuverability so the J-20 can pull off extreme aerial stunts.But what really makes the J-20 stand out are its awesome weapons. It's loaded with a deadly arsenal of air-to-air missiles to take out enemy planes from huge distances. The J-20 has special concealment bays to hide its missiles too so they're extra stealthy. And that's not all - it can also carry laser-guided bombs and anti-ship missiles to blow up targets on the ground or at sea. This fighter is like having a chunky video game weapon in real life!The cockpit interior is just as high-tech as the rest of the jet. The pilot has multiple digital displays showing radar, maps, targets and tons of other data. The controls are easy to use too, with a futuristic side-stick instead of a traditional joystick. It's like flying a extremely powerful video game simulator!Building a jet as amazing as the J-20 takes some serious effort though. Thousands of engineers, designers and workers were involved in developing it. The first test flight happened wayback in 2011 and it took years of further testing before the J-20 entered full military service in 2017.Even after all that work, the designers are still upgrading it with new abilities like bigger fuel tanks for longer range. Future versions might even be able to operate from aircraft carriers! China is also working on an advanced two-seat model for things like electronic warfare.So why did China build such an incredibly powerful fighter like the J-20? Well, it gives them a huge advantage over other airforces that don't have stealth jets yet. The J-20 can sneak past enemy radars and air defenses to kick some serious tail! It shows that China is a major force in military aviation technology.Just imagine how awesome it would be to pilot one of these stealth fighters. You'd be the ultimate ninja of the skies! Nothing could stop you as you blasted across the clouds, dodging missiles and outrunning everything else in the air. Every dogfight would be like an epic scene from a superhero movie.Even if I don't get to fly it myself, I'm still in awe of the J-20 and what it represents. This fighter proves that China can build incredibly sophisticated technology that rivals or even beats what other countries have. It makes me proud of my nation's capabilities in aviation and defense.The J-20 is definitely one of the most spectacular and futuristic warplanes ever created. With its mind-blowing speed, stealth, maneuverability and firepower, it can overcome nearly any airborne threat. And I bet the pilots feel like the ultimate maverick fighter aces when they take the J-20's controls!Stealth jets like this are crucial for a country to maintain a powerful military and keep its people safe. While I hope wars can be avoided, I feel a lot better knowing China has a jet as incredible as the J-20 protecting its skies. The J-20 makes me feel like my country is strong and secure.I could keep gushing about the awesomeness of the Chengdu J-20 all day, but I think you get the idea. This fighter is truly an amazing technological marvel and a new icon of Chinese power and innovation. The J-20's combination of cutting-edge stealth with brute force makes it arguably the most formidable jet in the modern age of aerial warfare. Just writing about it makes me wish I could see one of these bad boys in action!篇4The Amazing J-20 Stealth Fighter JetHave you ever dreamed of flying a super cool, top secret stealth fighter jet? Well, China has an incredible plane called theJ-20 that would blow your mind! It's one of the most advanced fighter jets in the world.The J-20 is designed to avoid being detected by enemy radar. Its sleek body is carefully shaped to minimize its radar cross-section, making it stealthy. The jet is coated in special radar-absorbing materials and uses other high-tech features to stay under the radar. This allows the J-20 to sneak up on targets without being seen.But the J-20 isn't just a silent hunter – it also packs a serious punch! It can be armed with a deadly assortment of air-to-air and air-to-ground missiles and precision guided bombs. The jet has an internal weapons bay to carry its munitions, further reducing its radar signature. With so much firepower, the J-20 can take on the best fighter jets of any other nation.And boy, can this jet fly! Powered by two hugely powerful turbofan engines, the J-20 can reach incredible speeds of over Mach 2 – that's more than twice the speed of sound! It can zoom across unfriendly airspace before anyone knows what hit them. The engines also give the J-20 a fantastic range, allowing it to patrol the skies for hours.The J-20's maneuverability is just as mind-blowing as its speed. With excellent aerodynamics and the ability to use thrustvectoring, it can pull off incredible high-g turns and aerial maneuvers that would make your head spin! Highly swept wings and all-moving tail surfaces ensure the J-20 can turn and burn better than virtually any other fighter.But it's not just about brawn – the J-20 is a technological marvel too. Its glass cockpit is packed with all the latest digital displays, keeping the pilot aware of everything they need to know. The jet can fuse data from multiple sensors into an integrated picture for unbeatable situational awareness. It even has an advanced digital flight control system that can keep the jet stable and recoverable at extremely high angles of attack.With all these incredible features, you'd think the J-20 would need a huge crew to operate. But remarkably, it only needs a single pilot! Through automation and well-designed interfaces, a lone aviator can fly this fearsome fighter all by themselves. The pilot does get assistance from a digital assistant and intelligent decision aids, but they're firmly in control.The J-20 really raised the bar when it comes to stealth and sensor fusion. But what's even more astounding is that it's made in China – not in Russia or the USA like most advanced jets! It shows just how quickly China's aerospace industry is advancing.The J-20 already outclasses many older fighters, and future upgraded variants will likely become even more capable.I don't know about you, but the J-20 sounds like the ultimate fighter jet to me! With its combination of stealth, speed, maneuverability, sensors and striking power, it can take on pretty much any opponent. Just imagining piloting a J-20 at Mach 2, dodging missiles and lining up that kill shot gets my heart racing with excitement!