The Calculation of Heat Transfer Coefficients from Skin Friction Coefficients in the Compressible Laminar Boundary Layer on an Aerofoil

1968 ◽  
Vol 19 (3) ◽  
pp. 243-253 ◽  
Author(s):  
R. E. Luxton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Strong Dependence ◽  
Transfer Coefficients ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Similar Solutions

SummaryIn this note a relation is established between the correlation parameters obtained by Cohen and Reshotko from similar solutions of the compressible laminar boundary layer, and the Pohlhausen-type pressure gradient parameter used in the approximate methods devised by Luxton and Young. A simple graphical procedure is presented to allow heat transfer coefficients to be obtained from known skin friction coefficients in the presence of a pressure gradient. In view of the restrictions of the similar solutions it cannot be claimeda priorithat the method gives accurate results. It does, however, reflect the strong dependence of the heat-transfer skin-friction relation on the pressure gradient and, by reference to calculated results published previously, it is suggested that the method may give adequate accuracy under quite severe conditions.

A note on expansions for the two-dimensional, compressible, laminar boundary layer equations near a point of zero skin friction

1983 ◽  
Vol 94 (1-2) ◽  
pp. 93-96 ◽  
Author(s):  
G. Wilks
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Boundary Layer Equations ◽  
Heat Transfer Coefficients

SynopsisThe first non-arbitrary coefficient, α12, of the Buckmaster expansions is evaluated in the context of the extended Goldstein-Stewartson theory. Leading terms of the next order contributions to the skin friction and heat transfer coefficients are also obtained.

Comparison of the Three-Dimensional Boundary Layer on Flat Versus Contoured Turbine Endwalls

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Stephen P. Lynch ◽  
Karen A. Thole
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Laser Doppler Velocimeter ◽  
Transfer Coefficients ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Passage Vortex ◽  
Dimensional Boundary

The boundary layer on the endwall of an axial turbomachine passage is influenced by streamwise and cross-stream pressure gradients, as well as a large streamwise vortex, that develop in the passage. These influences distort the structure of the boundary layer and result in heat transfer and friction coefficients that differ significantly from simple two-dimensional boundary layers. Three-dimensional contouring of the endwall has been shown to reduce the strength of the large passage vortex and reduce endwall heat transfer, but the mechanisms of the reductions on the structure of the endwall boundary layer are not well understood. This study describes three-component measurements of mean and fluctuating velocities in the passage of a turbine blade obtained with a laser Doppler velocimeter (LDV). Friction coefficients obtained with the oil film interferometry (OFI) method were compared to measured heat transfer coefficients. In the passage, the strength of the large passage vortex was reduced with contouring. Regions where heat transfer was increased by endwall contouring corresponded to elevated turbulence levels compared to the flat endwall, but the variation in boundary layer skew across the passage was reduced with contouring.

scholarly journals Heat transfer and skin-friction in channel with flow behind a cylinder

2021 ◽  
Vol 2088 (1) ◽  
pp. 012055
Author(s):  
N A Kiselev ◽  
A G Zditovets ◽  
Yu A Vinogradov
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Static Pressure ◽  
Thermal Imager ◽  
Transfer Coefficients ◽  
Reynolds Analogy ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Smooth Model ◽  
Transfer Method

Abstract The paper presents the results of an experimental study of the parameters of the boundary layer, distribution of static pressure, heat transfer and friction coefficients of smooth surface located in the wake behind the cylinder in the channel. Cylinders of various diameters were placed in a slotted channel with a height of 30 mm on its axis. In all experiments, the flow velocity at the inlet was 50 m/s. The cylinder was made unheated. The friction coefficients of the smooth model were determined both from the velocity profile in the boundary layer and by direct weighing of the model on a one-component strain-gage balance. The local values of the heat transfer coefficients were determined by transient heat-transfer method using a thermal imager. The values of the heat transfer and friction coefficients in the wake behind the cylinder, referred to the values on the smooth wall in the undisturbed flow, varied in the range 1.15–1.65 and 1.3–1.75, respectively. The value of the Reynolds analogy factor for all cylinder diameters turned out to be less than unity.

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.

Comparison of the Three-Dimensional Boundary Layer on Flat Versus Contoured Turbine Endwalls

2015 ◽  
Author(s):  
Stephen P. Lynch ◽  
Karen A. Thole
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Laser Doppler Velocimeter ◽  
Transfer Coefficients ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Passage Vortex ◽  
Dimensional Boundary

The boundary layer on the endwall of an axial turbomachine passage is influenced by streamwise and cross-stream pressure gradients, as well as a large streamwise vortex, that develop in the passage. These influences distort the structure of the boundary layer and result in heat transfer and friction coefficients that differ significantly from simple two-dimensional boundary layers. Three-dimensional contouring of the endwall has been shown to reduce the strength of the large passage vortex and reduce endwall heat transfer, but the mechanisms of the reductions on the structure of the endwall boundary layer are not well understood. This study describes three-component measurements of mean and fluctuating velocities in the passage of a turbine blade obtained with a laser Doppler velocimeter. Friction coefficients obtained with the oil film interferometry method were compared to measured heat transfer coefficients. In the passage, the strength of the large passage vortex was reduced with contouring. Regions where heat transfer was increased by endwall contouring corresponded to elevated turbulence levels compared to the flat endwall, but the variation in boundary layer skew across the passage was reduced with contouring.

