DEVELOPMENT OF A 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. Due to the inherent three- dimensional nature of the physics, most one-dimensional codes such as the Ramjet Performance Analysis Code (RJPA) separate the flow path components into connected control volumes. In the present paper, the addition of a modeling tool that enables more detailed analysis of flow physics within the combustor is developed as part of a MATLAB based model known as VTMODEL. The development of VTMODEL enables analysis of multiple injectors along with multiple analysis stations within a combustor. The model also integrates overall cycle analysis to support parameter studies of design changes on total thrust and engine performance. Using the functions within the model, components can be easily changed and modified to anchor to wind tunnel data. A c p dx f H h o M m P P t Q R T T t T TSFC u 5 V flow V e w W W x X x Greek γ η n 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 Static Temperature Total Temperature Thrust Thrust Specific Fuel Consumption Exit velocity Bulk Flow Velocity Nozzle Exit Velocity Mass Rate of Flow of Gas Stream Molecular Weight Work Drag Force Axial Location Ratio of Specific Heats Nozzle Adiabatic Efficiency Subscripts a At altitude 0 Inlet 1 Isolator Entrance 2 Combustor Entrance 3 Combustion Module Exit 4 Combustor Exit 5 Nozzle Exit s Isentropic Introduction One dimensional scramjet flowpath analysis codes can be a useful analytical tool for scramjet researchers and designers. There are many advantages to the appropriate use of a one dimensional code versus a two or three dimensional analysis such as CFD. These advantages include faster computational times and a more overall performance-based analysis. Though the analysis cannot predict effects of boundary layers and other multidimensional flow properties, the one dimensional code can provide reasonable ranges for thermodynamic and performance design criteria. Though scramjet internal flow is highly multidimensional, the use of one dimensional codes is still relevant. An industry standard, Ramjet Performance Analysis Code (RJPA) is a legacy code developed at the Applied Research Laboratory at John Hopkins University. RJPA is a onedimensional FORTAN code that analyzes ramjet and scramjet flowpaths. The program is an accepted method for 1D analysis of flow paths 1. The program uses control volume calculations and constant epsilon combustion. However, RJPA has some weaknesses. The program requires complex input Tran 1
lists, and is difficult to use. Though the program is very useful once the interface is learned, the program is governed by the Internal Traffic in Arms Regulations. This restriction limits the access and use of the program from public domain. In general, legacy one dimensional codes such as the Ramjet Performance Analysis Code use control volume approaches for modeling of components of the flow paths. These cycle analysis codes predict and analyze thermodynamic data only at the control volume entrances and exits. While these codes are useful for overall cycle analysis, details within the combustor cannot be resolved. The main focus of this paper is to describe an approach for a model that reduces these limitations, the one-dimensional modeling code, VTMODEL. VTMODEL is written in MATLAB using functions for each scramjet section. For the model, the scramjet flow path is divided into four components: the Inlet, Isolator, Combustor, and Nozzle. 1. Inlet Modeling The inlet function requires an input of the flight altitude and Mach number. The model uses the US Standard Atmosphere 2 properties at altitudes iterating every 5,000 feet. The incoming flight Mach number (M o ) is defined by the user and is used for determining supersonic inlet pressure recovery. The scramjet inlet is modeled using MIL Spec E-5007D 3 for inlet pressure recovery. Po2/Po1=1 from M o =0 to 1 (1) Po2/Po1=1-0.0776(M-1) 1.35 from M o >1 to 5 (2) Po2/Po1=800/(M 4 +935) for M o >5 (3) 2. Isolator The preliminary isolator model is comprised of two components. The first component enables modeling of pressure rises due to friction. The model uses Equation 4 and compressible flow relationships to calculate the pressure rise due to friction in a constant cross sectional area 4. 