Universal Law Of Wall Research Articles

Experimental Investigation of Drag Reducing Fluid Flow in Annular Geometry Using Particle Image Velocimetry Technique

Fully developed turbulent flow of drag reducing fluids through a horizontal flow loop with concentric annular geometry was investigated using the particle image velocimetry (PIV) technique. Experiments were conducted at solvent Reynolds numbers ranged from 38,700 to 56,400. Axial mean velocity profile was found to be following the universal wall law close to the wall (i.e., y+ < 10), but it deviated from log law results with an increased slope in the logarithmic zone (i.e., y+ > 30). The study was also focused on turbulence statistics such as near wall Reynolds stress distribution, axial and radial velocity fluctuations, vorticity and turbulent kinetic energy budget.

An Experimental Investigation of Turbulent Water Flow in Concentric Annulus Using Particle Image Velocimetry Technique

Fully developed turbulent flow of water through a horizontal flow loop with concentric annular geometry was investigated using high resolution particle image velocimetry (PIV). Reynolds number range varied from 17,700 to 66,900. Axial mean velocity profile was found to be following the universal wall law (u+ = y+) in the viscous sublayer (y+ < 10) and log law away from the wall (y+> 30). Radial position of zero shear stress and maximum velocity were found to be slightly different (2%). Root mean square values of velocity fluctuations velocity, Reynolds stresses, vorticity, and turbulent kinetic energy budget were also analyzed.

Calculation Mathod for Velocity and Shear Stress Distribution of Fully Developed Turbulent Pipe Flow Based on Defect Law and Universal Law of Wall and Integrated Turbulence Production.

Velocity and shear stress distribution of the fully developed turbulent pipe flow at any Reynolds number are calculated from another. Calculations are based on the defect law and the universal law of wall. Shear stress is based on the eddy viscosity model. Shear stress at the wall is calculated with the pressure drop which is based on the integrated turbulence energy production. Turbulence energy production is calculated from the velocity and shear stress distribution. Calculated results are compared with measured data reported by Nikuradse and Laufer.

Second-moment closure for the near-wall sublayer - Development and application

This paper extends the widely used second-moment closure of Gibson and Launder so as to be applicable within the near-wall sublayer where viscous effects are substantial. This extension, which allows the usual log-law/local-equilibrium matching to be discarded, enables boundary-layer problems to be tackled where the flow structure in the inner region departs from what is usually termed the universal wall law. Applications are reported of the flat-plate boundary layer and three cases in which strong streamwise pressure gradients are imposed. Agreement with experiment is better than when the simpler A-e model is adopted.

Linearized turbulent lubrication equation for finite self-acting porous bearings considering slip velocity over a hydrodynamically rough permeable boundary

A first attempt to derive a new lubrication equation for the hydrodynamic pressure generation in a three-dimensional self-acting porous metal bearing operating in a turbulent regime (fully developed) with single-phase Newtonian incompressible lubricant is presented considering simultaneously the slip velocity and the hydrodynamically rough permeable surface (in terms of the median diameter of the graded constituent particles of the sintered porous matrix and their standard deviation) with a hydrodynamically rough rotor. The analysis is analogous to boundary layer theory wherein the lubricant motion is treated as a generalized turbulent channel flow in which the rough porous wall is stationary and the impervious wall (also considered rough) is in longitudinal motion so that the flow is a turbulent shear flow coupled with codirectional and transverse turbulent pressure flow. A linearization or perturbation technique is used to decouple the two orthogonal turbulent flows by assuming that the turbulent shear stress in a finite bearing is a small perturbation of the shear stress for turbulent couette flow. Using Boussinesq's eddy viscosity formulation and the experimentally established logarithmic law as the universal law of wall, the governing pressure distribution equation is obtained from consideration of the conservation of momentum and continuity. The whole treatment is approached from the point of view of fluid film design. No ad hoc slip model is used, and the lubrication equation is fully analytical and can be applied to a number of particular bearing problems by applying suitable simplifying restrictive conditions. The derived lubrication equation can be used to predict bearing performance characteristics even in situations where the bearing permeability is non-isotropic.

A lubrication equation including slip velocity for hydrodynamic porous bearings in the lower turbulent regime — a perturbation approach

A first attempt is made to analyse pressure development in the form of a new lubrication equation including slip velocity for finite self-acting hydrodynamic porous metal bearings operating in the turbulent regime (fully developed) with a single phase Newtonian incompressible lubricant. The derivation is based on the analogy of boundary layer theory wherein lubricant motion is treated as a generalized turbulent channel flow in which the impermeable wall is in motion and the porous wall is stationary. The type of flow varies from pure couette flow to shear flow coupled with codirectional and transverse pressure flow. A linearization (or perturbation) technique is used to decouple the two orthogonal flows by assuming that the shear stress in a finite bearing is a small perturbation of the shear stress valid for couette flow. Using Boussinesq's eddy viscosity formulation and the wellestablished power law as a universal law of wall, the governing pressure distribution equation is obtained from considerations of the conservation of momentum and continuity. The surfaces are considered to be hydrodynamically smooth. The whole treatment is approached from the viewpoint of fluid film design rather than from a fundamental fluid mechanics approach. No slip model has been used. The lubrication equation is fully analytical and can be applied to a number of particular bearing problems by using the simplifying restrictive conditions. The lubrication equation derived can be used to predict the bearing performance characteristics even in situations where the permeability of the bearings is anisotropic and the Poiseuille flow in the porous matrix does not obey Darcy's law.