Computational Fluid Dynamic Study on Boundary Layer Efficiency of Liquid Propellant Rocket Engine Aung Myo Thu#1, Thet Nyi Nyi Shwe*2 #
Fluid Dynamic Analysis and Design Lab, Myanmar Aerospace Engineering University Meiktila, Myanmar 1
[email protected]
Abstract - This paper presents the systematic study of Computational Fluid Dynamic (CFD) simulation of liquid propellant rocket engine. The main purpose of this research is to calculate the boundary layer efficiency caused by friction losses between the fluid flow and wall surface based on characteristics exhaust velocity. In order to reach that goal, hot flow simulation, that assumes complete combustion of propellant, was firstly carried out and mesh sensitivity analysis was conducted to get a mesh independent solution. Then, three different turbulent models were used to analyse the flow physics inside the chamber. SST k-ω model showed the best boundary layer nature and was selected to simulate the rocket engine combustion flow utilizing eddy dissipation model (EDM). The boundary layer efficiency through this simulation showed good agreement with hot flow simulation results and NASA’s CEA result.
instability gain. Often it is not even possible to determine which mechanisms are responsible for a given combustion instability, much less to model it [4]. Huan et al [7] modelled the combustion stability based on chemistry. Transient two phase numerical simulation programs was developed to simulate gas-oxygen/kerosene, liquid oxygen/gas hydrogen and gas oxygen/gas hydrogen/kerosene combustion stability in his effort. He then studied influences of propellant combination and design of injector to combustion stability. Many researches [8-11] have tried to mathematically model and study boundary layer physics. The highest level of fidelity lies in direct numerical simulation (DNS), where all significant turbulent length scales are resolved. Jonathan et al and others [12-14] used a compromised model of implicit large eddy simulation with near wall resolution, in which the near wall region is well-resolved, but the mesh is coarsened away from the wall. Other researchers like Ahn et al [15] studied the effect of recess length on combustion characteristics. Anselm et tal [16] simulated the combustion in liquid propellant rocket engine by adding volume source and surface source method and concluded that the volume source created a more logical fluid flow, and also required less time for convergence. The current paper used reaction method and the resulted values were validated with the result of Anselm et al and NASA’s CEA results [17].
Keywords – CFD, Rocket, Combustion, Simulation, ANSYS, Numerical Modelling, Boundary Layer
I. INTRODUCTION The design of liquid propellant rocket engines requires tremendous effort to address the underlying issues such as performance, reliability, safety and so on. In order to address these issues, understanding the physics inside the chamber is very important. Many researchers around the world have been putting their labour in exploring underlying physics of rocket engines experimentally and numerically for decades. Nowadays, numerical prediction of physical problems has improved tremendously with the advancement of modern computer and its computing capacity. So, numerical simulation of complex flow phenomena becomes a must prior to testing experimentally that reduces large sum of money and time. In rocket engine, it is necessary to have accurate predictions of boundary layer and its transition to turbulent to get its performance. The earliest person who used numerical tool for rocket engine combustion is Priem et al [1]. This one was later modified by Hoffman [2]. However, they only handled one dimensional and two dimensional cases. Kim et al [3] tried to solve the reacting Navier-Stokes equations for axisymmetric and annular geometries. In recent years, high precision computing method has been applied to studying combustion instability. Laroche et al [4] developed MSD solver to simulate three dimensional acoustic. Grohens et al [5] used a numerical method, based on a network of elementary chemical reactors, to study the global performance of a ramjet. Venugopal et al [6] investigated the dynamics of a turbulent flow subjected to strong wall injection through Direct Numerical Simulations. However these numerical analyses are by no means fully matured and anchored. These models either assume artificially combustion response function or excite the combustion response through artificial initial disturbance. One of the key current limitations of analytical stability tools is the instability to predict the magnitude of the combustion
II. METHODOLOGY The modelling and analysis of the rocket engine configuration has been done by using CFD software package, ANSYS CFX. It uses finite volume method which is essentially a generalization of the finite difference methods but use the integral forms of the governing equations of flows rather than that of differential. They give greater flexibility on using complex domains, as the finite volume method need not be regular. Therefore, it is one of the best application software for the analysis of complex domains. III. GEOMETRY AND BOUNDARY CONDITIONS Due to the symmetry of the rocket chamber, only ¼ of the geometry was modelled to reduce the computational cost and ambient opening is extended for the nozzle exhaust plume, Fig.1. A small recess was added to get better mixing characteristics. Tetrahedral elements with thin prism layers at near wall region are used to reduce computational cost and obtain accurate boundary layer efficiency, Fig.2. The selected combustion case is shown in Table-I and is firstly run on NASA’s code CEA (Computer Program of Calculation of Complex Chemical Equilibrium Compositions and Applications) [17]. This code provides output values at critical point of rocket chamber based only on input condition to the rocket. It only makes 1D
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calculation and doesn’t take the geometry of rocket chamber into consideration. The code makes a number of assumptions for its solutions such as complete mixing, complete combustion, ideal gas and ideal system. The most current version of program was published 1994 (with the latest update in 2004) and contains numerous improvements to early version, published in 1976.
