ONE DIMENSIONAL ANALYSIS PROGRAM FOR SCRAMJET AND RAMJET FLOWPATHS Kathleen Tran and Walter F. O'Brien, Jr Center for Turbomachinery and Propulsion Research Virginia Polytechnic Institute and State University Abstract One-Dimensional modeling of dual mode scramjet and ramjet flowpaths is a useful tool for scramjet conceptual design and wind tunnel testing. Modeling tools that enable detailed analysis of the flow physics were developed and implemented as part of a one-dimensional MATLAB-based model named VTMODEL. VTMODEL divides ramjet or scramjet flow paths into four major components: inlet, isolator, combustor, and nozzle. The inlet module provides two options for supersonic inlet calculations: MIL Spec 5007D and a kinetic energy correlation with the option of a total temperature term. The isolator model calculates the pressure rise and the isolator shock train using two different methods. The two models are a combined Fanno flow and oblique shock system, and a rectangular shock train correlation. There are also two options for the combustor module: a non-equilibrium reduced-order hydrogen calculation using a mixing correlation. The second option is an equilibrium hydrogen calculation with a growing combustion sphere combustion model which is adaptable to any fuel. Both models calculate Mach number and thermodynamic flow properties using a 4 th order Runge Kutta solver. The model can take into account heat transfer, change in specific heat ratio, change in enthalpy, and other thermodynamic properties. A c p dx f H h o M P P t Q R Re θ T T t T TSFC u 5 V e w W W x Nomenclature Area Specific Heat at Constant Pressure Finite change in x Coefficient of Friction Enthalpy Stagnation Enthalpy per Unit Mass Mach Number Mass Rate of Flow Pressure Total Pressure Net Heat per Unit Mass of Gas Gas Constant Reynolds Number Based on Momentum Thickness Static Temperature Total Temperature Thrust Thrust Specific Fuel Consumption Exit velocity Nozzle Exit Velocity Mass Rate of Flow of Gas Stream Molecular Weight Work X x Greek γ θ η n Drag Force Axial Location Ratio of Specific Heats Boundary Layer Momentum Thickness Nozzle Adiabatic Efficiency Subscripts a At altitude 0 Inlet 1 Isolator Entrance Combustor Entrance 3 Combustion Module Exit 4 Combustor Exit 5 Nozzle Exit s Isentropic 1
Introduction One dimensional scramjet flowpath analysis codes are useful analytical tools for ramjet and scramjet researchers and designers. Despite the limitations of the flow physics, there are many advantages to one dimensional code versus two or three dimensional codes. One of the biggest advantages is faster computational times with an emphasis on overall performance-based cycle analysis. One dimensional analysis cannot predict the effects of boundary layers and other multidimensional flow properties. Though scramjet internal flow is highly multidimensional, the use of a one dimensional code is still relevant. There are multiple scramjet and ramjet flowpath analysis codes. These include codes that are developed by universities and government research labs. One of these codes is Ramjet Performance Analysis Code (RJPA). This code is an industry standard that was developed at the Applied Research Laboratory 1. The program uses control volume calculations and constant epsilon combustion. One of the biggest limitations of this program is the restrictions to US persons only since it is governed by the Internal Traffic in Arms Regulations. This restriction limits the access and use of the program from public domain. Another recent analysis code from Georgia Tech is SCCREAM. SCCREAM stands for Simulated Combined-Cycle Rocket Engine Analysis Module. This code was developed in C++ and combines three dimensional modules with a one dimensional combustor. The main focus of this paper is to describe an approach for modeling scramjet and ramjet flowpaths within a model known as VTMODEL. For the model, the scramjet flow path is divided into four components: the Inlet, Isolator, Combustor, and Nozzle 3. These components follow the main components of ramjet and scramjet flow paths as seen in Figure 1. VTMODEL anchors the analysis at one of three static pressure stations: (1) combustor