Analysis and Asymptotic Solutions of Compressible Turbulent Corner Flow

1982 ◽  
Vol 104 (3) ◽  
pp. 571-579 ◽  
Author(s):  
A. G. Mikhail ◽  
K. N. Ghia
Keyword(s):  
Heat Transfer ◽  
Turbulence Modeling ◽  
Algebraic Model ◽  
Far Field ◽  
Two Dimensional ◽  
Anisotropic Model ◽  
Field Boundary ◽  
Corner Flow ◽  
Dimensional Boundary ◽  
Marching Scheme

The turbulent compressible flow along an unbounded 90 deg axial corner has been analyzed. The limiting equations for the far-field boundary, simulating a two-dimensional boundary layer with crossflow, have been obtained appropriately. This latter set of equations have been solved using a semi-implicit second-order accurate numerical marching scheme. The turbulent stresses have been modeled first using a Cebeci-Smith type two-layer algebraic model in which isotropy is assumed. The turbulence stresses were also modeled using a modified form of the Gessner-Emery anisotropic model. Results have been presented for a range of Mach numbers between 0 and 2.0 with adiabatic as well as heat transfer boundary conditions at the corner walls. Effect of suction and injection have also been included. The anisotropy in the turbulence modeling showed insignificant effect on the flow field at far-field boundary, but it is believed to be essential in the inner corner region. The analysis presented recovers all previously available results for the simplified cases of this corner configuration.

Unsteady Two-Dimensional Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on an Accelerated Flat Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. R. Mozayyeni ◽  
Asghar B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Flat Plate ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Far Field ◽  
Two Dimensional ◽  
Flow And Heat Transfer ◽  
Wide Range

The general formulation and exact solution of the Navier–Stokes and energy equations regarding the problem of steady and unsteady two-dimensional stagnation-point flow and heat transfer is investigated in the vicinity of a flat plate. The plate is moving at time-dependent or constant velocity towards the main low Mach number free stream or away from it. The main stream impinges along z-direction on the flat plate with strain rate a and produces two-dimensional flow. The fluid is assumed to be viscous and compressible. The density of the fluid is affected by the existing temperature difference between the plate and potential far field flow. Suitably introduced similarity transformations are used to reduce the governing equations to a coupled system of ordinary differential equations. Finite Difference Scheme is used to solve these non-linear ordinary differential equations. The obtained results are presented over a wide range of parameters characterizing the problem. It is revealed that the significance of the increase of thermal expansion coefficient, β, and wall temperature on velocity and temperature distributions is much more noticeable for a plate moving away from impinging flow. Moreover, negligible shear stress and heat transfer is reported between the plate and fluid viscous layer close to the plate for a wide range of β coefficient when the plate moves away from incoming far field flow.

Singularities associated with separating boundary layers

1965 ◽  
Vol 257 (1084) ◽  
pp. 409-444 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Separation Line ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Line Of Singularities ◽  
Appl Math

This paper investigates the nature of flow in the neighbourhood of separation of a laminar boundary layer, and is based on the work of Goldstein (1948 Quart. J. Mech. Appl. Math. 1, 43), Stewartson (1958 Quart. J. Mech. Appl. Math. 11, 399), Terrill (1960 Phil. Trans. A, 253, 55) and Stewartson (1962 J.Fluid Mech. 12, 117). The problem of establishing the existence or nonexistence of a singularity at separation for incompressible two-dimensional flow is investigated in the first three of these papers, and the last mentioned finds that if heat transfer across the boundary is permitted no singularity occurs at a point of vanishing skin friction unless the heat transfer is also zero at this point. The present work examines the possibility of the non-occurrence of singularities in other physical situations including reference to three-dimensional separation. Particular problems considered include that of conefield flow of an incompressible fluid over a delta wing for which the separation line is shown to be a line of singularities, and that of compressible flow over a yawed cylinder in which case the conclusion is that the separation line is a line of regular points if the heat transfer is non-zero along its length. The problem of separation for a general three-dimensional boundary layer is considered but not resolved.

scholarly journals Calculation of Heat Transfer to Turbine Blading Using Two-Dimensional Boundary Layer Methods

1993 ◽  
Author(s):  
S. P. Harasgama ◽  
F. H. Tarada ◽  
R. Baumann ◽  
M. E. Crawford ◽  
S. Neelakantan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Suction Side ◽  
Operating Conditions ◽  
External Boundary ◽  
Test Case ◽  
Two Dimensional ◽  
Dimensional Boundary ◽  
Mach Numbers ◽  
Turbine Blading

