TRANSIENT SIMULATION OF LIQUID ROCKET ENGINES: A STEP TOWARDS A MORE EDUCATED PROPELLANT CHOICE BETWEEN KEROSENE AND METHANE.

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1 TRANSIENT SIMULATION OF LIQUID ROCKET ENGINES: A STEP TOWARDS A MORE EDUCATED PROPELLANT CHOICE BETWEEN KEROSENE AND METHANE Chiara Manletti Space Launcher Systems Analysis (SART), DLR, Cologne, Germany, chiara.manletti@dlr.de ABSTRACT It is renowned that transient simulation is a powerul tool which reveals undamental characteristics o any liquid engine. Using the program TLR-Sim (Transient Liquid Rocket Engine Simulator), whose development has recently begun, both LOX/Kerosene and LOX/Methane engine components have been closer examined whilst seeking or a clear indication o advantages associated with the use o one or the other in a number o potential engine applications. Results o the perormed simulations are presented and commented. The program TLR-Sim and its development are shortly presented. A short summary o the program structure and main characteristics precedes the detailed engine analysis and comparison. A brie conclusion will ollow, outlining both the main results o the inspection and a uture roadmap or a subsequent program evolution. NOMENCLATURE a Speed o sound m/s d (hydraulic) diameter m E Total energy per unit volume J/m 3 F Cross-sectional Area m h Surace roughness m h Surace roughness coeicient - l length m m Mass low kg/s n Factor o margin - p pressure bar κ Thermal conductivity W/mK Re Reynolds number - T temperature K u velocity m/s V volume m³ Finite dierence n.a. µ Viscosity Pa s ρ density kg/m 3 ϖ Frequency Hz ξ Friction actor /m 4. INTRODUCTION In the rame o an internal study at DLR, the program TLR-Sim is under development with the goal o perorming transient simulations o liquid rocket engine components. In the attempt o inding the best alternative to the cryogenic propellant couple LOX/LH, studies have been concentrated on comparisons between numerous propellant couples. Amongst the most targeted are LOX/Kerosene, or the latter's storability characteristics, and LOX/Methane, or possible lower acquisition costs, potentially higher achievable speciic impulse, lower pressure drop in cooling channels, superior cooling properties and higher coking limits []. Engine nominal operational point comparisons have already been examined and presented by the DLR Space Launcher Systems Analysis (SART) department. These have led to the conclusion that although the increased motor mass, booster size and hence drag, a reusable methane engine could provide a competitive solution to the extensively studied kerosene engines, with the premise o urther studies. The purpose o the study underway is to ill one o the gaps existing in previous studies, namely the examination and comparison o the transient behaviours o the propellants themselves under speciic conditions.. PROGRAM STRUCTURE The program TLR-Sim possesses a highly modular structure in order to assure as high a degree o lexibility as possible. The general program structure is illustrated in the scheme in Figure.

2 major techniques in the category o more detailed methods are the ollowing: - Method o characteristics (MOC) - Riemann Solvers (RS) The Method o Characteristics has a wide range o applications, thus an equally vast class o possible constructions. One can choose, or example, between explicit and implicit solving methods. A literature survey has revealed that implicit methods, when applied to sharp transients, can lead to initial errors which are carried through the entire calculation and may lead to questionable results. The choice thus alls on the explicit solving routines. Further decisions, coherent with the problem at hand, must be made in the uture. Fig.. TLR-Sim General Flow Diagram. TLR-Sim has been programmed to autonomously generate the components order o computation subsequently to having processed the user-deined input. The simulation is then perormed in three clearly deined steps. The irst part o this step-wise approach consists in calculating components that have been deined as elements. These include pumps, valves, combustion devices and the like. Subsequently, ducts, pipes, and lexibles are computed with the newly acquired boundary conditions stemming rom their neighbouring elements. Only ater this second step, does a complete engine run-through take place. 3. DUCT SIMULATION METHODS Within TLR-Sim, numerical routines or the simulation o a number o dierent components have already been implemented. Being, however, the ocus o this paper luid low through pipe lines, this section concentrates only on the simulation methods existing within TLR- Sim or the computation o duct lows. 3. Ducts All components alling under this category, that is, rigid and lexible pipes can be simulated by applying a number o dierent techniques. These techniques may be classiied according to the detail to which they examine the low. General ODEs (ordinary dierential equations) can be used to compute pressure changes, mass low variations etc. (see Section 5) More detailed schemes allow, not only the computation o the low properties, but also the evaluation o its structure. Two Riemann Solvers solve or the Riemann problem (RP) which is none other than a special case o the Initial Value Problem (IVP). Riemann solvers can be adopted to solve a local RP at any position along a duct. The solution to the RP is then used to solve or the Euler equations with or without additional source terms. Although being somewhat more complex, the use o Riemann solvers can be implemented in the solving o problems where the MOC is not suitable. As will be described in Section 6, the study here presented has made use o the Riemann solvers to solve the Navier- Stokes Equations. 4. KEROSENE METHANE COMPARISON 4. Analysis Background In previous studies conduced in the Launcher s Systems Analysis department o the German Aerospace Centre, DLR, two engines in the RD-80 class have been hypothesised to compare the perormance o methane and kerosene under nominal engine operation. The paper at hand has taken these engines as its starting point []. Table summarises the tank conditions or each o the methane and kerosene RD-80 class engines. Table.Propellant Tank Parameters Methane Kerosene RP Tank Pressure bar 3 Tank Temperature K 0 90 Density kg/m

