Recent results from a turbulent channel flow simulation using a vortex sheet and tube method will be described. The approach limits new vortex creation to just those arising from significant ejection events initiated by parent vortices. Together with the invocation of a hairpin removal algorithm and a technique for eliminating old highly stretched vortices, the number of vortex elements in a typical channel flow simulation achieves statistical equilibrium. Of particular interest is establishing that the algorithm represents the statistical and structural properties of physical turbulence. Clear evidence for a bona fide Reynolds shear stress is found in the computed averages, a persistent streaky structure in the near wall region, and the ability of the newly minted vortices to develop into substantial quasi-streamwise parent vortices over time. Toward the central region of the channel, the vortex elements display an increasingly anisotropic orientation. Preliminary results will also be presented from an application of the vortex method to the turbulent flow past a prolate spheroid.
[Cb.02] Approximate Wall Boundary Conditions in Simulations of Separated Flows
William Cabot, Jeffrey Baggett (\urllinkCenter for Turbulence Research http://www-fpc.stanford.edu/CTR/welcome.html, Stanford)
Large-eddy simulation at high Reynolds numbers is only practical if near-wall regions are modelled to provide suitable boundary conditions for the core flow, allowing the grid there to be specified in a Reynolds number-independent manner. Results are presented for wall model tests in separated flow on a flat plate subject to an adverse pressure gradient and in flow over a backward-facing step. The boundary conditions can take two forms: 1) wall stress conditions applied at the wall, and 2) velocity conditions applied off of the wall. Preliminary results show that it is more difficult to employ the latter conditions successfully; and even when the boundary conditions are sufficiently accurate, unresolved subgrid-scale stresses on the coarse near-wall grid also must be modelled accurately to provide a consistent description of both mass and momentum fluxes near the walls. This is currently beyond the capability of standard subgrid-scale models used in large-eddy simulation, which are based on assumptions of isotropic turbulence and resolved energy-containing scales of motion.
[Cb.03] Application of mixed SGS models to separated flows
Fabrizio Sarghini, Ugo Piomelli (Dept.~of Mechanical Engineering, University of Maryland, College Park, MD 20742), Craig L. Streett (NASA Langley Research Center, Hampton, VA 23681)
The separated flow behind a sharp corner has been the object of several numerical studies that have used both large-eddy (LES) and direct numerical simulations (DNS). In the present study, a mixed SGS model including a scale-similar formulation and a dissipative part is applied to the calculation of a backward-facing step and a shallow cavity. Mixed models have been shown to be the most active in the interaction with the unresolved, subgrid scales. Their ability to provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses that are well correlated with the locations where large Reynolds stress occurs allows them to give accurate prediction of the local flow structure in strongly non-equilibrium flows such as the ones under consideration, a capability required if the noise generated in these flows is desired.
[Cb.04] Self-similar filter for the dynamic procedure
Daniele Carati, Eric Vanden Eijnden (ULB)
Classically, the equation studied in a large eddy simulation (LES) is viewed as a spatially filtered version of the Navier-Stokes equation. However, the spatial filter is usually not specified and does not enter the LES equation explicitly. As a consequence, it is not clear how the LES results must be compared to direct numerical simulations or to experimental data. This problem became even more accurate with the introduction of the dynamic procedure which uses a second (test) filter for determining the model coefficients.
Here, we propose a new interpretation of the dynamic procedure in which the grid filter is given in terms of the test filter. By using a simple self-similarity assumption, the grid filter is formally expressed by an infinite convolution of test filters with smaller and smaller filter width.
The new formulation does not change the implementation of the dynamic procedure and only implies a new interpretation of the LES simulations. However, the possible ambiguity about the meaning of the resolved field disappears once the test-filter has been chosen. Alternatively, if the LES has to be done with a given grid filter then the test filter in the dynamic procedure cannot be chosen independently and can be determined again by using self-similarity arguments.
The relation between this new interpretation of the dynamic procedure and the renormalization group approach is discussed.
[Cb.05] Applications of B-spline Methodology to Three-Dimensional Simulations of Flow over a Cylinder
Arthur Kravchenko, Parviz Moin, Karim Shariff (CTR, Stanford University and NASA-Ames Research Center)
A numerical method based on B-splines(A.G. Kravchenko, P. Moin, R. Moser, J. Comp. Phys.), 127, 412-423 (1996) is generalized for turbulence simulations on zonal grids in curvilinear coordinates. The performance of the method is assessed in three-dimensional simulations of a flow over a circular cylinder. Numerical simulations at Re=300 show good agreement with the corresponding spectral calculations. Coefficient of drag and Strouhal shedding frequency agree well with the experimental data for this flow. Large eddy simulations at the subcritical Reynolds number, Re=3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the near-wake, all three simulations are in excellent agreement with each other and agree fairly well with the experimental data of Lourenco and Shih. In the far-wake, the results obtained from the B-spline computations are in better agreement with the experimental data of Ong and Wallace than those obtained in upwind and central finite-difference simulations. The influence of numerical resolution and the spanwise domain size on the three-dimensional simulations will be discussed.
