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Analysis of turbulence characteristics in a temporal dense gas compressible mixing layer using direct numerical simulation. (English) Zbl 07192803
Summary: This study investigates the effects of a Bethe-Zel’dovich-Thompson (BZT) dense gas (FC-70) on the development of a turbulent compressible mixing layer at a convective Mach number \(M_c=1.1\). Three-dimensional direct numerical simulations are performed with both FC-70 and air. The initial thermodynamic state for FC-70 lies inside the inversion region where the fundamental derivative of gas dynamics \((\Gamma )\) becomes negative. The complex Martin-Hou thermodynamic equation of state is used to reproduce thermodynamic peculiarities of the BZT dense gas (DG). The unstable growth phase in the mixing layer development shows an increase of \(xy\)-turbulent stress tensors in DG compared to perfect gas (PG). The following self-similar period has been carefully defined from the time evolution of the integrated streamwise production and transport terms. During the self-similar stage, DG and PG mixing layers at \(M_c=1.1\) display close values of the momentum thickness growth rate, which seems similarly affected by the well-known compressibility-related reduction for PG. The same mechanisms are at stake, related to the reduction of pressure-strain terms. Turbulent kinetic energy (TKE) spectra show a slower decrease of TKE at small scales for DG compared with PG. The filtered kinetic energy equation balance developed by H. Aluie [Physica D 247, No. 1, 54–65 (2013; Zbl 1308.76133)] is applied for the first time to a compressible mixing layer. The equation is reshaped to better account for TKE transport across the mixing layer. This new formulation brings out the role played by \(\Sigma_l\), the pressure strengths power. A detailed comparison of the contributions to the filtered TKE equation is provided for both PG and DG mixing layers.
76 Fluid mechanics
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[1] Almagro, A., García-Villalba, M. & Flores, O.2017A numerical study of a variable-density low-speed turbulent mixing layer. J. Fluid Mech.830, 569-601. · Zbl 1421.76109
[2] Aluie, H.2013Scale decomposition in compressible turbulence. Physica D247 (1), 54-65. · Zbl 1308.76133
[3] Anders, J. B., Anderson, W. K. & Murthy, A. V.1999Transonic similarity theory applied to a supercritical airfoil in heavy gas. J. Aircraft36 (6), 957-964.
[4] Argrow, B. M.1996Computational analysis of dense gas shock tube flow. Shock Waves6 (4), 241-248. · Zbl 0866.76052
[5] Bailly, C. & Comte-Bellot, G.2003 Turbulence. Sciences et techniques de l’ingénieur, CNRS Editions.
[6] Barre, S. & Bonnet, J. P.2015Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: towards an accurate description of compressibility effects in supersonic free shear flows. Intl J. Heat Fluid Flow51, 324-334.
[7] Batchelor, G. K.1953The Theory of Homogeneous Turbulence. Cambridge University Press. · Zbl 0053.14404
[8] Bethe, H. A.1942 The theory of shock waves for an arbitrary equation of state. Res. and Dev, Tech. Paper 545.
[9] Bogdanoff, D. W.1983Compressibility effects in turbulent shear layers. AIAA J.21 (6), 926-927.
[10] Borisov, A. A., Borisov, A. A., Kutateladze, S. S. & Nakoryakov, V. E.1983Rarefaction shock wave near the critical liquid-vapour point. J. Fluid Mech.126, 59-73.
[11] Bradshaw, P.1966The effect of initial conditions on the development of a free shear layer. J. Fluid Mech.26 (2), 225-236.
[12] Bradshaw, P.1977Compressible turbulent shear layers. Annu. Rev. Fluid Mech.9 (1), 33-52. · Zbl 0412.76049
[13] Breidenthal, R. E.1992Sonic eddy-a model for compressible turbulence. AIAA J.30 (1), 101-104. · Zbl 0739.76025
[14] Brown, B. P. & Argrow, B. M.1998Nonclassical dense gas flows for simple geometries. AIAA J.36 (10), 1842-1847.
[15] Brown, G. L. & Roshko, A.1974On density effects and large structure in turbulent mixing layers. J. Fluid Mech.64 (4), 775-816. · Zbl 1416.76061
[16] De Bruin, I.2001 Direct and large-eddy simulation of the spatial turbulent mixing layer. PhD thesis, Eindhoven University of Technology.
[17] Cadieux, F., Domaradzki, J. A., Sayadi, T., Bose, T. & Duchaine, F.2012DNS and LES of separated flows at moderate Reynolds numbers. In Proceedings of the 2012 Summer Program, pp. 77-86. Center for Turbulence Research, NASA Ames/Stanford University.
[18] Chung, T. H., Ajlan, M., Lee, L. L. & Starling, K. E.1988Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Engng Chem. Res.27 (4), 671-679.