The calculation of the external boundary layer and associated heat transfer to turbine blading is described. Three separate Two-Dimensional Boundary Layer programs were utilised in this study. The programs incorporated the k-epsilon turbulence model with several different formulations. The test case chosen for this study was the von Karman Institute blade VKI Tech. Note-174, Sept-1990. It is shown that in most cases all programs tend to predict the correct behaviour of the onset of transition. However, the transition length between the laminar and turbulent values is predicted too abruptly on the blade suction side. It was found that the magnitude of the predicted heat transfer coefficient was most consistent with experimental values for exit Mach numbers between 0.7–0.9, and for all inlet turbulence levels and Reynolds numbers. For higher blade exit Mach numbers in the transonic region (M > 0.95) it was difficult to correctly predict the heat transfer in comparison with experimental data. The predicted values were all higher than the measurement. For this blade, the pressure side is quite well predicted for most of the operating conditions.

scholarly journals A Two-Dimensional Boundary-Layer Program for Turbine Airfoil Heat Transfer Calculation

1982 ◽  
Author(s):  
R. M. C. So ◽  
I. H. Edelfelt ◽  
E. Elovic ◽  
D. M. Kercher
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Wind Tunnel ◽  
Gas Turbines ◽  
Two Dimensional ◽  
Gas Temperature ◽  
Suction Surface ◽  
Pressure Surface ◽  
Dimensional Boundary ◽  
Wind Tunnel Data

A two-dimensional boundary-layer program has been developed for the calculation of flow and heat transfer around turbine airfoils. The program is capable of carrying out the calculation from the forward stagnation point, and can account for such effects as compressibility, high inlet gas temperature, streamwise pressure gradient, transition, streamline curvature and freestream turbulence. Three comparisons with recent measurements are carried out. Two are with idealized wind tunnel data. One is with cascade data obtained at high gas-to-wall temperature ratio of 2.56–2.85, which compares with a normal range of 1.4 to 2.4 for real gas turbines. Good agreement is obtained with the wind tunnel data. As for the cascade data, good correlation on the suction surface of the turbine airfoil is achieved. However, discrepancy on the pressure surface is observed and is attributed to the occurrence of local separation and reattachment in the actual flow.

Heat Transfer Through a Pressure-Driven Three-Dimensional Boundary Layer

1991 ◽  
Vol 113 (2) ◽  
pp. 355-362 ◽  
Author(s):  
S. D. Abrahamson ◽  
J. K. Eaton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Transfer Data ◽  
Transverse Pressure ◽  
Dimensional Boundary ◽  
The Mean ◽  
Two Dimensional Flows

An experimental investigation of heat transfer through a three-dimensional boundary layer has been performed. An initially two-dimensional boundary layer was made three dimensional by a transverse pressure gradient caused by a wedge obstruction, which turned the boundary layer within the plane of the main flow. Two cases, with similar streamwise pressure gradients and different lateral gradients, were studied so that the effect of the lateral gradient on heat transfer could be deduced. The velocity flowfield agreed with previous hydrodynamic investigations of this flow. The outer parts of the mean velocity profiles were shown to agree with the Squire-Winter theorem for rapidly turned flows. Heat transfer data were collected using a constant heat flux surface with embedded thermocouples for measuring surface temperatures. Mean fluid temperatures were obtained using a thermocouple probe. The temperature profiles, when plotted in outer scalings, showed logarithmic behavior consistent with two-dimensional flows. An integral analysis of the boundary layer equations was used to obtain a vector formulation for the enthalpy thickness, HH≜∫0∞ρuisdyρ∞ii,o(u∞2+w∞2)1/2,0,∫0∞ρwisdyρ∞is,o(u∞2+w∞2)1/2 (where is is the stagnation enthalpy), which is consistent with the scalar formulation used for two-dimensional flows. Using the vector formulation, the heat transfer data agreed with standard two-dimensional correlations of the Stanton number and enthalpy thickness Reynolds number. It was concluded that although the heat transfer coefficient decreased faster than its two-dimensional counterpart, it was similar to the two-dimensional case. The vector form of the enthalpy thickness captured the rotation of the mean thermal energy flux away from the free-stream direction. Boundary layer three dimensionality increased with the strength of the transverse pressure gradient and the heat transfer coefficients were smaller for the stronger transverse gradient.

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