Engineering topics

Cabot, W.

Publications and source records attributed to Cabot, W..

13 records

NASA NTRS1996

Near-Wall Models in Large Eddy Simulations of Flow Behind a Backward-Facing Step

Accurate large eddy simulation (LES) of a wall-bounded flow generally requires a near-wall resolution comparable to that in direct numerical simulation (DNS). As much as 50% of the total grid points and computational costs are expended in the near-wall regions in a typical simulation. This limits LES to fairly low Reynolds numbers on current computers. To perform practical flow applications at realistically high Reynolds numbers, such as flow over an airfoil, it is desirable to replace very thin, near-wall regions in the LES with easily and inexpensively computed wall models to specify the near-wall boundary conditions.

Cabot, W.↗

NASA NTRS1996

Ensemble averaged dynamic modeling

The possibility of using the information from simultaneous equivalent Large Eddy Simulations (LAS) for improving the subgrid scale modeling is investigated. An ensemble average dynamic model is proposed as an alternative to the usual spatial average versions. It is shown to be suitable independently of the existence of any homogeneity directions, and its formulation is thus universal. The ensemble average dynamic model is shown to give very encouraging results for as few as 16 simultaneous LES's.

Carati, D.↗

NASA NTRS1996

Anisotropic eddy viscosity models

A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry.

Carati, D.↗

NASA NTRS1995

Large-eddy simulations with wall models

The near-wall viscous and buffer regions of wall-bounded flows generally require a large expenditure of computational resources to be resolved adequately, even in large-eddy simulation (LES). Often as much as 50% of the grid points in a computational domain are devoted to these regions. The dense grids that this implies also generally require small time steps for numerical stability and/or accuracy. It is commonly assumed that the inner wall layers are near equilibrium, so that the standard logarithmic law can be applied as the boundary condition for the wall stress well away from the wall, for example, in the logarithmic region, obviating the need to expend large amounts of grid points and computational time in this region. This approach is commonly employed in LES of planetary boundary layers, and it has also been used for some simple engineering flows. In order to calculate accurately a wall-bounded flow with coarse wall resolution, one requires the wall stress as a boundary condition. The goal of this work is to determine the extent to which equilibrium and boundary layer assumptions are valid in the near-wall regions, to develop models for the inner layer based on such assumptions, and to test these modeling ideas in some relatively simple flows with different pressure gradients, such as channel flow and flow over a backward-facing step. Ultimately, models that perform adequately in these situations will be applied to more complex flow configurations, such as an airfoil.

Cabot, W.↗

NASA NTRS1994

A Lagrangian dynamic subgrid-scale model turbulence

A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Meneveau, C.↗

NASA NTRS1991

A dynamic subgrid-scale model for compressible turbulence and scalar transport

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.

Moin, P.↗

NASA NTRS1990

Turbulent thermal convection in a differentially rotating channel

Differentially rotating disks of gases and solids occur in several astrophysical systems, in particular in the inner parts of protostellar nebulae, of which our own solar system is thought to be a relic. The objectives of this paper are to: (1) study localized turbulence in circumstances approximating those found in accretion disks using previously existing expertise in performing direct numerical simulation of turbulent, incompressible channel flows with low Reynolds numbers; (2) determine the limitations of such calculations; and (3) extend the type of numerical simulation (e.g., to include density and stratification and compressibility effects and to accommodate higher Reynolds numbers with sub-grid scale modeling) so that the relevant physical effects are realistically captured.

Cabot, W.↗

NASA NTRS1990

Direct Numerical Simulations of Turbulent Convection: Variable Gravity and Uniform Rotation - Part 1

Turbulent convection may have played a major role in determining the structure and evolution of the primordial solar nebula, but current, incomplete models of convection and turbulence give very different results and remain largely untested in the absence of detailed astronomical observations. Numerical simulations provide an 'experimental' database for comparison with these models, and, to this end, direct numerical simulations of turbulent convection were performed with modifications intended to mimic some of the unique physical features of thin accretion disks, such as the primordial solar nebula: internal heating, a gravitational acceleration that is linearly proportional to the distance from midplane of the nebula, and rapid rotation. Peclet numbers in the simulations are comparable to those in solar nebula models; Rossby numbers in the simulations are an order of magnitude larger than those in solar nebula models because of the unrealistically high Prandtl and low, Reynolds numbers required to resolve all scales of the convective flow. We find that, despite the loss of buoyancy at midplane, turbulent motions easily penetrate the midplane region with little loss of intensity, providing efficient transport of heat and turbulent kinetic energy throughout the interior. A simple mixing length model modified to include rotation is found to give convective heat fluxes for the interior flow in rough agreement with the numerical simulations. We discuss these preliminary results with regard to assumptions about heating distributions and convective heat fluxes made in standard solar nebula models. More definitive comparisons with solar nebula modelling will become possible when more realistic effects of shear, density, stratification, and compression are included.