entrance, () combustor exit, or (3) nozzle exit. Figure 1: Scramjet Schematic Courtesy of NASA Langley 1. Inlet Modeling The supersonic inlet is modeled in two different ways. Both methods require an input of flight altitude and Mach number. VTMODEL will use these inputs along with the US Standard Atmosphere 4 properties at altitudes iterating every 5,000 feet to calculate the flight conditions. The first method of determining pressure recovery uses MIL SPEC E-5007D 5. Po/Po1=1 from M o =0 to 1 (1) Po/Po1=1-0.0776(M-1) 1.35 from M o >1 to 5 () Po/Po1=800/(M 4 +935) for M o >5 (3) The second method of inlet calculation is based on the compilation of inlet information by Van Wie 6. He used experimental results to calculate two kinetic energy correlations. The two correlations are as follows: 10.581 /. (4) 10.41 / (5) From these correlations, the following equation is then used to find the inlet pressure recovery η KE = ( γ 1) γ 1 1 + M γ To1 0 γ 1 0 M 0 To 0 1 Po Po (6)
. Isolator There are also two isolator models to choose from. The first isolator model divides the isolator into two sections comprising of pressure rise due to Fanno flow and then pressure rise from the isolator shock train. The Fanno flow section uses the following equation and compressible flow relationships to calculate the pressure rise due to friction in a constant cross sectional area 7. where c f =0.0015 is chosen for the coefficient of friction (7) temperature prediction is the result of successive combustion calculations within each finite difference in x ( x) over the length of the combustor. The amount of fuel burned in each section is modeled using a fuel-air combustion sphere. A schematic of this sphere is shown in Figure. This model was developed based on the derivation found in Hill and Peterson 10. This sphere represents the amount of fuel burned in each finite section and is used to calculate the adiabatic flame temperature using complete combustion relationships dependent on the type of fuel used.. The second component models the pressure rise due to the shock train as a series of two reflected oblique shocks. The shock angles are iterated upon until the static pressure conditions at one of the three possible anchor points is satisfied. The second isolator model is based on an experimental shock train correlation in a rectangular duct. This correlation was published by Sullins and McLafferty 8. With this correlation (Eq. 8), only the thermodynamic properties at the beginning and the end of the isolator are calculated. Figure : Schematic of Growing Fuel-Air Combustion Product Sphere Model Concept /. / 3. Combustor 50 1170 1 (8) The ramjet/scramjet combustor is modeled using one of two different combustion methods in addition to an influence coefficient model. The first method uses an equilibrium chemistry model along with a local combustion efficiency model. The second method was developed based on the finite rate nonequilibrium chemistry model published by Jachimowski 9. The first combustion model uses a flame speed model in addition to complete combustion chemistry. This combustion chemistry assumes no dissociation of the combustion product species. The combustion The second model is a non equilibrium hydrogen kinetic model proposed by Jachimowski. He published a chemical kinetic mechanism of hydrogen scramjet combustion in a NASA report. From this report the following chemical equations were used for the chemical kinetics: H + O OH + OH H + O + M HO + M HO + H H + O HO + H OH + OH HO + H H O + O HO + O O + OH HO + OH H O + O HO + HO H O + O 3