篇5The Incredible J-20: China's Cutting-Edge Stealth Fighter JetHey there, fellow students! Today, I want to share with you something truly amazing – the J-20 stealth fighter jet. This incredible aircraft is like nothing we've ever seen before, and it's all thanks to the hard work and ingenuity of Chinese scientists and engineers.Let me start by telling you what "stealth" means. You know how in video games or movies, some characters can turn invisible or blend into their surroundings? Well, stealth technology in aviation works kind of like that. It allows planes to avoid being detected by enemy radar systems, making them harder to track and target.The J-20 is packed with cutting-edge stealth features that make it practically invisible to radar. Its body is designed with special shapes and materials that absorb or deflect radar signals, making it incredibly difficult for enemies to spot it on their screens. Imagine being able to fly undetected through the skies –how cool is that?But the J-20 isn't just about stealth; it's also a powerhouse of advanced technology. It's equipped with two powerful engines that can propel it at supersonic speeds, making it one of the fastest fighter jets in the world. And with its ability to carry a wide range of missiles and bombs, it can pack a serious punch against any target.One of the coolest things about the J-20 is its advanced avionics and sensor systems. It has a state-of-the-art cockpit filled with high-tech displays and controls that give the pilot an incredible amount of information and situational awareness. Imagine being able to see everything happening around you in real-time, from enemy aircraft to incoming missiles – it's like having a superpower!Speaking of pilots, flying the J-20 must be an incredible experience. These highly trained men and women are the best of the best, capable of performing daring maneuvers and handlingthe most challenging situations with skill and courage. Can you picture yourself in the cockpit, soaring through the skies and defending your country? It's like something straight out of a movie!But the J-20 isn't just about military might; it's also a symbol of China's technological prowess and innovation. The development of this advanced fighter jet showcases the country's ability to create cutting-edge technology and compete on a global scale. It's a source of pride for the nation and a testament to the hard work and dedication of its people.Now, you might be wondering why a stealth fighter jet is so important. Well, in today's world, countries need to be prepared to defend themselves against potential threats. The J-20 gives China a powerful deterrent and ensures that its airspace remains secure and protected.In the years to come, we can expect even more advanced versions of the J-20 to emerge, with even better stealth capabilities, more powerful weapons, and enhanced performance. Who knows, maybe some of you will even have the opportunity to work on developing future generations of this incredible aircraft!So, there you have it – the J-20 stealth fighter jet, a true masterpiece of Chinese engineering and a symbol of the country's technological prowess. Whether you're fascinated by aviation, interested in science and technology, or just love cool machines, the J-20 is sure to capture your imagination and inspire you to dream big.Remember, with hard work, dedication, and a love for learning, you too can contribute to creating incredible innovations like the J-20. So, keep studying, keep exploring, and keep reaching for the stars – the future is yours to shape!篇6The J-20 Mighty Dragon: China's Cutting-Edge Stealth FighterHave you ever dreamed of soaring through the skies like a mighty dragon? Well, China has made that dream a reality with the incredible J-20 stealth fighter jet! As a kid who loves everything about planes and flying machines, I was totally blown away when I first learned about this amazing aircraft.The J-20, also known as the "Mighty Dragon," is afifth-generation, single-seat, twin-engine, all-weather stealth fighter jet. It was developed and built by China's AviationIndustry Corporation (AVIC) for the People's Liberation Army Air Force (PLAAF). The J-20 is considered one of the most advanced fighter jets in the world, and it's really cool that it was made right here in China!One of the coolest things about the J-20 is its stealth technology. It's designed to be incredibly hard to detect on radar, which means it can sneak up on enemies without them even knowing it's there. The body of the jet is made from special radar-absorbing materials, and its shape is designed to minimize its radar signature. It's like a ninja of the skies!The J-20 is also incredibly fast and maneuverable. It can fly at supersonic speeds, which means it can go faster than the speed of sound. And with its advanced thrust vectoring control system, it can perform all sorts of crazy aerial maneuvers that would make your head spin. Imagine doing loops and barrel rolls at Mach 2 – how awesome is that?But the J-20 isn't just about speed and stealth. It's also packed with some serious firepower. It can carry a wide range of air-to-air and air-to-ground missiles, as well as precision-guided bombs. And with its advanced avionics and sensor systems, it can detect and track targets from incredibly far away. This thing is like a deadly dragon with razor-sharp claws and fiery breath!One of the most impressive things about the J-20 is its ability to conduct both air superiority and strike operations. That means it can engage and destroy enemy aircraft in the air, but it can also carry out bombing missions against targets on the ground. It's like having two amazing planes in one!The development of the J-20 was a huge undertaking, and it took years of hard work and dedication from some of China's top aerospace engineers and scientists. The first prototype took its maiden flight in 2011, and after years of testing and refinement, the J-20 finally entered service with the PLAAF in 