Application of Collaborative Optimization on a RBCC Inlet-Ejector System
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APPLICATION OF COLLABORATIVE OPTIMIZATION ON A RBCCINLET/EJECTOR SYSTEMZiaul Huque and Nayem Jahingir†CFD InstituteDepartment of Mechanical EngineeringPrairie View A & M UniversityPrairie View, TX.ABSTRACTCollaborative Optimization is a multidisciplinary design optimization architecture that allows coupled engineering design problems to be uncoupled and solved concurrently. This decentralized design strategy allows domain-specific issues to be accommodated by disciplinary analysts, while requiring interdisciplinary decisions to be reached by consensus. The present investigation focuses on application of the collaborative optimization architecture to the multidisciplinary design of an integrated inlet/ejector system of a 2-D axisymmetric rocket based combined cycle (RBCC) engine. Posed to suit the collaborative architecture, this design problem was characterized by three design variables and one constraint. An optimized primary thruster size and exit pressure were obtained. The CFD simulations of the inlet/ejector system were carried out with FDNS. The data from the response surface was used to train a neural network, which was used to approximate the objective function by a nonlinear gradient based optimizer code NPSOL.INTRODUCTIONThe low specific impulse of rocket-based vehicles along with the use of expendable stages results in a high cost per pound to deliver payload to orbit. A major goal driving current space propulsion research is to significantly decrease the cost of access to space. There are currently efforts underway to develop reusable launch vehicles that promise to decrease long-term costs as compared to the traditional expendable staged vehicles. One way to use high-efficiency airbreathing cycles during ascent in a reusable system is through the use of combined-cycle propulsion (CCP) systems. Associate Professor† Graduate Research Assistant CCP systems can be broadly divided into two categories: airbreathing combined-cycles and combined cycle systems which include a rocket sub-system. Airbreathing combined cycle engines are intended primarily for missions involving high –speed cruises in the atmosphere, but are not candidates for transatmospheric flight. While there are many types and variations of CCP systems, one class of rocket-based CCP systems shows promise for Earth-to-orbit (ETO) missions. These are engines that operate in rocket-ejector mode and also have the capability of operating in ramjet, scramjet, and rocket-only modes, and are typically referred to as rocket-based combined-cycle (RBCC) engines. A schematic of a RBCC engine is shown in figure 1. Many of the advantages of RBCC engines result from certain synergistic benefits that would not occur if the two units operated separately1. The ability to utilize the rocket as an ejector increases the thrust. Afterburning in rocket-ejector mode, using the ramjet/scramjet fuel injectors, further increased the thrust and specific impulse compared to the rocket alone. As the ratio of the bypass air to the rocket exhaust increases with increasing flight speed, the specific impulse continues to increase, as the cycle more closely resembles ramjet operation. In ramjet and scramjet modes, the rocket could be advantageously used as a fuel injector and mixing enhancer. In the rocket-only mode, the use of the engine duct as a highly expanded nozzle at high altitudes increases the specific impulse of that mode of operation. Another key advantages of RBCC systems is the reduction in the amount of onboard oxidizer required. This decreases the size and, therefore, the weight, of the tank and vehicle.An integrated inlet/ejector is one of the most critical parts of a RBCC engine propulsion system. Its design must be such that it delivers air to the engine at the desired mass flow rate and flow conditions for all flight Mach numbers. This delivery must be accompanied by as little losses, drag, weight, and complexity as possible. In short, the design is a trade-off or compromise between a high-pressure recovery and low drag. This38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit7-10 July 2002, Indianapolis, IndianaAIAA 2002-3604compromise can only be found after several propulsion and