This paper presents a reformulated version of the author'sk-ω model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-ω model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/ boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.

Formulation of the k-w Turbulence Model Revisited

Publisher Summary Accurate knowledge of the overall convective heat transfer from circular cylinders is of importance in a number of fields, such as boiler design, hotwire anemometry, and the rating of electrical conductors. The wide dispersion in the published experimental data for the heat transfer from smooth circular cylinders by natural and forced convection is attributed to various factors associated with the experiments. The error due to heat conduction to the supports is particularly important with natural convection, especially where the heat loss and the temperature rise of the cylinder are calculated from the voltage drop across it. A common cause of error is the use of too small a space ratio, so that the temperature and velocity fields are distorted. To reduce this error to less than l%, the space ratio D c /D for natural convection or D T /D for forced convection should exceed 100. The error caused by blockage with wind tunnel measurements can be calculated depending on the type of tunnel. One of the greatest sources of error with forced convection is the failure to allow for the effect of stream turbulence.

The Overall Convective Heat Transfer from Smooth Circular Cylinders

The turbulent wall jet, even limiting attention to the topographically simple cases beloved of academics, arguably provides more puzzles for those seeking an ordered set of rules to describe turbulence than any other class of turbulent shear layer. Formally, we can regard a wall jet as a boundary layer in which, by virtue of the initially supplied momentum, the velocity over some region in the shear layer exceeds that in the free stream. Wall jets are of great and diverse engineering importance. While some of the best known and most challenging applications lie in the field of advanced airfoil design, these aerodynamic roles are far outweighed in number and, probably, in economic importance by the use of wall jets in problems of heating, cooling or ventilating-areas where traditionally design has proceeded unfettered by any deep concern about the turbu­ lence structure of the flows in question. Two major industrial applications are the film-cooling of the lining walls of gas-turbine combustion chambers and of the leading stages of

The Turbulent Wall Jet Measurements and Modeling

Further experiments on the detailed study of annular jets are described in which the mean and fluctuating properties in the inner region have been measured. The experiments in the conical jetf have shown, besides the jet† vortices in the outer mixing region, another train of vortices in the inner region. This train of vortices is due to the wake formed by the boundary layer on the surface of the conical bullet. The experiments in the inner region of the basic annular jet have similar mean velocity profiles to those in the internal recirculating region. Good correlation is found for the location of the vortex centre, the location of reattachment, the minimum and maximum mean static pressure and their locations with the non-dimensional available pressure M°/AiP atm for entrainment behind the interface. A train of wake vortices is generated in the internal recirculating region and a train of jet vortices is found in the inner mixing region. Both types of vortices in the inner region seem to decay fairly rapidly within a distance of one outer diameter D° downstream. The disturbances associated with the wake vortices in the inner region seem to excite the outer mixing region. This results in another wave or train of vortices observed in the outer shear layer in addition to the jet vortices which are already in existence.

The inner regions of annular jets

https://hal.archives-ouvertes.fr/hal-00975626/document

Review of fluid flow and convective heat transfer within rotating disk cavities with impinging jet

Mean velocity and turbulence together with pressure distributions in a radial free jet flows were studied. By changing diameter and width of nozzles and discharge velocity, the flow pattern were measured. The concept of the equivalent nozzle width which contains the diameter and width of the nozzle can be usefully applied to describe both maximum flow velocity decay and growth of the jet half width with distance from a nozzle outlet. The maximum flow velocity decay and the growth of the jet half width lie on a single curve according to this equivalent nozzle width. In the main region at large nozzle Reynolds number, the maximum flow velocity decays following the same rule as in circular jet, and the growth of the jet half width is in good agreement with that in the two-dimensional jet.

Experimental Study of a Radial Turbulent Jet : 1st Report, Effect of Nozzle Shape on a Free Jet

Mean velocity and turbulence together with pressure distributions of jets issuing from ring nozzles with various openings, and spreading out radially over a flat smooth plate were studied. By changing the diameter and width of nozzles and discharge velocity, the flow pattern was measured. Flow field in the main region has been divided into two regions at the point of maximum flow velocity, that is, inner layer near the wall and outer layer away from the wall. Velocity profile in the inner layer is similar to Glauert's curve obtained for a radial wall jet, and the one in the outer layer agrees well with Goertler's curve for a two-dimensional free jet. Maximum flow velocity decays and growth of the jet half width lie on a single curve by making use of an equivalent nozzle width which contains the diameter and width of the nozzle.

Experimental Studies of a Radial Turbulent Jet : 2nd Report, Wall Jet on a Flat Smooth Plate

An experimental study has been made to determine the effect of vibration on the rate of heat transfer in natural convection from a horizontal fine wire to various fluids (air, water and ethylene glycol) Frequencies from 0 to 20 c/sec amplitudes from 05 to 35 mm and diameters of wire from 0031 to 0203 mm were employed The effect of vibrating motion may be considered in terms of a vibrating Reynolds number Re, based on the mean velocity of a wire Nusselt number may be predicted by the general experimental formula Nu=057Re1/2 where, Re is an equivalent vibrating Reynolds number defined by Re=320 (GrPr)1/3+RePr2/3 and Pr is Prandtl number and Gr is Grashof number Also, three modes in heat transfer were decided by the criterion that the coefficient of heat transfer deviates 5% from the one in pure natural and forced convection The boundaries of three modes may be controlled on the relative magnitudes of vibrating Reynolds and Grashof number and expressed by a dimensionless parameter X

Experimental Study on Effect of Vibration on Natural Convective Heat Transfer from a Horizontal Fine Wire

Pressure distributions on the disk surface and along the axis through the stagnation point have been measured. The settling place of rotating disk, the measuring point of velocity, and the dimensions of the disk model have been decided to refer well to the condition assumed in theoretical analysis. The results are summarized as follows. (1) The generalized experimental formulas which contained the effect of natural convection were established for the heat transfer from a rotating disk in the quiescent fluid and a stationary disk in the axial flow. (2) Experimental results in the presence of both rotating and axial stream velocities revealed good agreement with theory (2nd Report). (3) For the rotation alone, our results agreed with Cobb-Saunders and for the axial flow alone due to separation at the edge of the disk, Sogin's experimental data are about 17% larger than our results and theory.

Studies on the Convective Heat Transfer from a Rotating Disk : 5th Report, Experiment on the Laminar Heat Transfer from a Rotating Isothermal Disk in a Uniform Forced Stream

This paper presents the results of an experimental study on the reattachment of a radial turbulent jet flow discharged from a cylindrical nozzle on an adjacent offset disc plate, in the presence of a control flow. Static pressure distributions along the wall surface and across the jet flow were measured with a disc type pressure hole, and the effects of step height and control flow rate (suction and blowing) on them were investigated. Length and mean negative pressure in the recirculation region, and position of the attachment to the wall surface were examined. An oil film flow visualizing technique was also applied to determination of the flow pattern. The results were compared with those obtained from the pressure distributions.

Toshio Tanaka

Papers

Experimental Study of a Radial Turbulent Jet : 1st Report, Effect of Nozzle Shape on a Free Jet

Experimental Studies of a Radial Turbulent Jet : 2nd Report, Wall Jet on a Flat Smooth Plate

Experimental Study on Effect of Vibration on Natural Convective Heat Transfer from a Horizontal Fine Wire

Studies on the Convective Heat Transfer from a Rotating Disk : 5th Report, Experiment on the Laminar Heat Transfer from a Rotating Isothermal Disk in a Uniform Forced Stream

Study on Control of Radial Attaching Jet Flow : 2nd Report, Effects of Control Flow on Pressure Distributions