Eddy Viscosity Concept Research Articles

Helical Flow through Concentric Annulus

The object of this investigation is to study the properties of a fully developed turbulent helical flow in a concentric annulus. A steady axial flow is assumed to take place under a constant axial pressure gradient with the inner cylinder of the annulus rotating at a constant angular velocity. The generalized eddy viscosity concept is used and the equations of motion, in cylindrical coordinates, are solved to obtain the axial and tangential velocity distributions. The results compare favorably with some existing experimental data. The results of the present study ultimately lead to the determination of the axial resistance to the flow and torque required at the inner cylinder of an annulus to maintain a uniform flow under any given condition.

An Examination of Eddy Viscosity Models for Turbulent Free Shear Flows

The boundary layer equations based on an eddy viscosity concept are solved numerically in the Crocco coordinate plane. A multilevel linear difference scheme is employed. Four different viscosity models are examined and the resulting solutions are compared. The empirical constants in the viscosity models are evaluated by comparing the calculated velocity profiles with experimental data in the similarity region.

Extension of Heisenberg's model for spectral transfer to second order fluids in turbulent flow

A generalization of the eddy viscosity concept permits an extension of the Heisenberg model for spectral energy transfer. The results are applied to the isotropic homogeneous turbulent flow of an incompressible second order fluid.

Calculation of Incompressible Turbulent Boundary Layers With Mass Transfer, Including Highly Accelerating Flows

This paper describes a general method for calculating turbulent boundary layers with and without mass addition. The method, as in earlier studies, is based on the eddy-viscosity concept. However, the eddy-viscosity formulation presented in this paper differs from the previous ones in that the previous eddy-viscosity formulation has been generalized to handle flows with mass transfer. A large number of flows computed with this method show good agreement with experiment.

Calculation of compressible adiabatic turbulent boundary layers

A method of solution of the compressible turbulent boundary-layer equations for twodimensional and axisymmetric flows, with transverse-curvature effects, is presented. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept and the time mean of the product of a fluctuating velocity and temperature term appearing in the energy equation is eliminated by an eddy-conductivity concept. An implicit finite-difference method is used in the solution of both momentum and energy equations after they are linearized. Results are presented for several adiabatic compressible flows, with and without pressure gradients for Mach numbers up to 5. The results show that the method is quite accurate and fast; a typical flow can be calculated in one or two minutes on the IBM 360/65 computer.

A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers

This paper presents a finite-difference method for solving laminar and turbulent-boundary-layer equations for incompressible and compressible flows about two-dimensional and axisymmetric bodies and contains a thorough evaluation of its accuracy and computation-time characteristics. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept, and the time mean of the product of fluctuating velocity and temperature appearing in the energy equation is eliminated by an eddy-conductivity concept. The turbulent boundary layer is regarded as a composite layer consisting of inner and outer regions, for which separate expressions for eddy viscosity are used. The eddy-conductivity term is lumped into a “turbulent” Prandtl number that is currently assumed to be constant. The method has been programed on the IBM 360/65, and its accuracy has been investigated for a large number of flows by comparing the computed solutions with the solutions obtained by analytical methods, as well as with solutions obtained by other numerical methods. On the basis of these comparisons, it can be said that the present method is quite accurate and satisfactory for most laminar and turbulent flows. The computation time is also quite small. In general, a typical flow, either laminar or turbulent, consists of about twenty x-stations. The computation time per station is about one second for an incompressible laminar flow and about two to three seconds for an incompressible turbulent flow on the IBM 360/65. Solution of energy equation in either laminar or turbulent flows increases the computation time about one second per station.

Laminar and Turbulent Incompressible Boundary Layers on Slender Bodies of Revolution in Axial Flow

The boundary-layer equations for both laminar and turbulent incompressible flows over slender bodies of revolution in axial flow are solved by an implicit finite-difference method. The Reynolds shear-stress term is eliminated by means of an eddy-viscosity concept. Velocity profiles and values of local skin-friction coefficient are obtained for various slender circular cylinders in both laminar and turbulent flows. The deviation of the cylinder skin friction from that of a flat plate is studied. The calculated velocity profiles for turbulent flow are compared with those of both Richmond’s and Yasuhara’s experimental data and with Rao’s proposed formulation of the law of the wall in thick, axisymmetric turbulent boundary layers. In both cases excellent agreement is obtained.