2017.Since then, the J-20 has become a symbol of China's growing military strength and technological prowess. It's a source of great pride for many Chinese people, myself included. Whenever I see pictures or videos of the J-20 in action, I can't help but feel a sense of awe and excitement.But as impressive as the J-20 is, it's important to remember that it's just one part of China's larger military modernization efforts. China is also developing other cutting-edge weapons systems, including stealth drones, hypersonic missiles, and advanced naval vessels.While these developments may make some people nervous, I think it's important to understand that China's goal is to build astrong and capable military force for defensive purposes, not offensive ones. China has repeatedly stated its commitment to a peaceful rise and has no intention of seeking hegemony or engaging in aggression.Still, the J-20 and other advanced weapons systems have certainly caught the attention of the international community. Some countries have expressed concern about China's growing military capabilities, while others have sought to develop their own stealth fighter jets in response.Personally, I think the J-20 is an incredible feat of engineering and a testament to China's technological prowess. But I also hope that it will be used responsibly and for the purpose of maintaining peace and stability, rather than fueling conflicts or tensions.At the end of the day, the J-20 is a symbol of human ingenuity and our never-ending quest to push the boundaries of what's possible. It's a reminder that with hard work, perseverance, and a little bit of imagination, we can achieve amazing things.Who knows, maybe someday I'll even get the chance to fly one of these incredible machines myself. But for now, I'll just have to settle for admiring the Mighty Dragon from afar anddreaming of the day when I can soar through the skies like a true dragon rider!。
喷气航空史英语作文Jet aviation has played a pivotal role in the history of aviation, marking a significant milestone in the advancement of air travel. From the early days of experimentation to the modern era of commercial jetliners, the journey of jet aviation has been one of innovation, engineering prowess, and global connectivity.The roots of jet aviation can be traced back to the early 20th century, with the pioneering work of engineers and inventors like Frank Whittle and Hans von Ohain. These visionaries conceptualized and developed the fundamental principles of jet propulsion, laying the groundwork for the revolution that would follow.One of the key breakthroughs in jet aviation came with the development of the first operational jet engine during World War II. The German Messerschmitt Me 262, powered by the Junkers Jumo 004 engine, became the world's first operational jet-powered fighter aircraft in 1944. Thismarked a significant shift in military aviation, introducing unprecedented speed and altitude capabilities.Following the war, jet aviation entered a new phase of rapid expansion and innovation. In the civilian sector, the de Havilland Comet, introduced in 1952, became the world's first commercial jet airliner. Its revolutionary design and jet propulsion technology ushered in a new era of air travel, offering unprecedented speed and comfort to passengers.Throughout the latter half of the 20th century, jet aviation continued to evolve and flourish. The introduction of larger, more efficient jetliners, such as the Boeing 707 and the Douglas DC-8, transformed air travel into a mass-market phenomenon, making it accessible to people around the globe.The dawn of the 21st century brought further advancements in jet aviation, with the development of cutting-edge aircraft like the Airbus A380 and the Boeing 787 Dreamliner. These state-of-the-art jetliners pushed theboundaries of technology and design, offering unparalleled levels of fuel efficiency, comfort, and safety.Today, jet aviation plays a central role in the global transportation network, connecting cities and continentswith unprecedented speed and efficiency. Commercialjetliners ferry millions of passengers each day, while military jets patrol the skies, ensuring national security and defense.Looking ahead, the future of jet aviation appears promising, with ongoing research and development efforts focused on enhancing efficiency, reducing environmental impact, and pushing the boundaries of speed and performance. From supersonic passenger jets to advanced hypersonic aircraft, the next chapter in the history of jet aviation promises to be as exciting and transformative as those that have come before.In conclusion, jet aviation has been a remarkable journey of innovation, ingenuity, and progress. From its humble beginnings to its current status as a cornerstone ofmodern transportation, jet aviation has reshaped the world in profound ways, bringing people closer together and shrinking the distances that once separated us. As we look to the future, the sky remains the limit for the continued evolution of jet aviation.。
Investigating the properties of lightwavesLight is a form of electromagnetic radiation that is visible to the human eye. It has been studied extensively by scientists for centuries, but many of its properties are still not fully understood. In this article, we will explore some of the key properties of light waves and how they are investigated.Wavelength and FrequencyOne of the most fundamental properties of light waves is their wavelength, which refers to the distance between peaks in the wave. The wavelength of light determines its color, with longer wavelengths appearing as red and shorter wavelengths appearing as blue.Another important property of light waves is their frequency, which is the number of peaks that pass a given point in a given amount of time. Frequency is measured in hertz (Hz), with one hertz equal to one wave crest per second. The frequency of light is directly related to its energy, with higher frequencies corresponding to higher energies.Measurement TechniquesIn order to study the properties of light waves, scientists often use a variety of measurement techniques. One commonly used method is spectroscopy, which involves analyzing the wavelengths of