×

zbMATH — the first resource for mathematics

Comparison of energy-, pressure- and enthalpy-based approaches for modeling supercritical flows. (English) Zbl 1410.76468
Summary: At supercritical conditions, thermodynamics may become strongly nonlinear which is reflected by large thermodynamic Jacobian values. This means that small variations in density, momentum or energy can result in large pressure perturbations. Because of such nonlinearities, simulations of high-pressure flows are subject to stability issues when the conservative form of the Navier-Stokes system is employed. In high-Reynolds number simulations, transported quantities are altered by numerical scheme errors, stabilization methods and filtering procedures. These alterations affect density and energy independently and may lead to significant pressure oscillations due to the nonlinear behavior of the equation of state. The objective of the present work is to compare three methods based on different sets of transport equations, to measure their impact on pressure and mixing temperature. A classical fully-conservative approach based on the transport of internal energy is compared to two quasi-conservative methods: a pressure-based and an enthalpy-based formulation. A suite test cases of increasing complexity is employed to expose the main differences between these approaches, at conditions relevant for engineering applications. The analysis first confirmed that the energy-based formulation is prone to artificial pressure fluctuations caused by the interaction between thermodynamic nonlinearities and the numerical dissipation introduced by the stabilization scheme. It is also demonstrated that despite the stability properties of the pressure-based formulation, the mixing temperature is not properly captured since the pressure equation is not used in its conservative form. The enthalpy-based approach however, offers an improved representation of the mixing thermodynamic state while avoiding non-physical pressure variations.

MSC:
76V05 Reaction effects in flows
80A25 Combustion
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Software:
CHEMKIN
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hirschfelder, J.; Curtiss, F.; Bird, R., Molecular theory of gases and liquids, (1964), John Wiley & Sons: John Wiley & Sons New York
[2] Reid, R. C.; Prausnitz, J. M.; Polling, B. E., The properties of liquids and gases, Fourth ed., (1987), McGraw Hill, New York
[3] Oschwald, M.; Smith, J. J.; Branam, R.; Hussong, J.; Schik, A.; Chehroudi, B., Injection of fluids into supercritical environments, Combust Sci Technol, 178, 1-3, 49-100, (2006)
[4] Dahms, R. N.; Oefelein, J. C., On the transition between two-phase and single-phase interface dynamics in multicomponent fluids at supercritical pressures, Phys Fluids, 25, 092103, 1-24, (2013)
[5] Woodward, R. D.; Talley, D. G., Raman imaging of transcritical cryogenic propellants, AIAA Pap, 468, 1996, (1996)
[6] Hickey, J.; Ma, P.; Ihme, M.; Thakur, S., Large eddy simulation of shear coaxial rocket injector: Real fluid effects, 49th AIAA/ASME/SAE/ASEE joint propulsion conference, 4071-4085, (2013)
[7] Terashima, H.; Koshi, M., Approach for simulating gas-liquid-like flows under supercritical pressures using a high-order central differencing scheme, J Comput Phys, 231, 20, 6907-6923, (2012)
[8] Kawai, S.; Terashima, H.; Negishi, H., A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state, J Comput Phys, 300, 116-135, (2015)
[9] Schmitt, T.; Selle, L.; Ruiz, A.; Cuenot, B., Large-Eddy simulation of supercritical-pressure round jets, AIAA J, 48, 9, 2133-2144, (2010)
[10] Cutrone L, Ihme M, Herrmann M, Modeling of high-pressure mixing and combustion in liquid rocket injectors. In: Proceedings of the summer program; Center for Turbulence Research, NASA AMES, Stanford University, USA, 2006. p. 269-282.
