Showing papers by "Parviz Moin published in 1995"

A dynamic localization model for large-eddy simulation of turbulent flows

Abstract: In a previous paper, Germano, et al. (1991) proposed a method for computing coefficients of subgrid-scale eddy viscosity models as a function of space and time. This procedure has the distinct advantage of being self-calibrating and requires no a priori specification of model coefficients or the use of wall damping functions. However, the original formulation contained some mathematical inconsistencies that limited the utility of the model. In particular, the applicability of the model was restricted to flows that are statistically homogeneous in at least one direction. These inconsistencies and limitations are discussed and a new formulation that rectifies them is proposed. The new formulation leads to an integral equation whose solution yields the model coefficient as a function of position and time. The method can be applied to general inhomogeneous flows and does not suffer from the mathematical inconsistencies inherent in the previous formulation. The model has been tested in isotropic turbulence and in the flow over a backward-facing step.

Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence

Abstract: Direct numerical simulation is used to examine the interaction of turbulence with a wall in the absence of mean shear. The influence of a solid wall on turbulence is analysed by first considering two ‘simpler’ types of boundaries. The first boundary is an idealized permeable wall. This boundary isolates and elucidates the viscous effects created by the wall. The second boundary is an idealized free surface. This boundary complements the first by allowing one to isolate and investigate the kinematic effects that occur near boundaries. The knowledge gained from these two simpler flows is then used to understand how turbulence is influenced by solid walls where both viscous and kinematic effects occur in combination.Examination of the instantaneous flow fields confirms the presence of previously hypothesized structures (splats), and reveals an additional class of structures (antisplats). Statistical analysis of the Reynolds stresses and Reynolds stress transport equations indicates the relative importance of dissipation, intercomponent energy transfer, and energy transport. It is found that it is not the structures themselves, but the imbalance between structures which leads to intercomponent energy transfer. Remarkably, this imbalance (and hence near-wall intercomponent energy transfer) is controlled by viscous processes such as dissipation and diffusion. The analysis presented herein is a departure from past notions of how boundaries influence turbulence. The efficacy of these qualitative physical concepts is demonstrated in Part 2 where improved near-wall turbulence models are derived based on these ideas.

Direct computation of the sound from a compressible co-rotating vortex pair

Abstract: The far-field sound from corotating vortices is computed by direct computation of the unsteady, compressible Navier-Stokes equations on a computational mesh that extends to two acoustic wavelengths in all directions. The vortices undergo a period of corotation followed by a sudden merger. A 2D version of Moehring's equation is developed and used in conjunction with source terms computed in the simulation to predict the far-field sound. The prediction agrees with the simulation to within 3 percent. Results of far-field pressure fluctuations for an acoustically noncompact case are also presented for which the prediction is 66 percent too high. Results also indicate that the monopole contribution of 'viscous sound' is negligible for this flow.

On the representation of backscatter in dynamic localization models

Abstract: The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time‐step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that th...

The interaction of an isotropic field of acoustic waves with a shock wave

Abstract: Moore's (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail.The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuations decreases across the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.

Direct computation of the sound generated by vortex pairing in an axisymmetric jet

Abstract: The sound generated by vortex pairing in axisymmetric jets is determined by direct solution of the compressible Navier–Stokes equations on a computational grid that includes both the near field and a portion of the acoustic far field. At low Mach number, the far-field sound has distinct angles of extinction in the range of 60°–70° from the jet's downstream axis which can be understood by analogy to axisymmetric, compact quadrupoles. As the Mach number is increased, the far-field sound takes on a superdirective character with the dominant sound directed at shallow angles to the jet's downstream axis. The directly computed sound is compared to predictions obtained from Lighthill's equation and the Kirchhoff surface method. These predictions are in good agreement with the directly computed data. The Lighthill source terms have a large spatial distribution in the axial direction necessitating the introduction of a model to describe the source terms in the region downstream of the last vortex pairing. The axial non-compactness of the quadrupole sources must be adequately treated in the prediction method.

Shear-free turbulent boundary layers. Part 2. New concepts for Reynolds stress transport equation modelling of inhomogeneous flows

Abstract: Models for the dissipation tensor and (slow) pressure–strain terms of the Reynolds stress transport equations are presented which are applicable near boundaries. These models take into account the large inhomogeneity and anisotropy that can be present near walls and surfaces, and are inspired by the physical insights developed in Part 1 of this paper. The dissipation tensor model represents a fundamentally new approach to dealing with turbulence inhomogeneities. The pressure–strain model shows how the classic return-to-isotropy model of Lumley (1978) can be adapted to the near-wall region. The closure hypotheses underlying these two models are tested in an a priori fashion using direct numerical simulation (DNS) data.

