I.J. Information Technology and Computer Science, 2017, 3, 19-27
Published Online March 2017 in MECS (https://www.doczj.com/doc/aa14419415.html,/)
DOI: 10.5815/ijitcs.2017.03.03
A Real-Time 6DOF Computational Model to
Simulate Ram-Air Parachute Dynamics
Sandaruwan Gunasinghe
University of Colombo School of Computing, Colombo 07, 00700, Sri Lanka
E-mail: sandaruwan.gunasinghe@https://www.doczj.com/doc/aa14419415.html,
GKA Dias
University of Colombo School of Computing, Colombo 07, 00700, Sri Lanka
E-mail: gkad@ucsc.cmb.ac.lk
Damitha Sandaruwan and Maheshya Weerasinghe
University of Colombo School of Computing, Colombo 07, 00700, Sri Lanka
E-mail: dsr@ucsc.cmb.ac.lk, amw@ucsc.cmb.ac.lk
Abstract—Computer simulations are used in many disciplines as a methodology of mimicking behaviors of a physical system or a process. In our study we have developed a real-time six degree- of-freedom (6DOF), computational model that can replicate the dynamics of a ram-air parachute system which is the design of parachute that is widely used by the militaries worldwide for parachute jumps. The proposed model is expected to be adapted in to a real-time visual simulator which would be used to train parachute jumpers. A statistical evaluation of the proposed model is done using a dataset taken from NASA ram-air parachute wind tunnel test. Index Terms—Real-time, Parachute, 6DOF, Ram-air, Dynamics, Simulation.
I.I NTRODUCTION
Parachuting is a task that is at the interest of some researchers in the computer science field. It is an activity that has arisen with the human fascination of flying. Computational researches done in this area have mainly focused on the parachute type known as ring-sail parachutes. This is mainly due to the fact that many high-stake parachute landings that involve lot of calculations are done using this type of parachutes. One such example is the descent of the NASA spacecraft Orion. NASA is expecting to use ring-sail type parachutes to recover the Orion spacecraft that carries astronauts on the returning journey from outer space. This descent back to earth needs lot of precision and pre calculations and a real test would cost a lot. The cost involved in such a situation leaves no room for error. Because of that there are researches done in order to create accurate computational models that can simulate this scenario before testing the parachutes in a real environment [1].
One of the main focuses on this research area that many researchers are tried to propose fluid-structure interaction models for the parachutes. These computational models are made to evaluate how the air flow through a parachute affects the behavior of it [2]. There are also researches done to compute two-dimensional forces that are applied on parachutes [3]. These available researches are also focused on the forces applied on these parachutes and how the deceleration speed changes with the time. These are some of the variables that need to be calculated when creating a parachute simulation. But to calculate these values lot of computation power and time is needed because they use methods such as interface tracking methods [4]. Hence most of the available models proposed in this research area are non-real time.
Though there are some commercial real-time parachute simulators that simulate ram-air parachute dynamics, the implementation details of these simulators are not available for the public. Most of these simulators are deployed as serious games that are used by military and parachute training academies, which are proprietary. Due to these factors computationally less intensive but yet accurate model that simulates parachute dynamics (specifically for the ram-air parachute model) is required. This study is focused on the parachute type known as ram-air parachute, which is widely used by paratroopers and skydivers due to the maneuverability of the design. So, we have proposed a 6DOF model that is computationally feasible to be implemented in a real time simulation environment. This real time model is able to be adapted in to a real-time parachute simulation. To check the accuracy furthermore this real time model is tested against existing datasets.
The proposed model is implemented using Java programming language. Through the 6DOF model we calculate the position and the orientation of the ram-air parachute in a three dimensional world. On this research special cases like turbulences in air are not considered because in such scenarios the physics that are applied on the parachute differs. The parachute and the load it carries are considered as a single system. There are few steps in a parachute jump. During this research the focus
is on the para-gliding step, the point after deploying the parachute to the point before coming to the landing step. The research is also attempted to quantify data that can be garnered through the proposed model. The lack of datasets as well as the very low number of population that can be used to gather data is an issue in this research area. Hence the main focus when developing this model had to be given to existing computational and mathematical models. An approach that combines the available models and the knowledge on physics as well as the data that can be gathered through the existing datasets would be used to propose the real-time computational model, which would be the main purpose of this study.
II.S IMULATION A RCHITECTURE
A parachute is a device that is used to slow the motion of an object. Parachutes have been a fascination among humans since the ancient times. Earliest evidence of parachutes comes from the documents that are found in the renaissance era, most famously from the documents of Leonardo da Vinci (c.1495) [5]. Computational models for different aspects of parachute jumping have been proposed. Many of the computational models made for parachutes are done for the parachute type known as ribbon-ring parachutes. A Computational Method for Parachute Fluid–Structure Interactions of ribbon-ring parachute has been suggested by K.Takizawa and T.E.Tezdunyar [6].
But in the modern days many parachute jumpers use the parachute type known as ram-air parachutes or parafoils due to their maneuverability. The credit for introducing this model goes to Domina Jalbert. He patented his parafoil parachute design in 1966 as "Multi-cell wing type aerial device”[7]. The physics behind these two models are different due their shape. The traditional parachute models such as ribbon-ring parachutes slow the motion through the atmosphere by causing a drag. The ram-air parachutes do this by using aerodynamic forces of lift and drag. This enables a better control of speed and direction in these types of parachutes [8].
There are some computational models that are available for these ram-air parachutes which use non-real time calculations, due to their complexity and the amount of computation that has to be done. Most of the calculations done in these models require parallel computing and can't be adapted in to a real time model. One example for such a model is a parallel 3D computational method for fluid-structure interactions in parachute systems, suggested by Vinay Kalro and T.E.Tezduyar [9].
Fig. 1 showcases the architecture of the final system. The Six degree-of-freedom dynamic model is built from the physics equations taken from the literature which are then re-adjusted accordingly to calculate necessary values. The system is initiated using the environmental data as well as physical and mechanical data. The six degree-of-freedom model is then solved using a classic fourth-order Runge-Kutta (RK4) solver and the position and orientation as well as the velocity and angular rate parameters are then fed back in to the 6DOF dynamic model. External inputs to the system are the trailing edge deflection values which are used to calculate the effects of braking and asymmetric trailing edge deflection. In each calculation the 6DOF model calls the dynamic air density model which calculates the density of air at the given height.
Fig.1. System architecture for a real-time parachute dynamic simulation.
A. Environmental Properties
The most important environmental property that we have considered in this research is the wind. Which is an attribute that is at this stage is given as a static value which is represented using the earth fixed coordinate system. This value is fed to the 6DOF freedom model which is then considered in calculations.
B. Physical and Mechanical Properties
Data related to the parachute is gathered from NASA and University of Notre Dame wind tunnel tests [10] and also from Lingard [11]. These wind tunnel test data is available in a very sparse amount. These data is used in order to initiate each model. Also the data that is gathered from the data-sheets of standard parafoil designs of United States Air Force is used when initiating the parachute dimensions. These are stored in a database with the mechanical properties that are related to the parachute. These physical and mechanical properties of the parachute are fed in to the parachute dynamic model.
C. Dynamic Air Density Model
The air density changes with the altitude and the density is low in higher altitudes. We have used a dynamic air density model in our solution. Getting the exact values for air density involves lot of dynamic factors such as temperature, pressure of dry air and pressure of water vapor in air. Instead of using all these parameters we have used a model that follows the pattern of the density change with altitude [12]. The following equation is generated as an approximation to the actual pattern of the air density change with altitude in standard units.
ρ = ?17500h+1.2
ρ = Air Density
h = Altitude of the Parachute
III.6D EGREES OF F REEDOM M ODEL
In this research we are focused on proposing a 6DOF model to simulate the dynamic model of the ram-air parachute. We have used six degrees of freedom model to calculate the position and orientation of the parachute relative to an inertial frame. Three degrees of freedom is used to represent the position of the parachute and another three is used to represent the orientation. The position is presented using coordinates in the inertial reference frame (x, y and z) and the orientation is represented using Euler angles which are pitch, roll and yaw (θ,φand ψ). While building this model an assumption had to be made that the parachute and the payload is a single rigid body. Throughout the study the aerospace conventions have been used to build the 6DOF model.
A. Transformation Matrix
The velocities of the parachute system are expressed in the body reference frame and the parameter such as gravitational force is defined in the inertial frame. When we are using these parameters in equations of motion we have to convert the coordinate systems accordingly. Hence we need a transformation matrix to switch from one coordinate system to another. To do so we can define the each Euler rotation using the following transformation matrices where each transformation matrix represents roll, pitch and yaw respectively [13].