vehicle performance calculations, which strongly depends on the mission of the vehicle. Multidisciplinary optimization (MDO) promises to be the future design tool to provide guidance in making proper trade-off decisions.Collaborative optimization is new design architecture whose characteristics are well suited to large-scale, distributed design2. The fundamen-tal concept behind the development of this archi-tecture is the belief that disciplinary experts should contribute to the design decision process while not having to fully address local changes imposed by other groups of the system. This decentralized decision strategy is not only a practical approach to design, but may also allow for the use of existing disciplinary analyses without major modification.The objective of this study is to optimize a 2-D axisymmetric inlet/ejector geometry of a RBCC engine. (MDO) architecture, tied with response surface and neural networks technique has been used for this purpose.2. APPROACHES2.1 GENERAL:The RBCC flow path configuration for this analysis was axisymmetric with a single primary thruster on the engine centerline. The primary thruster was housed in a center body that created an annular constant area inlet. Figure 1 defines some of the RBCC design variables. The Inlet/Ejector plane is defined to be the exit plane of the primary thruster. The secondary inlet length (L) was a function of two of the trade space variables, L/D and A s/A5. A s is the area of the secondary flow area at the mixer inlet plane and A p is the area of the primary thruster exit area plus any base area surrounding the thruster. A5 is the total flow area at the ejector/mixer inlet plane (A s + A p) and A8is the flow area of the ramjet burner. The engine design variables that defined the trade space were: secondary inlet aspect ratio L/D;A s/A5, the ratio of secondary to total flow areas; and A8/A5, ratio of ramjet burner to ejector/mixer inlet areas. Each variable had three values so that the initial trade space was 27 configurations. But to implement the collaborative optimization concept successfully each discipline was considered independent the effect of others. So for each section (3X3)=9 cases were ran. The design variables are shown in table 1 and 2.The performance of the secondary inlet area was measured with the pressure recovery factor, which is the static pressure ratio of the secondary flow inlet to the ejector/mixture inlet. And the ejector/mixer performance was measured with by-pass ratio, which is the ratio of secondary to primary mass flow rate. The geometric definition of the 18 configurations was provided by an engine design spreadsheet. All grids contained the same number of nodes in the freestream, inlet, ram burner and nozzle portions of the domain. The number of nodes in the axial direction of the ejector/mixer varied because of their different lengths. A consistent axial delta-s was used in the ejector/mixer region.The FDNS computational fluid dynamics (CFD) code was implemented with a two-specie model: air and specie of average hot-gas properties. This analysis was non-reacting and the standard k- turbulence model was implemented. The free stream far field boundaries were set to conserve total pressure of one atmosphere at nozzle exit. All engine surfaces were set to no-slip adiabatic walls and the centerline of the engine was set to an axisymmetric boundary condition. The primary thruster’s mixture ratio was 4.0, with a chamber pressure of 500 psi. For this case there was no downstream introduction of GH2.This case was chosen as the baseline geometry to optimize. Primary thruster mass flow rates were kept constant for all configurations but each A s/A5 ratio resulted in a different primary thruster area ratio, therefore, a different primary thruster exit pressure. The A s/A5=0.64, 0.76 and 0.88 had exit pressures of 0.347, 0.52, and 1.04 atmospheres respectively. Primary thruster exit flow properties were defined as fixed inlet conditions for the ejector/mixer analysis.2.2 NEURAL NETWORK:Neural networks are composed of simple elements operating in parallel. These elements are inspired by biological nervous systems. As in nature, the network function is determined largely by the connections between elements3. A neural network (NN) can be trained to perform a particular function