Solution of the Incompressible Turbulent Boundary-Layer Equations With Heat Transfer

The boundary-layer equations for laminar and turbulent incompressible flows about two-dimensional and axisymmetric flows are solved by an implicit finite-difference method. An eddy-viscosity concept is used to eliminate the Reynolds shear-stress term, and an eddy-conductivity concept is used to eliminate the time mean of the product of fluctuating velocity and temperature. Several flows have been computed by this method, and comparisons with experimental data and with the Bradshaw-Ferriss method are made. In general, the agreement is quite good.

Turbulent Helical Flow in an Annulus

Turbulent flow of an incompressible fluid in the annular space between concentric rotating cylinders with an axial pressure gradient is investigated experimentally and theoretically. The concept of a tensor eddy viscosity is used to develop the theory which predicts mean velocity distributions and resistance characteristics of fully developed turbulent flow in an annulus with either rough or smooth boundaries. Resistance characteristics and transition phenomena are observed in an annulus with the inner cylinder rotating. For a given axial flow, the axial resistance increases with increasing speed of rotation, in agreement with theoretical predictions. The transition from purely turbulent flow to turbulent flow with vortices, as inferred from changes in axial pressure gradient, is found to occur at a constant value of the ratio of average axial velocity to tangential velocity. For a given angular velocity, the tangential resistance is found to be reduced by the introduction of axial flow.

Daytime Temperature Profiles

Abstract An equation for the daytime lapse rate of temperature as a function of z/L is derived assuming the lapse rate varies as z−⅔ in very light winds. This variation is presumed to result from the geometry of buoyant plumes. The equation, which agrees very well with some data taken by Dyer, predicts a maximum value for the lapse rate at a fixed height and with given heat flux, at intermediate values of z/L. This variation suggests the concept of eddy viscosity as usually applied does not adequately describe the heat flux in unstable conditions.

Production of longitudinal vortices in the boundary layer along a concave wall

Velocity measurements in the boundary layer along a concave wall reveal a spanwise variation having a definite wave number whether the boundary layer is laminar or turbulent. The variation is interpreted as produced by a system of vortices with axis in the streamwise direction. For the laminar boundary layer the vortices are identified with those predicted by the theory of laminar instability. The wave amplitude distribution and wave amplification rate are in good agreement with the theoretical prediction. For the turbulent boundary layer the concept of eddy viscosity is introduced to account for the observed phenomena by the theory of laminar instability. In both cases, however, the mechanism by which the wave number is determined remains an open question. Since the centrifugal force in the concavely curved boundary layer is analogous to the buoyant force in the thermally stratified boundary layer in giving rise to instability, some analogous phenomena may be expected in the boundary layer along a heated horizontal wall.

On the frictionally induced transverse circulation of the Antarctic Circumpolar Current

The stationary distribution of the transverse and vertical current velocities were computed from the distribution of the down stream velocity component using the eddy viscosity concept.

A turbulent equatorial jet

A recent study of a laminar jet in a rotating spherical shell of fluid is extended to the case of a turbulent planetary jet at the equator of a rotating, stratified atmosphere or ocean. General forms of the velocity, density and pressure functions of both the mean motion and the turbulence are derived by a dimensional analysis applied to the mean and perturbation equations. The horizontal and vertical dimensions are estimated, based on the three characteristic constants of the problem, which are the momentum transfer, the stability and a rotation parameter. The estimates are in good agreement with the dimensions of the Cromwell current, i.e. the equatorial undercurrent of the Pacific Ocean.To the first order of approximation, the mean axial velocity in the theory is independent of distance along the jet axis. The mean horizontal transverse velocity component is much smaller and decreases upstream. The mean vertical velocity is extremely small, also decreasing upstream. The two horizontal velocity components of the turbulence are of the same order and, in the undercurrent, are about one-fourth the mean axial velocity. The vertical turbulent component is much smaller. Finally, it is shown that the eddy-viscosity concept is inappropriate for this problem because at least one of the eddy coefficients would have to be negative.