[Cb.06] Subgrid-scale acceleration in the atmospheric surface layer
C. Tong, S. Khanna, J.C. Wyngaard (Penn State University)
In large-eddy simulations (LES), the subgrid-scale (SGS) acceleration is given by the difference between the SGS stress divergence, a, and the SGS pressure gradient. For unbounded incompressible flows this difference is the solenoidal part of the SGS stress divergence. In LES of the atmospheric boundary layer (ABL), the SGS pressure field contains boundary effects through its lower boundary condition given by the normal component of a at the surface. By decomposing a into an irrotational, a solenoidal, and an irrotational solenoidal part (the gradient of a harmonic function) and the SGS pressure gradient field into an irrotational and an irrotational solenoidal part, we show that for incompressible flows the net SGS acceleration is caused by the solenoidal SGS stress divergence a_so and by the SGS pressure gradient field determined only by the normal component of a_so at the surface. To study the SGS acceleration, LES data (128^3) of the ABL are filtered at scales larger than the LES cutoff to obtain resolvable- and SGS quantities. Preliminary results for a moderately convective ABL show larger anisotropy for a_so in the surface layer than for a. The SGS pressure gradient determined by a_so is important within the height of a few LES horizontal grid sizes and decreases exponentially with height. Results from detailed analyses of the a_so and the SGS pressure gradient field will be reported.
[Cb.07] High order finite difference schemes with good spectral resolution
Krishnan Mahesh (Center for Turbulence Research, Stanford University)
We present a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric, and may be considered a more general version of the standard compact (Padé) schemes. They are different from the standard Padé schemes, in that the first and second derivatives are evaluated simultaneously. For the same stencil width, the proposed schemes are two orders higher in accuracy, and have significantly better
spectral representation. Eigenvalue analysis, and numerical solutions of the one-dimensional wave equation are used to demonstrate the numerical stability of the schemes.
The computational cost of computing both derivatives is assessed, and shown to be essentially the same as the standard Padé schemes. The proposed schemes appear to be attractive alternatives to the standard Padé schemes for computations of the Navier Stokes equations.
[Cb.08] Performance of Smagorinsky and dynamic models in near surface turbulence
James G. Brasseur, Anurag Juneja (Penn State University)
In LES of high-Reynolds-number wall bounded turbulence such as the atmospheric boundary layer (ABL), a viscous sublayer either does not exist or is within the first grid cell, and some integral scale motions are necessarily under-resolved at the first few grid locations. Here the subgrid terms dominate the evolution of resolved velocity and the SGS model performance becomes crucial. To develop improved closures for surface layer turbulence (under-resolved and anisotropic), we explore (a) why current SGS closures fail and (b) what needs to be fixed. We evaluate the performance of the Smagorinsky and dynamic models using DNS data from shear- and buoyancy-driven turbulence as a function of filter cutoff location. We find that the underlying assumption of good alignment between the subgrid stress and resolved strain-rate tensors is not correct in general. More importantly, the Smagorinsky model incorrectly predicts a strong preference in the direction of the SGS stress divergence vector, a spurious prediction that is directly related to the anisotropic structure of the resolved turbulence field. This, and its under-estimation of the SGS pressure gradient, are likely sources of the errors observed in LES of the ABL. Whereas the dynamic formulations do a better job predicting some SGS dynamics, the model fails when the filter cutoff is near an integral scale, and predicts unreasonable fluctuation levels-- although performance is sensitive to type of averaging. *supported by ARO grant DAAL03-92-0117.
[Cb.09] DNS of Turbulent Flow over a Modeled Riblet Surface
Tai-Chang Tuan, David B. Goldstein (University of Texas at Austin)
An immersed boundary technique is used to model a riblet surface on one wall of a channel bounding fully developed turbulent flow. We employ a feedback scheme to apply a localized body force which makes the local flow velocity comply with the no-slip condition on the riblet surface. All simulations were done with a spectral code in a simple box computational domain without any mapping of the mesh.
An extensive grid resolution study has been done on simulations of both laminar and turbulent flows. The solutions are shown to converge with the grid refinement. A parametric study evaluating the effects of our modeling techniques on the no-slip condition demonstrates that the riblet surfaces are adequately simulated. Detailed comparisons with previous computational and experimental work indicate that our simulations correctly capture the physics.
Simulations with different riblet spacings and types were performed to study the geometry effects on near-wall flow structure. It is found that widely spaced riblets create a remarkable pattern of mean secondary flows consisting of pairs of streamwise vortices and a substantial increase in turbulent activity just above the riblet peaks, which may be tied to their loss of drag reduction performance.
[Cb.10] Temporal Eigenfunctions of Vorticity in Decaying Isotropic Turbulence
Haralambos Marmanis, G. Em. Karniadakis (Brown University)
A new approach in the theory of turbulence insinuates that the vorticity and the Lamb vector evince a wave-like behaviour. The objective of this work is to investigate the existence of these waves in turbulence. We start by assigning a special linear operator to every wavenumber in Fourier space. We subsequently analyze, by exact calculations, the eigenfunctions of this linear operator and show that they are capable to describe the decay of the individual Fourier modes of the vorticity field. This is verified by projecting the results of DNS onto these eigenfunctions, and comparing the relative magnitudes of the projection coefficients. For a specific wavenumber, only a couple of eigenfunctions are sufficient to represent the result obtained by DNS.