neglecting other flow losses except from boundary layer friction losses. Since kerosene is a complex fuel with multiple hydrocarbons and reactions, only the highest mass fraction gases (CO, CO2, H2, H, H2O, O, O2 and OH) were selected for simulation based on CEA output results. TABLE I INPUT VALUES FOR CEA
Parameters Mixture Ratio , O/F Contraction Ratio, Ac/At Initial Pressure, Pi (Bar) Pressure Ratio, Pi/Pe Combustion Temperature, Tc (Kelvin) Fuel Fuel Temperature, (Kelvin) Oxidizer Oxidizer Temperature, (Kelvin)
Values 3.2 5 20 19.74 3600 Jet A (Gas) 260 Oxygen (Gas) 240
TABLE II P ERFORMANCE P ARAMETERS AND MASS F RACTIONS OUTPUT FROM CEA
Performance Parameters C*, ms-1 CF, ms-1 Isp, ms-1 T, K
Combustion Chamber End 1729.4 0.0808 139.7 3543.00
Injector
CO CO2 H2 H2O O O2 OH H
Fig. 1 Geometry of model
0.28031 0.31108 0.00401 0.21153 0.02254 0.10199 0.06691 0.00133
Throat
Exit
1729.4 0.6507 1125.3 3392.45
1729.4 1.4307 2474.1 2832.12
Combustion Chamber End 0.28017 0.31131 0.00401 0.21159 0.02252 0.10197 0.06682 0.00133
Throat
Exit
0.26583 0.33386 0.00377 0.21864 0.01935 0.09705 0.06014 0.00118
0.19921 0.43855 0.00279 0.24566 0.00883 0.06965 0.03463 0.00066
IV. RESULTS AND DISCUSSION This CFD simulation allows us to understand the detailed internal flow dynamic of rocket combustion chamber that is difficult and too expensive to see in actual laboratory experiment. The simulation results were validated with ideal CEA results. The boundary layer efficiency based on characteristics exhaust velocity was calculated by the losses between no-slip and free-slip boundary conditions. The simulation results showed good agreement with CEA results and, of Anselm et tal [16].
Fig. 2 Meshed model of medium mesh density
The inlet velocity and mass flow of fuel and oxidizer are calculated based on continuity equation by using output values from CEA since the choked mass flow at the throat is maximum mass flow of the system. ( ρAv ) inlet = ( ρAv )throat The calculated initial velocity (144.4295 m/s2), fuel mass flow rate (0.098614 kg/s2) and oxidizer mass flow rate (0.305069 kg/s2) are used as the initial conditions for simulation. Adiabatic heat transfer was assumed for
V. HOT FLOW SIMULATION The very first attempt for the current research is to conduct hot flow simulation. The hot flow simulation assumes that the fully combusted hot gases are injected from the injector. For its fast convergence, different mesh densities are tested in order to get a mesh independent solution which is the life blood of every CFD simulation. The turbulence model study was also carried out with hot
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flow simulation and the best suited model was selected to simulate more realistic combustion reaction simulation. A. Mesh Sensitivity Analysis The aim of mesh sensitivity analysis is to obtain a mesh independent simulation. A number of mesh densities were tested and checked with CEA’s values. The mesh statistics used for three different simulations are shown in Table-III. Looking at Fig.3, the characteristics velocity value changed dramatically once the mesh density was increased. However, C* didn’t change much between mesh density B and C. The velocity profiles in Fig.4, Fig.5 and Fig.6 shows slightly different nature but the focus here is C*. Therefore, it comes to conclude that the mesh independent solution is reached and the lesser one was selected for further simulation regarding the lower computational cost.