[19] Cinnella, P. & Congedo, P. M.2005Aerodynamic performance of transonic Bethe-Zel’dovich-Thompson flows past an airfoil. AIAA J.43 (2), 370-378.
[20] Cinnella, P. & Congedo, P. M.2007Inviscid and viscous aerodynamics of dense gases. J. Fluid Mech.580, 179-217. · Zbl 1113.76046
[21] Colin, O. & Rudgyard, M.2000Development of high-order Taylor-Galerkin schemes for LES. J. Comput. Phys.162 (2), 338-371. · Zbl 0982.76058
[22] Colonna, P. & Guardone, A.2006Molecular interpretation of nonclassical gas dynamics of dense vapors under the van der Waals model. Phys. Fluids18 (5), 056101.
[23] Colonna, P., Guardone, A., Nannan, N. R. & Zamfirescu, C.2008Design of the dense gas flexible asymmetric shock tube. Trans. ASME J. Fluids Engng130 (3), 034501.
[24] Colonna, P. & Rebay, S.2004Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver. Intl J. Numer. Meth. Fluids46 (7), 735-765. · Zbl 1060.76586
[25] Congedo, P. M., Corre, C. & Cinnella, P.2007Airfoil shape optimization for transonic flows Bethe-Zel’dovich-Thompson fluids. AIAA J.45 (6), 1303-1316.
[26] Congedo, P. M., Corre, C. & Cinnella, P.2011Numerical investigation of dense-gas effects in turbomachinery. Comput. Fluids49 (1), 290-301. · Zbl 1271.76291
[27] Costello, M. G., Flynn, R. M. & Owens, J. G.2000 Fluoroethers and fluoroamines. In Kirk-Othmer Encyclopedia of Chemical Technology. John Wiley & Sons.
[28] Cramer, M. S.1989Negative nonlinearity in selected fluorocarbons. Phys. Fluids A1 (11), 1894-1897.
[29] Cramer, M. S.1991Nonclassical dynamics of classical gases. In Nonlinear Waves in Real Fluids, pp. 91-145. Springer.
[30] Cramer, M. S. & Crickenberger, A. B.1991The dissipative structure of shock waves in dense gases. J. Fluid Mech.223, 325-355. · Zbl 0717.76075
[31] Cramer, M. S. & Kluwick, A.1984On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech.142, 9-37. · Zbl 0577.76073
[32] Cramer, M. S. & Park, S.1999On the suppression of shock-induced separation in Bethe-Zel’dovich-Thompson fluids. J. Fluid Mech.393, 1-21. · Zbl 0970.76052
[33] Cramer, M. S. & Sen, R.1986Shock formation in fluids having embedded regions of negative nonlinearity. Phys. Fluids29 (7), 2181-2191. · Zbl 0623.76071
[34] Dai, Q., Jin, T., Luo, K. & Fan, J.2018Direct numerical simulation of particle dispersion in a three-dimensional spatially developing compressible mixing layer. Phys. Fluids30 (11), 113301.
[35] Desoutter, G., Habchi, C., Cuenot, B. & Poinsot, T.2009DNS and modeling of the turbulent boundary layer over an evaporating liquid film. Intl J. Heat Mass Transfer52 (25-26), 6028-6041. · Zbl 1177.80074
[36] Dura Galiana, F. J., Wheeler, A. P. S. & Ong, J.2016A study of trailing-edge losses in organic rankine cycle turbines. J. Turbomach.138 (12), 121003.
[37] Fergason, S. H. & Argrow, B. M.2001Simulations of nonclassical dense gas dynamics. In 35th AIAA Thermophysics Conference, Anaheim, CO.
[38] Fergason, S. H., Ho, T. L., Argrow, B. M. & Emanuel, G.2001Theory for producing a single-phase rarefaction shock wave in a shock tube. J. Fluid Mech.445, 37-54. · Zbl 1005.76051
[39] Freund, J. B., Lele, S. K. & Moin, P.2000Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech.421, 229-267. · Zbl 0998.76036
[40] From, C. S., Sauret, E., Armfield, S. W., Saha, S. C. & Gu, Y. T.2017Turbulent dense gas flow characteristics in swirling conical diffuser. Comput. Fluids149, 100-118. · Zbl 1390.76432
[41] Fu, S. & Li, Q.2006Numerical simulation of compressible mixing layers. Intl J. Heat Fluid Flow27 (5), 895-901.
[42] Garnier, E., Adams, N. & Sagaut, P.2009Large Eddy Simulation for Compressible Flows. Springer Science & Business Media. · Zbl 1179.76005
[43] Giauque, A., Corre, C. & Menghetti, M.2017Direct numerical simulations of homogeneous isotropic turbulence in a dense gas. J. Phys.: Conf. Ser.821 (1), 012017.