4c f L D = 4c fl x D 4c fx 1 D where c f =0.0015 is chosen for the friction. coefficient of (4) The total pressure rise due to friction is determined from the user-inputted static pressure profile. With the pressure profile, the pressure increase due to the oblique shock system can be identified from a significant change in the slope of the pressure graph. This pressure rise in the isolator due to the combustion process is modeled using a system of oblique shocks. This system of two reflected oblique shocks is the second component of the isolator model. Since the overall static pressure ratio is input by the user, the shock angles of the reflected oblique shock system can be calculated. From these angles, the Mach number and temperature following each shock is calculated. The isolator exit conditions, determined from the friction and shock pressure rise models, are used as the combustor entrance conditions in the following module. 3. Combustor The scramjet combustor is modeled using a combustion model and an influence coefficient model. The current combustor model requires a user inputted static pressure profile. This profile is used to calculate the change in temperature for constant given pressure due to combustion within each finite difference in x ( x). The temperature prediction is the result of equilibrium combustion calculations over the finite difference. The user inputted combustion efficiency and a hydrogen flame speed model are used to determine the amount of moles of hydrogen fuel that is burned in each section. The hydrogen flame speed model calculates the hydrogen-air combustion sphere caused by injection into the flowpath with following combustion. The model is based on an approach developed in Reference 5. The hydrogen flame speed is set to between 40-80 m/s and is calculated based on the desired combustion efficiency. The analysis uses the relationship between the combustor cross sectional area and the hydrogen sphere. Figure 1 depicts a schematic of the hydrogen flame speed model where V flow is the velocity of the air in the combustor. For the equilibrium combustion calculation, the equivalence ratio along with the hydrogen sphere model determines the moles of hydrogen burned in the section. The calculation assumes no dissociation and does not include any chemical kinetics. For the calculations a variable specific heat, c p is calculated based on the temperature of the flow. The adiabatic flame temperature combustion calculation is used as the temperature at each substation. Tran 2
bypass this oblique shock and continue using the influence coefficient equations for the remainder of the combustor. 4. Nozzle The nozzle module is an optional component of VTMODEL. With the nozzle module, the scramjet performance is calculated using a definite nozzle adiabatic efficiency in Equation 6. η n = h 04 h 5 h 04 h 5s (6) Figure 1: Schematic of Hydrogen Flame Speed Model 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 in Shaprio 6. Equation 5 calculates the local Mach number based on the change of various parameters. This equation is solved with respect to change in x using an explicit numerical integration method. Despite the possibility of the solver to be unstable, the programming for the initial version VTMODEL makes a numeric explicit solver ideal. dm 2 M 2 = 2 1+ γ 1 1 M 2 da + 1+γM2 dq dw x +dh + A 1 M 2 c p T γm 2 1+ γ 1 1 M 2 4f dx D + dx 1/2γPAM 2 2y dw w + 2 1+γM 2 1+ γ 1 1 M 2 dw 1+γM2 dw dγ w 1 M 2 W γ (5) One advantage of a user inputted pressure profile is the ability to analyze trends in the static pressure profile. In the wind tunnel data presented later in this paper, the decreasing pressure in the combustor sharply increases around x=0.227 meters. This increase is caused by an oblique shock, increasing the pressure to atmospheric pressure. When a pressure profile changes inflection at the end of the combustor, VTMODEL calculates the flow as an oblique shock with the static pressure ratio between the inflection point and the combustor exit point. With the oblique shock, VTMODEL assumes termination of combustion at the entrance to the shock. In the case with no inflection, the model will From the efficiency the exit Mach number and other performance criteria are calculated from Equations 7-9. M 5 2 = 2 γ 1 η n 1 P 5 P04 γ 1 γ 1 η n 1 P 5 P04 γ 1 γ (7) Thrust = m V e + P 5 P a A 5 (8) TSFC = m f Thrust Sample Analysis (9) In the following section, VTMODEL is used to predict property variations from a sample wind tunnel test that was run at the University of Virginia Direct Connect Wind Tunnel 7. The equivalence ratio for the run was 0.171 and the flow conditions were set to simulate flight at Mach 5 and 70,000 ft. Since the isolator entrance conditions were known, the inlet module was bypassed and the isolator conditions directly entered into the appropriate point in VTMODEL. For analysis of the University of Virginia Direct Connect Facility 7 the nozzle module is not used. The analysis was terminated at the end of the combustor. The geometry of the combustor is shown in Figure 2 below. The static pressure profile (Figure 3) was inputted into VTMODEL from a text file. Tran 3
