3 results
Velocity and temperature scalings leading to compressible laws of the wall
- P.G. Huang, G.N. Coleman, P.R. Spalart, X.I.A. Yang
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- Journal:
- Journal of Fluid Mechanics / Volume 977 / 25 December 2023
- Published online by Cambridge University Press:
- 22 December 2023, A49
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We exploit the similarity between the mean momentum equation and the mean energy equation and derive transformations for mean temperature profiles in compressible wall-bounded flows. In contrast to prior studies that rely on the strong Reynolds analogy and the presumed similarity between the instantaneous and mean velocity and temperature signals, the discussion in this paper involves the Farve-averaged equations only. We establish that the compressible momentum and energy equations can be made identical to their incompressible counterparts under appropriate normalizations and coordinate transformations. Two types of transformations are explored for illustration purposes: Van Driest (VD)-type transformations and semi-local-type or Trettel–Larsson (TL)-type transformations. In our derivations, it becomes clear that VD-type velocity and temperature transformations hold exclusively within the logarithmic layer. On the other hand, TL-type transformations extend their applicability to incorporate wall-damping effects, at least in principle. Each type of transformation serves its distinct purpose and has its applicable range. However, it is noteworthy that while VD-type transformations can be assessed using measurements obtained from laboratory experiments, TL-type transformations necessitate viscosity and density information typically accessible only through numerical simulations. Finally, we justify the omission of the turbulent kinetic energy transfer term, a term that is unclosed, in the energy equation. This omission leads to closed-form temperature transformations that are valid for both adiabatic and isothermal walls.
24 - Direct Numerical Simulations of Separation Bubbles
- Edited by B. E. Launder, University of Manchester Institute of Science and Technology, N. D. Sandham, University of Southampton
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- Book:
- Closure Strategies for Turbulent and Transitional Flows
- Published online:
- 06 July 2010
- Print publication:
- 21 February 2002, pp 702-719
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Summary
Abstract
In this chapter recent simulations of separation bubble flows are reviewed. This class of simulations contain a range of physical phenomena with laminar or turbulent separation and turbulent reattachment. Streamline curvature and extra rates of strain are present, compared to simple parallel shear flows. Simulations with initially laminar flow also contain a laminar–turbulent transition process. All this occurs within a simple geometry, providing good test cases for comparison with other predictive methods such as LES and RANS.
Introduction
Our discussion of separated flow DNS will be limited to separation of an incompressible laminar or turbulent boundary layer from a smooth flat surface. Either the boundary layer cannot follow a discontinuous change in the surface geometry, under nominally zero-pressure-gradient conditions (and the ‘surface separates from the flow’), or it is decelerated by an adverse pressure gradient (APG), with no change in surface curvature (and the ‘flow separates from the surface’). These cases are represented by, respectively, the flow over a backward-facing step, and the transpiration-induced detachment and reattachment of a flat-plate boundary layer. Both configurations include reattachment, leading to a closed separation bubble. The present focus is upon three-dimensional simulations in two-dimensional geometries, for Reynolds numbers low enough that all (or nearly all) relevant scales of motion can be explicitly resolved. Two-dimensional computations of transitional separation bubbles (e.g. Pauley et al. 1990), and higher-Reynolds-number LES of the backward-facing step are not considered here. Neither are the very low Reynolds number DNS of bluff-body flows (circular and elliptic cylinders, spheres, normal flat plates, and finite-thickness aerofoils), which often involve interaction of surface curvature and APG effects (Karniadakis and Triantafyllou 1992; Zhang et al. 1995; Najjar and Balachandar 1998; and Mittal and Balachandar 1995).
Application of DNS to separated flows is a challenging task. The heart of the challenge lies in the numerical issues introduced by the streamwise variation inherent to any separated flow.
The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study
- A. SIMONE, G.N. COLEMAN, C. CAMBON
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- Journal:
- Journal of Fluid Mechanics / Volume 330 / 10 January 1997
- Published online by Cambridge University Press:
- 10 January 1997, pp. 307-338
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The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md = S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.