Advanced Modeling Methods for Hypersonic Scramjet Evaluation

42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 9-12 July 2006, Sacramento, CaliforniaAIAA 2006-457842nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit9 - 12 July 2006, Sacramento, CAAIAA-2006-4578Advanced Modeling Methods for Hypersonic Scramjet EvaluationR.J. Ungewitter, J.D. Ott and S.M. Dash. Combustion Research and Flow Technology, Inc. (CRAFT Tech), Pipersville, PA 18947 Propulsive flowpaths for scramjet missiles are being evaluated using a high-fidelity CFD methodology to determine optimum performance and to extend ground test data to flight environments. With advances in parallel computer architecture, the use of CFD modeling is now playing a major role in the design phase of the propulsion system. Special attention has been paid to fuel injector design and modeling, which requires multi-element unstructured numerics with new grid adaptation techniques to obtain accurate values for combustion efficiency. The flow path physical modeling has been improved by use of new models for turbulence transition and turbulent scalar fluctuations. These new models add more equations but provide a higher level of fidelity to the solution. Genetic optimization techniques are used to establish optimal injector spacing / orientation, and nozzle shapes that maximize thrust and thus expand the role of CFD from an analysis tool to a design methodology.I.IntroductionCFD methodology has matured significantly over the past decade, permitting its application to hypersonic scramjet design studies with increasing levels of confidence. Via the availability of massively parallel hardware platforms and CFD codes optimized to perform efficiently on such platforms, end-to-end RANS simulations with resolved grids can now be obtained quickly using 128-512 processors. While RANS methodology has limitations in its ability to deal with the complex turbulent processes that occur in a scramjet, it is the only “practical” approach that can presently support complex designs accounting for the real three-dimensional nature of the flow path. The use of LES has been limited to unit problem studies, primarily used to support RANS turbulence model calibration where experimental data is lacking or inadequate. It has also been used “locally”, to bridge regions where larger scale unsteady effects predominate (i.e. where cavity flame holding is utilized). In our work over the past several years, CFD has been applied to support the design of scramjet propulsive systems for next-generation, hypersonic missiles. Overall work has entailed:• CFD code upgrades for enhanced accuracy and efficiency; • systematic validation of the turbulence and transitional models used in the CFD codes; • analysis of full-scale scramjet propulsive flow paths tested at CUBRC [1]; and, • design / optimization of scramjet components [2, 3]. With regard to CFD code upgrades, accuracy, which is critical for analyzing fuel/air mixing and flame holding, has been enhanced by use of multi-element UNS numerics with several levels of grid adaptation. Chemistry, solved using point implicit iterative techniques, requires more execution time in regions with stiff ignition or rapid combustion, leading to load imbalances, implementing conventional domain decomposition methodology (i.e. same number of nodes in each domain). New dynamic load balancing techniques based on work per node are being developed in an attempt to remedy this problem, having the potential to reduce overall CPU requirements substantially (see ref. 3 for more details). Today a reasonably well established capability exists to analyze and predict key performance parameters of scramjet propulsive flow paths when the modeling is limited to a few injector elements and where combustion is largely diffusion controlled and not ignition sensitive [4]. For more complex scramjet flow paths using inward turning inlet concepts the data comparison are being improved by the work described [5]. We are interested in improving the numerical fidelity of our analyses by enhancing the modeling of several key physical processes while still maintaining a reasonable turn around time. This paper will describe several new capabilities that are being incorporated into the methodology that will extend the applicability and accuracy of the tools. 