According to the Euler’s theorem any rigid body rotation can be expressed by a single rotation about fixed axis. According to this theorem any orientation can be achieved by the composition of the three elemental rotations. By using this we can create a transformation matrix between the earth-fixed reference frame and the body-fixed reference frame. To do so we have to first rotate the yaw angle over the z axis, then the pitch angle about the y axis and finally the roll angle about the x axis. Finally, we got the following transformation matrix [13]. The standard convention of shortening trigonometric symbols is used in the equation.
B. Forces and Moments Equations
According to Newton the force equation can be written as,
G
F ma
= (1)
G
dV
F m
dt
= (2)
In the above equation the velocity and the forces are defined in the earth fixed frame. But we are considering velocities in the body fixed frame. Hence we have to convert the equation to the body fixed frame. The acceleration can be transformed from the earth fixed frame to the body fixed frame using the following equation.
G
G
dV dV
a B V
dt dt
ω
==+? (3)
By using the above equation we can re-write the force equation as following [5].
dV
F m B m V
dt
ω
=+? (4)
There are two important external forces that act upon a parachute when it
is gliding. One is aerodynamic force and the other force is caused by the gravity. Gravitational force is acted upon the earth fixed inertial frame. But we need to calculate the forces that act upon the body fixed frame. Hence the body fixed gravitational force that acts upon the parafoil can be derived using the transformation
matrix as follows.
The completed
force equation for the body fixed system of the parachute can be written as follows.
We can rearrange the formula as following,
Also we have to consider about the moments that acts upon the parachute in each axis. The moment in the body-
(5)
(6)
(7)
fixed frame of the parachute can be written using the following formula where H is the angular momentum.
The angular momentum of a rigid body can be calculated using:
Here ω is the angular velocity vector of the parachute about the center of mass and I, is the moment of inertia. Moment of inertia can be defined using the following matrix [15].
If we rewrite the angular momentum formula for each axis it can be written as,
As in the scenario with the forces equation we have to re-write the moment equations to fit the body fixed frame as our parameters are defined in body fixed frame [14].
We can rearrange the formula as following,
C. Calculating Forces and Moments
There are basically two types of aerodynamic forces. One is the lift and the other one is the drag force both which are occurred by the movement of the parafoil through a fluid.
The formula to calculate the lift force:
The formula to calculate the drag force:
L = Total lift force of the parachute system.
D = Total drag force of the parachute system.
CL = Lift Coefficient
CD = Drag Coefficient
ρ = Air density.
V = Velocity of the System
S = Area of the parafoil
The drag and lift coefficients are dimensionless values which are determined by the type of aero-foil and it is changed with the angle of attack of the wing, or in this case the parachute. Also these coefficients change as the brakes are applied and as a deflection in a trailing edge occurs. What happens as these brakes are applied is also a change in the angle of attack. There are separate researches done in this area to study the behavior of these coefficient values. Practically these values are calculated through wind-tunnel tests. In this research we try to use the wind tunnel test data as well as the coefficient behavior equations found in other researches for calculations.
To calculate the aerodynamic force at each axis we have can use the following formula. Here α is the angle of attack and μ is the rigging angle [11].
Fig.2. Angles of a parachute system [2].
As we calculated the aerodynamic forces, aerodynamic moments should also calculate. We have to calculate the aerodynamic moments for the roll, pitch and yaw. They can be shown using the following equation.
The moment Ma can be represented through a matrix as following.
Each element in the matrix where each represents aero dynamic moment for roll, pitch and yaw respectively. The characteristic length matrix can be represented using the following matrix where the span of the parachute is b and the reference chord length is c.
(8)
(9)
(10)
(11)
(12)
(13)
(14) (15)
(16)
Each element in the aerodynamic moment coefficient matrix represents the dimensionless moment coefficients for pitch, roll and yaw moments respectively.
The aerodynamic forces and the moments are taken around the aerodynamic center of the parachute. But the values in the body fixed frame are considered from the center of the gravity of the parachute. Hence we have to take in to consideration the distance between these two centers and adjust the moment accordingly. If we assume the distance from the center of gravity to aerodynamic center is Z ag. This gives the following aerodynamic moment equation.
As the aerodynamic moments were taken about the aero-dynamic center and the inertia matrix we discussed in the earlier section was taken about the center of mass, we need to adjust the equation. Here to adjust this we use the parallel axis theorem. In parallel axis theorem it states that the moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space. The moment of inertia about any axis parallel to that axis through the center of mass is given by I paraxis = I cm +md2. When we adjust the inertia matrix accordingly we get the following:
D. Translational Kinematics
Translational kinematics concerns only about the velocity of the system relational to the ground. This velocity is called as the kinematic velocity and it can be described using the following matrix. This velocity is referred according to the earth fixed inertial system.
In the body fixed system the velocities are defined using u, v and w. We can use the inverse of the transformation matrix to get the kinematic velocities of the earth fixed inertial frame system.
If we write the earth fixed velocities as following,
By using integration we can calculate the distance that the parachute has traveled in each direction as following [5].
The integration gives the final position of the system. But what we are seeking for is a differential equation to calculate the distance value. If we assume that the matrix G represents the positions in the coordination system as [xyz]T. If so we can re-write the above equation as following.
When we write the earth fixed velocities using body fixed velocities by using the transformational matrix we can re-write the equation as,
E. Rotational Kinematics
Rotational kinematics is about the rotation of the parachute. If we take the Euler angle rates which are defined in the inertial frame system using matrix as E= [˙φ, ˙θ, ˙ψ]T. In the body fixed reference system the angular velocities are described using ω. The relation between these two can be shown using the following equation [14].
But what we are interested is the inertial system angular velocities. By inverting the above relationship we can get that equation.
If we define the transformation matrix above as R k T, then we can re-write the equation as follows.
An important thing that should be noticed is that this
(17)
(18) (19)
(20)
(21)
(22)
(23)
(24)
parameterization has singularities at pitch values of θ = π/2+n ?π radians. In the case of a vertical maneuver which rarely occurs when gliding a ram-air parachute; the above matrix would go to a singularity causing the simulation to stop.
F. Effects of Apparent Mass
When a large body moves through a fluid it generates some motion in a certain amount of fluid mass. Apparent mass is significant for flying objects when the mass of the air is greater than the mass of the object that is moving. The parameter that has to be considered here is the wing loading factor. If wing loading is less than 50 N/m2 then the apparent mass effects should be considered [15]. In this research we try to simulate the parachute model known as RA1 and at a suspended weight of 80kg the parachute has a wing load of 24 N/m2. Hence the need to calculate the apparent mass effect on a ram-air parachute occurs.
When calculating the forces that are applied on the parachute it is important to know the pressure distribution of the air. This depends on the relative fluid velocity and the acceleration of the fluid. If the fluid is an ideal fluid, stable motion of the parachute won’t cause any external force. Theoretical results have shown that the force necessary for a solid to accelerate in a fluid like air is greater than the force that is needed to accelerate in the vacuum due to the fact that the fluid resists the acceleration. This change in the motion of the parachute body causes changes in fluid flow and this causes inertial forces to occur due to the changes of the pressure field on the body surfaces. The increase of pressure on the parachute body is proportional to the acceleration of the parafoil. Hence additional forces are also proportional to this acceleration. This can be taken in to account in calculations by increasing the mass of the parachute system. This added mass is known as the apparent mass [16].
The apparent mass changes according to the direction of movement. The same effect occurs when the parachute rotates around its axis. Hence both the apparent mass forces as well as apparent mass moments should be calculated. The accurate values are determined using Computational Fluid Dynamic methods [2] [4]. But in this research we are using the simplified approximate values gained through analytical methods.
The following equations can be used to calculate the additional forces and moments generated due to the apparent mass. For the equations of forces and moments we derived earlier these new values should be taken in to consideration.
app F F dV
F M M V dt
ω=-- (25)
app F F F d M I I VM V dt
ω
ωω=--- (26)
Following equations represent the apparent mass and
moment of inertia matrices. These matrices can be represented as following.
The apparent mass and inertia terms are defined by Lissaman and Brown [15].
With the addition of the apparent mass effects we can rewrite the force equation for the parachute system as following.
As we are interested in the derivative of the velocity to create an ordinary we bring it to one side. There are two terms that has the derivation of velocity and we have to take the common element to separate it. But then the remaining values don’t have the same dimensions. We use an identity matrix to fix this and the equations are re-written as following.
(29)
The moment equation should also be also re-written with the addition of the apparent mass effect.