Heat Transfer in a Supersonic Parallel Diffuser

1965 ◽  
Vol 7 (1) ◽  
pp. 1-7 ◽  
Author(s):  
P. J. Baker
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Cross Section ◽  
Static Pressure ◽  
Positive Pressure ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Flows ◽  
Pressure Distributions ◽  
The Mean

This paper presents the results of heat transfer measurements taken on a two-dimensional supersonic parallel diffuser. The wall static pressure distributions and the corresponding heat transfer coefficients and fluxes have been measured for a range of initial total pressures. The effects of varying the area of the diffuser cross-section for the same upstream generating nozzle have also been studied. Mach number profiles measured at sections along the diffuser show that in the presence of shock waves and a positive pressure gradient the flow is very much underdeveloped. In general, the mean level of heat transfer is found to be much greater than that predicted by conventional empirical equations for subsonic pipe flows with zero pressure gradient. Further, on comparison between normal and oblique shock diffusion the former is found to give the higher level of heat transfer.

Darryl E. Metzger Memorial Session Paper: Comparison of Calculated and Measured Heat Transfer Coefficients for Transonic and Supersonic Boundary-Layer Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 248-254 ◽  
Author(s):  
C. Hu¨rst ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Supersonic Boundary Layer ◽  
Nozzle Wall ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Three Dimensional Finite Element

The present study compares measured and computed heat transfer coefficients for high-speed boundary layer nozzle flows under engine Reynolds number conditions (U∞=230 ÷ 880 m/s, Re* = 0.37 ÷ 1.07 × 106). Experimental data have been obtained by heat transfer measurements in a two-dimensional, nonsymmetric, convergent–divergent nozzle. The nozzle wall is convectively cooled using water passages. The coolant heat transfer data and nozzle surface temperatures are used as boundary conditions for a three-dimensional finite-element code, which is employed to calculate the temperature distribution inside the nozzle wall. Heat transfer coefficients along the hot gas nozzle wall are derived from the temperature gradients normal to the surface. The results are compared with numerical heat transfer predictions using the low-Reynolds-number k–ε turbulence model by Lam and Bremhorst. Influence of compressibility in the transport equations for the turbulence properties is taken into account by using the local averaged density. The results confirm that this simplification leads to good results for transonic and low supersonic flows.

The Effects of Small Changes of Prandtl Number and the Viscosity-Temperature Index on Skin Friction

1964 ◽  
Vol 15 (4) ◽  
pp. 392-406 ◽  
Author(s):  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Wall Temperature ◽  
External Pressure ◽  
Main Stream ◽  
Pressure Gradients ◽  
Temperature Index

SummaryThe analytic simplifications in boundary-layer analysis that result from the assumptions that the Prandtl number σ and the viscosity-temperature index ω are unity make it desirable to be able to assess the effects of the departures of the actual values of these parameters from unity. In this paper only the effects on skin friction are considered. Formulae of acceptable validity and wide application are first used to produce generalised curves for these effects for given main-stream Mach numbers and wall temperature conditions for the case of zero external pressure gradient for both laminar and turbulent boundary layers (Figs. 1 and 2).A number of calculated results for the laminar boundary layer with favourable and adverse pressure gradients is then analysed (Figs. 3, 4 and 5) and it is shown that these results are consistent with the assumption that, for a given wall temperature, the effects of small changes of σ and ω on skin friction are independent of the external gradient, so that the appropriate curves of Figs. 1 and 2 apply. Where the change of a- is associated with a change of wall temperature (e.g. if the heat transfer is specified as zero) then the interaction between pressure gradient and this temperature change can be significant in its effects on skin friction for the laminar boundary layer and can only be assessed if the effects of changes of wall temperature with constant σ and ω have been separately determined for the pressure distribution considered. It is inferred that in all cases, except with large adverse pressure gradients and imminent separation, the effects of changes of ω and σ for the turbulent boundary layer are reliably predicted by the zero pressure gradient curves of Figs. 1 and 2 and the effect of any associated change of wall temperature can then be reliably inferred from the zero pressure gradient formula (equation (15)) in the absence of more specific calculations covering a range of wall temperatures.

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