1 American Institute of Aeronautics and AstronauticsCopyright © 2006 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.AIAA-2006-4578II. Numerical Modeling OverviewThe analysis capability is based on use of two computational fluid dynamics codes; the structured grid, CRAFT CFD® code and the multi-element unstructured (UNS) grid, CRUNCH CFD® code whose most recent features for scramjet analyses are described in ref. 3. Each code is applied to different sections of the scramjet flow path, depending on the grid topology. The UNS solver is utilized for the fuel injection region, which has several different length scales requiring high resolution and thus grid adaptation. It is also applied to complex geometric shapes like the inward turning design. In other areas where the geometry is easily modeled by a structured solver, the CRAFT CFD® code is used since it is computationally faster. Both codes have nearly identical capabilities. The scramjet analyses performed to date have utilized “first-generation” or basic models. Improvements being made leading to “second generation” or advanced models are discussed in ref. 6. The availability of massively parallel computer platforms has increased so that analyses with 256 or more processors are starting to become routine, allowing for rapid turn around of nose-to-tail studies, even at higher levels of physical modeling. Table 1 lists the progression of models used in scramjet analyses from a basic level to newer advanced level. The basic level is the level at which all of our “routine” scramjet analyses have been performed. The advanced level adds more complex physics and includes better turbulence transitional model, improved turbulence models, enhanced grid adaptation, a stiff chemistry solver, and automated design optimization techniques that can be applied to flow path definition studies. Several of these advanced capabilities have matured to the point where they can be applied to routine scramjet analyses. Further validation of these advanced capabilities is still on going to ensure that the modeling techniques and coefficients are optimal for hypersonic scramjet flow paths of interest.Table 1. Scramjet Numerical Modeling DefinitionMODELING Transitional Models Turbulence Models Grid Adaptation Turbulent Scalar Transport H/N/O Thermochemistry BASIC Algebraic Onset/Intermittency Unified kε with extensions Single pass, tet/prism refinement Constant Prt/Sct Standard/extended mechanisms with ignition and air reactions Trial and error ADVANCED PDE’s for onset/intermittency EASM non-linear model Multi-pass, grid refinement and grid movement Local valued from PDE’s PDF turbulent combustion model, vibrational nonequilibrium Multi-Variate Genetic Design OptimizationFlow Path DesignIII.Advanced Modeling MethodsThe PDE-based turbulence transition modeling has developed to the point where it can be applied to standard two dimensional analyses and some three dimensional analyses. Papp et. al. documents the latest modeling improvement in ref. 7. The transitional modeling uses an additional equation to determine the onset location, and another equation that models the intermittency, which is the blending from laminar to turbulent conditions. This capability is demonstrated, shown in Figure 1, on a data set from LENS I showing flow transition on a twodimensional compression ramp. The only model parameter prescribed (not fixed) was that of quantifying tunnel noise (see ref. 7). Once calibrated, the model was very effective in predicting turbulent onset for all dynamic pressures tested. Pressure measurements were well matched while heat transfer comparison show a variation in the comparisons, but provide good estimates on the thermal environment. The turbulent transition model is a regular part of our design methodology and provides a means to extend ground test designs to flight environments.2 American Institute of Aeronautics and AstronauticsAIAA-2006-4578exp. data CRAFT -CFDFigure 1. Heat Transfer Comparison of 2D Inlet ramp At typical flight profiles of scramjet missiles, it is necessary to promote the transition to turbulent conditions through the use of transition aids, or trips. These transition trip mechanisms add an additional level of complexity to the modeling and may require modifications to the turbulence model to accurately predict the small scale features not captured by the numerical model. A recent numerical