In the above chemical equations M represents a non reactive species. The rate coefficients for each reaction were also obtained from the NASA report by Jachimowski. The rate coefficient is defined as follows: k=at n exp(-e/rt) (9) To simplify this non equilibrium calculation, a steady state assumption was made. This assumption allowed kinetic calculation without a full kinetic code. In addition to the above reaction equations, Jachimowski also published a mixing efficiency developed by Anderson et al 9. This efficiency was given in the form of η mix =1-exp(-ax) (10) where a is a constant dependent on Mach number and x is the distance from the fuel injection in centimeters. Along with the combustion model, an influence coefficient model is used to determine the change in Mach number at each station. With the Mach number, other desired properties are calculated such as stagnation pressure and stagnation temperature. The calculation of Mach number using influence coefficients was presented by Shaprio 11. The following equation was solved using a 4 th order Runge-Kutta solver. 4 + / + (11) Basic heat transfer is included in VTMODEL as an option to calculate the cooling load and heat transfer in the combustor. The model uses Reynolds Analogy as a basic heat transfer model. In addition to this analogy, the heat transfer can also be entered directly into the program. 4. Nozzle The nozzle module is an optional component of VTMODEL. This module is bypassed when analyzing data from a direct connect tunnel. The following equation defines the nozzle efficiency. = (1) From the efficiency the exit Mach number and other performance criteria are calculated from Equations 13-15. = (13) h= + (14) = Comparisons of Results with Other Models (15) To further demonstrate the validity of VTMODEL has an option for analysis of scramjet and ramjet flowpaths, VTMODEL was run with various geometries to compare with other models in the literature. The first model was developed at Georgia Tech as part of a Rocket Combined Cycle Analysis program. This model is called SCCREAM and the geometry and the flow conditions were taken from the doctorate dissertation of Bradford. Since Bradford also compared his model to SRGULL and RJPA, these comparisons are included also. In Figure 3, Bradford is comparing SSCREAM to SRGULL. SRGULL was developed at NASA Langley Research Center. SRGULL models the inlet and nozzle in two dimensions with 3 D corrections 1 4
Bradford s dissertation. He varied the flight Mach number from 3 to 1 and compared the I SP obtained by SCCREAM and RJPA. VTMODEL was used to calculate the ISP at the same conditions and are plotted with the RJPA and SCCREAM results in Figure 5. Figure 3: Bradford Comparison of SCCREAM and SRGULL (Bradford 001) VTMODEL was used to analyze Bradford s geometry and compared to his results. Since Figure 3 only shows the Mach number decrease in the combustor, only these results are shown below in Figure 4. Mach Number 5 4.5 4 3.5 3.5 1.5 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x/l Figure 4: VTMODEL Prediction of Bradford Combustor - Mach number As can be seen above, VTMODEL predicted the Mach number decreases in the combustor to be on the same order of magnitude as Bradford s calculations 3. The benchmark program for scramjet and ramjet performance analysis is RJPA. This program was developed at John Hopkins University and is a control volume cycle analysis. Since the results of RJPA were ITAR restricted, published results from two dissertations were used for comparison with VTMODEL. The first set of results was taken from Figure 5: ISP vs. Mach number as Predicted by SSCREAM, RJPA (Bradford 001), and VTMODEL (,3) From the results it can be seen that VTMODEL consistently overpredicts I SP with respect to RJPA and SCCREAM. Some of the reasons for this overprediction include an unknown equivalence ratio and neglected heat transfer through the combustor walls. Also the inlet and nozzle in Bradford s model uses two dimensional analyses while VTMODEL is entirely one dimensional. VTMODEL was also used to compare to another RJPA analysis where the heat transfer and equivalence ratios were known. In Bonanos dissertation, he used RJPA to perform cycle analysis and combustion efficiency analysis on experimental data obtained from the University of Virginia direct connect wind tunnel. His results with an aeroramp and flame holder were compared to a physical ramp. VTMODEL was used to analyze the Bonanos flow path for air specific impulse. In the analysis, no aeroramp was assumed, and an inlet total temperature of 1010K was used. In Figures 6 and 7, VTMODEL results are overplotted with Bonanos RJPA analysis 13. 5