As with the force equation in this equation we are interested in the derivative of the angular velocity
(27)
(28)
(30) (31)
IV. S IMULATED R ESULTS
The computational model we have proposed is modeled as a Real-Time Fixed Step Simulation. We have chosen an explicit solver to solve the initial value problem. In our simulation to select a suitable step size for the solver we have used different combinations of step sizes with varying number of iterations. The step size 0.01 gave the best performance in these tests and we are using that value in our model. A. Fourth-Order Runge-Kutta Method
In this study we have used the RK4 method as the solver to address the initial value problem and solve the dynamic model. Initial value problem is the problem that arises in modeling of physics attributes where an initial condition has to be given to a set of ordinary differential equations at the given point of domain in the solution. In our scenario the domain is time and we have to give an initial condition at a point of time (generally at t 0). The solver is an evolution equation specifying in which way the dynamic model will evolve with time given initial conditions.
RK4 method can only be used to solve ordinary differential equations of the form,
This means that only first order differential equations can be solved using RK4 and it is not an issue as all the equations we derived are in first order. The RK4 method for our implementation can be written as following.
1(,)n n k f t y = (34)
21(,)22
n n h h
k f t y k =++ (35)
32(,)22
n n h h
k f t y k =++ (36)
43(,)n n k f t h y hk =++ (37)
Here the h is the step size we are using in the simulation. The calculated value of y n+1 and the t n+1 can be written as,
1123(224)6
n n h
y y k k k k +=++++ (38)
1n n t t h +=+ (39)
B. Parameters for Simulation
We have selected a parachute design which is used by the United States Air Force for the simulation purposes. The model is known as the RA1 and the parachute attributes are shown in the Table 1. The thickness and the distance from the aerodynamic center to gravitational center is an approximation taken from Lingard [xxx]. The proposed model was tested for different test cases in the study.
Table 1. RA1 Parachute Attributes
Fig.3. Trajectory of the parachute when no brakes are applied.
Fig.4. Trajectory of the parachute when half brakes are applied.
We try to analyze the trajectory of the parachute in the 3D space. The trajectory is plotted under three conditions. One test is done without any brakes and the other one is done when half brakes are applied gradually and released. The final test is done when there is an asymmetric trailing edge deflection. When there are no forces applied in the
(32)
(33)
direction of Y, values across Y axis doesn't change. Hence the plot is done for X and Z axes for the first two test cases (Fig.3 and Fig.4).
The asymmetric brake deflection is kept for the full trajectory time period. The deflection is 0.5 radians. The parachute starts to move in a rotational movement throughout the period (Fig.5).
Fig.5. Trajectory of the parachute when trailing edges are deflected
asymmetrically.
V.C ONCLUSION
In this study we developed a real-time computational model that can be adapted in to a ram-air parachute simulator. The model we proposed behaves according to the principles of aerodynamics. The proposed model can be adapted in to various types of ram-air parachutes that are used for parachute jumping by changing the physical properties of it. One barrier that had to be faced when developing such a model is getting actual data for these properties. Especially parameters such as aerodynamic coefficients were not available to specific models and in reality these can be changed slightly than the values we have calculated using equations. The proposed model can be used to train the basic maneuvers of parachute control such as turning, braking, and flaring which are important to the novice jumpers. But the model doesn’t handle emergency situations such as entanglements of parachute lines and stalling. Hence this model is not provided a hundred percent training though it covers all the basics.
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Authors’ Profiles
Sandaruwan Gunasinghe received his BSc
in Computer Science (2016) from the
University of Colombo School of Computing,
Sri Lanka.
Served as the President of Computer
Science Society of University of Colombo,
UCSC (University of Colombo School of
Branch Chair of the IEEE Student Branch of University of Colombo School of Computing (2015-2016)
He is currently a Software Engineer, at the MillenniumIT, Sri Lanka. His Research Interests are Modelling and Simulation, Real-time Simulation, Physics based Modelling, Distributed Systems.