analysis of a typical inward turning inlet resolved each individual trip using a hybrid grid of prisms, hexahedral, pyramid and tetrahedral elements that exceeded 6 million elements. Accurately resolving the flow field changes caused by the trips plays a key role in predicting the overall flow path. Details of the trip modeling is reported by Dash et. al. [8]. Figure 2 shows the test hardware and flow path tested at CUBRC under the HYCAUSE program [9] with analysis results reported in ref. [5].Inward Turning Model Tested at CUBRCInward Turning Concept FlowpathFigure 2. Inlet Section and Numerical Model from S. Walker, et. al. (AIAA paper 2005-3254, [9]). Grid adaptation is a tool that allows the quality of the analysis to be improved automatically. By refining the grid in regions of strong gradients we can enhance the accuracy of the solution. CRAFT Tech has developed a stand alone grid adaptation tool called CRISP [10]. This tool has been very effective at identifying regions where the grid has limited resolution and in refining the grid, independent of the type of computational cells. For example, Figure 3 shows the change in mixing efficiency as a single injector of a multi-injector round scramjet combustor is refined. Also shown is an axial cut of the product composition on the original and adapted grids. The refined grid side shows how the gradient hexahedral cells were refined in the fuel air interface region. Early in the domain the product was isolated in a purely tetrahedral region which was also adapted. Mixing efficiency changes due to grid resolution was also discussed in ref. 3.3 American Institute of Aeronautics and AstronauticsAIAA-2006-4578Circular Injector Design StudyOriginal Grid Refined GridAdapted OriginalProduct Species Conc.Figure 3. Cell splitting Grid Refinement The current grid adaptation employed (cell splitting) can lead to substantial increases in grid sizes. CRAFT Tech has been pursuing a new stretching-based “r (redistribution)” methodology where no additional cells are added and instead the grid is moved to the regions of high gradients. This capability is shown in Figure 4 where a symmetry plane of a three dimensional analysis of a flush injector is shown that used a hybrid unstructured grid. In this analysis both the tetrahedral and hexahedral cells are relocated so that the resulting grid better resolves the strong gradients. In this case the fuel starts to burn at an earlier location due to the better shear layer resolution. This improved accuracy was achieved with out any increase in grid size and is now also being incorporated into the design methodology.Original Grid ResultsAdapted Grid ResultsFigure 4. Cell Movement Grid Refinement Another modeling improvement that raises the fidelity of an injector analysis is the simulation of turbulent temperature and species fluctuations [11, 12]. These parameters permit obtaining variable turbulent Prandtl and Schmidt numbers, which for most CFD analyses are assumed constant and are used to determine the turbulent thermal and species diffusivity. To demonstrate the variation of these turbulent quantities, an LES study was performed on single flush injector unit test case. A flush angled wall jet is introduced to a turbulent boundary layer flow and the mixing between the fuel jet and free stream air is analyzed. Figure 5 shows a schematic of the sample problem with the axial results of the LES and a corresponding RANS analysis using the new scalar turbulent model. The axial cuts show the comparison of the mean temperature, temperature fluctuation, the fuel concentration, and species variation fluctuations. The comparison shows reasonable agreement between the RANS and more accurate LES analysis. Specifically, the temperature and species variation shows that the advanced RANS turbulence model is able to capture the basic features of these fluctuations but seem to be under-predicting the fluctuations. Using the 4 American Institute of Aeronautics and AstronauticsAIAA-2006-4578RANS model results with the turbulent scalar fluctuation model, a local turbulent Prandlt number and Schmidt number are created. These are shown in Figure 6 along with the ratio of the two, the Lewis number. In most CFD analyses the turbulent Prandlt and Schmidt numbers are taken to be a constant ranging between .4 and .9 with the effective Lewis ranging from 1 to 2. The