Heat-Transfer Measurements in an Inexpensive Supersonic Wind Tunnel: 2—Results for a Laminar Boundary Layer Based on a Two-Dimensional Flow Model

1955 ◽  
Vol 22 (3) ◽  
pp. 297-304
Author(s):  
Joseph Kaye ◽  
G. A. Brown
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Supersonic Flow ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Two Dimensional ◽  
Round Tube ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

Abstract Reliable experimental data on local heat-transfer coefficients for supersonic flow of air in a round tube are reanalyzed in detail with the aid of an approximate two-dimensional flow model. The results are compared with similar results based on a one-dimensional flow model and with the theoretical predictions for supersonic flow over a flat plate and for flow in the entrance region of a tube when a laminar boundary layer is present. The two-dimensional flow model yields a better understanding of the phenomena which occur for diabatic supersonic flow of air in a round tube than that obtained with the aid of the one-dimensional flow model. The two-dimensional flow model shows that the core Mach number is nearly constant along the length of test section for a range of values of the inlet diameter Reynolds number. For a laminar boundary layer the values of the local Stanton number agree within a few per cent with the theoretical values for plate flow at the largest values of the inlet diameter Reynolds number.

Measurement of Recovery Factors and Friction Coefficients for Supersonic Flow of Air in a Tube: 2—Results Based on a Two-Dimensional Flow Model for Entrance Region

1952 ◽  
Vol 19 (2) ◽  
pp. 185-194
Author(s):  
J. Kaye ◽  
T. Y. Toong ◽  
R. H. Shoulberg
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Variable Mass ◽  
Entrance Region ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Change Of State ◽  
Two Dimensional Flow

Abstract The first part of a program to obtain reliable data on the rate of heat transfer to air moving at supersonic speeds in a tube has been devoted to measurements made on adiabatic supersonic flow of air in a tube. The details of these measurements have been described in a previous paper. The calculated quantities such as the local apparent friction coefficient, recovery factor, Mach number, and so forth, were obtained from the simple one-dimensional flow model for which the properties of the stream are uniform at any section, and boundary-layer effects are ignored. The analysis of some of the same data given in the previous paper is undertaken here with the aid of a simplified two-dimensional flow model. The supersonic flow in the tube is divided into a supersonic core of variable mass with the fluid remaining in the core undergoing a reversible adiabatic change of state, and a laminar boundary layer of variable mass. The compressible laminar boundary layer increases in thickness in the direction of flow, and then undergoes a transition to a turbulent boundary layer. The two-dimensional flow model is limited here to the region where a laminar boundary layer appears to be present in the entrance region of the tube. The results of the analysis based on the two-dimensional flow model indicate that where the flow in the tube boundary layer appears to be laminar, the measured pressures and temperatures in the tube for adiabatic supersonic flow of air could have been predicted, with sufficient accuracy for engineering problems, from measured data for supersonic flow of air over a flat plate with a laminar boundary layer, and with zero pressure gradient.

Heat-Transfer Measurements in an Inexpensive Supersonic Wind Tunnel: 1—Apparatus and Results for a Laminar Boundary Layer Based on a Simple One-Dimensional Flow Model

1955 ◽  
Vol 22 (3) ◽  
pp. 289-296
Author(s):  
Joseph Kaye ◽  
J. H. Keenan ◽  
G. A. Brown ◽  
R. H. Shoulberg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Transfer Coefficients ◽  
Supersonic Wind Tunnel ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Dimensional Flow

Abstract Reliable experimental data, obtained at relatively low cost, are presented in the form of heat-transfer coefficients for air moving at supersonic speeds in a round tube. These data are analyzed, interpreted, and compared with available data in the literature. The experimental local heat-transfer coefficients are for laminar, transitional, and turbulent boundary layers. The data for a laminar boundary layer, comprising 17 runs, are discussed here for Mach numbers at tube inlet of 2.8 and 3.0. The range of values of diameter Reynolds number covered is from 20,000 to 100,000 for these laminar-flow tests, while the length Reynolds number extends to about 4,000,000. The computed quantities are obtained on the basis of a simple one-dimensional flow model, but a companion paper will analyze the same data in greater detail on the basis of a two-dimensional flow model.

Measurement of Recovery Factors and Friction Coefficients for Supersonic Flow of Air in a Tube: 1—Apparatus, Data, and Results Based on a Simple One-Dimensional Flow Model

1952 ◽  
Vol 19 (1) ◽  
pp. 77-96
Author(s):  
J. Kaye ◽  
J. H. Keenan ◽  
K. K. Klingensmith ◽  
G. M. Ketchum ◽  
T. Y. Toong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Flow Model ◽  
Supersonic Stream ◽  
Round Tube ◽  
Adiabatic Wall ◽  
One Dimensional ◽  
Dimensional Flow

Abstract For the past few years a program has been under way to obtain reliable data on the rate of heat transfer to air moving at supersonic speeds. The investigation was limited to air flowing at supersonic speeds in a round tube. The program was divided into two separate parts, the first for measurement of the adiabatic wall temperatures of a supersonic stream and the second for the heat-transfer rate. The first part of this program is described here. The details of three experimental test combinations used to measure the adiabatic wall temperature and local state of a supersonic stream of air are presented. The experimental data for forty runs, in the form of measured pressure and temperature distributions, are included. The range of diameter Reynolds number covered is from 0.15 × 105 to 5 × 105. The length Reynolds number extends to 120 × 105. The Mach number at the inlet to the round tube is about 2.6. The calculated quantities such as the local apparent friction coefficient, recovery factor, local Mach number, and so forth, are obtained from the simple one-dimensional flow model for which the properties of the stream are uniform at any cross section of the tube and boundary-layer effects are ignored. A subsequent paper deals with the calculation of these quantities when account is taken of the boundary-layer growth in the tube on the basis of a two-dimensional flow model.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

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