[44] Grieser, D. R. & Goldthwaite, W. H.1963 Experimental determination of the viscosity of air in the gaseous state at low temperatures and pressures. Tech. Rep. Battelle Memorial Institute, Columbus, OH.
[45] Guardone, A., Vigevano, L. & Argrow, B. M.2004Assessment of thermodynamic models for dense gas dynamics. Phys. Fluids16 (11), 3878-3887. · Zbl 1187.76193
[46] Harinck, J., Colonna, P., Guardone, A. & Rebay, S.2010aInfluence of thermodynamic models in two-dimensional flow simulations of turboexpanders. J. Turbomach.132 (1), 011001.
[47] Harinck, J., Turunen-Saaresti, T., Colonna, P., Rebay, S. & Van Buijtenen, J.2010bComputational study of a high-expansion ratio radial organic Rankine cycle turbine stator. Trans. ASME J. Engng Gas Turbines Power132 (5), 054501.
[48] Hayes, W. D.1958The basic theory of gasdynamic discontinuities, fundamentals of gas dynamics. In High Speed Aerodynamics and Jet Propulsion (ed. Emmons, H. W.), pp. 416-481. Princeton University Press.
[49] Invernizzi, C. M.2010Stirling engines using working fluids with strong real gas effects. Appl. Therm. Engng30 (13), 1703-1710.
[50] Kirillov, N. G.2004Analysis of modern natural gas liquefaction technologies. Chem. Petrol. Engng40 (7-8), 401-406.
[51] Kluwick, A.2004Internal flows of dense gases. Acta Mech.169 (1-4), 123-143. · Zbl 1063.76083
[52] Kolmogorov, A. N.1941The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR30 (4), 299-303.
[53] Kritsuk, A. G., Norman, M. L., Paolo Padoan, A. N. D. & Wagner, R.2007The statistics of supersonic isothermal turbulence. Astrophys. J.665 (1), 416-431.
[54] Kutateladze, S. S., Nakoryakov, V. E. & Borisov, A. A.1987Rarefaction waves in liquid and gas-liquid media. Annu. Rev. Fluid Mech.19 (1), 577-600.
[55] Liepmann, H. W. & Laufer, J.1947 Investigations of free turbulent mixing. NACA Tech. Note 1257.
[56] Luo, K. H. & Sandham, N. D.1994On the formation of small scales in a compressible mixing layer. In Direct and Large-Eddy Simulation I, pp. 335-346. Springer.
[57] Martin, J. J. & Hou, Y.1955Development of an equation of state for gases. AIChE J.2 (4), 142-151.
[58] Martin, J. J., Kapoor, R. M. & De Nevers, N.1959An improved equation of state for gases. AIChE J.5 (2), 159-160.
[59] Martínez Ferrer, P. J., Lehnasch, G. & Mura, A.2017Compressibility and heat release effects in high-speed reactive mixing layers I. Growth rates and turbulence characteristics. Combust. Flame180 (M), 284-303.
[60] Mathijssen, T., Gallo, M., Casati, E., Nannan, N. R., Zamfirescu, C., Guardone, A. & Colonna, P.2015The flexible asymmetric shock tube (FAST): a Ludwieg tube facility for wave propagation measurements in high-temperature vapours of organic fluids. Exp. Fluids56 (10), 1-12.
[61] Menikoff, R. & Plohr, B. J.1989The Riemann problem for fluid flow of real materials. Rev. Mod. Phys.61 (1), 75. · Zbl 1129.35439
[62] Merle, X. & Cinnella, P.2014Bayesian quantification of thermodynamic uncertainties in dense gas flows. Reliability Engng Syst. Safety134, 305-323.
[63] Moin, P. & Mahesh, K.1998Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech.30 (1), 539-578. · Zbl 1398.76073
[64] Monaco, J. F., Cramer, M. S. & Watson, L. T.1997Supersonic flows of dense gases in cascade configurations. J. Fluid Mech.330, 31-59. · Zbl 0895.76038
[65] Okong’O, N. A. & Bellan, J.2002Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen. J. Fluid Mech.464, 1-34. · Zbl 1062.76029
[66] Pantano, C. & Sarkar, S.2002A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech.451, 329-371. · Zbl 1156.76403
[67] Papamoschou, D. & Roshko, A.1988The compressible turbulent shear layer: an experimental study. J. Fluid Mech.197, 453-477.