G.K.A Dias received his BSc in Physical
Science (1982) from the University of
Colombo, Sri Lanka, Postgraduate Diploma
in Computer Studies from University of
Essex,UK (1986), and MPhil in Computer
Science from University of Wales, UK
(1995).
Served as the Head/Department of Communication and Media Technologies, UCSC (University of Colombo School of Computing) 2010-2015
Coordinator of the Third Country and In-Country Training Programme conducted by UCSC and JICA (Japanese International Cooperation Agency (2005-2010)
He is currently a Senior Lecturer Gr. I, at the UCSC, Sri Lanka. His Research Interests are Computer Aided Software Engineering, Multimedia for Education, Modelling and Simulation, Rich internet Web applications, Conceptual Modeling, Model Driven Engineering.
Damitha Sandaruwan received his BSc in
Physical Science from the University of
Colombo, Sri Lanka, PhD in Computer
Science from University of Colombo School
of Computing (2015).
Media Coordinator of the Advanced
Digital Media Technology Centre (ADMTC) UCSC (2008-2014). Co-investigator of the Modelling and Simulation Research Group, UCSC, Sri Lanka.
He is currently a Senior Lecturer Gr. II, at the UCSC, Sri Lanka. His Research Interests are Real-time Simulation, Modelling and Simulation, Computer Graphic and Vision.
Maheshya Weerasinghe received her BSc
in Computer Science (2014) from the
University of Colombo School of
Computing, Sri Lanka.
Student Member of the Computer Society
and IEEE Student Branch of University of
Colombo School of Computing (2010-
2014). Member of the Modelling and Simulation Research Group, UCSC, Sri Lanka 2014-Present. She is currently a Research Assistant, at the Modelling and Simulation Research Group, UCSC, Sri Lanka. Her Research Interests are Modelling and Simulation, Cognitive Neuroscience, Game based Learning, Cognitive Rehabilitation, Quantum Computing.
How to cite this paper: Sandaruwan Gunasinghe, GKA Dias, Damitha Sandaruwan, Maheshya Weerasinghe,"A Real-Time 6DOF Computational Model to Simulate Ram-Air Parachute Dynamics", International Journal of Information Technology and Computer Science (IJITCS), Vol.9, No.3, pp.19-27, 2017. DOI: 10.5815/ijitcs.2017.03.03
1、气动力的计算 2、重心位置计算 先将参考点设为（0,0,0），根据对焦点取力矩，力矩始终不变的原理来计算。设焦点距离参
考点d，迎角a1的压心位于距离参考点X1的地方（具体是什么位置不用管）升力为C L1，迎角a2的压心位于X2，升力为C L2，则L1*X1=M1，L2*X2=M2，L1（X1-d）=L2（X2-d），可以解出d的表达式，d=c*（C M2-C M1）/（C L2-C L1） 1、a=2°C L=0.37526体轴系 2、a=4°C L=0.50923体轴系 可得d=0.35745即X cg=0.35745 要使静稳定裕度等于10%，平均气动弦长c=0.4m 则Xac-Xcg=0.1*c=0.04，所以重心距离前缘位置应该为0.35745-0.04=0.31745m 在参数设定中将参考点从（0,0,0）变为重心（0.31745,0,0） 3 根据极曲线，设计升力系数取迎角为12°时，C L设计=1.02493 4、配平计算 由题目3得出的结论，巡航迎角为12°。所以在迎角为12°前提下改变升降舵的角度，直至俯仰力矩系数C M=0为止，通过计算，最终升降舵配平角度为-14.6°即向上偏转14.6°此时CLtot = 0.51514，CDtot = 0.03309，CYtot = 0.00000 ，Cmtot = 0.00021 附录： feiyi-DaiXinxi 0.00 !Mach 0.0 0.0 0.0 !iYsym iZsym Zsym 0.800 0.40 2.00 !Sref Cref Bref 0.31745 0.0 0.00 !Xref Yref Zref 0.017 !CDo # #============================================= SURFACE WING 5.0 1.0 31.0 0.0
实用标准文案 飞机空气动力学复习 一．概念： 1．升力、翼型分离、压差阻力、压力中心和失速P116-120 2. 机翼展向压强变化P135-136 3．马蹄涡系、下洗与诱导阻力P137-140 4. 声速、马赫数、马赫线、马赫角和马赫锥P187-200 5. 亚声速、超声速与截面积关系P197-201 6. 亚声速小扰动理论P273-282 7. 跨声速翼型气动特性284-294 8. 超声速翼型P314-321 9. 超声速机翼P330-335，338-340 10．高超声速流P363-371 二．论述： 1.低速翼型气流分离的原因？论述后缘分离对压强分布的影响，并绘图示意。 P129-130 2.低速翼型的前缘气泡？论述产生前缘气泡的原因，并绘图示意前缘气泡对压强分布的影响。P130-131 3．分别论述后掠翼的前、后缘是亚声速流还是超声速流？并画出各机翼中某翼型处的压强系数与翼弦的分布示意图。P330-331,338 4．分别论述高超声速有粘性干扰的边界层和激波，并画出流动简图和压强分布图。P363-364 5. 论述超音速机翼锥形流法的含义，描述机翼前后缘均为超声速后掠机翼锥形流理论的处理方法，画出用锥形流法处理的区域示意图。P334 三．计算 1．已知某机翼平板二维机翼翼型参数，求二维机翼翼型升力及升力系数。 2．已知单翼椭圆机翼飞机飞行状态，求诱导阻力及根部剖面处的环量。 3．机翼为椭圆机翼低速平飞,已知重量、速度和翼展、展弦比，求飞机的升力系数﹑阻力系数和阻力。 4.一架飞机以某马赫数高速飞行，求飞机的飞行速度和皮托管测出的总压。 5．翼型以某马赫数和迎角运动,已知翼型参数, 用线化理论算翼型的升力系数和波阻系数。 精彩文档
低速、亚音速飞机的空气动力 环境c091 王亚飞 飞机上的空气动力学和现在的流体力学有着相同的特点，研究空气动力学可以间接的学习流体力学，而空气动学上的最突出的应用就是飞机，所以现在着重讲述下飞机的空气学特点， 翼型的升力和阻力 飞机之所以能在空中飞行，最基本的事实是，有一股力量克服了它的重量把它托举在空中。而这种力量主要是靠飞机的机翼与空气的相对运动产生的。 迎角的概念飞行速度（飞机质心相对于未受飞机流场影响的空气的速度）在飞机参考平面上的投影与某一固定基准线（一般取机翼翼根弦线或机身轴线）之间的夹角，称为迎角(图2.3.5(a))，用α表示。当飞行速度沿机体坐标系（见2.4.1节）竖轴的分量为正时，迎角为正。 如果按照相对气流（未受飞机流场影响的气流）方向，则相对气流速度（未受飞机流场影响的空气相对于飞机质心的运动速度）在飞机参考平面上的投影与某一固定基准线之间的夹角就是迎角，且当相对速度沿机体坐标系竖轴的分量为负时，迎角为正(图2.3.5(b))。
图2.3.5 迎角图2.3.6小迎角α下翼剖面上的空气动力 1—压力中心 2—前缘 3—后缘 4—翼弦 升力和阻力的产生根据我们已经讨论过的运动的转换原理，可以认为在空中飞行的飞机是不动的，而空气以同样的速度流过飞机。如图2.3.6所示，当气流流过翼型时，由于翼型的上表面凸些，这里的流线变密，流管变细，相反翼型的下表面平坦些，这里的流线变化不大(与远前方流线相比)。根据连续性定理和伯努利定理可知，在翼型的上表面，由于流管变细，即流管截面积减小，气流速度增大，故压强减小；而翼型的下表面，由于流管变化不大使压强基本不变。这样，翼型上下表面产生了压强差，形成了总空气动力R，R的方向向后向上。根据它们实际所起的作用，可把R分成两个分力：一个与气流速度v垂直，起支托飞机重量的作用，就是升力L；另一个与流速v平行，起阻碍飞机前进的作用，就是阻力D。此时产生的阻力除了摩擦阻力外，还有一部分是由于翼型前后压强不等引起的，称之为压差阻力。总空气动力R与翼弦的交点叫做压力中心(见图 2.3.6)。好像整个空气动力都集中在这一点上，作用在翼型上。 根据翼型上下表面各处的压强，可以绘制出翼型的压强分布图(压力分布图)，如图 2.3.7(a)所示。图中自表面向外指的箭头，代表吸力；指向表面的箭头，代表压力。箭头都与表面垂直，其长短表示负压(与吸力对应)或正压(与压力对应)的大小。由图可看出，上表面的吸力占升力的大部分。靠近前缘处稀薄度最大，即这里的吸力最大。