local turbulent numbers show significant variation at each axial location with the effective local Lewis number varying significantly in the shear layer.Single Flush Injector, LES vs. RANSComparison at X=5”LES RANS LES RANSFigure 5. Sample Test Case showing LES validation case to RANS model predictionVariable PrtX=1” X=3” X=1”Variable SctX=3”Effective LetX=5”X=7”X=5”X=7”Figure 6. Results of local turbulent Prandlt and Schmidt numbers for sample test caseThe scalar fluctuation model has produced very good results for coaxial jets and non-reacting flows [13,14]. The model continues to be extended using reacting data sets like the Scholar experiment [15] shown in Figure 7. Here a hydrogen jet is injected into a supersonic stream and combustion occurs. The mixing of the hydrogen and air stream is sensitive to the turbulent transport quantities as shown by Figure 8 as reported by Mattick et. al. [16]. The figure compares contours of temperature and H20 concentrations at Prt = Sct = .9 (Le=1) and using Prt =.9 but Sct = .45 (Le = 2). This comparison shows that use of Le=2 in the near-field leads to an over-prediction of mixing just 5 American Institute of Aeronautics and AstronauticsAIAA-2006-4578downstream of the jet and hence premature combustion. Extending the scalar fluctuation model to reacting wall bounded flows is on going, but will lead to more accurate modeling of critical fuel air mixing phenomena.Experimental Conditions:● ● ●H2 injector: 30º, Mach 2.5, 130K Air inflow: Mach 2.0, 1187K, vitiated Inflow Mass Fractions 0.2 H2O, 0.23 O2, 0.57 N2Figure 7. Schematic of SCHOLAR combustion experiment.Figure 8. SCHOLAR combustion experiment, (a) Predicted vs. Measured Static Temperature, and(b) Predicted H2O Mole Fraction Distribution; Sct = 0.45 and 0.9 (Prt =0.9).Design optimization is a methodology to extend CFD analysis from point design evaluation into a tool for geometry definition. For example, the injector pattern is a function of the injector size, pressure, angle and spacing. Also injectors can be axially off set to take advantage of additional shock mixing. To help define an optimum design, genetic-based optimization theory is used. This provides a mechanism to efficiently converge on a high performance design when investigating several parameters. Genetic based optimization has been shown to work well in an environment were there are multiple design variables [2]. A genetic algorithm based design optimization procedure has been coupled to the multi-element unstructured CRUNCH CFD® code and the grid generation package GRIDGEN. This methodology has been chosen because the search procedure in the genetic algorithm is inherently parallel and has worked well in other multi-variant design applications. Figure 9 shows an original design concept for a flush injector design and the mixing efficiency of multiple design variations performed before a final design was determined. Significant improvement in overall mixing efficiency was achieved and the whole design process occurred nearly seamlessly. Although expensive for complex three dimensional flows, the methodology is becoming practicable because of massively multi-processor computers and has become a viable tool in the design process.6 American Institute of Aeronautics and AstronauticsAIAA-2006-4578Mixing Efficiency Curves for 2D Injector Design StudyOriginal Baseline DesignFinal Optimal DesignMixing EfficiencyOriginal DesignFinal Optimized DesignAxial DistanceFigure 9. Genetic Design Optimization for injector patternIV.ConclusionsThis paper has provided an overview of the new technologies that are presently being incorporated into scramjet flow path design methodology at CRAFT Tech. A baseline approach has proven reasonably successful in matching several scramjet flow paths where geometry is limited to one or two injector elements and the combustion process is largely diffusion controlled. For problems where mixing and ignition processes are more complex, data comparisons are not as good. To extend the analysis capability several new computational techniques have been developed that improve the accuracy of the numerical modeling. These capabilities include redistribution grid adaptation, and advanced turbulence modeling for flow transition, and turbulent model extensions to predict scalar temperature and species fluctuations. Coupled three dimensional design