by adjusting the values of the connections (weights) between elements. Commonly neural networks are adjusted, or trained, so that a particular input leads to a specific target output. The network is adjusted, based on a comparison of the output and the target, until the network output matches the target. Typically many such input/target pairs are used, in this supervised learning, to train a network. In this study back-propagation neural network was used. Standard back propagation is a gradient descent algorithm. The term back propagation refers to the manner in which the gradient is computed fornonlinear multi-layer networks. Present study used NN to build a response surface from 18 CFD runs of a steady sate flow of an inlet/ejector system and later it was used for evaluating an objective function. The data was entered into the net as [3x1] matrix. In the first layer “tangsig” function from MATLAB NN toolbox was used as transfer function in three neurons. In the second layer “purelin” was used in one neuron.2.3 COLLABORATIVE OPTIMIZATIONThe collaborative optimization (CO) architecture, a form of multidisciplinary optimization method, is designed to promote disciplinary autonomy while achieving interdisciplinary compatibility. Development of collaborative optimization is discussed in4. The algorithm has been applied by researchers to a number of different design problems; the trajectory of a lunar ascent vehicle5, the sizing of a medium range transport aircraft6, and the design of a single-stage-to-orbit booster7. In all of these problems the algorithm successfully converged to an optimal solution. In this paper CO is applied to optimize an integrated inlet/ejector system of a 2D RBCC engine.The CO architecture is described in figure 8. In this approach the problem is decomposed along analysis-convenient boundaries and subspace optimizers are integrated with each analysis-block. Through subspace optimization each group is given control over its own set of local design variables and is charged with satisfying its own domain-specific constraints. Explicit knowledge of the other groups constraints or design variables are not required. The objective of each subspace optimizer is to agree upon the values of the interdisciplinary variables with the other groups. A system-level optimizer is employed to orchestrate this interdisciplinary compatibility process while minimizing the overall objective. The system level optimizer module, minimizes (or maximizes) an objective function subject to constraints just like any standard optimization problem. The design variables (known as target variables) are set by the system level optimizer to improve the objective function.An inlet/ejector in a RBCC engine is a single discipline system from multidisciplinary optimization point of view. Since any change in geometry or flow condition on boundaries, will affect the whole system from entrance to the nozzle at the end. On the other hand, as problem gets bigger by including more and more variables, using a single optimizer will be more difficult even by isolating the inlet/ejector from other disciplines in the vehicle design. So it is logical to start the inlet/ejector as a multidisciplinary optimization problem.The design was decomposed into two disciplines named as Inlet section (secondary flow area, red enclosure in fig.1) and Ejector/Mixture section (isolator and diffuser section, blue enclosure in fig.1) for implementing CO. In this study only the geometric variables at the baseline design were optimized. The secondary to primary area ratio A s/A5 was the only coupling variable for this CO algorithm. The limiting value for L/D was 1.0-4.0, for A s/A5was 0.6-0.9 and for A8/A5 was 1.0-3.0. One linear constraint was applied to the ejector mixture section. The objective function in the inlet was the static pressure recovery, and for the mixture/ejector it was by pass ratio, . The objective function used in this analysis wasMin F = 1/ + 1/ .i.e Min F= P i/P s + m p/m swhere, Pi.= Static pressure at the free inlet, Ps.