Eddy Viscosity Distribution Research Articles

Parametric Relations for Ordinary and Confluent Turbulent Boundary-Layer Flows

Theme T paper presents the results of an investigation of parameters associated with the confluent boundary layer shown schematically in Fig. 1. It is shown that with a suitable choice of parameters, velocity profiles in both jet and wake layers become similar, with the same similarity function obtained for different pressure gradients. Moreover, local dynamic similarity allows suitable functional representation of shear stress at the loci of maximum and minimum velocity. Measured eddy viscosity distributions for the confluent boundary layer is presented for one velocity ratio at slot exit. An analytical solution for the conventional flat plate turbulent boundary layer is shown for comparison purposes.

Kinematic eddy viscosity at low Reynolds numbers.

with A = A + v(tw/p)~]-/2, and showed that when Eqs. (3) (with a = 0.0168) and (5) were used as the eddy- viscosity formulation in the solution of the boundary-layer equations, the agreement with experiment was improved. Bushnell and Morris6 made measurements in hypersonic turbulent boundary layers at low Reynolds numbers. They observed that when they calculated the eddy-viscosity distribution from their data, the variations with Reynolds number of the parameters K and a in the inner and the outer eddy-viscosity formulas were similar to those in Refs. 5 and 4. Recently Huffman and Bradshaw7 concluded, after examining a large number of experimental data, that the parameter K in Eq. (5) was a constant. As may be seen from all these studies, the question of the universality of these constants is not settled. In the present Note we attempt to settle the question by showing that the parameter a is not a universal constant, but that K is— at least according to the calculations done by the author.

Heat, Mass, and momentum transfer analogies for the fully developed turbulent flow of power law fluids in circular tubes

AbstractA new correlation is presented to describe heat and mass transfer at large Prandtl or Schmidt numbers to power law fluids in fully developed turbulent flow in a pipe. The resulting expression for the Stanton number differs from earlier semiempirical correlations in that it is based on a continuous eddy viscosity distribution from the wall to the center of the pipe and contains no adjustable parameters to be determined from heat transfer data. Nusselt numbers determined by the new correlation are in excellent agreement with data on heat transfer to both pseudoplastic and dilatant fluids.

Self-Aerated Flow Characteristics in Wall Region

Characteristics of self-aerated flows in the wall region are studied. The distribution of velocity and air concentration in the wall turbulent zone is studied by dividing the wall turbulent zone into an inner and outer region according to the eddy viscosity distribution. It is shown that the inner region ceases to exist under certain conditions. Air concentration on the wall is estimated. The values of the Karman constant and Manning’s roughness coefficient show an increase in their value as air concentration increases. An estimation of the average velocity and the probable diameter of an air bubble shows a definite relation with mean air concentration in the wall region.

Eddy Viscosity Distributions in Compressible Turbulent Boundary Layers with Injection

SummaryShear stress, eddy viscosity and mixing length distributions have been obtained from measured boundary-layer developments over porous surfaces with air and carbon dioxide injection at Mach numbers up to M=3·6. It is found that, if the eddy viscosity is non-dimensionalised by dividing by the product of the free-stream velocity and the kinematic displacement thickness then this non-dimensional ratio is almost independent of injection ratio, but decreases slightly with Mach number.

Eddy viscosity distributions in a Mach 20 turbulent boundary layer

Shear stress and eddy viscosity distribution in Mach 20 compressible turbulent boundary layer, using mixing length flow theory

On the mass transport induced by oscillatory flow in a turbulent boundary layer

Oscillatory flow in a turbulent boundary layer is modelled by using a coefficient of eddy viscosity whose value depends upon distance from a fixed boundary. A general oscillatory flow is prescribed beyond the layer, and the model is used to calculate the mass transport velocity induced by this within the layer. The result is investigated numerically for a representative distribution of eddy viscosity and the conclusions interpreted in terms of the mass transport induced by progressive and standing waves. For progressive waves, the limiting value of the mass transport velocity at the outer edge of the layer is the same as for laminar flow. For standing waves, the limiting value is reduced relative to its laminar value but, within the lowermost 25% of the layer, there is a drift which is reversed relative to the limiting value. This is considerably stronger than its counterpart in the laminar case and, in view of the greater thickness of the turbulent layer, it may make a dominant contribution to the net movement of loose bed material by a standing wave system.

Cell Method for Computing Lake Circulation

The equations of fluid motion are solved using finite differences for the three-dimensional, wind-driven circulation in a homogeneous lake of arbitrary bottom topography. The method allows arbitrary choices for the wind stress, the horizontal and vertical eddy viscosities, and the distribution of vertical eddy viscosity. For the examples investigated the nonlinear terms of the equations contributed little or nothing, indicating that lake circulation is well described by linear equations. The magnitudes of the horizontal and vertical eddy viscosities have a strong effect on the current velocity but only a minor effect on the circulation patterns. The distribution of the vertical eddy viscosity appears to play a minor role in the circulation pattern. Sample calculations indicate that some combinations of horizontal eddy viscosity, vertical eddy viscosity, and distribution of vertical eddy viscosity are nearly equivalent in that these combinations produce similar response curves, similar current velocities and circulation patterns having small differences.