3 4. Analysis Breakdown The study here presented is based on a two-old analysis. The irst is based on non-linear ODEs (ordinary dierential equations) describing the evolution o pressure and mass low along a duct and is perormed with an ODE integrating tool. The second aspect o the analysis is a more detailed one consisting in the implementation o the Navier-Stokes equations to evaluate the potential dierences between kerosene and methane. Viscosity [ kg/ms ] 4,0e-03 3,0e-03,0e-03,0e-03 Jet A Viscosity vs. Temp. (along cnst. p curves) Jet A 0. MPa Jet A MPa Jet A MPa Jet A 3 MPa JetA 4 MPa In the ollowing sections each o the above-mentioned assessments is introduced, the underlying model is highlighted and the out-coming major results are presented. 4.3 Propellant Properties It should be noted that Jet A data has been used due to its easy availability. Dierence between RP and Jet A due exist but or present purposes are o minor importance [4], [6]. Figures and 3 illustrate the viscosity o methane and kerosene as unctions o temperature and pressure. The plots show that, within the pressure and temperature range o interest, methane viscosity values can be an order o magnitude smaller than those o kerosene. Similar curves depicting methane and kerosene density show in this case the ratio is only two-old. Viscosity [ Pa*s ],5e-04,0e-04,5e-04,0e-04 5,0e-05 Methane Viscosity vs. Temp. (along cnst. p curves) 0.0 MPa 0. MPa 0.5 MPa 0.5 MPa MPa 5 MPa 0 MPa 0 MPa 0,0e Temperature [ K ] Fig.. Methane Viscosity Plot as a ( T, p ) Fn. 0,0e Temperature [ K ] Fig. 3. Kerosene Viscosity Plot as a ( T, p ) 5. ODE ANALYSIS 5. Introduction Fn. The ODE analysis has been perormed with a program widely used at DLR or the simulation control laws such as those existing in aviation light control systems. The tool has the capability o integrating ordinary dierential equations and allows or eedback loops. 5. ODE Equations The luid parameters, pressure and mass low, characterising the luid low though a duct can be expressed according to the ollowing ODEs [3]: dm dp dt in dt F = l a = V p in p out [ m in m out ] ρ ξ m out where the subscript stands or { M } kerosene and methane respectively. () () K, or The riction actor ξ is a unction o the Reynolds number, and or turbulent lows, i.e. Re 300 is deined as: 4 68 l ξg ξ = 0. h + + (3) Re d F F h where h =. d

4 5.3 ODE Model The model used in the ODE analysis is aimed at reproducing, in more simple terms, the start sequence o a rocket engine employing a burst disk and includes a tank directly connected with a duct. Bends and areavariations have not been taken into account. Acceleration eects stemming rom the launcher system have also been neglected. In the model the burst disk is assumed to be located just beore the irst duct section. The duct is broken down into sections each having an inlet pressure, an outlet pressure and inlet and outlet mass lows. Figure 4 illustrates the model used. Each duct section is o equal length and is user deined according to: πa l max (4) ϖ n max where ϖ max is the maximum requency that is to be examined. Under the spectrum o the ODE analysis, three models have been used. Each model diers in the length o its duct sections. Table summarises the main details o each model coniguration. Table. Model Conigurations and Corresponding Frequencies Model Section Length [m] ϖ [Hz] max Model Model Model ODE Results Fig. 4. ODE Model The graphs shown below have been obtained by implementing the three dierent models described above. Although each model diers rom the others in the length o its duct sections the total duct length examined has been kept. Each graph depicts normalised pressure, i.e. the pressure in the duct normalised to the pressure in the respective tanks (3 bar or methane and bar or kerosene), against time in seconds. In addition to centre o the duct where the evolution o pressure is shown, two urther locations have been plotted or each model. These are the entrance and exit locations o the duct. The initial pressure within the duct has been assumed to be one bar lower than pressure existing within the tank (corresponding to a normalised pressure o 0.5 or kerosene and approximately 0.67 or methane)..0e+00 Kerosene & Methane Normalised Pressure vs. Time - Model.00E E E E-0.00E E Fig. 5. ODE Model Test Results Methane Duct Entrance Methane Duct Exit Kerosene Duct Entrance Kerosene Duct Exit