= Static pressure at the secondary inlet, m s= secondary mass flow rate and m p = primary mass flow rateSystem Level:P= [A s/A5, F]Min F (Z) = (Z1, Z2,) + (Z2, Z3)s.t. 2,1;0)(==jzgjSubsystem 1:P1=[L/D, A s/A5, ]Min21121111)()()(iiiizyzxxg+=s.t.iiiuxl<< for i = 1, 2Subsystem 2:P2=[A s/A5, A8/A5, ]Min22222222)()()(iiiizyzxxg+=s.t.iiiuxl<< for i = 2, 3X1 represents L/DX2 represents A s/A pX3 represents A8/A5Linear Constraints: Secondary area (A s) should be equal or grater than 1/3 of Ram burner area (A8)i. e, X2 > (1/3) X33X2– X3 > 0.03. RESULTS AND DISCUSSIONS3.1 Flow Field overview:Color contours of static pressure and Mach number on the RBCC internal flow path for two configurations; case-1 and case-3are shown in figure-2 and 3 respectively.The freestream zones downstream of the nozzle were omitted from these images. The rocket engine plume is clearly visible on the horizontal centerline. The Mach number contours indicate that the flow is entirely subsonic as it entered the diffuser section of the duct. The average Mach number at the nozzle exit was approximately 0.75.The Mach number contours of the A s/A5=0.64 (case-1) configuration indicate the primary flow attached to the mixer wall sooner and incurred significantly stronger shocks than the A s/A5=0.88 (case-3) configuration. The shocks were caused by the primary flow’s interaction with the secondary flow and the mixer wall. The increasing length of inlet section reduces the inlet angle, which increases the pressure recovery. The effect of pressure recovery with L/D ratio is shown in Figure4. Figure 5 indicates the largest driver in the by-pass ratio was A s/A5.This was a result of the different primary thruster exit pressures. For the range ofA s/A5 studied, the primary thruster exit pressure0.52 atm. (A s/A5=0.76), pumped the most secondary air flow. A8/A5 had less dramatic but yet significant effects on by pass-ratio. The trends of pressure recovery and by pass ratio for all configurations are summarized in figure 4 and 5 respectively.3.2 Optimization results:The CFD data of 18 cases were used to generate a response surface. This response surface was used for training the neural network and later it was used for objective function evaluation, during the optimization process. At first step the decomposition was done for a simple bounded from in which two disciplines are both limited to the domain variables. In this form the collaborative optimization will converge in first iteration because two disciplines will agree with system level suggestion. In the second run, one linear constraint was applied in one of the disciplines such that when that discipline receive the suggested value from the system level, that will not necessarily agree, and start sending back the new suggestions as it was trying to decrease the discrepancy between the system level variable and it’s own suited variable. Some of the optimally constraints are mentioned in [8]but the applied constraint was chosen arbitrarily to show the effect of constraints existence.After 63 iterations, system level converged to the optimum value. Figure 6shows a convergence history of system level objective function and constraints. The value of objective function jumps from one solution domain to another, as it tries to reduce the interdisciplinary discrepancies. The results show that the minimum value of the function always occurred when the constrains are relatively big and the iterations continue. Figure 7 shows the system level convergence of design variables.CONCLUSIONSIn this investigation, the collaborative optimization architecture was used to perform multidisciplinary design of an inlet/ejector of 2-D RBCC engine. Posed to suit the collaborative architecture, this design problem was characterized by 3 design variables and 1 constraint. A moderate primary thruster size and exit pressure less than ambient concept was obtained which is very much consistent with current research9,10 on RBCC engine. It appears a primary thruster exit pressure moderately below than ambient is more desirable than primary thruster exit pressure significantly more or less than ambient. The practical advantages of collaborative optimization like the ability to use domain-specific analyses, inherent system flexibility and modularity, distributed analysis optimization capability and significant reduction in communication requirements make the architecture well-suited for the optimization of a 2D RBCC inlet/ejector system.ACKNOWLEDGEMENTThis work has been supported by NASA Marshall Space Flight Center under grant No. NAG8-1668.REFERENCES1. Escher, William