采用MHD(磁流体动力学)方法实现高超声速流动控制是一种新颖的流动控制概念,与常规空气动力学方法采用的飞行器表面气流接触式干扰不同,MHD方法不改变飞行器外形,而是通过电磁场对电离流场进行有距离影响,这是MHD流动控制方法具有的最大优点。此类方法具有较大地改善高超声速飞行器性能的潜力,包括防热控制,增加进气道流量捕获、增强燃烧室燃烧效率等。本文针对高超声速MHD流动控制概念,基于磁流体动力学数值模拟方法研究,结合理论分析进行了数值模拟与控制机理分析。工作包括高超声速MHD数值方法研究和高超声速MHD流动控制模拟与机理研究两大部分。第一部分为MHD数值模拟方法研究。MHD流动依据特征磁雷诺数分为高磁雷诺数和低磁雷诺数两大类,分别对应于全MHD方程组形式和低磁雷诺数近似方程组形式。本文分别针对这两种形式发展了相应的数值模拟方法。全MHD方程组形式对应于磁雷诺数较高情况,针对当前研究中存在的伪磁场散度问题、方程组奇性和修正形式的守恒性问题,本文提出了八波形式方程附加源项的模拟形式,该方法同时具备八波形式和原七波MHD方程组的优点,既可以采用八波形式特征向量,同时又保证方程组整体守恒。在数值方法上,将CFD模拟中采用的有限体积方法、Roe的近似Riemann 求解器、OC-TVD限制器以及时间格式推广到MHD模拟中。此外,作为全MHD 模拟的辅助步骤,本文建立了三维投影方法,能够有效清除磁场的伪散度。低磁雷诺数MHD方程组的求解形式较全MHD方程组形式简单,为了使之能够更好地实现高超声速复杂流场结构变化的精细捕捉,提高计算效率,本文发展了一套完整的三维自适应各向异性叉树网格方法应用于低磁雷诺数MHD流动模拟。该网格方法的工作主要包括:建立了三维叉树形网格的数据结构,以及在此基础上完善了包括自适应判别、合并/分裂、网格级别审查等步骤,并提出了对流场结构进行“保护”性加密等网格优化方式,实现了对激波等流场结构的细致捕捉。针对上述发展的数值模拟方法,本文编制了三维结构网格全MHD流动模拟程序FMHD,三维结构网格低磁雷诺数MHD流动模拟程序LSMHD,以及三维各向异性叉树网格低磁雷诺数MHD流动程序LTMHD。这些程序经过了多个经典算例的计算,验证了其有效性和准确性,能够应用于针对高超声速飞行器MHD流动控制的模拟中。第二部分为高超声速MHD流动控制机理研究。本文主要结合理论分析,开展了钝体MHD防热控制和斜激波MHD控制的模拟研究,并对控制机理进行了分析。对于马赫5来流,考虑理想气体,且假设激波层内电导率均布的高超声速钝头绕流,气动热MHD控制的数值模拟结果显示,随着控制磁场的加强,弓形激波脱体距离增大,壁面压强变化很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了26%。基于高温空气电导率模型和化学平衡热力学关系,成功进行了40km高空马赫15钝头MHD绕流数值模拟。结果显示考虑空气化学平衡效应的驻点热流小于理想气体。随着互涉参数Q的增大,弓形激波脱体距离增大,但很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了24%。模拟结果说明了MHD钝体热流控制在很高马赫数下的可行性。数值研究了高磁雷诺数的理想无粘斜激波MHD流动控制规律。模拟清晰地捕捉到激波结构。磁场大小和方向对流场和激波影响较大。在多数磁场较大情况下得到了MHD流动特有的快—慢激波结构;而磁场垂直于来流方向时,始终未有慢激波产生。这些现象都通过群速度图方法进行了理论上的解释。数值研究了低磁雷诺数无粘MHD斜激波流动控制规律,自由来流马赫数6,考虑电子束激发使局部区域产生电导率,采用自适应各向异性叉树网格。结果显示,MHD作用能够使斜激波向远离壁面的方向偏离,激波控制效应明显。磁场和电导率的大小是MHD作用的决
物理学前沿论文（设计）论文题目：计算物理学的发展与应用 学生姓名：袁强 学号：2012118504147 院系：信息系 班级：电子信息1212班 完成日期：2013年12月11日
目录 一、计算机物理学的定义 (1) 二、计算物理学的发展与现状 (1) 三、计算物理学的应用 (2) （一）计算机在物理学中的应用 (2) 1.计算机数值分析 (2) 2.实验数据处理 (2) 3.计算机模拟 (2) 4.计算机符号处理 (2) （二）计算机在其他方面的应用 (2) 四、总结 (3) 参考文献 (4)
计算物理学的发展与应用 摘要 计算物理学是伴随着电子计算机的出现和发展而逐步形成的一门新兴的边缘学科。它是以电子计算机为工具,应用数学的方法,解决物理问题的应用科学。它是物理、数学和计算机三者结合的产物。计算物理学起源于第二次世界大战期间美国对核武器的研制,它是由于核科学技术的需要而产生,并且随着电子计算机的发展而发展。现在这门科学已广泛地应用于其他领域。本文就其发展和应用领域，阐述了计算物理在物理学中的重要性和作用。 关键词：计算物理学发展应用领域
The development and application fields of Computational physics Abstract Computational physics is along with the emergence and development of the electronic computer and gradually formed a new edge discipline.it was based on the electronic computer as the tool,applied mathematics,the method of the application to solve the problem of physical science.It is the product of physics,mathematics,and computer https://www.doczj.com/doc/aa14419415.html,putational physics originated during the second world war the United States for the development of nuclear weapons,it is produced due to the need of nuclear science and technology,and develops with the development of the electronic computer.now the science has been widely used in other areas.In this paper,the development and the application field,this paper expounds the importance of computational physics in physics and function. Key word:computational physics application fields develop
第一章 一、大气的物理参数 1、大气的(7个)物理参数的概念 2、理想流体的概念 3、流体粘性随温度变化的规律 4、大气密度随高度变化规律 5、大气压力随高度变化规律 6、影响音速大小的主要因素 二、大气的构造 1、大气的构造（根据热状态的特征） 2、对流层的位置和特点 3、平流层的位置和特点 三、国际标准大气（ISA） 1、国际标准大气（ISA）的概念和基本内容 四、气象对飞行活动的影响 1、阵风分类对飞机飞行的影响（垂直阵风和水平阵风*） 2、什么是稳定风场？ 3、低空风切变的概念和对飞行的影响 五、大气状况对飞机机体腐蚀的影响 1、大气湿度对机体有什么影响？ 2、临界相对湿度值的概念 3、大气的温度和温差对机体的影响 第二章 1、相对运动原理 2、连续性假设 3、流场、定常流和非定常流 4、流线、流线谱、流管 5、体积流量、质量流量的概念和计算公式。 二、流体流动的基本规律 1、连续方程的含义和几种表达式（注意适用条件） 2、连续方程的结论:对于低速、不可压缩的定常流动，流管变细，流线变密，流速变快；流管变粗，流线变疏，流速变慢。 3、伯努利方程的含义和表达式 4、动压、静压和总压 5、伯努利方程的结论:对于不可压缩的定常流动，流速小的地方，压力大；而流速大的地方压力小。（这里的压力是指静压） 重点伯努利方程的适用条件：1）定常流动。2）研究的是在同一条流线上，或同一条流管上的不同截面。3）流动的空气与外界没有能量交换，即空气是绝热的。4)空气没有粘性，不可压缩——理想流体。 三、机体几何外形和参数 1、什么是机翼翼型； 2、翼型的主要几何参数； 3、翼型的几个基本特征参数 4、表示机翼平面形状的参数（6个） 5、机翼相对机身的角度（3个） 6、表示机身几何形状的参数四、作用在飞机上的空气动力 1、什么是空气动力？ 2、升力和阻力的概念 3、应用连续方程和伯努利方程解释机翼产生升力的原理 4、迎角的概念 5、低速飞行中飞机上的废阻力的种类、产生的原因和减少的方法； 6、诱导阻力的概念和产生的原因和减少的方法； 7、附面层的概念、分类和比较；附面层分离的原因 8、低速飞行时，不同速度下两类阻力的比较 9、升力与阻力的计算和影响因素 10、大气密度减小对飞行的影响 11、升力系数和升力系数曲线（会画出升力系数曲线、掌握升力随迎角的变化关系，零升力迎角和失速迎角的概念） 12、阻力系数和阻力系数曲线 13、掌握升阻比的概念 14、改变迎角引起的变化（升力、阻力、机翼的压力中心、失速等） 15、飞机大迎角失速和大迎角失速时的速度 16、机翼的压力中心和焦点概念和区别 六、高速飞行的一些特点 1、什么是空气的可压缩性？ 2、飞行马赫数的含义 3、流速、空气密度、流管截面积之间关系 4、对于“超音速流通过流管扩张来加速”的理解 5、小扰动在空气中的传播及其传播速度 6、什么是激波？激波的分类 7、气流通过激波后参数的变化 8、什么是波阻 9、什么是膨胀波？气流通过膨胀波后参数的变化 10、临界马赫数和临界速度的概念 11、激波失速和大迎角失速的区别 12、激波分离 13、亚音速、跨音速和超音速飞行的划分* 14、采用后掠机翼的优缺点比较 第三章 一、飞机重心、机体坐标和飞机在空中运动的自由度 1、机体坐标系的建立 2、飞机在空中运动的6个自由度 二、飞行时作用在飞机上的外载荷及其平衡方程 外载荷组成平衡力系的2个条件*： ①、外载荷的合力等于零（外载荷在三个坐标轴投影之和分别等于零）∑x = 0 ∑Y = 0 ∑Z = 0 ②、外载荷的合力矩等于零(外载荷对三个坐标轴力矩之和分别等于零) ∑Mx=0 ∑My= 0 ∑Mz= 0 1、什么是定常飞行和非定常飞行？ 2、定常飞行时，作用在飞机上的载荷平衡条件和平衡方程组