[68] Pirozzoli, S., Bernardini, M., Marié, S. & Grasso, F.2015Early evolution of the compressible mixing layer issued from two turbulent streams. J. Fluid Mech.777, 196-218. · Zbl 1381.76115
[69] Poinsot, T. J. & Lele, S. K.1992Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys.101 (1), 104-129. · Zbl 0766.76084
[70] Rogers, M. M. & Moser, R. D.1994Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids6 (2), 903-923. · Zbl 0825.76329
[71] Rusak, Z. & Wang, C.-W.1997Transonic flow of dense gases around an airfoil with a parabolic nose. J. Fluid Mech.346, 1-21. · Zbl 0913.76042
[72] Sandham, N. D. & Reynolds, W. C.1990Compressible mixing layer – linear theory and direct simulation. AIAA J.28 (4), 618-624.
[73] Sarkar, S.1995The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech.282, 163-186. · Zbl 0825.76309
[74] Sarkar, S., Erlebacher, G., Hussaini, M. Y. & Kreiss, H. O.1991The analysis and modelling of dilatational terms in compressible turbulence. J. Fluid Mech.227, 473-493. · Zbl 0721.76037
[75] Sarkar, S. & Lakshmanan, B.1991Application of a Reynolds stress turbulence model to the compressible shear layer. AIAA J.29 (5), 743-749.
[76] Sciacovelli, L., Cinnella, P., Content, C. & Grasso, F.2016Dense gas effects in inviscid homogeneous isotropic turbulence. J. Fluid Mech.800, 140-179.
[77] Sciacovelli, L., Cinnella, P. & Gloerfelt, X.2017aDirect numerical simulations of supersonic turbulent channel flows of dense gases. J. Fluid Mech.821, 153-199. · Zbl 1383.76293
[78] Sciacovelli, L., Cinnella, P. & Grasso, F.2017bSmall-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech.825, 515-549. · Zbl 1374.76084
[79] Shuely, W. J.1996 Model liquid selection based on extreme values of liquid state properties in a factor analysis. Tech. Rep. Edgewood Research Development and Engineering Center, Aderbeen Proving Ground, MD.
[80] Spinelli, A., Dossena, V., Gaetani, P., Osnaghi, C. & Colombo, D.2010Design of a test rig for organic vapours. In ASME Turbo Expo 2010: Power for Land, Sea, and Air, pp. 109-120. Paper N.
[81] Spinelli, A., Pini, M., Dossena, V., Gaetani, P. & Casella, F.2013Design, simulation, and construction of a test rig for organic vapors. Trans. ASME J. Engng Gas Turbines Power135 (4), 042304.
[82] Stephan, K. & Laesecke, A.1985The thermal conductivity of fluid air. J. Phys. Chem. Ref. Data14 (1), 227-234.
[83] Stull, D. R. & Prophet, H.1971 Janaf thermochemical tables. Tech. Rep. National Standard Reference Data System.
[84] Sutherland, W.1893LII. The viscosity of gases and molecular force. Lond. Edin. Dublin Phil. Mag. J. Sci.36 (223), 507-531. · JFM 25.1544.01
[85] Tanahashi, M., Iwase, S. & Miyauchi, T.2001Appearance and alignment with strain rate of coherent fine scale eddies in turbulent mixing layer. J. Turbul.2 (6), 1-17. · Zbl 1082.76538
[86] Thompson, P. A.1971A fundamental derivative in gasdynamics. Phys. Fluids14 (9), 1843-1849. · Zbl 0236.76053
[87] Thompson, P. A. & Lambrakis, K. C.1973Negative shock waves. J. Fluid Mech.60 (1), 187-208.
[88] Vadrot, A., Giauque, A. & Corre, C.2019Investigation of turbulent dense gas flows with direct numerical simulation. In Congrès français de mécanique. AFM.
[89] Vreman, A. W., Sandham, N. D. & Luo, K. H.1996Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech.320, 235-258. · Zbl 0875.76159
[90] Wagner, B. & Schmidt, W.1978Theoretical investigations of real gas effects in cryogenic wind tunnels. AIAA J.16 (6), 580-586.
[91] Wang, C.-W. & Rusak, Z.1999Numerical studies of transonic BZT gas flows around thin airfoils. J. Fluid Mech.396, 109-141. · Zbl 0967.76046
[92] Wang, J., Wan, M., Chen, S. & Chen, S.2018Kinetic energy transfer in compressible isotropic turbulence. J. Fluid Mech.841, 581-613. · Zbl 1419.76252
[93] Wheeler, A. P. S. & Ong, J.2013The role of dense gas dynamics on organic Rankine cycle turbine performance. Trans. ASME J. Engng Gas Turbines Power135 (10), 102603.
[94] White, F. M.1998Fluid Mechanics. McGraw-Hill Series in Mechanical Engineering.
[95] Zel’Dovich, J.1946On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz.16 (4), 363-364.
[96] Zeman, O.1990Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A2 (2), 178-188.
[97] Zhou, Q., He, F. & Shen, M. Y.2012Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties. J. Fluid Mech.711, 1-32. · Zbl 1275.76133
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