[11] Pohl, S.; Jarczyk, M.; Pfitzner, M.; Rogg, B., Real gas CFD simulations of hydrogen/oxygen supercritical combustion, Progress in propulsion physics, 4, 583-614, (2013), EDP Sciences
[12] Demoulin, F.; Zurbach, S.; Mura, A., High-pressure supercritical turbulent cryogenic injection and combustion: a single-phase flow modeling proposal, J Propul Power, 25, 2, 452-464, (2009)
[13] Poschner, M.; Pfitzner, M., CFD-simulation of the injection and combustion of LOX and H2 at supercritical pressures, 1144-1156, (2010), Am Inst AeronautAstronaut
[14] Qiu, L.; Reitz, R. D., Simulation of supercritical fuel injection with condensation, Int J Heat Mass Transf, 79, 1070-1086, (2014)
[15] Banuti, D. T.; Hannemann, K., Supercritical pseudo-Boiling and its relevance for transcritical injection, 2014-3571, (2014), Am Inst AeronautAstronaut
[16] Banuti, D.; Hannemann, K., The absence of a dense potential core in supercritical injection: a thermal break-up mechanism, Phys Fluids, 28, 3, 035103, (2016)
[17] Banuti, D.; Hannemann, V.; Hannemann, K.; Weigand, B., An efficient multi-fluid-mixing model for real gas reacting flows in liquid propellant rocket engines, Combust Flame, 168, 98-112, (2016)
[18] Bellan, J., Supercritical (and subcritical) fluid behavior and modeling : drops, streams, shear and mixing layers, jets and sprays, Prog Energy Combust Sci, 26, 329-366, (2000)
[19] Miller, R.; Harstad, K.; Bellan, J., Direct numerical simulations of supercritical fluid mixing layers applied to heptane-nitrogen, J Fluid Mech, 436, 6, 1-39, (2001)
[20] Okong’o, N.; Bellan, J., Consistent boundary conditions for multicompoment real gas mixtures based on characteristic waves, J Comput Phys, 176, 330-344, (2002)
[21] Okong’o, N.; Bellan, J., Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. part 1. Direct numerical simulation, formulation and a priori analysis, J Fluid Mech, 499, 1-47, (2004)
[22] Bellan, J., Theory, modeling and analysis of turbulent supercritical mixing, Combust Sci Technol, 178, 1-3, 253-281, (2006)
[23] Masi, E.; Bellan, J.; Harstad, K. G.; Okong’o, N. A., Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition, J Fluid Mech, 721, 578-626, (2013)
[24] Foster, J.; Miller, R. S., A priori analysis of subgrid mass diffusion vectors in high pressure turbulent hydrogen/oxygen reacting shear layer flames, Phys Fluids, 24, 7, 075114, (2012)
[25] da Silva, C. B.; Balarac, G.; Metais, O., Transition in high velocity ratio coaxial jets analysed from direct numerical simulations, J Turbul, 4, 24, 1-18, (2003)
[26] Tani, H.; Teramoto, S.; Yamanishi, N.; Okamoto, K., A numerical study on a temporal mixing layer under transcritical conditions, Comput Fluids, 85, 93-104, (2013)
[27] Oefelein, J. C.; Yang, V., Modeling high-pressure mixing and combustion processes in liquid rocket engines, J Propul Power, 14, 5, 843-857, (1998)
[28] Zong, N.; Ribert, G.; Yang, V., A flamelet approach for modeling of liquid oxygen (lox)/methane at supercritical pressures, Forty-sixth AIAA aerospace sciences meeting and exhibit, AIAA, 946, 1-16, (2008)
[29] Petit, X.; Ribert, G.; Lartigue, G.; Domingo, P., Large-eddy simulation of supercritical fluid injection, J Supercrit Fluids, 84, 61-73, (2013)
[30] Lacaze, G.; Misdariis, A.; Ruiz, A.; Oefelein, J. C., Analysis of high-pressure diesel fuel injection processes using LES with real-fluid thermodynamics and transport, Proc Combust Inst, 35, 1603-1611, (2015)
[31] Tramecourt, N.; Masquelet, M.; Menon, S., Large-eddy simulation of unsteady wall heat transfer in a high pressure combustion chamber, 41 st AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit, 1-17, (2005)
[32] Petit, X.; Ribert, G.; Domingo, P., Lox/ch4 mixing and combustion under supercritical conditions, 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 713-723, (2013)
[33] Tramecourt, N.; Menon, S.; Amaya, J., LES of supercritical combustion in a gas turbine engine, 40th AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, 3381-3392, (2004)
[34] Matsuyama, S.; Shinjo, J.; Ogawa, S.; Mizobuchi, Y., Large eddy simulation of LOX/GH2 shear-coaxial jet flame at supercritical pressure, 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 208-218, (2010)
[35] Matsuyama, S., Correlation of optical emission and turbulent length scale in a coaxial jet diffusion flame, Combust Flame, 161, 4, 937-949, (2014)
[36] Oefelein, J. C., Thermophysical characteristics of shear-coaxial LOX-H2 flames at supercritical pressure, Proc Combust Inst, 30, 2, 2929-2937, (2005)
[37] Oefelein, J. C., LES of supercritical LOX-H2 injection and combustion in a shear-Coaxial Uni-Element rocket, 1-13, (2003), Am Inst AeronautAstronaut
[38] Oefelein, J. C., Mixing and combustion of cryogenic oxygen-hydrogen shear-coaxial jet flames at supercritical pressure, Combust Sci Technol, 178, 1-3, 229-252, (2006)
