Temperature Effects in a Laminar Compressible-Fluid Boundary Layer Along a Flat Plate

1941 ◽  
Vol 8 (3) ◽  
pp. A105-A110
Author(s):  
H. W. Emmons ◽  
J. G. Brainerd
Keyword(s):  
Boundary Layer ◽  
Equilibrium Temperature ◽  
Perfect Gas ◽  
Boundary Layer Problem ◽  
Wide Range ◽  
Dimensional Boundary ◽  
Fluid Boundary ◽  
New Phenomena ◽  
Steady Laminar ◽  
Layer Problem

Abstract In this paper the two-dimensional boundary-layer problem of the steady laminar flow of a perfect gas along a thin flat insulated plate has been solved for a wide range of gas velocities and properties. It is found that compressibility and Prandtl number do not introduce any new phenomena, but do alter the drag on the plate, the equilibrium temperature of the plate, and the velocity and temperature distribution through the boundary layer. The drag coefficient for the plate is given by Equation [24] together with Fig. 2. The temperature of the plate is given by Equation [27 a or b], and approximately by Equation [26] or by Figs. 3 or 4. Typical velocity and temperature distributions are given in Figs. 5 to 10, inclusive.

scholarly journals Stability of the laminar boundary layer in a streamwise corner

1984 ◽  
Vol 393 (1804) ◽  
pp. 101-116 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Viscous Incompressible Flow ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Mean ◽  
Layer Region ◽  
The Stability ◽  
Infinite Boundary Value Problem ◽  
Layer Problem

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.

Application of a General Finite-Difference Method to Boundary Layer Flows

1972 ◽  
Vol 1 (3) ◽  
pp. 146-152
Author(s):  
S. D. Katotakis ◽  
J. Vlachopoulos
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Boundary Layer Flows ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Temperature Boundary ◽  
Dimensional Boundary ◽  
Finite Difference Solution ◽  
Suction Or Injection ◽  
Layer Problem

A straight-forward and general finite-difference solution of the boundary layer equations is presented. Several problems are examined for laminar flow conditions. These include velocity and temperature boundary layers over a flat plate, linearly retarded flows and several cases of suction or injection. The results obtained are in excellent agreement with existing accurate solutions. It appears that any kind of steady, two-dimensional boundary layer problem can be solved thus with accuracy and speed.

Effect of Variable Viscosity on Boundary Layers, With a Discussion of Drag Measurements

1942 ◽  
Vol 9 (1) ◽  
pp. A1-A6
Author(s):  
J. G. Brainerd ◽  
H. W. Emmons
Keyword(s):  
Boundary Layer ◽  
Variable Viscosity ◽  
Equilibrium Temperature ◽  
Flow Coefficient ◽  
Boundary Layer Problem ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Viscosity Functions ◽  
Passage Efficiency ◽  
Test Result

Abstract This work extends a previously reported investigation of the boundary-layer problem associated with the steady laminar flow of a perfect gas along a thin flat insulated plate. In the earlier study the viscosity was assumed constant and the distributions of velocity and temperature were obtained for a wide range of conditions. Part I of the present paper shows, for Prandtl number 0.733 (air) and Mach number of the undisturbed stream 2, the velocity and temperature distributions in the boundary layer under various assumed viscosity variations. Part II gives the distributions for various Prandtl numbers and Mach numbers, assuming the same viscosity functions as used by von Kármán and Tsien. Part III is devoted to a discussion of the method of interpretation of traverse tests of the efficiency and flow coefficients of nozzles or other passages. The results of Part I show that the variation of viscosity with temperature does not alter the equilibrium temperature of the plate, and hence the reading of a plate thermometer. This result is extended in Part II where it is shown that θ at the plate wall is equal to the same quantity when μ is taken constant to within 1 per cent in all cases studied. Furthermore, φU′ at the plate wall does not vary greatly, so that the drag coefficient CD is equal to 1.28/(Re)1/2 to within 5 per cent for most of the cases investigated. In Part III a passage efficiency as usually calculated is found to be subject to two errors, one of which reduces and the other of which increases the test result. The net effect is to cause the standard traverse test to give a conservative estimate of the efficiency. The flow coefficient as determined by traverse tests is somewhat higher than the correct one.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

Validation of MISES Two-Dimensional Boundary Layer Code for High-Pressure Turbine Aerodynamic Design

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Philip L. Andrew ◽  
Harika S. Kahveci
Keyword(s):  
Boundary Layer ◽  
High Pressure ◽  
Operating Cost ◽  
Design Tool ◽  
Operating Conditions ◽  
Aerodynamic Design ◽  
High Pressure Turbine ◽  
Reduce Operating Cost ◽  
Wide Range ◽  
Dimensional Boundary

Avoiding aerodynamic separation and excessive shock losses in gas turbine turbomachinery components can reduce fuel usage and thus reduce operating cost. In order to achieve this, blading designs should be made robust to a wide range of operating conditions. Consequently, a design tool is needed—one that can be executed quickly for each of many operating conditions and on each of several design sections, which will accurately capture loss, turning, and loading. This paper presents the validation of a boundary layer code, MISES, versus experimental data from a 2D linear cascade approximating the performance of a moderately loaded mid-pitch section from a modern aircraft high-pressure turbine. The validation versus measured loading, turning, and total pressure loss is presented for a range of exit Mach numbers from ≈0.5 to 1.2 and across a range of incidence from −10 deg to +14.5 deg relative to design incidence.

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

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