第三章 - 飞行空气动力学 飞行空气动力学介绍作用于飞机上的力的相互关系和由相关力产生的效应。作用于飞机的力 至少在某些方面，飞行中飞行员做的多好取决于计划和对动力使用的协调以及为改变推力，阻力，升力和重力的飞行控制能力。飞行员必须控制的是这些力之间的平衡。对这些力和控制他们的方法的理解越好，飞行员执行时的技能就更好。 下面定义和平直飞行(未加速的飞行)相关的力。 推力是由发动机或者螺旋桨产生的向前力量。它和阻力相反。作为一个通用规则，纵轴上的力是成对作用的。然而在后面的解释中也不总是这样的情况。 阻力是向后的阻力，由机翼和机身以及其他突出的部分对气流的破坏而产生。阻力和推力相反，和气流相对机身的方向并行。 重力由机身自己的负荷，乘客，燃油，以及货物或者行礼组成。由于地球引力导致重量向下压飞机。和升力相反，它垂直向下地作用于飞机的重心位置。 升力和向下的重力相反，它由作用于机翼的气流动力学效果产生。它垂直向上的作用于机翼的升力中心。 在稳定的飞行中，这些相反作用的力的总和等于零。在稳定直飞中没有不平衡的力(牛顿第三定律)。无论水平飞行还是爬升或者下降这都是对的。也不等于说四个力总是相等的。这仅仅是说成对的反作用力大小相等，因此各自抵消对方的效果。这点经常被忽视，而导致四个力之间的关系经常被错误的解释或阐明。例如，考虑下一页的图3－1。在上一幅图中的推力，阻力，升力和重力四个力矢量大小相等。象下一幅图显示的通常解释说明(不保证推力和阻力就不等于重力和升
力)推力等于阻力，升力等于重力。必须理解这个基本正确的表述，否则可能误解。一定要明白在直线的，水平的，非加速飞行状态中，相反作用的升力和重力是相等的，但是它们也大于相反作用的推力和阻力。简而言之，非加速的飞行状态下是推力和阻力大小相等，而不是说推力和阻力的大小和升力重力相等，基本上重力比推力更大。必须强调的是，这是在稳定飞行中的力平衡关系。总结如下： ?向上力的总和等于向下力的总和 ?向前力的总和等于向后力的总和 对旧的“推力等于阻力，升力等于重力”公式的提炼考虑了这样的事实，在爬升中，推力的一部分方向向上，表现为升力，重力的一部分方向向后，表现为阻力。在滑翔中，重力矢量的一部分方向向前，因此表现为推力。换句话说，在飞机航迹不水平的任何时刻，升力，重力，推力和阻力每一个都会分解为两个分力。如图3－2
并行计算流体力学的研究与应用 1 计算流体力学（CFD）概况 自然界存在着大量复杂的流动现象，随着人类认识的深入，开始利用流动规律改造自然界。最典型的例子是人类利用空气对运动中的机翼产生升力的机理发明了飞机。航空技术的发展强烈推动了流体力学的迅速发展。 流体运动的规律由一组控制方程描述。计算机没有发明前，流体力学家们在对方程经过大量简化后能够得到一些线形问题解析解。但实际的流动问题大都是复杂的强非线形问题，无法求得精确的解析解。计算机的出现以及计算技术的迅速发展使人们直接求解控制方程组的梦想逐步得到实现，从而催生了计算流体力学这门交叉学科。 计算流体力学（CFD，Computational Fluid Dynamics）是一门用数值计算方法直接求解流动主控方程（Euler或Navier-Stokes方程）以发现各种流动现象规律的学科。它综合了计算数学、计算机科学、流体力学、科学可视化等多种学科。广义的CFD包括计算水动力学、计算空气动力学、计算燃烧学、计算传热学、计算化学反应流动，甚至数值天气预报也可列入其中。 自二十世纪六十年代以来CFD技术得到飞速发展，其原动力是不断增长的工业需求，而航空航天工业自始至终是最强大的推动力。传统飞行器设计方法试验昂贵、费时，所获信息有限，迫使人们需要用先进的计算机仿真手段指导设计，大量减少原型机试验，缩短研发周期，节约研究经费。四十年来，CFD在湍流模型、网格技术、数值算法、可视化、并行计算等方面取得飞速发展，并给工业界带来了革命性的变化。如在汽车工业中，CFD和其它计算机辅助工程（CAE）工具一起，使原来新车研发需要上百辆样车减少为目前的十几辆车；国外飞机厂商用CFD取代大量实物试验，如美国战斗机YF-23采用CFD进行气动设计后比前一代YF-17减少了60％的风洞试验量。目前在航空、航天、汽车等工业领域，利用C FD进行的反复设计、分析、优化已成为标准的必经步骤和手段。 当前CFD问题的规模为：机理研究方面如湍流直接模拟，网格数达到了109（十亿）量级，在工业应用方面，网格数最多达到了107（千万）量级。 2 并行计算流体力学（Parallel CFD）研究与应用现状 2.1 Parallel CFD的推动力 随着计算机技术的迅猛发展，CFD得以迅速发展和普及。单机性能的提高使过去根本无法解算的问题在普通微机上可以解算，从而推动了CFD成为尖端工业、乃至一般过程工业的基本设计分析手段，从而大大激发了其应用，但人们一直难以解决以下问题： （1）工业应用方面的大规模设计计算问题。如飞机设计中全机气动性能计算，火箭发动机复杂多变的燃烧和跨音速流动模拟，导弹的气动隐身性能评估，低阻力系数高性能汽车外形的设计和分析，透平机械复杂叶型及组合的设计分析，潜艇尾迹模拟，高超音速航天器空气动力学设计分析，核电站水蒸汽两相流流动分析，非定常状态的物理过程如飞机起飞降落、过载下空间推进剂晃动分析等。这些大规模设计计算问题不但单个作业计算量庞大，且需不断调整，重复计算。
基于空气动力学的车身设计方法 14车辆卓越雷方龙1408032214 现如今工业技术急速进步，为汽车工业发展创造了良好的契机，汽车变得越来越普及、越来越高速，由此车身空气动力学曲线问题得到诸多研究人员的热点关注。 众所周知，车速越快阻力越大，空气阻力与汽车速度的平方成正比。如果空气阻力占汽车行驶阻力的比率很大，会增加汽车燃油消耗量或严重影响汽车的动力性能。据测试，一辆以100km/h速度行驶的汽车，发动机输出功率的80%将被用来克服空气阻力，减少空气阻力，就能有效地改善汽车的行驶经济性。如图1为空气流动对汽车的各方面影响。 图1 自卡尔·本次在1886年发明生产出世界上第一辆汽车起，汽车已有了百年的发展历史。从汽车造型角度而言，自最初的马车型汽车(无空气动力学阶段)，到现如今的复合型汽车(空气动力学高度化阶段)，车身空气动力学曲线发展收获了显著的成效[1]。车身空气动力学一方面重要影响着汽车的各式各样关键性能，好比动力性能、安全性能、环保性能以及经济性能等，另一方面也重要影响着汽车的外观转变及审美发展潮流。随着社会经济发展，人们生活水平日益改善，人们对于出行必备交通工具汽车的性能要求愈来愈高，汽车生产商对于车辆的气动特征也越来越关注，气动性能的好坏以转变成汽车行业竞争的关键因素。 汽车在行驶中由于空气阻力的作用，围绕着汽车重心同时产生纵向，侧向和垂直等三个方向的空气动力量，对高速行驶的汽车都会产生不同的影响，其中纵向空气力量是最大的空气阻力，大约占整体空气阻力的80%以上。
一、在研究汽车空气动力学的过程中的三种方法。 （1）、理论研究方法理论研究方法通过抓住所分析问题的主要影响因素，抽象出合理的简化理论模型，并根据总结出来的相关物理定律和有关介质性质的试验公式来建立描述介质运动规律的积分或微分方程。然后利用各种数学工具及相应的初始、边界条件解出方程组，通过对解分析来揭示各种物理量的变化规律，包括将它与实验或观察资料对照，确定解的准确度和适用范围。 （2）、数值计算研究方法由于数学发展水平的局限，理论研究只能建立较为简单的近似模型，无法完全满足研究更复杂更符合实际的气流的要求。于是近年来出现了依托快速电子计算机进行有效数值计算的方法CFD，其中包括有限元法、有限差分法等，它属于汽车计算机辅助空气动力学CAA的设计范畴，并已成为与理论分析和实验并列或具有同等重要性的研究方法。其优点是能够用来预测或解决一些理论及实验无法处理的复杂流动问题，取代部分实验环节，省时省工。但它要求事前对问题的物理特性有足够的理解，提炼出较精确的数学方程及相应的初始、边界条件等。但这些都离不开试验和理论方法的支持，并且数值方法通常无法直接反映同类问题中有普遍指导意义的结论或规律。 （3）、试验研究方法试验研究方法在空气动力学研究中占有重要地位，如风洞试验法、道路试验法。它使人们能在与所研究问题相同或相近条件下进行观测，提供建立运动规律及理论模型的依据，检验理论或计算结果的准确性、可靠性和适用范围，其作用是不可替代的。但试验方法受限于试验手段、设备和经费等物质条件，甚至有些问题尚无法在实验室中进行研究。 理论、数值计算和试验三种方法相互促进，彼此影响，取长补短从而推动汽车空气动力学的不断发展。 二、轿车外形设计的两种方法 （1）、局部最优化方法。基本思路是在满足功能、工艺学、人机工程学、安全法规以及美学造型等方面的要求下设计出汽车车身造型，然后再进行空气设计程序。此方法的优点是：操作简单，在流线型较差的车上有较好的效果。通过对原始模型仿真，从结果中得出某细节修改的模型，再重新进行仿真分析。像这样循环反复，最终达到自己预期的目标。这种方法在现实设计中运用广泛。 （2）、整体最优化方法。整体最优化是基于空气动力学原理，在汽车造型设计初期获得极佳的气动特性的理想外形，接着再根据功能结构需求，调整集合的局部外形，使其满足人机工程学、国家安全法规等各个必要因素的汽车[1]。所以，对于这种汽车的空气动力学设
计算流体力学的发展及应用 计算流体力学的发展： 20世纪30年代，由于飞机工业的需要、要求用流体力学理论来了解和指导飞机设计，当时由于飞行速度很低，可以忽略粘性和旋涡，因此流动的模型为拉普拉斯方程，研究工作的重点是椭圆型方程的数值解。利用复变函数理论和解的迭加方法来求解析解。随着飞机外形设计越来越复杂，出现了求解奇异边界积分方程的方法。以后为了考虑粘性效应，有了边界层方程的数值计算方法，并发展成以位势方程为外流方程，与内流边界层方程相结合，通过迭代求解粘性干扰流场的计算方法。同一时期许多数学家研究了偏微分方程的数学理论，Courant，Fredric等人研究了偏微分方程的基本特性、数学提法的适定性、物理波的传播特性等问题，发展了双曲型偏微分方程理论。以后，Courant，Fredric，Lowy等人发表了经典论文，证明了连续的椭圆型、抛物型和双曲型方程组解的存在性和唯一性定理，并针对线性方程的初值问题，首先将偏微分方程离散化，然后证明了离散系统收敛到连续系统，最后利用代数方法确定了差分解的存在性；他们还给出了著名的稳定性判别条件：CFL条件。这些工作是差分方法的数学理论基础。20世纪40年代，V onNeumann，Richmyer，Hopf，Lax和其他一些学者建立了非线性双曲型方程守恒定律的数值方法理论，为含有激波的气体流动数值模拟打下了理论基础。