The velocity and vorticity fields of the turbulent near wake of a circular cylinder

Abstract: The purpose of this research is to provide a detailed experimental database of velocity and vorticity statistics in the very near wake (x/d less than 10) of a circular cylinder at Reynolds number of 3900. This study has determined that estimations of the streamwise velocity component in flow fields with large nonzero cross-stream components are not accurate. Similarly, X-wire measurements of the u and v velocity components in flows containing large w are also subject to the errors due to binormal cooling. Using the look-up table (LUT) technique, and by calibrating the X-wire probe used here to include the range of expected angles of attack (+/- 40 deg), accurate X-wire measurements of instantaneous u and v velocity components in the very near wake region of a circular cylinder has been accomplished. The approximate two-dimensionality of the present flow field was verified with four-wire probe measurements, and to some extent the spanwise correlation measurements with the multisensor rake. Hence, binormal cooling errors in the present X-wire measurements are small.

Large Eddy Simulation of Backward-Facing Stop Flow with Application to Coaxial Jet Combustors.

Abstract: : Large eddy simulations (LES) have been performed for two massively separated flows: a planar backward-facing step and a coaxial jet combustor. The backward-facing step case was used to develop and validate both the numerical method and the subgrid-scale model. Backward-facing step simulations were performed at Reynolds numbers 5100 and 28000. Both cases agree well with experimental data; the low Reynolds number case is also in excellent agreement with DNS data. Two versions of the dynamic subgrid-scale model as well as the classical Smagorinsky model were tested and little difference was found among them. The coaxial jet combustor simulations were used as a first step to study the flame stability problem known as lean blow-out. The study focused on the entrainment and mixing of fuel and air within the combustion chamber, using a passive scalar tracking technique. Chemical reactions and the effects of heat release were ignored in this initial study. Mean statistics at Reynolds number 38000 are in good agreement with experimental data. A motion picture of the unsteady motion revealed intermittent pockets of fuel-rich fluid crossing the annular air jet and becoming entrained in the recirculation zone. A larger source of entrainment, however, was found to be the upstream redirection of the fuel jet near the instantaneous impingement point on the combustor wall.

The Sound Generated by a Two-Dimensional Shear Layer: A Comparison of Direct Computations and Acoustic Analogies

Abstract: The sound generated by vortex pairing in a two-dimensional mixing layer is studied by solving the N avier-Stokes equations (DNS) for the layer and a portion of its acoustic field, and by solving acoustic analogies with source terms determined from the DNS. Predictions for the acoustic field based on Lilleys equation are in excellent agreement with the DNS results giving detailed verification of Lilleys acoustic analogy for the first time. We show that parts of the full source term which arise when the left-hand-side of Lilleys equation is linearized should not be neglected solely because they are attributable to refraction and scattering, nor because they are proportional to the dilatation. Lilleys source, -2Ui,jUj,kUk,i, appears to be mainly responsible for the overall directivity of the acoustic field produced by the vortex pairings, which is highly focused at shallow angles to the streamwise axis. Scattering of the waves by the flow appears also to be significant, causing the directivity to be more omnidirectional than the Lilley source alone would predict. We also show how small errors in determining the sources, especially those due to scattering, can sometimes lead to large errors in the predictions.

Large Eddy Simulation of Turbulent Flow Over an Airfoil.

Abstract: : The turbulent flow over a NACA 4412 airfoil at angle of incidence corresponding to maximum lift (12 degree) has been computed via large-eddy simulation Two different numerical approaches, one based on a conventional structured mesh and one with a more economical unstructured mesh, have been employed Results from both simulations differ considerably from each other and from the available experimental data Differences are found with respect to occurrence of transition near the suction peak and with respect to the amount of backflow (incipient separation) near the trailing edge The unstructured mesh code predicts rapid boundary layer growth and separation near the trailing edge, whereas the flow remains attached in the structured mesh simulation It was concluded that a better matching of the transition mechanism (boundary layer tripping) which was employed in the experiments is paramount for an accurate simulation of this flow and for convergence of solutions from the two codes (AN)

Direct and large eddy simulation of separated turbulent boundary layers

Abstract: : Space-time characteristics of pressure fluctuations were analyzed using the databases generated from the direct numerical simulation. In the separated flow, the wall-pressure fluctuations are significantly reduced in the separation zone. However, they are significantly enhanced in the reattachment region. The streamwise and spanwise vorticities are lifted away from the wall in the separation zone and the pressure fluctuations are significantly enhanced in this shear layer. The contours of space-time correlations show that the convection velocities of wall-pressure fluctuations are reduced significantly inside the separation bubble. The reattachment region is characterized by large scale structures which are formed in the shear layer above the separation bubble. Frequency spectra downstream of incipient detachment shows that maximum turbulent shearing stress appears to be the proper scale to normalize wall-pressure fluctuations in the turbulent boundary layers in the presence of large adverse pressure gradient. (AN)