combustion models comprising of a simplified kinetic equilibrium model and a complete combustion nonequilibrium model. Figure 6: Air Specific Impulse Predicted by VTMODEL Overlay over Bonanos (Bonanos 005) (3,13) Figure 7: Air Specific Impulse Predicted by VTMODEL for To=1010K Overlay over Bonanos (Bonanos 005) (3,13) From the above figures it can be seen that with the addition of heat transfer and the knowledge of some specific modeling parameters, VTMODEL was able to predict air specific impulse values close to RJPA predicted values. Without the addition of heat transfer, VTMODEL overpredicts the values of air specific impulse. The values were approximately 11%-17% higher than the numbers presented in Figures 6 and 7. Summary VTMODEL was created to be a modular code that can be improved upon and expanded. The code was constructed with four main sections to reflect the four main sections of a ramjet or scramjet: inlet, isolator, combustor, and nozzle. For each of the first three sections, the user has two different options for modeling paths. The inlet provides two options for pressure recovery: MIL Spec and kinetic energy correlation. The isolator model also has two options for analysis. The first is a Fanno flow/ oblique shock system that iterates on shock angles and the second is a shock train correlation. The most complex model section is the combustor section. There are two In this paper, VTMODEL was used to compare to published modeling results. The model closely predicted air specific impulse with the addition of heat transfer to the combustor module. Several improvements can be made to VTMODEL. The program is written in a manner that requires programming knowledge. A visual graphical interface can be developed. One of the first improvements that should be made is the addition of l Hopital s rule or another mathematical technique to enable calculation through M=1 in the combustor with the influence coefficient method. Another major improvement would be the addition of a more detailed heat transfer analysis. Currently, VTMODEL uses Reynolds Analogy. Due to the modular nature of VTMODEL, these improvements can be made and implemented easily without reprogramming the entire code. References 1. Pandolfini, P.P., and Friedman, M.A. Instructions for using Ramjet Performance Analysis (RJPA) IBM-PC Version 1.4. JHU/APL, June 199.. Bradford, J. E. A Technique for Rapid Prediction of Aftbody Nozzle Performance for Hypersonic Launch Vehicle Design. Aerospace Engineering. Atlanta, Georgia Institute of Technology. Doctor of Philosophy. 001. 3. Tran, K.N. One Dimensional Modeling of Scramjet and Ramjet Flowpaths. Mechanical Engineering. Blacksburg, Virginia Polytechnic Institute and State University. Masters of Science. 010. 4. United States Government Printing Office.US Standard Atmosphere. Washington DC. 1976. 5. MIL-E-5007D. Handbook from Pratt and Whitney. 6
6. Van Wie, D. M. (001). Scramjet Inlets. Scramjet Propulsion (Progress in Astronautics and Aeronautics). P. Zarchan. pp 189. 7. Hill, Philip and Peterson, Carl. Mechanics and Thermodynamics of Propulsion. nd Edition. New York: Addison Wesley Longman, 199. 8. Sullins, G. and McLafferty. (199). Experimental Results of Shock Trains in Rectangular Ducts. AIAA Fourth International Aerospace Planes Conference. Orlando, FL, 199. 9. Jachimowski, C. An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion. NASA Langley Research Center. Hampton, VA, 1988 10. Hill, Philip and Peterson, Carl. Mechanics and Thermodynamics of Propulsion. 1 st Edition: 3 rd Printing. Reading: Addison Wesley Longman, 1975. pp. 18-0. 11. Shaprio, Ascher H. The Dynamics and Thermodynamics of Compressible Fluid Flow in Two Volumes. New York: Ronald Press Company, 1953. 1. Zweber, J. V., Hanee Kabis, William W. Follett, and Narayan Ramabadran. Towards an Integrated Modeling Environment for Hypersonic Vehicle Design and Synthesis. AIAA/AAAF 11th International Space Planes and Hypersonic Systems and Technologies Conference. New Orleans, American Institute of Aeronautics and Astronautics. 00. 13. Bonanos, A. M. Scramjet Operability Range Studies of an Integrated Aerodynamic- Ramp-Injector/Plasma-Torch Igniter with Hydrogen and Hydrocarbon Fuels. Aerospace Engineering. Blacksburg, Virginia Polytechnic Institute and State University. Doctor of Philosophy. 005 7