A Transformation for the Numerical Solution of Two-Dimensional Free Mixing Flow Problems

1973 ◽  
Vol 95 (1) ◽  
pp. 103-107
Author(s):  
R. J. Elassar
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Difference Scheme ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Coordinate Plane ◽  
Free Shear Layer ◽  
Layer Width ◽  
Boundary Layer Equations ◽  
Flow Problems

A coordinate transformation which removes the variation of the mixing layer width is introduced. The boundary layer equations are then solved in the new coordinate plane using a multilevel difference scheme. The calculated results for two-dimensional symmetric mixing and free shear layer flows for turbulent flow are compared with experimental data and with other solutions.

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.

Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems

2015 ◽  
Vol 70 (12) ◽  
pp. 1031-1037
Author(s):  
Imran Naeem ◽  
Rehana Naz ◽  
Muhammad Danish Khan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Invariant Solution ◽  
Heat Transfer Analysis ◽  
Two Dimensional ◽  
Group Invariant ◽  
Boundary Layer Equations ◽  
Flow Problems ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

AbstractThis article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem.

A Viscous-Inviscid Interaction Procedure—Part 1: Method for Computing Two-Dimensional Incompressible Separated Channel Flows

1986 ◽  
Vol 108 (1) ◽  
pp. 64-70 ◽  
Author(s):  
O. K. Kwon ◽  
R. H. Pletcher
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Turbulent Flows ◽  
Inviscid Flow ◽  
Companion Paper ◽  
Separated Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Interaction Scheme ◽  
Laminar And Turbulent Flows

A viscous-inviscid interaction scheme has been developed for computing steady incompressible laminar and turbulent flows in two-dimensional duct expansions. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is computed by numerically solving the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively along displacement surfaces. Details of the procedure are presented in the present paper (Part 1), along with example applications to separated flows. The results compare favorably with experimental data. Applications to turbulent flows over a rearward-facing step are described in a companion paper (Part 2).

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.

Velocity Profiles of Turbulent Boundary Layers

1969 ◽  
Vol 73 (698) ◽  
pp. 143-147 ◽  
Author(s):  
M. K. Bull
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Experimental Work ◽  
Constant Pressure ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Equations

Although a numerical solution of the turbulent boundary-layer equations has been achieved by Mellor and Gibson for equilibrium layers, there are many occasions on which it is desirable to have closed-form expressions representing the velocity profile. Probably the best known and most widely used representation of both equilibrium and non-equilibrium layers is that of Coles. However, when velocity profiles are examined in detail it becomes apparent that considerable care is necessary in applying Coles's formulation, and it seems to be worthwhile to draw attention to some of the errors and inconsistencies which may arise if care is not exercised. This will be done mainly by the consideration of experimental data. In the work on constant pressure layers, emphasis tends to fall heavily on the author's own data previously reported in ref. 1, because the details of the measurements are readily available; other experimental work is introduced where the required values can be obtained easily from the published papers.

A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1

1980 ◽  
Vol 98 (1) ◽  
pp. 65-95 ◽  
Author(s):  
M. Sokolov ◽  
A. K. M. F. Hussain ◽  
S. J. Kleis ◽  
Z. D. Husain
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Large Scale ◽  
Mixing Layer ◽  
Streamwise Velocity ◽  
Reynolds Stresses ◽  
Free Shear Layer ◽  
Turbulent Spot ◽  
Air Jet ◽  
Phase Average

A three-dimensional ‘turbulent spot’ has been induced in the axisymmetric free mixing layer of a 12.7 cm diameter air jet by a spark generated at the nozzle boundary layer upstream of the exit. The spot coherent-structure signature, buried in the large-amplitude random fluctuating signal, has been educed at three downstream stations within the apparent self-preserving region of the mixing layer (i.e. x/D = 1.5, 3.0 and 4.5) at the jet exit speed of 20 ms−1. The eduction has been performed through digital phase averaging of the spot signature from 200 realizations. In order to reduce the effect of the turbulence-induced jitter on the phase average, individual filtered signal arrays were optimally time-aligned through an iterative process of cross-correlation of each realization with the ensemble average. Further signal enhancement was achieved through rejection of realizations requiring excessive time shifts for alignment. The number of iterations required and the fraction of realizations rejected progressively increase with the downstream distance and the radial position.The mixing-layer spot is a large-scale elongated structure spanning the entire width of the layer but does not appear to exhibit a self-similar shape. The dynamics of the mixing-layer spot and its eduction are more complicated than those of the boundary-layer spot. The spot initially moves downstream essentially at a uniform speed across the mixing layer, but further downstream it accelerates on the high-speed side and decelerates on the low-speed side. This paper discusses the data acquisition and processing techniques and the results based on the streamwise velocity signals. Phase average distributions of vorticity, pseudo-streamlines, coherent and background Reynolds stresses and further dynamics of the spot are presented in part 2 (Hussain, Kleis & Sokolov 1980).

scholarly journals Planar flows past thin multi-blade configurations

1996 ◽  
Vol 324 ◽  
pp. 355-377 ◽  
Author(s):  
F. T. Smith ◽  
S. N. Timoshin
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Laminar Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Require Solution ◽  
Lift And Drag ◽  
Planar Flows ◽  
Steady Laminar

Two-dimensional steady laminar flows past multiple thin blades positioned in near or exact sequence are examined for large Reynolds numbers. Symmetric configurations require solution of the boundary-layer equations alone, in parabolic fashion, over the successive blades. Non-symmetric configurations in contrast yield a new global inner–outer interaction in which the boundary layers, the wakes and the potential flow outside have to be determined together, to satisfy pressure-continuity conditions along each successive gap or wake. A robust computational scheme is used to obtain numerical solutions in direct or design mode, followed by analysis. Among other extremes, many-blade analysis shows a double viscous structure downstream with two streamwise length scales operating there. Lift and drag are also considered. Another new global interaction is found further downstream. All the interactions involved seem peculiar to multi-blade flows.

Elastico-viscous boundary-layer flows I. Two-dimensional flow near a stagnation point

1964 ◽  
Vol 60 (3) ◽  
pp. 667-674 ◽  
Author(s):  
D. W. Beard ◽  
K. Walters
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Viscous Boundary Layer ◽  
Boundary Layer Equations ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Viscous Boundary

AbstractThe Prandtl boundary-layer theory is extended for an idealized elastico-viscous liquid. The boundary-layer equations are solved numerically for the case of two-dimensional flow near a stagnation point. It is shown that the main effect of elasticity is to increase the velocity in the boundary layer and also to increase the stress on the solid boundary.

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