light emitted or absorbed by a particular substance. This can provide valuable information about the chemical makeup of the substance and how it interacts with light.Another technique is interferometry, which involves combining multiple sources of light waves to create interference patterns. This can be used to measure very small changes in distance or to create highly precise measurements of wavelength or frequency.ApplicationsThe properties of light waves have a wide range of applications in science and technology. For example, the colors of light are crucial for understanding the behavior of chemical compounds, as well as for designing and testing new photonic materials and devices.Light waves are also used extensively in communications technology, with high-frequency waves such as radio waves and microwaves being used for things like Wi-Fi signals and cell phone transmissions. In addition, scientists are actively exploring the potential of using lower-frequency waves like infrared and terahertz radiation for a wide range of applications, from imaging and sensing to biomedical research and cancer treatment.ConclusionIn conclusion, the properties of light waves are incredibly complex and diverse, with a wide range of applications in science and technology. Studying these properties requires sophisticated measurement techniques and a deep understanding of the underlying physics, but the potential benefits are vast. Whether we are exploring the outer reaches of the cosmos or designing new forms of communication technology, light waves will continue to play a crucial role in shaping our world.。
Interactions of a Light Hypersonic Jet with a Non-Uniform Interstellar MediumRalph S.Sutherland and Geoffrey V.BicknellResearch School of Astronomy and Astrophysics,Australian National University,ACT 0200,Australia.ABSTRACTWe present three dimensional simulations of the interaction of a light hypersonic jet with an inhomogeneous thermal and turbulently supported disk in an elliptical galaxy.These simulations are applicable to the GPS/CSS phase of extragalactic radio sources.The interstellar medium in these simulations consists of a conventional hot (T ∼107K)component together with a warm (T ∼104K )turbulently supported disk whose local density is described by a log-normal density distribution and whose spatial structure is realized from a fractal power-law.We model the jet as a light,supersonic non-relativistic flow with parameters selected to be consistent with a relativistic jet with kinetic power just above the FR1/FR2break.We identify four generic phases in the evolution of such a jet with the inhomogeneous in-terstellar medium:1)an initial “flood and channel”phase,where progress is characterized by high pressure gas finding changing weak points in the ISM,flowing through channels that form and re-form over time,2)a spherical,energy-driven bubble phase,were the bubble is larger than the disk scale,but the jet remains fully disrupted close to the nucleus,3)a subsequent,rapid,jet break–out phase the jet breaks free of the last obstructing dense clouds,becomes col-limated once more and pierces the spherical bubble,and 4)a classical phase,the jet propagates in a momentum-dominated fashion similar to jets in single component hot haloes,leading to the classical jet –cocoon –bow-shock structure.Mass transport in the simulations is investigated,and we propose a model for the morphology and component proper motions in the well-studied Compact Symmetric Object 4C31.04.Subject headings:Radio Galaxies —GPS/CSS,ISM —Turbulence,Fractal medium.1.Introduction There is a substantial literature on jet simulations going back to the time when the first supercomputersbecame available for computational astrophysics (Norman et al.1982).The simulations of extragalactic radio jets that have been carried out typically have axisymmetric or cartesian slab-jet geometries;a smaller number of three dimensional simulations have also been conducted.One of the most important features has generally been the assumption of a hot,tenuous and smoothly distributed ambient atmosphere.These simulations have been extremely informative,leading to significant insights into the physics of extragalactic jets.For example the production of jet knots and filamentary structure has been associated with non-linear development of Kelvin-Helmholtz modes (Norman et al.1984;Hardee et al.1992);slab-jet simulations have shown how the extragalactic dentist drill (Scheuer 1982)may work in practice (Hardee &Norman 1990)and simulations of jets in atmospheres with density gradients (Hardee et al.1991)have shown how the stability/instability of jets is influenced by the gradients in the ambient atmosphere.More recently,Krause (2003)has mapped out a region of the parameter space of jet density ratio,ηand Mach number,M and hasa r X i v :0707.3668v 1 [a s t r o -p h ] 25 J u l 2007also simulated the progress of a light jet through a dense(but uniform)medium typical of Gigahertz Peak Spectrum(GPS)or Compact Steep Spectrum(CSS)radio sources.Notwithstanding the insights provided by the above work,until recently one key element has not been addressed in detail and this is the nature of the background medium.In the case of classical double radio sources,there is ample justification for assuming an homogeneous medium.However,there is excellent observational motivation for the disruption or modification of radio source morphologies by an inhomogeneous medium.For example,the existence offilamentary optical line-emitting gas adjacent to the inner radio lobes in M87has been known for some time(Ford&Butcher1979)as has the hierarchical structure of M87 evident in both radio and X-ray images(Owen et al.2000;B¨o hringer et al.1995).Moreover,recent Chandra observations of the inner few kpc of M87,indicate significant interaction of the inner radio plasma in M87 with the hot X-ray gas leading to the production of X-rayfilaments.There is also evidence for jet–ISM interaction in high redshift radio galaxies such as4C41.17Bicknell et al.