在20世纪50年代，仅采用当时流体力学的方法，研究比较复杂的非线性流动现象是不够的，特别是不能满足高速发展起来的宇航飞行器绕流流场特性研究的需要。针对这种情况，一些学者开始将基于双曲型方程数学理论基础的时问相关方法用于求解宇航飞行器的气体的定常绕流场问题，这种方法虽然要求花费更多的计算机时，但因数学提法适定，又有较好的理论基础，且能模拟流体运动的非定常过程，所以在60年代这是应用范围较广的一般方法。以后由Lax、Kais和其他著者给出的非定常偏微分方程差分逼近的稳定性理论，进一步促进了时间相关方法。当时还出现了一些针对具体问题发展起来的特殊算法。 进人2O世纪80年代以后，计算机硬件技术有了突飞猛进的发展，计算机逐渐进人人们的实践活动范围。随着计算方法的不断改进和数值分析理论的发展高精度模拟已不再是天方夜谭。同时随着人类生产实践活动的不断发展，科学技术的日新月异，一大批高新技术产业对计算流体力学提出了新的要求，同时也为计算流体力学的发展提供了新的机遇。实践与理论的不断互动，形成计算流体力学的新热点、新动力，从而推动计算流体力学不断向前发展。首先，在计算模型方面，又提出了一些新的模型，如新的大涡模拟模型、考虑壁面曲率等效应的新的湍流模式、新的多相流模式、新的飞行器气动分析与热结构的一体化模型等这就使得计算流体力学的计算模型由最初的Euler和Ⅳ—s方程，扩展到包括湍流、两相流、化学非平衡、太阳风等问题研究模型
研究性学习论文 小组成员： 班级：机电1011 指导教师：卢梅
汽车车身的空气动力学应用 摘要：汽车在行驶中由于空气阻力的作用，围绕着汽车重心同时产生纵向，侧向和垂直等三个方向的空气动力量，对高速行驶的汽车都会产生不同的影响。因此轿车的车身设计既要服从空气动力学，要有尽量低的空阻系数，降低发动机的输出负担，又要采取措施，降低诱导阻力，以保证轿车的行驶安全。 关键词：空气动力学，车身外形设计，导流板，扰流板 背景：迄今为止，汽车的发展已经过了112年，无论是汽车的速度，还是汽车的配置，或者是汽车的造型多有了长足的发展。随着汽车速度的提高，空气阻力成为汽车前进的最大障碍。在此因素下，汽车造型经历了马车型汽车,箱型汽车,甲壳虫型汽车,船型汽车,鱼型汽车以及楔型汽车等六个阶段的演变，从而越来越符合空气动力学的要求，越来越符合人们的审美观。在这一发展历程，也可看做是人们对空气动力学的认识及应用过程。 1934年，流体力学研究中心的雷依教授，采用模型汽车在风洞中试验的方法测量了各种车身的空气阻力，这是具有历史意义的试验。它标志着人们开始运用流体力学原理研究汽车车身的造型。1937年，德国设计天才费尔南德·保时捷开始设计类似甲壳虫外形的汽车。它是第一代大量销售的空气动力学产物的汽车。1949年福特公司推出了福特V8汽车,这种车型改变了以往汽车造型模式、使前翼子板和发动机罩,后翼子板和行李舱溶于一体,大灯和散热器罩也形成整体,车身两侧是一个平滑的面,驾驶室位于中部,整个造型很象一只小船,因此,我们把这类车称为“船型汽车”。船形汽车不论从外形上还是从性能上来看都优于甲壳虫形汽车，并且还较好地解决了甲壳虫形汽车对横风不稳定的问题。船型汽车尾部过分向后伸出,形成阶梯状,在高速行驶时会产生较强的涡流,为了克服这一缺点,人们把船型车的后窗玻璃逐渐倾斜,倾斜的极限即成为斜背式。由于这个背部很象鱼的背脊,所以这类车称为“鱼型汽车”。“鱼”型虽然解决了涡流的困难，但也引起了一些空气动力学缺陷。是当汽车高速行驶时汽车的升力会比较大。鉴于鱼形汽车的缺点，设计师在鱼形汽车的尾部安上了一个上翘的“鸭尾巴”以此来克服一部分空气的升力，这便是“鱼形鸭尾式”车型。这是最早为克服气动升力而做的空气动力学设计。为了从根本上解决鱼型车的升力问题,科学家们设想了种种方案,最后终于找到了一种楔型造型。就是将车身整体向前下方倾斜,车身后部像刀切一样平直，这种造型有效地克服了升力。目前,各种身价过百万元的超级跑车设计都基本上采用楔型。各大车厂也都开发带有楔型效果的小客车，如两厢式旅行车,子弹头面包车等形式的轿车。在此基础上，增加扰流板等装置，进一步解决了空气升力的问题。 正文： 汽车气动阻力分析： 从种类上分，汽车气动阻力由形状阻力、干扰阻力、摩擦阻力、诱导阻力和内部阻力五部分迭加构成。 形状阻力：由于气流分离现象。在汽车后面形成尾流区，前后气流压力不相等，从而形成压差阻 力。压差阻力的大小是由车身外部形状决定的，所以一般称为形状阻力。它约占空气阻力的58％，是气动阻力的主要部分。 干扰阻力：车身表面凸起物、凹槽和车轮等局部影响气流流动，从而引起空气阻力，约占14％。
计算流体力学在化工中的应用 摘要：计算流体力学（CFD）用于求解固定几何形状设备内的流体的动量、热量和质量方程以及相关的其它方程，是化学工程师用于分析问题和解决问题强有力的和用途广泛的工具。本文综述了CFD 在化学工程领域的应用进展及发展趋势。 关键词：计算流体力学；流体流动；化学工程；数值模拟 计算流体力学（Computational Fluid Dynamics, CFD）是流体力学的一个分支，用于求解固定几何形状空间内的流体的动量、热量和质量方程以及相关的其他方程，并通过计算机模拟获得某种流体在特定条件下的有关数据[1]。CFD最早运用于汽车制造业、航天事业及核工业，解决空气动力学中的流体力学问题。CFD计算相对于实验研究，具有成本低、速度快、资料完备、可以模拟真实及理想条件等优点，从而使CFD成为研究各种流体现象，设计、操作和研究各种流动系统和流动过程的有利工具。20世纪60年代末，CFD技术已经在流体力学各相关行业得到了广泛的应用，化学工程的模拟计算始于20世纪90年代后期，如今CFD已经成为研究化工领域中流体流动和传质重要工具。CFD可以用于各种化工装置的模拟、分析及预测，如模拟搅拌槽混合设备的设计、放大；可以预测流体流动过程中的传质、传热，如模拟加热器中的传热效果，蒸馏塔中的两相传质流动状态；可以描述化学反应及反应速率，进行反应器模拟，如模拟出燃烧反应器、生化反应器中的反应速率；还可有效模拟分离、过滤及干燥等设备及装置内流体的流动。 一、CFD在化学工程中的基本原理 CFD是通过数值计算方法来求解化工中几何形状空间内的动量、热量、质量方程等流动主控方程，从而发现化工领域中各种流体的流动现象和规律，其主要以化学方程式中的动量守恒定律、能量守恒定律及质量守恒方程为基础。一般情况下，CFD的数值计算方法主要包括有限差分法、有限元法及有限体积法[2]。CFD是多领域交叉的学科，涉及计算机科学、流体力学、偏微分方程的数学理论、计算几何、数值分析等学科。这些学科的交叉融合,相互促进和支持,推动着这些学科的深入发展。CFD的真实模拟，其主要目的是对流体流动进行预测，以获得流体流动的信息，从而有效控制化工领域中的流体流动。随着信息技术的发展，市场上也出现了CFD软件，其具有对流场进行分析、计算、预测的功能，计算流体力学软件操作简单，界面直观形象，有利于化学工程师对流体进行准确的计算。常见的CFD软件有：FLUENT、PHOENICS、CFX、STAR-CD、FIDIP等。其中FLUENT由美国FLUENT公司于1983年推出的，是目前功能最全面、适用性最广、国内使用最广泛的CFD软件之一。 二、CFD在化学工程中的应用
2005年9月系统工程理论与实践第9期 文章编号:100026788(2005)0920137205 微型飞行器空气动力学研究 李占科,宋笔锋,张亚锋 (西北工业大学航空学院,陕西西安710072) 摘要: 围绕与微型飞行器相关的低雷诺数空气动力学问题,进行了低雷诺数翼型气动特性的数值分析 研究、低马赫数低雷诺数流场数值计算方法研究、考虑扑翼结构弹性变形的气动特性估算方法研究、微 型飞行器气动特性估算的非定常涡格法研究和微型飞行器的风洞试验研究,取得的研究成果对微型飞 行器的发展具有重要的参考价值和指导意义. 关键词: 微型飞行器;雷诺数;扑翼;风洞试验 中图分类号: V27912 文献标识码: A Aerodynamics Research on M icro Air Vehicles LI Zhan2ke,S ONG Bi2feng,ZHANG Y a2feng (School of Aeronautics,N orthwestern P olytechnical University,X i’an710072,China) Abstract: In the paper,Based on the low Reynolds number aerodynamics of the micro air vehicles(M AVs),s ome researches were done.such as aerodynamics characteristic numerical analysis research on the air foil at low Reynolds numbers,numerical calculation method of low Mach low Reynolds numbers fluid field,estimation method research on aerodynamic characteristic of the aeroelastic flapping wing,unsteady v ortex method of aerodynamics characteristic estimation and wind tunnel test of M AVs.The results of this paper have im portant reference value and instructive meaning to the development of M AVs. K ey w ords: micro air vehicles(M AVs);Reynolds number;flapping wing;wind tunnel test 1 引言 近年来,微型飞行器作为一种新型的航空飞行器,在国内外形成了新的研究热潮.低速和小尺寸共同决定了微型飞行器的飞行雷诺数很低(105左右),这远低于传统飞行器(包括普通的无人驾驶飞机)的飞行雷诺数范围(106～108以上).微型飞行器必须在低雷诺数条件下仍能保持良好的气动性能,而这方面的研究目前尚处在探索阶段.本文主要围绕与微型飞行器有关的低雷诺数空气动力学问题,进行了数值计算和风洞试验等方面的研究,取得了具有一定参考价值的研究成果. 2 微型飞行器空气动力学研究 211 低雷诺数翼型气动特性的数值分析研究 微型飞行器外形尺寸小,速度低,基于微型飞行器尺寸的雷诺数也比较小,粘性效应相对强烈,流动易分离,准确求解这种低雷诺数的流场对湍流模型乃至整个数学模型都是一个极大的挑战.本研究针对低雷诺数问题,利用求解雷诺平均的NS方程,数值模拟了绕翼型的低雷诺数流动,分析了与低雷诺数流动有关的不稳定性.研究表明,分离流动都是不稳定的,会产生周期性的脱出涡.结合绕翼型的低雷诺数流动,对采用的计算模型进行了以下研究: 1)FNS方程与T LNS方程数值准确性的对比研究 分别采用FNS方程和T LNS方程计算了在条件:Ma=012,雷诺数Re=110×105,攻角α=1°时绕 收稿日期:2003207207 资助项目:总装气动预研项目(413130401)及国防基础科研项目(J1500C001)联合资助 作者简介:李占科(1973-),男,陕西岐山人,西北工业大学飞机系博士,主要从事与微型飞行器有关的研究.
