â¢Coupling of pressure and velocity is realized using the PIMPLE approach, which was adapted to real gas demands. ⢠Diffusion is modeled using the assumption ...
Numerical Computation of Real Gas CH4/O2 Counterflow Diffusion Flames using OpenFOAM® H. Müller, S. Pohl, M. Jarzcyk, M. Pfitzner Thermodynamics Institute, Faculty for Aerospace Engineering, University of the Federal German Armed Forces Munich
Introduction In state-of-the-art liquid rocket combustion engines the propellants are typically injected at high pressures of up to 25 MPa and at cryogenic temperatures. Computations of the mixture and combustion in such engines by means of CFD require consistent modelling of the real gas effects which have a considerable impact on the fluid structure. In the past, a consistent description of real gas behaviour was implemented and successfully validated for inert mixing with the open-source CFD software OpenFOAM [1]. For further investigations the capabilities of OpenFOAM were extended to allow for computations which include both real gas thermodynamics and chemical reactions. The present work presents the according implementation and the results for a 2D-counterflow diffusion flame configuration at high pressures using CH4 and air as propellants.
Theoretical Formulation and Numerical Details Numerical Setup: •The configuration which is simulated is schematically shown in Figure 1.
Thermodynamic- and Transport Properties: • All thermodynamic properties are calculated as the sum of an ideal reference value and a departure function accounting for real gas effects which is calculated using a real gas equation of state. ∂ Vm h (T , p ) = h0 (T ) + ∫ Vm − T dp ∂T p p0 p
∂p c p (T , Vm ) = cV (T , Vm ) − T ∂ T Vm 2
∂p ∂ V m T
• The molar volume is related to pressure and temperature using the PengRobinson EOS with an additional volume correction for low temperatures due to Harstad et al. [2]. a (T ) RT p= − Vm − b Vm2 + 2Vmb − b 2
• The mixture properties are calculated using the relations which were proposed by Harstad et al. [2]. 0.4572( RTc ,αβ ) T 1 + Cm 1 − a (T ) = ∑∑ xα xβ ⋅ pc ,αβ Tc ,αβ α β RTc ,αα b(T ) = ∑ xα ⋅ 0.0778 pc ,αα α 2
2
Tc ,αβ = Tc ,α Tc , β (1 − kαβ ) pc ,αβ =
pc ,α pc , β
• The transport properties, i.e thermal conductivity and viscosity, are calculated according to the model by Chung et al. [3]. • Chemical reactions are calculated using the reduced chemistry mechanism proposed by Smooke et al. [4] which comprises 16 species and 46 reactions.
Results Figure 1: Schematic of the counterflow setup Table 1: boundary conditions
• The geometry is discretized with a 1-layer wedge geometry and 160x40 cells in axial and radial direction, respectively. • For spatial discretization a 2nd-order central scheme is used. • The boundary conditions are summarized in Table 1. Governing equations: • A pressure based solution algorithm is used which solves for the full set of laminar Navier-Stokes equations. • Coupling of pressure and velocity is realized using the PIMPLE approach, which was adapted to real gas demands. • Diffusion is modeled using the assumption of unity Lewis number.
Figure 2 displays the results of the real gas CFD simulation for the counterflow diffusion flame in comparison with results which were obtained from a perfect gas simulation. The lack of comparable simulations in the literature makes a detailed assessment of the profiles tedious. It can however be said that the outcome is plausible and the properties on either side of the flame are captured correctly. Furthermore, the comparison shows that real gas effects have a considerable influence on important flame features, such as flame thickness and maximum temperature. Further work is in progress, in particular a comparison with flamelet computations is planned to validate the presented results.
Figure 2: Profiles for temperature, density and mass fractions plotted over the centerline.
Conclusion • The current work shows the capability of our OpenFOAM solver to simulate combustion with the propellants being injected at transcritical conditions. • The future work will focus on the extension of the currently used models to allow for turbulent combustion with a PDF/stochastic fields method in conjunction with real-gas effects.
Literature [1] Jarczyk M., Pfitzner M., Large eddy simulations of supercritical nitrogen jets, AIAA2012-1270, 2012 [2] Harstad K.G., Miller R.S., Bellan J., Efficient high pressure state equations, A.I.Ch.E.J., p. 1605-1610, 1997 [3] Chung T.-H., Ajlan M., Lee L.L., Starling K.E., Generalized multiparameter correlation for nonpolar and polar fluid transport properties, Ind. & Eng. Chem. Res., 27(4), p. 671-679, 1988 [4] Smooke M.D., Puri I.K., Seshadri K. 21st Symposium (International) on Combustion, The Combustion Institute, p. 1783–1792, 1988
