Isotropic Turbulent Viscosity Research Articles

A modified hypothesis of Reynolds stress tensor modeling for mixed turbulent convection in crystal growth

Within implicit large eddy simulation, we have provided unsteady 3D numerical study of turbulent melt convection during 100 mm diameter Si Cz growth, using refined time step and material properties. Comparison of calculated and measured time-averaged temperature profiles along the melt/crucible interface has demonstrated advantages of using updated material properties. Reference data on the spatial distributions of the turbulent stress tensor and heat fluxes in the melt have been obtained and used for validation of the conventional and modified hypothesis of Reynolds stress tensor modeling. Contrary to the conventional Boussinesq assumption of isotropic turbulent viscosity, our modified hypothesis has reproduced qualitative and quantitative details of reference Reynolds stress tensor distributions, including the boundary layer anisotropy due to the wall and free surface effects, mean velocity shear effect, and the buoyancy contribution to enhance vertical velocity fluctuations. Using our modified hypothesis and generalized Reynolds analogy for turbulent heat transport modeling, it become feasible to reproduce quantitatively the distributions of the turbulent heat flux, shear and buoyancy production terms of the kinetic energy transport equation, which is the necessary basis for further turbulence model development.

A Reynolds-averaged turbulence modelling approach to the maintenance of the Venus superrotation

A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modelling approach. The basic framework is similar to that of Gierasch (Meridional circulation and maintenance of the Venus atmospheric rotation. J. Atmos. Sci. 1975, 32, 1038–1044) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a non-local time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the non-local time scale. The relationship of the present model with the current general circulation model simulation is discussed in light of a crucial role of the vertical viscosity.

Turbulent-viscosity modeling applicable to swirling flows, based on a composite time scale with mean flow helicity partially incorporated

Helical motion contributes to the stabilization of turbulent flows, as is recognized through their mean velocity profiles. This feature indicates that swirl is capable of suppressing momentum transport. In the current Reynolds-averaged modeling, the flow is regarded as beyond the scope of the explicit algebraic modeling with the turbulent-viscosity representation as a key ingredient, and the second-order modeling is utilized as the sole approach at the cost of the increase in mathematical and computational complexity. The present work aims at reproducing primary features of swirling flows within the framework of an isotropic turbulent-viscosity model and extending the ability of the explicit algebraic modeling. Its cornerstone is the introduction of a composite time scale with the mean flow helicity partially incorporated without violating the Galilean invariance. The time scale is synthesized with the single ones familiar in the current modeling, on the basis of which the turbulent viscosity is modeled and incorporated into the two-equation modeling. The model is tested in a swirling pipe flow and is confirmed to reproduce its primary features, showing that the momentum transport is suppressed by the partial mean flow helicity due to the circumferential flow and the vorticity resulting from the retarded axial flow.

Modeling of Indoor Thermally Stratified Flows on the Basis of Eddy Viscosity/Diffusivity Model: State of the Art Review

Modeling of indoor air flow is one subject of significance in the area of building physics. As a multidisciplinary issue, the physics of air flow has been insufficiently investigated, especially for the thermally stratified flows that is widely encountered in indoor environment, and for the perimeter zones where exterior environment contributes much to the indoor thermal environment through envelops. This article tries to do an extensive survey about how to model thermally stratified flows within the RANS framework based on a literature review. First, turbulence phenomenon with the indoor thermally stratified flow is briefly interpreted. Second, the nonisotropic modification of Reynolds stress and heat flux is analyzed and the direct vertical correction is suggested to keep the simplicity of traditional EVM/EDM. Finally, a simpler nonisotropic correction is discussed, which adapts turbulent diffusion to the attenuated turbulence through modifying the isotropic turbulent viscosity and/or turbulent Prandtl number. This study, based on a limited but in-depth literature review, intends to sum up some useful suggestion on the modeling of indoor thermally stratified flows on the principles of simplicity and reliability. The motivation and objective of the present work is to achieve some fundamental guidelines for the evaluation of existing models and the exploration of new models.

Numerical prediction of turbulent boundary layer subjected to a sudden transverse strain at the wall

This study is about the behaviour of a two dimensional turbulent boundary layer on a flat plate subjected to a transverse motion of the bounding wall, producing a sudden shear force. The resulted flow is three-dimensional. Numerical prediction is achieved using the k-e model at high Reynolds number with the assumption of an isotropic turbulent viscosity. Close wall treatment constitutes the main difficulty within the three-dimensional turbulent boundary layer modelling. Therefore, we propose a law of wall along the transverse direction. Whilst the standard logarithmic function suggested in the literature for the two-dimensional case is used for the longitudinal component.

Experimental study of three-dimensional separation on a large-scale model

Three-dimensional separation was studied by analyzing the flow past a large-scale model consisting of a half-prolate ellipsoid extended by a circular cylinder ending in a flat base at 45 deg with respect to the cylinder axis. The flow past the model, including boundary layer and vortical structures, was investigated in great detail using a three-component laser Doppler velocimetry system and three-hole pressure probes actuated by a displacement system installed inside the model. This last device allowed probing of the separating three-dimensional boundary layer very close to the surface. We observed how the boundary layer evolved as it gradually sheared into a vortex roll-up and then into an organized vortex. When skewing of the boundary layer increased, the difference in direction between the velocity gradient vector and the shear stress vector also increased. For this type of flow, turbulence models based on the assumption of isotropic turbulent viscosity are inadequate for numerical analysis.

On the Calculation of Flow and Heat Transfer Characteristics for CANDU-Type 19-Rod Fuel Bundles

A numerical study is reported of flow and heat transfer in a CANDU-type 19 rod fuel bundle. The flow domain of interest includes combinations of triangular, square, and peripheral subchannels. The basic equations of momentum and energy are solved with the standard k–ε model of turbulence. Isotropic turbulent viscosity is assumed and no secondary flow is considered for this steady-state, fully developed flow. Detailed velocity and temperature distributions with wall shear stress and Nusselt number distributions are obtained for turbulent flow of Re = 4.35 × 104, 105, 2 × 105, and for laminar flow of Re ∼ 2400. Friction factor and heat transfer coefficients of various subchannels inside the full bundle are compared with those of infinite rod arrays of triangular or square arrangements. The calculated velocity contours of peripheral subchannel agreed reasonably with measured data.

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.

The prediction of turbulent swirling jet flow

A space marching integration procedure is used to solve the Reynolds equations governing the axisymmetric incompressible turbulent swirling jet flow. Turbulence is modelled by the k− ε model with an isotropic turbulent viscosity. Besides mean velocity field, turbulent properties—such as Reynolds stresses, turbulent kinetic energy and dissipation rate—are obtained and the results are compared with experimental data. Agreement is quite encouraging and shows that the assumption of isotropic turbulent viscosity seems plausible.