optimization methods have also become an integral part of the design cycle. The modeling enhancements outlined in this paper provides an improved design methodology for the basic analysis capability that can provide a higher level of accuracy for scramjet flow path evaluations.AcknowledgmentsComputational resources for the design optimization studies were provided under the HPCC challenge project “Hypersonic Scramjet Technology Enhancement for Long Range Interceptor Missile”. The authors thank their coworkers at CRAFT-Tech for all the help and support they have provided.References1 23Holden, M.S., “Studies of Scramjet Performance in the LENS Facilities”, AIAA Paper 2000-3604, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, AL, July 17-19, 2000. Ahuja, V., and Hosangadi, A., “Design Optimization of Complex Flowfields Using Evolutionary Algorithms and Hybrid Unstructured CFD,” Paper No. AIAA-2005-4985, 17th Computational Fluids Dynamic Conference, Toronto, Ontario, CA, Jun. 6-9, 2005 Ungewitter, R.U., Ott, J.D. ,Ahuja, V., and Dash, S.M., “CFD Capabilities for Hypersonic Scramjet Propulsive Flowpath Design”, AIAA Paper 2004-4131, 40th AIAA Joint Propulsion Conference, Fort Lauderdale, FL, July 11-14, 2004.7 American Institute of Aeronautics and AstronauticsAIAA-2006-457845 6 7 8910 11121314 15 16Ungewitter, R.J., Papp, J.L., Dash, S.M., and Kennedy, K.,”Structured/Unstructured RANS Simulations of Hypersonic Scramjet Propulsive Flowpaths and Comparisons with CUBRC/LENS Test Data”, 2002 JANNAF 26th Airbreathing Propulsion Subcommitte (APS) Meeting, Sandestin, FL, April 8-12 2002. Ungewitter, R.J., Ott, J.D., Mattick, S, and Dash, S.M., “CFD Design and Evaluation of Mach 10 Propulsive Flow Paths”, 2005 JANNAF 28th Airbreathing Propulsion Subcommitte (APS) Meeting, Charleston, SC, April 13-17 2005 Dash, S.M., “Perspective on Flow field Modeling Advances Needed to Support Hypersonic Scramjet Design and Evaluation”, 2005 JANNAF 28th Airbreathing Propulsion Subcommitte (APS) Meeting, Charleston, SC, April 13-17 2005 Papp, J.L. and Dash, S.M., “A Rapid Engineering Approach To Modeling Hypersonic Laminar To Turbulent Transitional Flows,” Journal of Spacecraft and Rockets, Vol. 42, No. 3, May-June, 2005 Dash, S.M., Hosangadi, A., R.J. Ungewitter, Ott, J.D, and Brinckman, K.W.,”Hypersonic Scramjet Technology enhancements for Long Range Interceptor Missile”, DOD HPCMO 2005 User’s Group Conference, Dever, CO June 2629 2006 Walker, S.H., Rodgers, F.C., Esposita, A.L., “Hypersonic Collaborative Australia/United States Experiment (HYCAUSE)”, Paper No. 2005-3254, AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies Conference, Capua, Italy, May. 2005 Cavallo, P.A., and Grismer, M.J., “Further Extension And Validation Of A Parallel Unstructured Mesh Adaptation Package” Paper No. AIAA-2005-0924, 43rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 10-13, 2005 Brinckman, K.W., Kenzakowski, D.C., and Dash, S.M., “Progress in Practical Scalar Fluctuation Modeling for High-Speed Aeropropulsive Flows,” Paper No. AIAA-2005-0508, 43rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 1013, 2005 Ott, J.D., Kannepalli, C., Brinckman, K.W., and Dash, S.M., “Scramjet Propulsive Flowpath Prediction Improvements Using Recent Modeling Upgrades,” AIAA Paper No. AIAA-2005-0432, 43rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 10-13, 2005 Calhoon, W.H., Jr., Brinckman, K., Tomes, J., Mattick, S. and Dash, S.M.., “Variable Turbulent Prandtl Number Modeling for Application to High Speed Reacting Flows” Extended abstract submitted to 44th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 9-12, 2006 Brinckman, K., Calhoon, W.H., Jr., Mattick, S.J., Tomes, J., and Dash, S.M., “Variable Turbulent Schmidt Number Modeling for High-Speed Reacting Flows” , 44th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 9-12, 2006. O’Byrne, S., Danehy, P. M., Cutler, A. D., “Dual-Pump CARS Thermometry and Species Concentration Measurements in a Supersonic Combustor,” AIAA-2004-0710, 42nd Aerosciences Meeting and Exhibit, Reno NV, Jan 5-8, 2004 Mattick, S.J, Calhoon,W.H. Jr,., Brinkman, K, Ott, J.D. and Dash, S.M., “Improvements in Analyzing Scramjet Fuel Injection Problems Using Scalar Fluctuation Modeling” abstract submitted to 45th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 8-11, 20078 American Institute of Aeronautics and Astronautics。