(2000),quasars such as3C48(Wilkinson et al.1991),blazars such as MKN501(Giroletti et al.2004; Bicknell et al.2005),and the general class of GPS and CSS sources(De Vries et al.1999;Bicknell et al. 1997),which motivated our current line of research in thefirst place.All of these sources show clear evidence for the interaction of a jet with a clumpy medium which substantially distorts the morphology of the radio source,in most cases producing accompanying emission line luminosity from the disturbed dense gas.There are other compelling reasons for considering the interaction of radio jets with an inhomogeneous medium.Ever since the paper of Silk&Rees(1998),proposing an explanation for the Magorrian et al. (1998)relation between black hole mass and bulge mass,there has been an increasing appreciation of the importance of feedback processes involving active galactic nuclei and the evolving interstellar medium of forming galaxies.In principle,jets,winds and radiation emitted from the environs of the black hole can impede continued accretion into a forming galaxy thereby limiting its growth.The importance of jets stems from the realisation that disrupted jets can process4πsteradians of solid angle in the interstellar medium (e.g.Saxton et al.(2005))and that they transport a large amount of momentum.For similar reasons the importance of jet–ISM interactions has been appreciated in attempts to resolve the questions posed by coolingflows as well as the X-ray cavities associated with radio bubbles that are now being observed in these environments(e.g.Nulsen et al.(2005)).In recent work we have begun to investigate these phenomena through the simulation of two-dimensional slab jets issuing into an inhomogeneous medium(Bicknell et al.2003,?;Saxton et al.2005).We have shown that a numerous different radio morphologies can arise as a result of the interaction of both the jet and lobes with a clumpy interstellar medium and we have compared the resulting radio morphologies with a number of well–known radio sources.Some preliminary three-dimensional simulations have also been published (Sutherland2005;Bicknell2006).In this paper we present a high resolution simulation of a radio jet interacting with an inhomogeneous interstellar medium in the form of a turbulently supported disk which extends our previous work in several different directions:(1)The simulation is three dimensional with a resolution of512cells in the(cartesian) coordinate directions and a spatial scale of2parsecs per cell.(2)The density structure of the warm disk is described by a log-normal distribution,typical of the warm interstellar medium in a number of different environments.(3)The initial distribution of the warm medium is that of a thick,almost Keplerian disk supported by a combination of thermal pressure and a,dominant,supersonic velocity dispersion.This type of distribution is one of several that may be contemplated and is supported by the observation of such disks in M87(Dopita et al.1997)and NGC7052(van der Marel&van den Bosch1998).(Other types ofdistributions of warm gas that may be contemplated include that typical of the Lyman-αhaloes observed in many high redshift radio galaxies.These will be considered in future papers in this series.)(4)The hard and soft X-ray emissivity and surface brightness of the thermal plasma is calculated,in conjunction with the radio surface brightness image.These synthetic images provide valuable insights for the interpretation of observational data.This simulation illustrates four important phases in the evolution of a young radio galaxy:(1)An initial “flood and channel”phase wherein the radio source is beginning to be established,but is still interacting strongly with the disk material.(2)A quasi-spherical jet-driven bubble phase where the jet is fully disrupted and drives a pseudo-spherical bubble into the surrounding medium.(3)a rapid jet establishment phase where the last obstruction is ablated away and the jet reforms and crosses the spherical bubble rabidly until it breaks out.(4)A classical jet–cocoon–bow-shock phase familiar from previous studies of radio sources in a single component,hot ISM.We also determine the X-ray morphology associated with the interaction of the radio source with the disk and show that the luminosity from the disk may persist.We begin,in the following section,by describing the key elements and assumption in some detail.We discuss our justification of,and constraints on,the parameters chosen for the simulations.2.The Jet-Galaxy System:Key Model Element and Parameters2.1.Host galaxy potentialElliptical galaxies contain both baryonic and dark matter.The former dominates on scales close to the core and the latter dominates at large radii,say of order10kpc.Since jet simulations frequently extend over this range of scales,we have constructed a family of potentials which we use to represent a combined, self-consistent distribution of baryonic(luminous)and dark matter.In the simulation presented here,the scale of the simulation is such that the potential is dominated by the baryonic component close to the core. However,the dark matter does have some influence.Hence,we present here a generic potential that is useful here and which can also be used in future simulations with a larger overall spatial scale,in which the dark matter has an even greater influence.The potential is based on isothermal distributions of baryonic and dark matter,described in terms of isotropic distribution functions,as follows.Let,(σB,ρB,0)and(σD,ρD,0)be the line of sight velocity dispersions and central densities of baryonic and dark matter respectively and let the total specific energy of a baryonic particle(star,gas),or dark matter ‘particle’,be E=1/2v2+φG where v is the velocity andφG is the gravitational potential.The central value of the potential is taken as,φG(0)=0.We assume Maxwellian distributions for the distribution functions, for both dark and baryonic matter:f D(E)=ρB,0(2π)3/2σ3Bexp(−E/σ2D),f B(E)=ρD,0(2π)3/2σ3Dexp(−E/σ2B).(1)As for the classic single component isothermal sphere(c.f.King(1966)),we define dark and baryonic matter core radii,r D and r B,via the relations:4πGρD,0r2Dσ2D =4πGρB,0r2Bσ2B=9.