5 .0E+00 Kerosene & Methane Normalised Pressure vs. Time - Model.00E E E-0 Methane Duct Entrance 4.00E-0 Methane Duct Exit Kerosene Duct Entrance.00E-0 Kerosene Duct Exit 0.00E Fig. 6. ODE Model Test Results.0E+00 Kerosene & Methane Normalised Pressure vs. Time - Model 3.00E E E E-0.00E E+00 Methane Duct Entrance Methane Duct Exit Kerosene Duct Entrance Kerosene Duct Exit Fig. 7. ODE Model 3 Test Results 6. -DIMENSIONAL NAVIER-STOKES ANALYSIS 6. Introduction The one-dimensional Navier-Stokes analysis has been built on the Euler equations with the addition o a series o sources terms deemed as important or luid low in ducts. These source terms include area variations as well as viscous and heat contributions. 6. Navier-Stokes Equations and Riemann Solvers The Navier-Stokes equations in conservative orm are as ollows: U t ρ ρu E t + + u F( U ) ρu x ( ρu + p ) ( E + p ) x = S + S = S + S (5) where S and S are source terms accounting or areavariation and viscous and heat eects and which upgrade the one-dimensional Euler equations to the one-dimensional Navier-Stokes equations with areavariations.

6 By adopting the WAF (Weight Averaged Flux) method proposed by Toro [5], and using an exact Riemann solver and an appropriate lux limiter, the Riemann problem can be solved or each U ( i, i + ), along the duct. The result to the local Riemann problem in conjunction with a conventional TVD (Total Variation Diminishing) scheme can then be implemented to obtain the result to the Euler equations or all positions, i along the duct or a given time, n. Subsequently the source term eects are added to obtain the solution to the Navier-Stokes equations. 6.3 Results Figure 8, as Figures 5 through 7 or the ODE analysis, depicts normalised pressure vs. time. The results correspond to a shock-tube problem set up to have the same starting conditions as the ODE analysis. The purpose o this evaluation is to provide an indirect comparison to the ODE results or a somewhat dierent problem and thus validate the general characteristics shown by kerosene and methane. 9.00E E-0 Normalised Pressure vs. Time (Navier Stokes) 8.00E E E E E E E Fig. 8. Navier-Stokes Results 7. CONCLUSIONS AND OUTLOOK The two-old analysis here presented has highlighted three undamental aspects. Firstly: the dynamic behaviours o kerosene and methane have been shown to possess substantial dierences, thus underlying the importance o a transient analysis. Secondly: the ODE and Navier-Stokes analyses have led to coherent results though applied to dierent test cases. This shows that the transient analysis can be perormed with tools having dierent ocuses, thus allowing the choice o the best tool to suit the problem at hand and thus holding a considerable advantage. Thirdly: a more advanced transient simulation which includes additional engine components and examines their interactions or a range o operating conditions represents an advantage in engine analysis and should be pursued. Thus, urther examinations and program developments are underway not only or dierent ambient conditions but or more complex models, comprehending other LRE components such as valves and combustion devices. 8. REFERENCES [] Anderson, J. D.: Fundamentals o Aerodynamics, Mc-Graw Hill, Singapore, 99. [] Burkhardt, H., et al.: Kerosene vs Methane: A Propellant Tradeo or Reusable Liquid Booster Stages, to appear in Journal o Spacecrat and Rockets. [3] Belyaev, E.N., et al.: Mathematical Simulation o the Operating Processes o Liquid Rocket Engines, MAI, Moscow, 999. [4] Rachner, M.: Die Stoeigenschaten von Kerosin Jet A-, Deutsches Zentrum uer Lut- und Raumahrt e.v., Koeln, March 998. [5] Toro, E.F.: Riemann Solvers and Numerical Methods or Fluid Dynamics, A Practical Introduction, Springer-Verlag, Berlin Heidelberg, 997. [6] N.N.: NIST Chemistry WebBook, [Online March 004].