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Journal ArticleDOI

A dynamic subgrid‐scale eddy viscosity model

01 Jul 1991-Physics of Fluids (American Institute of Physics)-Vol. 3, Iss: 7, pp 1760-1765
TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the subgrid-scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses.
Abstract: The subgrid‐scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.

3,730 citations

Journal ArticleDOI
TL;DR: In this paper, a subgrid scale model is proposed for large eddy simulations in complex geometries, which accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations.
Abstract: A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y 3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

2,855 citations

Journal ArticleDOI
TL;DR: In this paper, a second-order accurate, highly efficient method is developed for simulating unsteady three-dimensional incompressible flows in complex geometries, which is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid.

1,643 citations

Journal ArticleDOI
TL;DR: Germano et al. as discussed by the authors generalized the dynamic subgrid-scale (SGS) model for the large eddy simulation (LES) of compressible flows and transport of a scalar.
Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

1,588 citations

Journal ArticleDOI
TL;DR: In this article, a method for generating three-dimensional, time-dependent turbulent inflow data for simulations of complex spatially developing boundary layers is described, which is essentially a variant of the Spalart method, optimized so that an existing inflow?outflow code can be converted to an inflow-generation device through the addition of one simple subroutine.

1,462 citations

References
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Journal ArticleDOI
TL;DR: In this article, an extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation, and the solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically.
Abstract: An extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation. The solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically. The vertical structure permits as dependent variables the horizontal wind at two internal levels and a single temperature, with the static stability entering as a parameter. The incoming radiation is a function of latitude only corresponding to the annual mean, and the outgoing radiation is taken to be a function of the local temperature. With the requirement for thermal equilibrium, the domain mean temperature is specified as a parameter. The role of condensation is taken into account only as it effectively reduces the static stability. All other external sources and sinks of heat are assumed to balance each other locally, and are thus omitted. The kinematics are th...

12,952 citations

Journal ArticleDOI
TL;DR: In this article, a direct numerical simulation of a turbulent channel flow is performed, where the unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points.
Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

4,788 citations

Journal ArticleDOI
TL;DR: In this article, a dynamic renormalization group (RNG) method for hydrodynamic turbulence was developed, which uses dynamic scaling and invariance together with iterated perturbation methods, allowing us to evaluate transport coefficients and transport equations for the large scale (slow) modes.
Abstract: We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumCK=1.617; turbulent Prandtl number for high-Reynolds-number heat transferPt=0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-\(\bar \varepsilon \) model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/\(\bar \varepsilon \), decay of isotropic turbulence asK=O(t−1.3307), and the von Karman constantκ=0.372. A differential transport model, based on differential relations betweenK,\(\bar \varepsilon \), andν, is derived that is not divergent whenK→ 0 and\(\bar \varepsilon \) is finite. This latter model is particularly useful near walls.

3,342 citations

Journal ArticleDOI
TL;DR: In this article, the three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers.
Abstract: The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

1,868 citations

Journal ArticleDOI
TL;DR: In this paper, the authors defined the distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosities size of roughness friction factor = 8rw/p V 2
Abstract: y* h k* a* A* = = = = = = = = = = = = = = = = = = = = = = = = = = = = distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosity size of roughness friction factor = 8rw/p V 2

1,710 citations