Fig. 5 Velocity distribution of mesh density B
TABLE III MESH STATISTICS FOR MESH SENSITIVITY ANALYSIS
Number of Nodes
Mesh Density A Mesh Density B Mesh Density C
3836
Number of Tetrahedr-al Elements 5170
Number of Prism Elements
81908
260493
61958
95
496973
2074629
249967
151
4143
Number of Pyramid Elements 119
Fig. 6 Velocity distribution of mesh density C
B. Turbulence Model Study The aim of turbulence model study is to understand the advantages and disadvantages of turbulence model and to select the most suitable model for reaction combustion flow with appropriate boundary layer accuracy. The three turbulence models (k-ε, SST k-ω and SSG Reynolds Stress) were studied with selected mesh density B by using same time step. The k-ε contains variables that measured the turbulence kinetic energy (k) and turbulence eddy dissipation (ε). It provides good predictions for engineering interest for free stream flow properties for linear fluid flow. The SST k-ω calculates the transport of the turbulence shear stress with turbulence kinetic energy (k) and turbulence frequency (ω) and gives highly accurate boundary layer simulations. The SSG Reynolds Stress model is based on transports equations for all components of the Reynolds stress tensors and the dissipation rates. It is recommended for complex swirling flow. By studying on the graphical results of present numerical simulation, all of three models showed the existence of large recirculation zone above the injection flow as expected. This recirculation flow can help to improve the combustion efficiency of rocket chamber by recirculating the no combusted fuel to the combustion zone. The k-ω model (Fig.8) gave more reasonable boundary layer flow than k-ε model (Fig.7) while studying the velocity vector of simulations results. However the SSG Reynolds Stress model (Fig.9) shows the existence of a pressing vortex core (PVC), which occurs as the central vortex core is perturbed by external disturbances.
1685 C
B C*
1680
1675 A 1670 0.00E+00
2.00E+05 4.00E+05 number of nodes
6.00E+05
Fig. 3 Mesh densities VS C*
Fig. 4 Velocity distribution of mesh density A
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kerosene and available in ANSYS CFS, was used. Pure jet A and gaseous oxygen were injected from the inlet at their initial temperatures and maximum eight gas species (CO, CO2, H2, H, H2O, O, O2 and OH) were used as the product gases by accounting to three decimal from CEA result. Temperature distribution of reaction combustion with EDM model is shown in Fig.10. The simulation captures reasonable combustion flow with flame propagation than hot flow simulation. Maximum temperature distribution is occurred along the wall because of the reduction of turbulence kinetic energy and increasing of dissipation rate when flow is approached to wall. Due to the increasing of near wall temperature, the size of recirculation zone is reduced and just can see at the corner of the combustion chamber. The calculated boundary layer efficiency is 0.95, which is slightly lower than hot flow simulation and Anselm et tal [16]’s volume and surface source adding method, because of domination of side wall flow and flame propagation.
Recirculation due to fluid expansion
Fig. 7 Velocity distribution of k-ε model simulation
Fig. 8 Velocity distribution of k-ω model simulation
Fig. 10 Total temperature distribution of EDM model
VII. CONCLUSIONS The step by step simulation of liquid propellant rocket engine combustion was done. In order to get reliable boundary layer efficiency, complete combustion hot flow simulation was carried out and, mesh sensitivity analysis was carried out to get mesh independent solution. Three different turbulent models were also tested. Out of three models used, SST k- ω turbulence model showed good boundary layer development along the wall and lesser computational time. SSG Reynolds stress model showed central recirculation zone and accompanying pressed vortex core while other models only depicted recirculation zone near the wall. The reaction combustion simulation with EDM showed good flame propagation and the resulted boundary layer efficiency is acceptable with hot flow simulation result and other peer’s work.
PVC
Fig. 9 Velocity distribution of SSG Reynolds Stress model simulation
C. Performance Efficiency Calculation Accounting boundary layer transition characteristics and associated computational cost, SST k-ω model was selected for further studies. Boundary layer efficiency based on characteristics exhaust velocity was calculated based on the results of free-slip and no-slips simulations with mesh density B and SST k- ω turbulence model. ηc*Bl = no-slip/free-slip = 1683.53/1754.52 = 0.96 VI. REACTION FLOW SIMULATION After hot flow simulation, the more realistic reaction flow simulation of rocket engine combustion was carried out by using Eddy Dissipation Model (EDM). The EDM model can be used in a wide range of turbulent reacting flows covering premixed and diffusion flame and is the best applied to turbulent flows when chemical reaction is fast relative to the transport processes in the flow. As a fuel, jet aviation fuel (Jet A), that has closest combination to
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