[39] Matsuyama, S.; Shinjo, J.; Mizobuchi, Y.; Ogawa, S., A numerical investigation on shear coaxial LOX/GH2 jet flame at supercritical pressure, 44th AIAA aerospace sciences meeting and exhibit, 761-772, (2006)
[40] Smith, R.; Xia, G.; Anderson, W. A.; Merkle, C. L., Computational simulations of the effect of backstep height on nonpremixed combustion instability, AIAA J, 48, 9, 1857-1868, (2010)
[41] Park, T. S., LES And RANS simulations of cryogenic liquid nitrogen jets, J Supercrit Fluids, 72, 232-247, (2012)
[42] Müller, H.; Pfitzner, M.; Matheis, J.; Hickel, S., Large-eddy simulation of coaxial LN2/GH2 injection at trans-and supercritical conditions, J Propul Power, 32, 1, 46-56, (2015)
[43] Matheis, J.; Müller, H.; Lenz, C.; Pfitzner, M.; Hickel, S., Volume translation methods for real-gas computational fluid dynamics simulations, J Supercrit Fluids, 107, 422-432, (2016)
[44] Meng, H.; Yang, V., A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme, J Comput Phys, 189, 1, 277-304, (2003)
[45] Masquelet, M.; Menon, S.; Jin, Y.; Friedrich, R., Simulation of unsteady combustion in a LOX-GH2 fueled rocket engine, Aerosp Sci Technol, 13, 8, 466-474, (2009)
[46] Wang, X.; Yang, V., Supercritical mixing and combustion of liquid-oxygen/kerosene bi-swirl injectors, J Propul Power, 33, 2, 316-322, (2016)
[47] Huo, H.; Yang, V., Large-eddy simulation of supercritical combustion: model validation against gaseous H2-O2 injector, J Propul Power, 33, 5, 1272-1284, (2017)
[48] Terashima, H.; Kawai, S.; Yamanishi, N., High-resolution numerical method for supercritical flows with large density variations, AIAA J, 49, 12, 2658-2672, (2011)
[49] Zong, N.; Meng, H.; Hsieh, S.; Yang, V., A numerical study of cryogenic fluid injection and mixing under supercritical conditions, Phys Fluids, 16, 4248-4261, (2004)
[50] Zong, N.; Yang, V., A Numerical study of high-pressure oxygen/methane mixing and combustion of a shear coaxial injector, 43rd AIAA aerospace sciences meeting and exhibit, 152, 1-15, (2005)
[51] Zong, N.; Yang, V., Cryogenic fluid jets and mixing layers in transcritical and supercritical environments, Combust Sci Technol, 178, 1-3, 193-227, (2006)
[52] Zong, N.; Yang, V., Near-field flow and flame dynamics of LOX/methane shear-coaxial injector under supercritical conditions, Proc Combust Inst, 31, 2, 2309-2317, (2007)
[53] Schmitt, T.; Méry, Y.; Boileau, M.; Candel, S., Large-eddy simulation of oxygen/methane flames under transcritical conditions, Proc Combust Inst, 33, 1, 1383-1390, (2011)
[54] Schmitt, T.; Rodriguez, J.; Leyva, I.; Candel, S., Experiments and numerical simulation of mixing under supercritical conditions, Phys Fluids, 24, 5, (2012)
[55] Selle, L.; Schmitt, T., Large-eddy simulation of single-species flows under supercritical thermodynamic conditions, Combust Sci Technol, 182, 4-6, 392-404, (2010)
[56] Hakim, L.; Ruiz, A.; Schmitt, T.; Boileau, M.; Staffelbach, G.; Ducruix, S., Large eddy simulations of multiple transcritical coaxial flames submitted to a high-frequency transverse acoustic modulation, Proc Combust Inst, 35, 2, 1461-1468, (2015)
[57] Urbano, A.; Selle, L.; Staffelbach, G.; Cuenot, B.; Schmitt, T.; Ducruix, S., Exploration of combustion instability triggering using large eddy simulation of a multiple injector liquid rocket engine, Combust Flame, 169, 129-140, (2016)
[58] Ma, P.; Bravo, L.; Ihme, M., Supercritical and transcritical real-fluid mixing in diesel engine applications, Proceeding of the summer program 2014, 99-108, (2014), CTR Stanford
[59] Rinaldi, E.; Pecnik, R.; Colonna, P., Exact Jacobians for implicit Navier-Stokes simulations of equilibrium real gas flows, J Comput Phys, 270, 459-477, (2014)
[60] Taşkinoğlu, E.; Bellan, J., Subgrid-scale models and large-eddy simulation of oxygen stream disintegration and mixing with a hydrogen or helium stream at supercritical pressure, J Fluid Mech, 1, 1, 1-38, (2011)
[61] Selle, L.; Okong’o, N.; Bellan, J.; Harstad, K., Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study, J Fluid Mech, 593, 1, 57-91, (2007)
[62] Karni, S., Hybrid multifluid algorithms, SIAM J Sci Comput, 17, 5, 1019-1039, (1996)
[63] Terashima, H.; Koshi, M., Unique characteristics of cryogenic nitrogen jets under supercritical pressures, J Propul Power, 29, 6, 1328-1336, (2013)
[64] Jarczyk, M.-M.; Pfitzner, M., Large eddy simulation of supercritical nitrogen jets, 1-13, (2012), Am Inst AeronautAstronaut
[65] Matheis J, Müller H, Pfitzner M, Hickel S, Large eddy simulation of cryogenic coaxial LN2/GH2 injection under supercritical pressures. In: International symposium on turbulence and shear flow phenomena (TSFP-9); Melbourne, Australia, 2015. p. 1-6.