(2)Forκ=σD/σB 1andλ=r D/r B 1,the density is dominated by the baryonic component near r=0 and by the dark component near r=r D.In this case,the core radii have the conventional interpretation of being the radii at which the surface densities of the respective components drop to approximately half of their central values.Taking =ρB,0/ρD,0,the dark and baryonic matter densities are given in terms of the dimensionless potentialψ=φ/σ2Dby:ρDρD,0=exp(−ψ),ρB B,0=ρB,0D,0exp−σDB2ψ(3) = exp−κ2ψ.(4)Defining the normalized radius by r =r/r D,the dimensionless version of Poisson’s equation is:d2ψdr 2+2rdψdr=9exp(−ψ)+ exp−κ2ψ.(5)We may take the parameters of this double isothermal distribution to beκ,the ratio of the dark to baryonic velocity dispersions,and ,the central baryonic to dark matter densities.However,it is generally more convenient to takeκ,and the ratio of core radii,λ,as defining parameters,use =λ2/κ2,andfind the central densities from equations(2),ρD,0=9σ2D4πGr2D,ρB,0=9σ2B4πGr2B.(6)We refer below to the double potential function for givenκandλparameters asψκ,λ.Equation(5)is numerically integrated for chosen parameters,tabulated and interpolated with cubic splines when required by the hydrodynamic code.In the present modeling we useκ=2,andλ=10, referring to the potential asψ2,10.The central density is dominated by baryonic material over dark matter by a ratio of25:1.Figure1in the next section shows the resulting equilibrium density distribution of the hot galactic atmosphere in theψ2,10potential,compared to two single isothermal potentials.2.2.The Hot Galactic AtmosphereGenerally,in radio galaxies,there are at least two components of the interstellar medium,a tenuous, smoothly distributed hot atmosphere with central density∼0.01−1particles cm−3and T∼107K,and a cold/warm unevenly distributed component with number densities∼1−100cm−3and temperatures ∼103−4K.The tenuous,hot interstellar medium in our simulations is isothermal,although it is relatively straight-forward to relax this condition by adopting,for example,an empirically determined radial temperature profile.Let T be the gas temperature.The virial temperature corresponding to the dark matter is defined by T∗=¯mσ2D/k,where¯m=µm u≈1.035×10−24g,is the mean particle mass(including electrons,hydrogen and heavier ions),usingµ=0.6224,the mean molecular weight in fully ionised solar metallicity gas,andm u,the atomic mass unit.Assuming hydrostatic equilibrium,the particle number density,n h of the hot gas is given simply by:n h n h,0=exp−T∗Tψ.(7)(Note that this defines the total particle density,not the Hydrogen number density,often denoted by n H). On the1kpc scales simulated here,the sound crossing time for the region at400kms−1is about2.5Myr,so the hydrostatic formalism used requires the atmosphere to have settled into place for longer than this prior to the jet interaction,which we assume to be the case.Figure1shows how the T=T∗hot atmospherefills the double isothermal,ψ2,10,potential with r D=3.5kpc.For comparison,corresponding functions for single isothermal potentials,one each for a core radius of r c=3.5kpc,and r c=350pc,are overplotted.The upper logarithmic plot shows the large scale behavior,and the lower linear panel focuses on the1kpc range used in the simulations here.The key feature is that between the inner radius and outer radius,the density decreases with radius with an intermediate slope.Within the1kpc range on the grid,the hot atmosphere density has fallen to approximately40%of its central value,and is essentially uniform(within10%)inside200pc,and is described by a radial powerlaw with a slope of index−0.68in the outer regions to1.0kpc.2.3.The non-uniform,fractal,warm interstellar mediumThe warm and cold interstellar medium has been known to be non-uniform ever since thefirst obser-vations of nebulae in the late19th and early20th centuries(although recognition of an interstellar medium as such came later in the20th century).In these simulations we introduce a non-uniform medium,which is describable semi-analytically,with the view to assessing qualitatively the influence on inhomogeneity on the energetics of dynamical interactions–even if a full theoretical understanding of the non-uniformity un-available.We compare a homogeneous model with an inhomogeneous model,at two resolutions,in order to comprehend the consequences of non-uniformity will take,in a global dynamical sense.To establish non-uniform medium we make use of an obvious analogy with a turbulent medium.The physics literature on turbulence is vast,with results and models in a manyfields of physical sciences,and astrophysics is is no exception.Rather than attempt to review this huge topic here however,we refer the reader to the recent astrophysically oriented annual reviews of(Elmegreen&Scalo2004),and(Scalo& Elmegreen2004)as a starting point for background material,and then refer simply to some specific results that we use below to arrive at reasonable(although not necessarily unique)parameters for our non-uniform medium.It must be emphasized that for the present work we are not modelling actual turbulence in a genuine causally generated ISM(see Kritsuk et al.(2006)for a recent large scale isothermal ISM turbulence simula-tion).Rather,we are taking a parameterisation for the non-uniform properties of generic turbulent media focusing on characteristics such as the variance,σ2,the intermittency(in skewed distributions),and two–point self-similar power-law structures,relying on a range of previous experimental and theoretical results from thefield of turbulence.Hence the initial distribution of the ISM that we employ should be regarded as a physically motivated generalisation of a homogeneous model,whilst not necessarily representing an accurate physical model of a turbulent ISM.Fig.1.