Stagnation Temperature(Kelvin) Static Pressure (kpa) Static Temperature (Kelvin) In Figure 5 below, note that the stagnation temperature predicted by VTMODEL is rising through the combustor, but remains constant in the combustor exit oblique shock. This follows the assumption of termination of combustion at the entrance to the shock. 1600 1500 Figure 2: Schematic of UVA Combustor 8 1400 1300 1200 1100 120 110 1000 900 100 90 80 70 60 800 700 Figure 4: Static Temperature Calculated by VTMODEL for Φ=0.171 50 1500 40 1450 Figure 3: Internal Static Pressure Profile from wind tunnel data for Φ=0.171 Entered into VTMODEL The experimental static pressure data was provided by C. Goyne at the University of Virginia for analysis. For this first test of the model, the nozzle module was excluded for the analysis. The x axis shown in the Figures below is Distance from the Ramp Fuel Injector. Since the injection point is at x=0, negative x values designate the isolator and positive x values are in the combustor. Figures 3-4 are the results from VTMODEL assuming 70% hydrogen combustion efficiency with the hydrogen flame speed models; that is, the flame speed model was adjusted to 75.5 m/s to produce 70% combustion of the fuel at the end the combustor. 1400 1350 1300 1250 1200 Figure 5: Stagnation Temperature Predicted by VTMODEL for Φ=0.171 Tran 4
Mach Number 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 Figure 6: Mach Number Predicted by VTMODEL for Φ=0.171 Summary The initial development of VTMODEL was in response to the difficulty of using the Ramjet Performance Analysis Code and the cited limitations of the program. The current version of VTMODEL has many limitations due to the assumptions necessary for the one-dimensional code. Despite these limitations, VTMODEL provides a improved tool for the analysis of a scramjet combustor, beyond a defined control volume code. Since the combustor is segmented, thermodynamic data and Mach numbers can be predicted at any axial location. The hydrogen flame speed model for combustion efficiency also enables the analysis of multiple injection locations. Currently VTMODEL is solely an analytic model due to the requirement of input pressure data. This analytic model can be used to analyze wind tunnel results and parameterizations of the effect of heat transfer, friction, and other variables on the flow. However, the program cannot be used to predict static pressures and the complete profile. To remove these limitations, the author is currently working on making VTMODEL a fully predictive program that will iterate on internal flow properties and external boundary conditions to find the physically correct solution. The combustor modules will also iterate on a combustor exit pressure along with the isolator modules to predict the pressure profile along the entire flow path. The predictive program will only require user inputs of flight Mach number, altitude, combustor geometry, heat transfer, combustion efficiency, and combustor exit pressure. Future Work As discussed, the intent of the VTMODEL modeling effort is to produce an entirely predictive onedimensional internal flow path model for Scramjets. A number of the required modeling steps have been implemented, and completion of the model is near References 1. Pandolfini, P.P., and Friedman, M.A. Instructions for using Ramjet Performance Analysis (RJPA) IBM-PC Version 1.24. JHU/APL, June 1992. 2. United States Government Printing Office.US Standard Atmosphere. Washington DC. 1976. 3. MIL-E-5007D. Handbook from Pratt and Whitney. 4. Hill, Philip and Peterson, Carl. Mechanics and Thermodynamics of Propulsion. 2 nd Edition. New York: Addison Wesley Longman, 1992. 5. Hill, Philip and Peterson, Carl. Mechanics and Thermodynamics of Propulsion. 1 st Edition: 3 rd Printing. Reading: Addison Wesley Longman, 1975. pp. 218-220. 6. Shaprio, Ascher H. The Dynamics and Thermodynamics of Compressible Fluid Flow in Two Volumes. New York: Ronald Press Company, 1953. 7. Experimental Data Given by Robert Rockwell at the University of Virginia. January 2009-January 2010. 8. Le, D.B., Goyne, C.P, Krauss, R.H., and McDaniel. J.C., Experimental Study of a Dual-Mode Scramjet Isolator, Journal of Propulsion and Power, Vol. 25, No. 5, 2008, pp. 1050-1057 Tran 5