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Effects of distributed pressure gradients on the pressure–strain correlations in a supersonic nozzle and diffuser

Published online by Cambridge University Press:  21 February 2014

Somnath Ghosh
Lehrstuhl für Aerodynamik und Strömungsmechanik, TU München, D-85748 Garching bei München, Germany
Rainer Friedrich*
Lehrstuhl für Aerodynamik und Strömungsmechanik, TU München, D-85748 Garching bei München, Germany
Email address for correspondence:


Direct numerical simulation (DNS), based on high-order numerical schemes, is used to study the effects of distributed pressure gradients on the redistribution of fluctuating kinetic energy in supersonic nozzle and diffuser flow with incoming fully developed turbulent pipe flow. Axisymmetric geometries and flow parameters have been selected such that shock waves are avoided and streamline curvature remains unimportant. Although mean extra rates of strain are quite small, strong changes in Reynolds stresses and their production/redistribution mechanisms are observed, in agreement with findings of Bradshaw (J. Fluid Mech., vol. 63, 1974, pp. 449–464). The central role of pressure–strain correlations in changing the Reynolds stress anisotropy is highlighted. A Green’s function-based analysis of pressure–strain correlations is presented, showing remarkable agreement with DNS data.

© 2014 Cambridge University Press 

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Adams, N. A. & Shariff, K. 1996 A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comput. Phys. 127, 2751.Google Scholar
Bradshaw, P. 1967 The response of a constant-pressure turbulent boundary layer to the sudden application of an adverse pressure gradient. In ARC R and M 3575 Aero. Res. Counc. England.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. (AGARDograph) , vol. 169. NATO Science and Technology Organization.Google Scholar
Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449464.Google Scholar
Coleman, G. N., Fedorov, D., Spalart, P. R. & Kim, J. 2009 A numerical study of laterally strained wall-bounded turbulence. J. Fluid Mech. 639, 443478.Google Scholar
Coleman, G. N., Kim, J. & Spalart, P. R. 2003 Direct numerical simulation of a decelerated wall-bounded turbulent shear flow. J. Fluid Mech. 495, 118.Google Scholar
Duffy, D. G. 2001 Green’s Functions with Applications. Chapman and Hall.Google Scholar
Dussauge, J. P. & Gaviglio, J. 1987 The rapid expansion of a supersonic turbulent flow: role of bulk dilatation. J. Fluid Mech. 174, 81112.Google Scholar
Fernando, E. M. & Smits, A. J. 1990 A supersonic turbulent boundary layer in an adverse pressure gradient. J. Fluid Mech. 211, 285307.Google Scholar
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. (AGARDograph) , vol. 253. AGARD.Google Scholar
Fernholz, H. H. & Finley, P. J. 1981 A further compilation of compressible boundary layer data with a survey on turbulence data. (AGARDograph) , vol. 263. AGARD.Google Scholar
Fernholz, H. H., Smits, A. J., Dussauge, J. P. & Finley, P. J. 1989 A survey of measurements and measuring techniques in rapidly distorted compressible turbulent boundary layers. (AGARDograph) , vol. 315. AGARD.Google Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207216.Google Scholar
Gatski, T. B. & Bonnet, J. P. 2009 Compressibility, Turbulence and High Speed Flow. Elsevier.Google Scholar
Ghosh, S., Foysi, H. & Friedrich, R. 2010 Compressible turbulent channel and pipe flow: similarities and differences. J. Fluid Mech. 648, 155181.Google Scholar
Ghosh, S. & Friedrich, R. 2010 Direct numerical simulation of turbulent flow in an axisymmetric supersonic diffuser. J. Turbul. 11, 122.Google Scholar
Ghosh, S., Sesterhenn, J. & Friedrich, R. 2008 Large-eddy simulation of supersonic turbulent flow in axisymmetric nozzles and diffusers. Intl J. Heat Fluid Flow 29, 579590.Google Scholar
Jayaram, M., Donovan, J. F., Dussauge, J.-P. & Smits, A. J. 1989 Analysis of a rapidly distorted, supersonic turbulent boundary layer. Phys. Fluids 1, 18551864.Google Scholar
Jayaram, M., Taylor, M. W. & Smits, A. J. 1987 The response of a compressible turbulent boundary layer to short regions of concave surface curvature. J. Fluid Mech. 175, 343362.Google Scholar
Lee, J. & Sung, H. J. 2008 Effects of an adverse pressure gradient on a turbulent boundary layer. Intl J. Heat Fluid Flow 29, 568578.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.Google Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157, 787795.Google Scholar
Nagano, Y., Tagawa, M. & Tsuji, M. 1993 Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In Turbulent Shear Flows (ed. Durst, F., Friedrich, R., Launder, B. E., Schmidt, F. W., Schumann, U. & Whitelaw, J. W.), vol. 8, Springer.Google Scholar
Panchapakesan, N. R., Nickels, T. B., Joubert, P. N. & Smits, A. J. 1997 Lateral straining of turbulent boundary layers. Part 2. Streamline convergence. J. Fluid Mech. 349, 130.Google Scholar
Piomelli, U., Balaras, E. & Pascarelli, A. 2000 Turbulent structures in accelerating boundary layers. J. Turbul. 1, 116.Google Scholar
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.Google Scholar
Pompeo, L., Bettelini, M. S. & Thomann, H. 1993 Laterally strained turbulent boundary layers near a plane of symmetry. J. Fluid Mech. 257, 507532.Google Scholar
Saddoughi, S. G. & Joubert, P. N. 1991 Lateral straining of turbulent boundary layers. Part 1. Streamline divergence. J. Fluid Mech. 229, 173204.Google Scholar
Sarkar, S. 1992 The pressure-dilatation correlation in compressible flows. Phys. Fluids A4 (12), 26742682.Google Scholar
Sesterhenn, J. 2001 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30, 3767.Google Scholar
Smith, D. R. & Smits, A. J. 1991 The rapid expansion of a turbulent boundary layer in a supersonic flow. Theor. Comput. Fluid Dyn. 2, 319328.Google Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. 2nd edn. Springer.Google Scholar
Smits, A. J. & Wood, D. H. 1985 The response of turbulent boundary layers to sudden perturbations. Annu. Rev. Fluid Mech. 17, 321358.Google Scholar
Spalart, P. R. 1986 Numerical study of sink flow boundary layers. J. Fluid Mech. 172, 307328.Google Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287319.Google Scholar