Interacting Turbulent Boundary Layer over a Wavy Wall

1978 ◽  
Vol 100 (4) ◽  
pp. 678-683 ◽  
Author(s):  
A. Polak ◽  
M. J. Werle
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Relaxation Method ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Flow Conditions ◽  
Boundary Layer Equations ◽  
Eddy Viscosity Model ◽  
Turbulence Effects

This paper is concerned with the two-dimensional supersonic flow of a thick turbulent boundary layer over a train of relatively small wave-like protuberances. The flow conditions and the geometry are such that there exists a strong interaction between the viscous and inviscid flow. Here the interacting boundary layer equations are solved numerically using a time-like relaxation method with turbulence effects represented by the inclusion of the eddy viscosity model of Cebeci and Smith. Results are presented for flow over a train of up to six waves for Mach numbers of 2.5 and 3.5, Reynolds numbers of 10 and 32 × 106/meter, and wall temperature ratios Tw/T0 of 0.4 and 0.8. Limited comparisons with independent experimental and analytical results are also given.

Measurement Investigation of Complex Eddy Viscosity Model in Non-Equilibrium Wavy Wall Turbulence with TRPIV

2013 ◽  
Vol 718-720 ◽  
pp. 1657-1662
Author(s):  
An Tong Zhang ◽  
Nan Jiang
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strain Rate ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Wavy Wall ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Phase Differences

The spatial flow fields of turbulent boundary layer over a wavy wall were measured by TRPIV at three different Reynolds numbers in a water channel, the mean streamwise and wall-normal velocities near the wall were calculated from the time series of instantaneous spatial 2D-2C flow fields of turbulent boundary layer, and the periodic distributions of the streamwise and wall-normal velocity in streamwise direction influenced by the wavy wall were found. The spatial distributions of Reynolds stress and mean velocity strain rate were obtained by ensemble average. Using the spatial cross-correlation technique, the spatial phase relationship in streamwise direction between mean velocity strain rate and Reynolds stress was investigated. It is found that there exist spatial phase differences between Reynolds stress components and mean velocity strain rate components, the phase differences increase gradually after decrease gradually from zero away from the wavy wall in wall-normal direction and reach a minimum at 0.4~0.5 times the wavelength of wavy wall, and in a certain range the effect of the Reynolds number on the phase differences is very small. The reasonability of the complex eddy viscosity model is confirmed by these experimental evidences in order to forecast non-equilibrium turbulence accurately.

Turbulent boundary-layer effects on transient wave propagation in shallow water

2006 ◽  
Vol 462 (2075) ◽  
pp. 3481-3491 ◽  
Author(s):  
Philip L.-F Liu
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Order Effects ◽  
Convolution Integral ◽  
Transient Wave ◽  
Bottom Stress ◽  
Eddy Viscosity Model ◽  
Damping Rate ◽  
Transient Wave Propagation

The depth-integrated continuity and momentum equations developed by Liu & Orfila are extended to include the effects of turbulent bottom boundary layer. The eddy viscosity model is employed in the boundary layer, in which the eddy viscosity is assumed to be a power function of the vertical elevation from the bottom. The leading-order effects of the turbulent boundary layer appear as a convolution integral in the depth-integrated continuity equation because of the boundary-layer displacement. The bottom stress is also expressed as a convolution integral of the depth-averaged horizontal velocity. For simple harmonic progressive waves, the analytical expression for the phase shift between the bottom stress and the depth-averaged velocity is obtained. The analytical solutions for the solitary wave damping rate due to a turbulent boundary layer are also derived. Prandtl's one-seventh power law is described in detail as an example.