Cabot, W.↗

NASA NTRS1987

The role of turbulent convection in the primitive solar nebula. I - Theory. II - Results

A model of convective turbulence which takes radiative dissipation, rotation, and convective motion anisotropy into account, on the basis of a closure for the nonlinear interactions that employs the growth rates of hydrodynamic instabilities, is used to obtain a theoretical framework for modeling the primordial solar nebula. It is assumed that convection is the sole source of turbulence causing the solar nebula to evolve. Vertical structure equations in the thin disk approximation are developed and a detailed comparison with the previous solar nebula convective models of such workers as Lin et al. (1981, 1982) is undertaken. The present values for the turbulent efficiency are much lower and more sensitive to opacity and surface density, resulting in low turbulent speeds, a more massive disk, a lower accretion rate 'best value', and a longer characteristic dispersal time for the disk. It is concluded that convection may not be the dominant source of turbulence needed to evolve young solar/stellar nebulae.

Cabot, W.↗

NASA NTRS1985

Is the Kolmogoroff model applicable to large-scale turbulence?

In view of the present discussion, the Heisenberg-Kolmogoroff (HK) model of turbulence that is often used for turbulent phenomena on all scales is actually valid for a turbulent spectrum wavelength band typically much smaller than the size of the system, and cannot describe phenomena at large scales in astrophysical systems. The results of mixing length theory cannot be accommodated within the HK model's framework without the adoption of an unreasonable coupling constant. It is also noted that the use of the observed velocity-size relationship in molecular clouds with turbulent velocity values of about l to the 1/2-power, within the HK model, gives rise to a growth rate that does not correspond to any known physical processes suspected of operating in molecular clouds.

Canuto, V. M.↗

NASA NTRS1985

Accretion disk oscillations - A local analysis in a disk of finite thickness

Two types of oscillations are observed to occur in dwarf novae: 'coherent' and 'quasi-periodic' oscillations. These may be associated with the pulsation of the white dwarf or the accretion disk components of the dwarf nova. Here a local (short-wavelength) analysis is utilized to study the oscillation of a self-consistent, two-dimensional model of an accretion disk. The linearized equations describing adiabatic, inviscid, nonaxisymmetric oscillations are used to derive a fifth-order algebraic equation for the (complex) pulsation frequency of the disk. The solutions of this equation for various values of the wavevector k reveal that the disk is capable of supporting (1) a pair of high-frequency acoustic modes (p-modes); (2) a pair of intermediate-frequency modes which may share the characteristics of internal gravity waves (g-modes) and inertial waves; and (3) a mode associated with a dynamical instability (purely imaginary frequency). The role played by the shear in determining the stability or instability of these modes is also considered. Finally, the global oscillation frequencies of the disk are discussed.

Carroll, B. W.↗

NASA NTRS1984

The nonaxisymmetric baroclinic instability in thin accretion disks

The instability of linear, nonaxisymmetric baroclinic waves in the radiative regions of a thin accretion disk is investigated with simplifying assumptions used in the representation of the structure of the basic state. As in stars with rotation laws deviating from rotation on cylinders, the departure from barotropy ('baroclinicity') resulting from such rotation feeds potential energy from the basic state into the kinetic energy of the baroclinic motions. The baroclinic instability is considered as a possible mechanism for driving turbulence in disks. Estimations of the Reynolds stress from baroclinic waves indicate that the degree of baroclinicity in stationary disk models is insufficient to account for the large viscosity inferred from observations of, e.g., cataclysmic variables.

Cabot, W.↗

NASA NTRS1982

Meridional circulation in optically thick accretion disks

Thermal imbalances in stars due to rotation are known to drive mass motions in the meridional plane. A preliminary analytic investigation has been made of a similar effect in optically thick accretion disks using conventional thin-disk approximations. It is found that estimated circulation times can be as short as thermal timescales, resulting in rapid transport of heat and angular momentum. This indicates that the simple approximations commonly used are incomplete with regard to detailed, two-dimensional disk structure.

Cabot, W.↗