Turbulent Boundary Layers With Unsteady Injection-Suction

1980 ◽  
Vol 102 (3) ◽  
pp. 364-371 ◽  
Author(s):  
D. T. Tsahalis
Keyword(s):  
Flat Plate ◽  
Skin Friction ◽  
Eddy Viscosity ◽  
Steady Flows ◽  
Outer Flow ◽  
Boundary Layer Equations ◽  
Eddy Viscosity Model ◽  
Viscosity Models ◽  
Porous Flat Plate ◽  
Theoretical Results

The time dependent turbulent boundary-layer equations with a two-layer eddy viscosity model are integrated numerically over a porous flat plate for a steady outer flow and a sinusoidally distributed injection-suction that varies harmonically with time. The dependence of the unsteady wall shear on the frequency and strength of injection-suction is investigated. The present results indicate that the time-averaged skin friction is always larger than the skin friction observed over a nonporous flat plate. Comparison with previous theoretical results indicates that the time-averaged skin friction is always smaller than the skin friction observed over a porous flat plate with steady, simultaneous injection-suction of the same strength. The extension of eddy viscosity models, developed for steady flows, to unsteady flows is discussed.

The Application of Eddy-Viscosity Stress Limiters for Modeling Cross-Flow Separation

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
P. A. Gregory ◽  
P. N. Joubert ◽  
M. S. Chong ◽  
A. Ooi
Keyword(s):  
Kinetic Energy ◽  
Skin Friction ◽  
Turbulent Kinetic Energy ◽  
Flow Separation ◽  
Eddy Viscosity ◽  
Cross Flow ◽  
The Body ◽  
Mean Flow ◽  
Viscosity Models ◽  
Experimental Apparatus

The ability of eddy-viscosity models to simulate the turbulent wake produced by cross-flow separation over a curved body of revolution is assessed. The results obtained using the standard k−ω model show excessive levels of turbulent kinetic energy k in the vicinity of the stagnation point at the nose of the body. Additionally, high levels of k are observed throughout the wake. Enforcing laminar flow upstream of the nose (which replicates the experimental apparatus more accurately) gives more accurate estimates of k throughout the flowfield. A stress limiter in the form of Durbin’s T-limit modification for eddy-viscosity models is implemented for the k−ω model, and its effect on the computed surface pressures, skin friction, and surface flow features is assessed. Additionally, the effect of the T-limit modification on both the mean flow and the turbulent flow quantities within the wake is also examined. The use of the T-limit modification gives significant improvements in predicted levels of turbulent kinetic energy and Reynolds stresses within the wake. However, predicted values of skin friction in regions of attached flow become up to 50% greater than the experimental values when the T-limit is used. This is due to higher values of near-wall turbulence being created with the T-limit.

scholarly journals Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions for Flat Plate without/with Suction

Aerodynamics ◽  
2021 ◽  
Author(s):  
Chedhli Hafien ◽  
Adnen Bourehla ◽  
Mounir Bouzaiane
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layer Suction ◽  
Analytical Approximations ◽  
Approximate Integral ◽  
Porous Flat Plate ◽  
Analytical Expressions ◽  
Approximate Integral Method ◽  
Lambert Functions ◽  
Theoretical Results

In this work, we investigated the problem of the boundary layer suction on a flat plate with null incidence and without pressure gradient. There is an analytical resolution using the Bianchini approximate integral method. This approximation has been achieved by Lambert or Error functions for boundary layer profiles with uniform suction, even in the case without suction. Based on these new laws, we brought out analytical expressions of several boundary layer features. This gives a necessary data to suction effect modeling for boundary layer control. To recommend our theoretical results, we numerically studied the boundary layer suction on a porous flat plate equipped with trailing edge flap deflected to 40°. We showed that this flap moves the stagnation point on the upper surface, resulting to avoid the formation of the laminar bulb of separation. Good agreement was obtained between the new analytical laws, the numerical results (CFD Fluent), and the literature results.

An Examination of Eddy Viscosity Models for Turbulent Free Shear Flows

1971 ◽  
Vol 93 (4) ◽  
pp. 624-630
Author(s):  
R. J. Elassar ◽  
P. P. Pandolfini
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Difference Scheme ◽  
Eddy Viscosity ◽  
Shear Flows ◽  
Coordinate Plane ◽  
Boundary Layer Equations ◽  
Viscosity Models ◽  
Calculated Velocity ◽  
Empirical Constants

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.

