Solution of the Incompressible Turbulent Boundary-Layer Equations With Heat Transfer

1970 ◽  
Vol 92 (1) ◽  
pp. 133-141 ◽  
Author(s):  
T. Cebeci ◽  
A. M. O. Smith ◽  
G. Mosinskis
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Incompressible Flows ◽  
Reynolds Shear Stress ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Incompressible Turbulent Boundary Layer ◽  
Implicit Finite Difference ◽  
Stress Term ◽  
Made In

The boundary-layer equations for laminar and turbulent incompressible flows about two-dimensional and axisymmetric flows are solved by an implicit finite-difference method. An eddy-viscosity concept is used to eliminate the Reynolds shear-stress term, and an eddy-conductivity concept is used to eliminate the time mean of the product of fluctuating velocity and temperature. Several flows have been computed by this method, and comparisons with experimental data and with the Bradshaw-Ferriss method are made. In general, the agreement is quite good.

COMPUTATION OF TWO-DIMENSIONAL INCOMPRESSIBLE TURBULENT BOUNDARY LAYER FLOWS WITH EQUILIBRIUM AND NONEQUILIBRIUM TURBULENCE MODELS

1994 ◽  
Vol 05 (02) ◽  
pp. 207-210
Author(s):  
Daniel Wong ◽  
Salahuddin Ahmed
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Turbulence Models ◽  
Two Dimensional ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Viscosity Models ◽  
Incompressible Turbulent Boundary Layer

Two-dimensional incompressible turbulent boundary layer flows over a flat plate were predicted using turbulent boundary layer equations. Reynolds stresses were calculated using Cebeci-Smith, Baldwin-Lomax, and Johnson-King eddy viscosity models. Computational results of mean-flow properties based on Cebeci-Smith model and Baldwin-Lomax model are in excellent agreement with experimental data, and, those based on Johnson-King model are not as accurate as the other two models.

A Finite Difference Solution of the Two and Three-Dimensional Incompressible Turbulent Boundary Layer Equations

1973 ◽  
Vol 95 (3) ◽  
pp. 445-458 ◽  
Author(s):  
W. F. Klinksiek ◽  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Three Dimensional ◽  
Mixing Length ◽  
Mean Velocity ◽  
Boundary Layer Equations ◽  
Incompressible Turbulent Boundary Layer ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Transverse Stresses

A modified Crank-Nicholson implicit finite difference formulation is presented for two and three-dimensional turbulent boundary layers. The turbulent stresses are treated after Prandtl’s early mixing length model. “Boundary layer like” assumptions result in only the streamwise and transverse stresses remaining. The specific empirical input is the Maise and McDonald mixing length model. Excellent agreement with two independent experiments is obtained for mean velocity field data. Both experiments included a plane of symmetry to provide a transverse coordinate initial condition.

Calculation of unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity

1977 ◽  
Vol 355 (1681) ◽  
pp. 225-238 ◽  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Boundary Layer Equations

A numerical method is presented for calculating unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity. The method used an eddy-viscosity formulation to model the Reynolds shear stress term appropriate to turbulent flow and an efficient two-point finite-difference method to solve the governing boundary-layer equations. The method is used to calculate phase angles between the wall shear stress and an oscillating external laminar boundary layer over a flat plate. The results are in excellent agreement with the analytic solutions of Lighthill for the high- and low-frequency limits and provide information in the region between. Similar calculations for turbulent flows are compared with experimental data and the method shown to be more precise than previously described attempts to represent flows of this type. The agreement between calculations and measurements is imperfect but probably within the resolution of the experiments and adequate for engineering purposes.

Heat and Mass Transfer in an Incompressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (1) ◽  
pp. 23-28 ◽  
Author(s):  
E. Brundrett ◽  
W. B. Nicoll ◽  
A. B. Strong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Plate ◽  
Mixing Length ◽  
Two Dimensional ◽  
Transfer Data ◽  
Incompressible Turbulent Boundary Layer ◽  
Wide Range ◽  
Incompressible Boundary

The van Driest damped mixing length has been extended to account for the effects of mass transfer through a porous plate into a turbulent, two-dimensional incompressible boundary layer. The present mixing length is continuous from the wall through to the inner-law region of the flow, and although empirical, has been shown to predict wall shear stress and heat transfer data for a wide range of blowing rates.

The response of a turbulent boundary layer to lateral divergence

1979 ◽  
Vol 94 (2) ◽  
pp. 243-268 ◽  
Author(s):  
A. J. Smits ◽  
J. A. Eaton ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Structural Parameters ◽  
Axial Flow ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Transition Section ◽  
Two Dimensional Flow ◽  
Made In

Measurements have been made in the flow over an axisymmetric cylinder-flare body, in which the boundary layer developed in axial flow over a circular cylinder before diverging over a conical flare. The lateral divergence, and the concave curvature in the transition section between the cylinder and the flare, both tend to destabilize the turbulence. Well downstream of the transition section, the changes in turbulence structure are still significant and can be attributed to lateral divergence alone. The results confirm that lateral divergence alters the structural parameters in much the same way as longitudinal curvature, and can be allowed for by similar empirical formulae. The interaction between curvature and divergence effects in the transition section leads to qualitative differences between the behaviour of the present flow, in which the turbulence intensity is increased everywhere, and the results of Smits, Young & Bradshaw (1979) for a two-dimensional flow with the same curvature but no divergence, in which an unexpected collapse of the turbulence occurred downstream of the curved region.

scholarly journals Two-Phase Dusty Fluid Flow Along a Rotating Axisymmetric Round-Nosed Body

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Sadia Siddiqa ◽  
Naheed Begum ◽  
M. A. Hossain ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Boundary Layer ◽  
Flow Characteristics ◽  
Leading Edge ◽  
Solid Particles ◽  
Dust Particles ◽  
Computational Domain ◽  
Two Phase ◽  
Carrier Fluid ◽  
Boundary Layer Equations ◽  
Implicit Finite Difference

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axisymmetric round-nosed body. By using the method of transformed coordinates, the boundary layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidate the heat transfer mechanism near the surface of round-nosed bodies. We will investigate whether the presence of dust particles in carrier fluid disturbs the flow characteristics associated with rotating hemisphere or not. A comprehensive parametric analysis is presented to show the influence of the particle loading, the buoyancy ratio parameter, and the surface of rotating hemisphere on the numerical findings. In the absence of dust particles, the results are graphically compared with existing data in the open literature, and an excellent agreement has been found. It is noted that the concentration of dust particles’ parameter, Dρ, strongly influences the heat transport rate near the leading edge.

scholarly journals Nonclassical Symmetry Analysis of Boundary Layer Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Rehana Naz ◽  
Mohammad Danish Khan ◽  
Imran Naeem
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Similarity Solution ◽  
Symmetry Analysis ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.

Evaluation of Turbulence Models Using Direct Numerical and Large-Eddy Simulation Data

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Hassan Raiesi ◽  
Ugo Piomelli ◽  
Andrew Pollard
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Predictive Accuracy ◽  
Turbulence Models ◽  
Special Treatment ◽  
Two Dimensional ◽  
Square Duct ◽  
Eddy Simulation ◽  
Large Eddy

The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the k−ε, ζ−f, k−ω, and Spalart–Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in k−ε models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζ−f, k−ω, and Spalart–Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

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