空气动力学 崔尔杰* (中国航天科技集团第701研究所) 本文简要回顾空气动力学发展的历史及其在航空航天飞行器研制中的作用，对现代空气动力学新的发展趋势和新一代航天飞行器研制中可能遇到的关键气动力问题进行探讨和分析，并对今后发展提出看法。 一、空气动力学与航空航天飞行器发展 空气动力学是研究空气和其他气体的运动规律以及运动物体与空气相互作用的科学，它是航空航天最重要的科学技术基础之一。 1．空气动力学推动20世纪航空航天事业的发展 1903年莱特兄弟研制成功世界上第一架带动力飞机，实现了人类向往已久的飞行梦想。为了研制这架飞机，他们进行过多次滑翔试验，还为此建造了一座试验段为0.01m2的小型风洞。正是这些努力，加上综合运用早期的空气动力学知识，最终获得了成功。 20世纪初，建立在理想流体基础上的环量和升力理论以及普朗特提出的边界层理论奠定了低速飞机设计基础，使重于空气的飞行器成为现实。40年代中期至50年代，可压缩气体动力学理论的迅速发展，以及对超声速流中激波性质的理论研究，特别是跨音速面积积律的发现和后掠翼新概念的提出，帮助人们突破“音障”，实现了跨音速和超音速飞行。50年代中期，美、苏等国研制成功性能优越的第一代喷气战斗机，如美国的F-86、F-100，苏联的米格-15、米格-19等。50年代以后，进入超音速空气动力学发展的新时期，第二代性能更为先进的战斗机陆续投入使用，如美国的的F-4、F-104，苏联的米格-21、米格-23，法国的幻影-3等。 1957年苏联发射第一颗地球人造卫星和1961年第一艘载人飞船“东方号”升空，被认为是空间时代的开始。美、苏两国在战略导弹和航天器发展方面的激烈角逐，促使超音速和高超音速空气动力学得到迅速发展。两个超级大国都投入巨大力量，致力于发展地面模拟设备，开邻近高超出音速空气动力学和空气热力学的研究。航天方面的研究重点放在如何克服由于高超音速飞行和再入大气层，严重气动加热所引起的“热障”问题上在钱学森先生倡导下诞生了一门新的学科，即物理力学，为航天器重返大气层奠定了科学基础。航空方面的研究重点则放在了发展高性能作战飞机、超音速客机、垂直短距起落飞机和变后掠翼飞机。这一时期，空气动力研究方面的另一项重要成就是“超临界机殿”新概念的提出，它可以显著提高机翼的临界马赫数。20世纪70年代后，脱体涡流型和非线性涡升力的发现和利用，是空气动力学的又一重要成果。它直接导致了第三代高机动性战斗机的产生，如美国的F-15、F-16，苏联苏-27、米格-29和法国的“幻影2000”。
三．面元法和涡格法是基于什么方程求解，有什么异同，简述涡格法求解步骤答：面元法和涡格法都是拉普拉斯方程 2，同：a基本求解都是基于一个面上 b边界条件在控制点上是不可穿透的 c求解高维线性方程组得知每个基本解的强度 异：a涡格法强调升力，不能模拟厚度 b边界条件不一样，涡格法布置在中性面上，不在实际的面上 c基本解布置位置不一样，涡格法不是布置在整个面上 d涡格法考虑的是薄面，面元法对厚度没限制
3，涡格法求解步骤 a 对某个近似平面用四边形划分涡格 b 在每个涡格上布置马蹄涡（1/4c) c 每个涡格控制点满足不可穿透条件 d 根据每个马蹄涡的环量强度，计算每个马蹄涡的升力，然后据此计算全机的升力 4.面元法求解步骤： 将翼型上下表面打断城直线段，假定在每一线段或者每一块面内点源强度是一个常量，每个快之间是不同的值，而涡格强度对每个面内都是常量。 四，简述CFD 求解方程 答：1建立控制方程——2确立初始条件及边界条件——3划分网格，生成计算节点——4建立离散方程——5离散初始条件和边界条件——6给定求解控制参数——7求解离散方程——8判断解是否收敛（不收敛则返回4）——9显示和输出计算结果 五．什么是离散化？常用离散化的方法，各自的特点。 答：1，离散化：在对制定问题进行CFD 计算之前，首先要将计算区域离散化，即对空间上 连续计算的区域进行划分，把他划分成多个子区域，并确定每个区域中得节点，从而生成网格。然后将控制方程在网格上离散，即将偏微分格式的控制方程转化为各个节点上的代数方程组。对于瞬态问题，还要进行时间域的离散。 即对计算区域进行空间和时间方向的离散。 2，常用的离散化有： a 有限差分法：直接将微分问题变成代数问题的近似数值解法，这种方法发展较早，比较成 熟，适用于求解双曲型和抛物型问题，但求解边界条件复杂、尤其是椭圆问题不如有限元或有限体积法方便。 b 有限元法：具有广泛的适应性，特别适用于集合无力条件比较复杂的问题（尤其是对椭圆 问题有更好的适用性）。求解速度比有限差分法和有限体积法慢，故在CFD 软件里应用并不普遍。 c 有限体积法：简单地说，子域法加离散，就是有限体积法的基本方法。特点是计算效率高， 在CFD 领域得到了广泛应用。 九．当地时间步长，多重网格，预处理的加速收敛机理？ 答：当地时间步长：max max t λx ?≈?，ij NF j i s c n v CFL t ?+?∑Ω=?→→-)(1 多重网格： 多重网格是一种非常有效的加速收敛技术，即可用于显式格式，又可用于隐式格式。其思想是，为了是密网格上的流场计算尽可能快地收敛到最终的定常解，同时在另外几套依次变稀的网格上做计算，稀网格的计算结果再反馈给密网格。其加速收敛的机理是： 大多数的计算是在稀网格上进行的，可取较大的时间步长，而且计算量较小。（收敛快，计算机时少） 绝大部分显式或隐式时间推进和迭代求解方法降低高频误差有效，对降低低频误差效果很差。计算域内所有频段的误差都得到降低才能达到最终的定常解（一般地，对一给定的网格，经过若干迭代步，可以很快消除掉高频误差，而低频误差则需要更多的迭代步数）。多重网