A Model of Coherent Disturbances in Compressible Mixing Layers

2002 ◽  
Author(s):  
Hong Yang ◽  
Anatoli Tumin
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Mixing Layer ◽  
Governing Equations ◽  
Turbulent Mixing Layer ◽  
Eddy Viscosity Model ◽  
Temperature And Pressure ◽  
Mean Time ◽  
Theoretical Results

A theoretical model of harmonic perturbations in a compressible turbulent mixing layer is proposed. The model is based on the triple decomposition method. It is assumed that the instantaneous velocities, temperature, and pressure consist of three distinctive components: mean (time-averaged), coherent (phase-averaged), and random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large-scale coherent disturbances is incorporated by the Newtonian eddy viscosity model. The governing equations for the coherent disturbances have the same form as in laminar flow with substitution of the Reynolds number and the Prandtl number by their turbulent counterparts. A slight divergence of the flow is also taken into account. Theoretical results and comparison with experimental data reveal the significance of interaction between the coherent and random constituents of the flow.

Direct measurement of skin friction on a porous flat plate with massinjection.

AIAA Journal ◽  
1967 ◽  
Vol 5 (11) ◽  
pp. 1934-1939 ◽  
Author(s):  
HARVEY DERSHIN ◽  
CHARLES A. LEONARD ◽  
WILLIAM H. GALLAHER
Keyword(s):  
Flat Plate ◽  
Skin Friction ◽  
Direct Measurement ◽  
Porous Flat Plate

Numerical Simulation of Backward Facing Step Flow Using Nonlinear Eddy Viscosity Model

2010 ◽  
Vol 163-167 ◽  
pp. 4120-4124
Author(s):  
Ting Ting Wang ◽  
Qing Shan Yang
Keyword(s):  
Numerical Simulation ◽  
Eddy Viscosity ◽  
Pressure Coefficient ◽  
Viscosity Model ◽  
Building Structures ◽  
Complex Flow ◽  
Backward Facing Step ◽  
Step Flow ◽  
Eddy Viscosity Model ◽  
Viscosity Models

Nonlinear eddy viscosity models have received significant interest because of the shortcomings of linear eddy viscosity models used in the numerical simulation of flow around building structures. There are many kinds of nonlinear eddy viscosity models. This paper adopts one of them to simulate backward facing step flow, which aims to evaluate the properties of this turbulence model. Compared with linear eddy viscosity model and experimental measurements, the simulation of nonlinear eddy viscosity model gives better results, especially for the reattachment length and pressure coefficient values. For this reason, this nonlinear eddy viscosity model is more suitable for numerical simulation of complex flow around building structures than linear eddy viscosity model.

scholarly journals EFFECTS OF THERMAL CONDUCTIVITY OF FLUID ON FREE CONVECTION FLOW ALONG A VERTICAL FLAT PLATE WITH TRANSVERSE CONDUCTION

2015 ◽  
Vol 44 (2) ◽  
pp. 105-111
Author(s):  
A K M Safiqul Islam ◽  
M. A. Alim ◽  
Md Rezaul Karim ◽  
ATM M Rahman
Keyword(s):  
Thermal Conductivity ◽  
Flat Plate ◽  
Skin Friction ◽  
Linear Equations ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Boundary Layer Equations ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Vertical Flat Plate

This paper reports the effects of transverse conduction variation with thermal conductivity on freeconvection flow along a vertical flat plate. The governing equations with associated boundary conditions reduceto local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms usinga suitable transformation. The transformed non-linear equations are then solved using the implicit finitedifference method together with Keller-box technique. Numerical results of the velocity and temperature profiles,skin friction and surface temperature profiles for different values of the thermal conductivity parameter, thePrandtl number and the transverse conduction variation parameters are presented graphically. Detaileddiscussion is given for the effect of the aforementioned parameters. Mentionable effect is found in skin friction andsurface temperature for the transverse conduction variation parameter.

Orthogonal Flow Impinging on a Wall with Suction or Blowing

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Asmat Ara ◽  
Syed Anwer Ali ◽  
Muhammad Jamil
Keyword(s):  
Incompressible Fluid ◽  
Perturbation Method ◽  
Flat Plate ◽  
Skin Friction ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Viscous Incompressible Fluid ◽  
Approximate Solutions ◽  
Homotopy Perturbation ◽  
Porous Flat Plate

The goal of this work is the approximate solutions of a viscous incompressible fluid impinging orthogonally on a porous flat plate. The equation governing the flow of an incompressible fluid is investigated using the homotopy perturbation method (HPM) with the aid of Padé-approximants. The approximate solutions can be successfully applied to provide the value of the skin-friction. The reliability and efficiency of the approximate solutions were verified using numerical solutions in the literature.

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.

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