EDDY VISCOSITY AND UNIVERSAL VELOCITY PROFILE IN TURBULENT FLOW IN A STRAIGHT PIPE

Simple but systematic expressions for eddy viscosity based on the available experimental results are presented and the universal velocity profile is obtained from the eddy viscosity distribution. The present analysis takes account of the Reynolds number effect on the eddy viscosity. The friction factor based on the universal velocity profile was in good agreement with the Blasius formula, which was derived from the (1/7)-power law of the velocity profile, and was sepresented precisely by the Prandtls universal law of friction.

Turbulent prandtl number in thermally stratified shear flows of air

Turbulent Prandtl number and eddy viscosity distribution in the thermally stratified turbulent. boundary layer of an air flow are found to be functions of distance from the wall and thermal stabilities of the flow field. Turbulent Prandtl number in thermally stable shear flow of air is generally greater than that in thermally unstable shear flow of air.

Velocity distribution in the core of turbulent pipe flow

A general expression is proposed for the distribution of mean velocity in the core of turbulent pipe flow. This expression, based on the Reichardt general distribution but with alternative values of the constants, covers the range of turbulent Reynolds Numbers fro 50,000 to 350,000. The expression is compatible with experimental evidence relating to the distribution of eddy viscosity.

The velocity and eddy viscosity distribution in the wall region of turbulent pipe flow

Instantaneous axial and circumferential components of both velocity and turbulent intensity were measured in the wall region (to y + = 0·2) for water flowing in a 2 in. glass pipe of Reynolds numbers of 8000 to 50,000. A flow-visualization technique was employed, involving dark-background multiple exposure microphotography of minute tracer particles. Differentiation of the measured velocity profiles yields values of the eddy viscosity which are several times greater than those commonly assumed to apply at y + < 5 in the development of the analogies between momentum and mass or heat transfer. The axial intensity data agree well with those of Laufer. The circumferential intensity data show a minimum of about 5 per cent at y + ≅ 3, rising to 8 per cent as y + → 0.

The damping of gravity waves in shallow water by energy dissipation in a turbulent boundary layer

The method of matched asymptotic expansions is applied to the determination of the damping of gravity waves propagating in turbulent conditions. The effect of the turbulence is introduced by a general system of coefficients of eddy viscosity, whilst the turbulence itself is supposed to be confined to boundary layers adjacent to a rigid impermeable bottom and the free surface. The lowest order damping in the system is found to be independent of surface turbulence and computations are made for a physically meaningful distribution of eddy viscosity in the lower boundary layer. DOI: 10.1111/j.2153-3490.1968.tb00375.x

Fully Developed Turbulent Flow in Annuli

For annular pipes with diameter ratios from 0.0625 to 0.562 and with Reynolds numbers from 46,000 to 327,000, mean-velocity distributions and the location of the maximum mean velocity for each flow condition are presented. The point of maximum mean velocity in turbulent flow occurs at a smaller radius than in laminar flow. Velocity profiles are compared with the law of the wall and the velocity-defect law and are found to deviate from the usual correlations whenever the radial distribution of Reynolds stress, which was also measured, is far from linear. This occurs in the inner profiles for small diameter ratios. Mixing length and eddy-viscosity distributions were determined from accurate measurements of velocity gradients. Turbulence intensity distributions are presented, and these in conjunction with already published distributions for flow in circular pipes and for flow between parallel planes provide knowledge of turbulence-intensity distributions for all cases of fully developed, one-dimensional flow.

Turbulent exchange of momentum, mass, and heat between fluid streams and pipe wall

A new correlation is presented to describe mass and heat transfer to a fluid in a fully developed turbulent flow in a pipe. The correlation differs from earlier empirical relations in that it is based on a theoretical continuous eddy-viscosity distribution from the wall to the center of the pipe. Transfer rates calculated from the new correlation are in excellent agreement with experimental data on mass and heat transfer to fluid streams.

A numerical experiment with wind variations in the planetary boundary layer

The equations of motion applied to the planetary boundary layer are numerically integrated for certain special eddy viscosity distributions. Accelerations are retained, eddy viscosity varied with height and, to a lesser extent, with time. The resulting inertial oscillations, although very limited in generality, show agreement with observations. Not only clockwise but also counterclockwise rotation of the end point of the wind vector can occur in some cases. Some solutions agree and others disagree with the analytical solutions for unbounded eddy viscosity.

Distribution of eddy viscosity and mixing length in smooth tubes

AbstractProfiles of eddy viscosity and Prandtl mixing length in fluids flowing steadily and isothermally in smooth tubes have been calculated from the velocity data of several investigators for Reynolds numbers between 1.2 × 103 and 3.2 × 106. In the transition range unusually high values of eddy viscosity and mixing length are obtained in some portions of the stream. In the fully turbulent range the effect of Reynolds number is small and the mixing length tends toward zero at the center of the tube. The parameters for turbulent flow between parallel plates have been correlated through the concept of an equivalent tube. The results are of importance in designing equipment for heat and mass transfer and mixing.