[66] Pantano, C.; Saurel, R.; Schmitt, T., An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows, J Comput Phys, 335, 780-811, (2017)
[67] Peng, D. Y.; Robinson, D. B., A new two-constant equation of state, Ind Eng Chem Fundam, 15, 1, 59-64, (1976)
[68] Linstrom, P.; Mallard, W., NIST chemistry webbook, NIST standard reference database, 69, (2005), National Institute of Standards and Technology (NIST): National Institute of Standards and Technology (NIST) Gaithersburg MD, 20899
[69] Gordon, S.; McBride, B. J., Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman-Jouguet detonations, Tech. Rep. SP-273, (1971), NASA
[70] Kee, R. J.; Rupley, F. M.; Miller, J. A., Chemkin-II: a fortran chemical kinetics package for the analysis of gas-phase chemical kinetics, Tech. Rep., (1991), Sandia National Laboratories
[71] Poinsot, T.; Veynante, D., Theoretical and numerical combustion, (2005), R.T. Edwards, 2nd edition.
[72] Ely, J.; Hanley, H. J.M., Prediction of transport properties. 2. Thermal conductivity of pure fluids and mixtures, Ind Eng Chem Fundam, 22, 1, 90-97, (1983)
[73] Takahashi, S., Preparation of a generalized chart for the diffusion coefficients of gases at high pressures, J Chem Eng Jpn, 7, 6, 417-420, (1974)
[74] Bird, R.; Stewart, W.; Lighfoot, E., Transport phenomena, (1960), John Wiley: John Wiley New York
[75] Jameson, A.; Schmidt, W.; Turkel, E., Numerical solution of the euler equations by finite volume methods using Runge-Kutta time stepping schemes, 14th fluid and plasma dynamics conference, 1259-1278, (1981), American Institute of Aeronautics and Astronautics
[76] Gaitonde, A. L., A dual-time method for two-dimensional unsteady incompressible flow calculations, Int J Numer Methods Eng, 41, 6, 1153-1166, (1998)
[77] Leonard, B., A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput Methods Appl Mech Eng, 19, 1, 59-98, (1979)
[78] Swanson, R. C.; Turkel, E., On central-difference and upwind schemes, J Comput Phys, 101, 2, 292-306, (1992)
[79] Ruiz, A. M.; Lacaze, G.; Oefelein, J. C.; Mari, R.; Cuenot, B.; Selle, L., Numerical benchmark for high-Reynolds-number supercritical flows with large density gradients, AIAA J, 54, 5, 1445-1460, (2015)
[80] Sod, G., A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J Comput Phys, 27, 1, 1-31, (1978)
[81] Prosser, R., Improved boundary conditions for the direct numerical simulation of turbulent subsonic flows. I. Inviscid flows, J Comput Phys, 207, 2, 736-768, (2005)
[82] Oefelein, J., Large eddy simulation of turbulent combustion processes in propulsion and power systems, Prog Aerosp Sci, 42, 1, 2-37, (2006)
[83] Van Wylen, G. J.; Sonntag, R. E., Fundamentals of classical thermodynamics, (1986), Wiley, New York
[84] Roe, P., Approximate Riemann solvers, parameter vectors and difference schemes, J Comput Phys, 43, 357-372, (1981)
[85] Van Leer, B., Towards the ultimate conservative difference scheme IV. A new approach to numerical convection, J Comput Phys, 23, 276-299, (1977)
[86] Jorgenson, P.; Turkel, E., Central difference TVD schemes for time dependent and steady state problems, J Comput Phys, 107, 2, 297-308, (1993)
[87] Lacaze, G.; Oefelein, J. C., Modeling high-density-gradient flows at supercritical pressures, 49th AIAA/ASME/SAE/ASEE joint propulsion conference, 3717-3734, (2013), American Institute of Aeronautics and Astronautics
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.