CFD Advanced Modeling Methods for Hypersonic Scramjet AIAA-2006-4578.pdf

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American Institute of Aeronautics and Astronautics

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Advanced Modeling Methods for Hypersonic Scramjet

Evaluation

R.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. Introduction

FD methodology has matured significantly over the past decade, permitting its application to hypersonicscramjet 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 approachthat 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 beingdeveloped 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 islargely 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.

C

42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit9 - 12 July 2006, Sacramento, CA


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II. Numerical Modeling Overview

The analysis capability is based on use of two computational fluid dynamics codes; the structured grid, CRAFTCFDcode and the multi-element unstructured (UNS) grid, CRUNCH CFDcode 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 CRAFTCFDcode 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 becomeroutine, 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 gridadaptation, 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 Definition

Multi-Variate Genetic Design

Optimization

Trial and errorFlow Path Design

PDF turbulent combus tion

model, vibrational

nonequilibrium

Standard/extended mechanisms

with igniti on and air reactions

H/N/O Thermochemistr y

Local valued from PDEsConstant Prt/SctTurbulent Scalar

Transport

Multi-pass, grid refinement and

grid mov ement

Single pass, tet/prism

refinement

Grid Adaptation

EASM non-linear modelUnified k with extensionsTurbulence Models

PDEs for onset/intermittencyAlgebraic Onset/In termittencyTransitional Models

ADVANCEDBASICMODELING

Multi-Variate Genetic Design

Optimization

Trial and errorFlow Path Design

PDF turbulent combus tion

model, vibrational

nonequilibrium

Standard/extended mechanisms

with igniti on and air reactions

H/N/O Thermochemistr y

Local valued from PDEsConstant Prt/SctTurbulent Scalar

Transport

Multi-pass, grid refinement and

grid mov ement

Single pass, tet/prism

refinement

Grid Adaptation

EASM non-linear modelUnified k with extensionsTurbulence Models

PDEs for onset/intermittencyAlgebraic Onset/In termittencyTransitional Models

ADVANCEDBASICMODELING

III. Advanced Modeling Methods

The 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. Thiscapability is demonstrated, shown in Figure 1, on a data set from LENS I showing flow transition on a two-

dimensional compression ramp. The only model parameter prescribed (not fixed) was that of quantifying tunnelnoise (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 thecomparisons, 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.


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exp. dataexp. data

CRAFT -CFD

exp.dataexp. data

CRAFT -CFD

Figure 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 tothe 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 overallflow 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 Flowpath

Inward Turning Model Tested at CUBRCInward Turning Concept Flowpath

Figure 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, Figure3 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 theproduct was isolated in a purely tetrahedral region which was also adapted. Mixing efficiency changes due to grid

resolution was also discussed in ref. 3.


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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 symmetryplane 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 thedesign methodology.

Adapted Grid ResultsOriginal Grid Results Adapted Grid ResultsOriginal Grid Results

Figure 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 turbulentthermal 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 sampleproblem 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 modelis able to capture the basic features of these fluctuations but seem to be under-predicting the fluctuations. Using the

Circular Injector Design Study

Origina l Grid

Refined GridAdapted Original

Product Species Conc.Circular Injector Design Study

Origina l Grid

Refined GridAdapted Original

Product Species Conc.


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RANS 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.

Comparison at X=5

Single Flush Injector,

LES vs. RANS

LES RANS LES RANS

Comparison at X=5

Single Flush Injector,

LES vs. RANS

LES RANS LES RANS

Figure 5. Sample Test Case showing LES validation case to RANS model prediction

Variable Prt Variable Sct Effective LetX=1 X=3

X=5 X=7

X=1 X=3

X=5 X=7

Variable Prt Variable Sct Effective LetX=1 X=3

X=5 X=7

X=1 X=3

X=5 X=7

Figure 6. Results of local turbulent Prandlt and Schmidt numbers for sample test case

The 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 streamis 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


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downstream 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:H2injector: 30, Mach 2.5, 130K

Air inflow: Mach 2.0, 1187K, vitiated

Inflow Mass Fractions

0.2 H2O, 0.23 O2, 0.57 N2

Figure 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 highperformance 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 afinal 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, themethodology is becoming practicable because of massively multi-processor computers and has become a viable tool

in the design process.


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Final Optimized Design

Original Baseline

Design

Mixing Efficiency Curves for 2D Injector Design Study

Axial Distance

MixingEfficienc

Final Optimal Design

Original Design Final Optimized Design

Original Baseline

Design

Mixing Efficiency Curves for 2D Injector Design Study

Axial Distance

MixingEfficienc

Final Optimal Design

Original Design

Figure 9. Genetic Design Optimization for injector pattern

IV. Conclusions

This 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 islargely 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 designmethodology for the basic analysis capability that can provide a higher level of accuracy for scramjet flow path

evaluations.

Acknowledgments

Computational 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 co-workers at CRAFT-Tech for all the help and support they have provided.

References1 Holden, 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, 2000.2 Ahuja, V., and Hosangadi, A., Design Optimization of Complex Flowfields Using Evolutionary Algorithms and Hybrid

Unstructured CFD, Paper No. AIAA-2005-4985, 17thComputational Fluids Dynamic Conference, Toronto, Ontario, CA,

Jun. 6-9, 20053 Ungewitter, R.U., Ott, J.D. ,Ahuja, V., and Dash, S.M., CFD Capabilities for Hypersonic Scramjet Propulsive Flowpath

Design, AIAA Paper 2004-4131, 40thAIAA Joint Propulsion Conference, Fort Lauderdale, FL, July 11-14, 2004.


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4 Ungewitter, R.J., Papp, J.L., Dash, S.M., and Kennedy, K.,Structured/Unstructured RANS Simulations of HypersonicScramjet Propulsive Flowpaths and Comparisons with CUBRC/LENS Test Data, 2002 JANNAF 26th Airbreathing

Propulsion Subcommitte (APS) Meeting, Sandestin, FL, April 8-12 2002.5 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 20056 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

7 Papp, J.L. and Dash, S.M., A Rapid Engineering Approach To Modeling Hypersonic Laminar To Turbulent TransitionalFlows,Journal of Spacecraft and Rockets, Vol. 42, No. 3,May-June,2005

8 Dash, S.M., Hosangadi, A., R.J. Ungewitter, Ott, J.D, and Brinckman, K.W.,Hypersonic Scramjet Technologyenhancements for Long Range Interceptor Missile, DOD HPCMO 2005 Users Group Conference, Dever, CO June 26-29 2006

9 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 TechnologiesConference, Capua, Italy, May. 2005

10 Cavallo, P.A., and Grismer, M.J., Further Extension And Validation Of A Parallel Unstructured Mesh Adaptation PackagePaper No. AIAA-2005-0924, 43rdAerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 10-13, 2005

11 Brinckman, K.W., Kenzakowski, D.C., and Dash, S.M., Progress in Practical Scalar Fluctuation Modeling for High-SpeedAeropropulsive Flows, Paper No. AIAA-2005-0508, 43rdAerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 10-13, 2005

12 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

13 Calhoon, W.H., Jr., Brinckman, K., Tomes, J., Mattick, S. and Dash, S.M.., Variable Turbulent Prandtl Number Modelingfor Application to High Speed Reacting Flows Extended abstract submitted to 44thAerospace Sciences Meeting and

Exhibit, Reno, NV, Jan. 9-12, 200614 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 , 44thAerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 9-12, 2006.15 OByrne, 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, 200416 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 45 th Aerospace Sciences Meeting andExhibit, Reno, NV, Jan. 8-11, 2007

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