J. D. and B. J. Flomes:A Study of Composite Propulsion Systems For Advanced Launch Vehicle Application, Contract NAS7-377, The Marquardt Corporation, Van Nuys, California, 1966,Vol.1-7.2. Braun, R.: Collaborative Optimization: An Architecture for Large-Scale Distributed Design, PhD thesis, Stanford University, June 1996.3. Sparks Jr., D.W., and Maghami, P. G.: Neural Networks for Rapid Design and Analysis, AIAA-98-1779.4. R.D. Braun: Collaborative Optimization -An Architecture/or Large-Scale Distributed Design, PhD thesis, Stanford University, June 1996.5. R.D. Braun and I.M. Kroo: Development and Application of the Collaborative Optimization Ar c hitecture in a Multidisciplinary Design Environ-ment, SIAM, 1996.6. I. Sobieski and I. Kroo: Collaborative Optimization Applied to an Aircraft Design Problem, AIAA Paper 96-0715, Jan. 1996.7. R. Braun, I. Kroo, and A. Moore: Use of the Collaborative Optimization Architecture for Launch Vehicle Design, AIAA Paper 96-4018, Bellevue, WA, Sept. 1996.8. Pretzel, P. W., Palumbo, D. L., and Arras, M. K.: Fault Tolerance of Artificial Neural Networks with Applications in Critical Systems, NASA Technical Paper 3187.9. Stroup, K., and Pontzer,R., “Advanced Ramjet Concepts, Volume I. Ejector Ramjet Systems Demonstration,” Air Force Aero Propulsion Lab., TR-67-118, Van Nuys, CA, June 1968.10. Siebenhaar, A., and Bulman, M., “The Strutjet Engine: The Overlooked Option for Space Launch,” AIAA paper 95-3124, July 1995.11. Carpenter, W. C., and Barthelemy, J.F. M.: A comparison of Polynomial Approximations and Artificial Neural Nets as Response Surface, Structural Optimization 5,pp. 166-174, Springer-Veriag, 1993.12. Olds, J., and Bradford, J.: SCCREAM (Simulated Combined-Cycle Rocket Engine Analysis Module) - A Conceptual RBCC Engine Design Tool, AIAA Paper 97-2760, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA, July 6-9, 1997.13. Daines, R. L. and Merkle, C. L.: Computational Analyses of Mixing and Jet Pumping in Rocket Ejector Engines, AIAA Paper 95-2477, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, San Diego, CA, July 10-12, 1995.14. Billig, F. S.: Low-Speed Operation of an Integrated Rocket-Ram-Scramjet for a Trans atmospheric Accelerator, in Developments in High-Speed-Vehicle Propulsion Systems, ed. by Murthy, S.N.B. and Curran, E.T., published by American Institute of Aeronautics and Astronautics, Inc., Virginia, U.S.A., 1995.Figure 1: Schematic View of a 2-D Axissymetric RBCC Engine.Secondary Inlet Ejector/MixerL/D A s /A 5A 8/A sA s /A 51.1750.64 1.50.642.350.76 2.00.763.5270.882.50.88Table 1: Design Variables for Generating Response SurfaceCase No.A8/A5L/D As/A5Pressure Recovery By Pass Ratio Objective Function 12 1.1750.640.7293 2.31641.80288222 1.1750.760.8392.3138 1.62408532 1.1750.880.8675 2.4803 1.55591542 2.350.640.7712 1.8984 1.82344052 2.350.760.8437 2.3066 1.61879462 2.350.880.8635 2.1163 1.630600723.5270.640.8714 1.8717 1.68185282 3.5270.760.8964 1.9626 1.62510292 3.5270.880.9095 2.3946 1.51711210 1.5 2.350.640.7189 1.8684 1.926231112 2.350.640.8388 2.0894 1.67078612 2.5 2.350.640.8709 2.4509 1.55625113 1.5 2.350.760.8069 2.0819 1.719640142 2.350.760.8496 2.3066 1.61056315 2.5 2.350.760.8973 2.7342 1.48019216 1.5 2.350.880.7108 1.8831 1.937905172 2.350.880.9173 2.1163 1.562679182.52.350.880.87012.52271.545694Table 2. Figures of Merit Results for the Inlet/Ejector Trade StudyFigure: 2(a) Pressure contour of the RBCC internal flow path for the configuration, L/D=1.175,A s /A p =0.64 and A 8/A 5=2.0 (CASE-1).Figure: 2(b) Mach contour of the RBCC internal flow path for the configuration, L/D=1.175,A s /A p =0.64 and A 8/A 5=2.0 (CASE-1).Figure: 3(a) Enlarged view of Pressure contour of the ejector section of RBCC internal flow path for theconfiguration, L/D=1.175, A s /A p =0.88 and A 8/A 5=2.0 (CASE-3).Figure: 3(b) Enlarged view of Mach contour of the ejector section of RBCC internal flow path for theconfiguration, L/D=1.175,A s /A p =0.88 and A 8/A 5=2.0 (CASE-3).L/D RatioP r e s s u r e R e c o v e r y (%)A 8/A 5 RatioB y P a s s R a t i oFigure: 5: Comparison of By Pass Ratio ofEjector Section.10203040506070C o n s t r a i n t s , L o g ||g i *||-5-4-3-2-1O b j e c t i v e F u n c t i o n1.4751.4801.4851.4901.4951.5001.5051.5101z 2g Figure 8: The Collaborative Optimization Architecture in Detail。