—The density distribution of the normalized two component isothermal potential,ψ2,10.The solid curve represents the normalized total density distributionρ/ρ0=exp[ψ2,10],scaled to a dark matter radius of r D=3.5kpc,implying a baryonic core radius of r B=350pc.The short dashed curve is the density distribution corresponding to an isothermal potential with a core radius of3.5kpc.The dash-dot curve is a density distribution for an isothermal sphere with a core radius of350pc.The upper panel uses logarithmic coordinates,the lower panel is linear and covers the domain of the simulated hot atmosphere.Seetext for details.2.3.1.Log-normal density distributionTurbulence naturally gives rise to non-uniform structure,in velocity and densityfields.We neglect the velocity structure,and focus on choosing statistical parameters to describe the density.This is justified numerically by the relatively small turbulent velocities expected when compared to the very large velocities found in our global jet–ISM interaction.The velocities observed in typical warm ISM conditions fall in a range of transonic to mildly supersonic values,Mach1-4(e.g.Heiles(2004)).At temperatures at or below104K this corresponds to velocities<50km s−1.In our1kpc simulations over105yr timescales, the resulting displacements amount to less than2or3cells,and are insignificant compared to those of the radio jet and the energy bubble/cocoon generated by the main outburst,wherein velocities of hundreds or thousands of km/s occur.Consequently,we do not impose a turbulent velocityfield on the warm medium, and focus instead on constructing the densityfield.We use a log–normal distribution to describe the single point statistics of the densityfield of our nonuniform ISM.The log–normal distribution is a skewed continuous probability distribution.Unlike the normal distribution,it has a non-zero skewness,variable kurtosis,and in general the mode,median and mean are unequal.The log-normal distribution appears to be a nearly universal property of isothermal turbulent media in experimental,numerical and analytical studies(e.g.Nordlund&Padoan(1999),see also Warhaft (2000),and Pumir(1994)).Moreover,it is encouraging that the log–normal distribution is the limiting distribution for the product of random increments,in the same way that the normal distribution plays that role for additive random increments.It is thus compatible,at least conceptually,with a generic cascading process consisting of repeated folding and stretching.We begin by describing parameters for an inhomogeneous interstellar medium densityfield,which is on average isotropic.That is,there is no dependence on location.In§2.3.4below,we describe how this standard distribution is modified to reflect the potential.With a log–normal distribution,the natural logarithm of the ISM densityfield is a Gaussian which has a mean m and variance s2.The probability density function for the log-normal distribution of the mass densityρis,P(ρ)=1s√2πρexp−(lnρ−m)2.(8)The meanµand varianceσ2of the density are given byµ=exp[m+s2/2].(9)σ2=µ2(exp[s2]−1)(10)Additional statistical properties of the log-normal distribution are summarized in Appendix A.In this simulation we adoptµ=1.0,σ2=5.0,as our standard log–normal distribution.These values are compatible with the favored ranges in Fischera et al.(2003)and Fischera&Dopita(2004)from star burst galaxy reddening and extinction considerations.The variance measures how concentrated the mass is in dense cores,or conversely how much volume is occupied by voids,and these parameters give aflatness parameter F=1836,indicative of an intermittent distribution(see Appendix A).With these parameters, densities below the mean,z=µ,comprise one quarter of the mass,and occupy three quarters of the volume, and the mean is approximately20times the mode(see§C for further details).Other values are possible of course,and a proposed relationship between the log-normal variance and the isothermal Mach number of the turbulence given by(Nordlund&Padoan1999),viz.σ2≈0.25M2,(11)suggests that higher mach numbers in an AGN medium for example,could be compatible with larger variances.Below,when we use turbulent velocity support to determine the scale height of the warm ISM disk in the galactic potential,we adopt a turbulent velocity that is consistent with the valueσ2=5.0adopted here;hence the turbulent velocity is not a completely independent parameter in the model.2.3.2.Power-law density structureThe two–point structure of a homogeneous turbulent medium is best described in Fourier space.We denote the Fourier transform of the densityρ(r)by F(k)(where k is the wavenumber vector).The isotropic power spectrum D(k)is the integral over solid angle in Fourier space of the spectral density F(k)F∗(k).Inthree dimensions:D(k)=k2F(k)F∗(k)dΩ.(12).Even if the spectral density is anisotropic,the angular integral averages the spectral density into a one dimensional function of k only.For a power-law dependence on k,D(k)∝k−βandβ=5/3,the spectrum is referred to as Kolmogorov turbulence.It has been shown that a scalar tracer(density)of the turbulentfield also shows the Kolmogorov structure index(Warhaft2000).We follow Fischera et al.(2003)and adopt a standard density power spectrum with a Kolmogorov power-law withβ=5/3to generate a spatial structure power-law for the density in our non-uniform ISM. Given our assumption above that the(isothermal)disk is mainly supported by supersonic turbulence,a slightly different value ofβ=2.0associated with shock turbulence may be a reasonable alternative(e.g. Boldyrev et al.(2004))but we postpone investigation of the variation ofβto future work.2.3.3.Iterative Generation and Fractal ResolutionFor our inhomogeneous ISM we selectµ=1.0andσ2=5.0as our standard log–normal densityfield parameters,and a Kolmogorovβ=5/3power-law spatial index.This structure is modified as described below in§2.3.4to take account of a spatially variable mean density.The selected parameters may be representative in view of the results of Fischera et al.