Numerical investigation of the turbulent boundary layer over a bump

1998 ◽  
Vol 362 ◽  
pp. 229-271 ◽  
Author(s):  
XIAOHUA WU ◽  
KYLE D. SQUIRES
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Eddy Viscosity ◽  
Subgrid Scale ◽  
Internal Layers ◽  
Mean Flow ◽  
Eddy Viscosity Model ◽  
The Mean ◽  
Shear Production

Large-eddy simulation (LES) has been used to calculate the flow of a statistically two-dimensional turbulent boundary layer over a bump. Subgrid-scale stresses in the filtered Navier–Stokes equations were closed using the dynamic eddy viscosity model. LES predictions for a range of grid resolutions were compared to the experimental measurements of Webster et al. (1996). Predictions of the mean flow and turbulence intensities are in good agreement with measurements. The resolved turbulent shear stress is in reasonable agreement with data, though the peak is over-predicted near the trailing edge of the bump. Analysis of the flow confirms the existence of internal layers over the bump surface upstream of the summit and along the downstream trailing at plate, and demonstrates that the quasi-step increases in skin friction due to perturbations in pressure gradient and surface curvature selectively enhance near-wall shear production of turbulent stresses and are responsible for the formation of the internal layers. Though the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall is not followed by mean-flow separation. Certain turbulence characteristics in this region are similar to those previously reported in instantaneously separating boundary layers. The present investigation also explains the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements of Webster et al. (1996), i.e. the simultaneous uninterrupted development of an inner energy-equilibrium region and the monotonic decay of elevated turbulence shear production away from the wall. LES results were also used to examine response of the dynamic eddy viscosity model. While subgrid-scale dissipation decreases/increases as the turbulence is attenuated/enhanced, the ratio of the (averaged) forward to reverse energy transfers predicted by the model is roughly constant over a significant part of the layer. Model predictions of backscatter, calculated as the percentage of points where the model coefficient is negative, show a rapid recovery downstream similar to the mean-flow and turbulence quantities.

Numerical simulation of non-buoyant pollutants dispersion in a turbulent boundary layer

2011 ◽  
Vol 225 (8) ◽  
pp. 1903-1912
Author(s):  
M S Shin ◽  
S K Kang ◽  
S J Byun ◽  
J Y Yoon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Settling Velocity ◽  
Concentration Field ◽  
Continuous Phase ◽  
Eddy Viscosity Model ◽  
Layer Flow ◽  
Concentration Equation ◽  
Settling Process

A pollutant-laden transport in fully developed turbulent boundary-layer flow has been investigated using the k–ω turbulence model. The scalar transport equation of the pollutants concentration, which is based on the continuous-phase approach, is adopted. The pollutant settling process is taken into account with a modified settling velocity appearing in the pollutant concentration equation. A new eddy viscosity model is proposed in the turbulence modelled equations to couple the velocity field and the concentration field. The numerical results are compared with the experimental data, and good general agreement is achieved.

A Two-Region Model of the Turbulent Boundary Layer, With Emphasis on Interfacial Conditions

1969 ◽  
Vol 36 (4) ◽  
pp. 664-672
Author(s):  
J. L. Gaddis ◽  
J. P. Lamb
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Eddy Viscosity ◽  
Outer Region ◽  
Variable Density ◽  
Density Variation ◽  
Interfacial Conditions ◽  
Eddy Viscosity Model ◽  
Region Model ◽  
Matching Criteria

Presented herein is a turbulent boundary-layer analysis which is based on a two-region characterization for eddy viscosity. The eddy viscosity for the inner region is described with the usual wall law whereas the outer region, which is characterized by large eddy scales, is treated through an application of Prandtl’s eddy viscosity model for free shear flows. A similarity solution for the outer region is obtained for a linearized motion equation and suitably joined to the inner solution by requiring continuity of shear stress and eddy viscosity. The present matching criteria for the two regions result in the preservation of the velocity profile shape in the defect plane while simultaneously yielding the correct longitudinal development of all layer parameters. It is shown that interfacial conditions are, collectively, the particular feature of incompressible flow which can serve as the point of reference for variable density transformations. A simple, parametric density scaling of the eddy viscosity is employed to demonstrate that the inner layer is much less sensitive to the density variation than the outer region. An improved compressibility transformation, based on ρε = ρ¯ε¯, is advanced.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

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