(2003)and Fischera&Dopita(2004)noted above. However,at this stage not a lot is known about the parameters of the inhomogeneous ISM of radio galaxies.In order to simultaneously achieve log-normal single-point statistics and a power-law self-similar struc-ture,we have implemented the practical method developed by atmospheric scientists,for constructing two and three dimensional terrestrial cloud models,which are used in radiative transfer calculations(Lewis& Austin2002).Thefirst step of the procedure involves constructing a cube in which each cell has a Gaussian distribution of mean zero.This cube is Fourier transformed and then apodized by a power-law in wave number.The apodized cube is then Fourier transformed back to the spatial domain and retains its Gaussian statistics because a sum of Gaussians is still a Gaussian.A cube with log-normal statisitics is then produced by exponentiating the Gaussian cube.However,as re-transformation to Fourier space shows this alters the power-law in wave number property.Essentially the generation of dense cores and large voids consistent with the log-normal parameters,alters the low and high wavenumber ends of an original power-law,breaking self-similarity.Hence,the deviation from a power-law is calculated and this is used to estimate a correction to the power-law of the Gaussian distribution.Successive corrections are applied until satisfactory convergenceto a power-law(within approximately1%)is obtained,usually in about4–6iterations for distributions with modest variances(σ2<10).The process converges more slowly as the target variance,σ2,increases,and variances>10were not attempted.The reader is referred to Lewis&Austin(2002)for further details of this method.From this process a library of cubes with a range of resolutions and variances were pre-computed for use in a range of simulations,from which our standard set:µ=1.0andσ2=5.0,β=5/3was selected.The remaining choice in this procedure is to select the range of wave numbers over which to generate the fractal,in particular the minimum wave number k min,which determines the largest structure scale in the resulting fractal with respect to the spatial grid.With the scale height of the disk in the simulations being of order100pc in a domain of1kpc extent,a minimum wave number of k min=20is used to ensure that the largest‘clouds’are of order50pc,and appropriate to the scale of the disk everywhere.In thefinal structure used to form the disk,the wave numbers in the Fourier domain range from k=20to the Nyquist limit, N/2−1=255,covering just over1.1decades of scale.This is limited by the computational requirements for the overall grid,and the fact that the disk is only a small part of the domain.Significant improvement requires a substantial increase in computing resources than are available to treat more than say2decades of structure in the fractal disk alone.That said however,we did perform the simulation with two resolutions,low and high,discussed in§3.3, to investigate resolution dependent differences,and the differences of the low and high resolution fractal simulations from a uniform model.The evolution of these different simulations is evidence that at least some of the fractal properties are being captured.2.3.4.Equilibrium turbulent disksAs noted in§1many radio galaxies exhibit a turbulent disk of gas in the central regions,motivating us to consider the interaction of a jet with such a disk.Let us now consider the establishment of a disk-like distribution of gas in some detail.There are two elements to establishing a turbulent disk.We begin with the fractal,power-law distribu-tion described above.This may be scaled to give a fractal distribution with a specific,but constant,mean density.This is unsatisfactory since the distribution of gas would not reflect the potential of the galaxy. Hence,we derive below expressions for the mean density of a turbulent gas disk in the potential discussed in§2.1.We use the spatially dependent mean density to scale the fractal cube.Essentially this provides a single realization from an ensemble of turbulent fractal disks.Let the density of the warm disk gas beρand its velocity be v i.We express the density and velocity as statistical averages,as follows,with the angle brackets expressing ensemble averages:ρ=¯ρ+ρ ρ =0,(13)v i=˜v i+v i ρv i =0.For a recent description of this mass-averaged approach to a statistical description of turbulentflow,see Kuncic&Bicknell(2004).We derive the relevant equations for our warm clumpy disk in the appendix, showing en-route that the azimuthal velocity in the turbulent disk is a function of the cylindrical radius only.Following,Strickland&Stevens(2000)we also adopt the ansatz of an almost Keplerian disk.Letv K=(r∂φ(r,0)/∂r)1/2be the Keplerian velocity in the disk mid-plane and put˜vφ=e K v K=e KσDr∂ψ(r,0)∂r1/2,(14)where e K is a constant close to unity.Taking the mean temperature of the disk to be˜T and the line-of-sight turbulent velocity dispersion to beσt,the mean density of gas in the potential is given by:¯ρ(r,z)¯ρ(0,0)=exp−σ2Dσ2gψ(r,z)−e2ψ(r,0)−(1−e2)ψ(0,0).(15)whereσ2g=σ2t+k˜T/µm and as previouslyσD is the velocity dispersion of the dark matter.(Equation(15) assumes that˜T andσt are constant throughout the disk.)The main differences from the development of a similar equation by Strickland&Stevens(2000)is the (mandatory)lack of dependence of e K on z and the formal introduction of a turbulent velocity.The latter avoids the difficulty of prescribing an unphysically large temperature in order to achieve a reasonable disk scale height.In summary then,we use the double isothermal potentialψκ,λwithκ=2,λ=10,scaled by r D=3.5kpc, andσD=400km/s,and a rotation parameter e K=0.93,plus a velocity dispersion of the warm gas of σg=40km/s for the disk.This velocity dispersion corresponds to an adiabatic Mach number,M∼4, which is approximately consistent with the log–normal variance parameterσ2=5.0we adopted for the densityfield,if the Nordlund&Padoan(1999)relation(equation(11)holds.3.Jet ParametersWe use a non-relativistic code for these simulations.Other aspects of the code are discussed in§4.The use of such a code to simulate phenomena that involve relativisticflow in parts of the grid,is not ideal. Nevertheless,a large part of theflowfield is non-relativistic and is driven by the energy or momentum flux provided by the jet.Hence,we establish jet parameters in such a way that the energyflux of the non-relativistic jet corresponds to the jet energyflux of a given relativistic jet using relationships derived by Komissarov&Falle(1996).The relationships between the respective densities and Mach numbers are given by the following rela-tionships for relativistic and non-relativistic jets with the same energyflux,velocity and pressure:ρnr=2γγ−1pc2Γ21+ΓΓ+1χ.(16)M2nr=2M2rel2−γ1+ΓΓ+1χ1+χ2−γ−1.(17)(Komissarov&Falle1996).We use these relationships to determine the ratio of the non-relativistic jet density to the background and the non-relativistic jet Mach number.First note that the relativistic Mach number is given by:M2rel=2−γγ−1Γ2β21+χ2−γ.(18)。