An appraisal of ‘flat plate’ closure for the approximate solution of boundary layer problems

1987 ◽  
Vol 91 (908) ◽  
pp. 373-389
Author(s):  
D. I. A. Poll ◽  
C. M. Hellon
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Flat Plate ◽  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Similarity Solutions ◽  
Laminar Flows ◽  
Reynolds Analogy

SummaryThe usefulness of zero pressure gradient, flat plate closure relations in providing approximate solutions for the boundary layer momentum and energy integral equations is examined. Expressions are obtained for skin friction, surface heat transfer rate and local Reynolds analogy factor under general compressible flow conditions. For laminar flows the predictions are compared with well known similarity solutions, with some exact solutions for non-similar flows and with experimental heat transfer data for high speed flow over a blunt cone. Consideration is also given to situations in which the surface temperature is a function of position. For turbulent flow situations comparisons are made with experimental data obtained from two-dimensional and axi-symmetric tests. Conditions vary from low Mach number incompressible flows through to high Mach number compressible flows with highly cooled walls. Some comparisons are also made with other prediction techniques.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.

scholarly journals Experimental study of the impact of N-wave on heat transfer in a boundary layer of a flat plate at the Mach number 2

2021 ◽  
Author(s):  
V. L. Kocharin ◽  
A. A. Yatskikh ◽  
D. S. Prishchepova ◽  
A. V. Panina ◽  
Yu. G. Yermolaev ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Experimental Study ◽  
Mach Number ◽  
Flat Plate ◽  
N Wave ◽  
The Impact

Heat transfer from a hypersonic turbulent boundary layer on a flat plate

1973 ◽  
Vol 60 (2) ◽  
pp. 257-271 ◽  
Author(s):  
G. T. Coleman ◽  
C. Osborne ◽  
J. L. Stollery
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Friction Coefficient ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Reasonable Agreement ◽  
Skin Friction Coefficient ◽  
Number Range

A hypersonic gun tunnel has been used to measure the heat transfer to a sharpedged flat plate inclined at various incidences to generate local Mach numbers from 3 to 9. The measurements have been compared with a number of theoretical estimates by plotting the Stanton number against the energy-thickness Reynolds number. The prediction giving the most reasonable agreement throughout the above Mach number range is that due to Fernholz (1971).The values of the skin-friction coefficient derived from velocity profiles and Preston tube data are also given.

scholarly journals An Ultra-Fast TSP on a CNT Heating Layer for Unsteady Temperature and Heat Flux Measurements in Subsonic Flows

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 657
Author(s):  
Martin Bitter ◽  
Michael Hilfer ◽  
Tobias Schubert ◽  
Christian Klein ◽  
Reinhard Niehuis
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Surface Temperature ◽  
Flat Plate ◽  
High Speed ◽  
Ambient Pressure ◽  
Frame Rate ◽  
Temperature Fields ◽  
Test Case ◽  
Unsteady Temperature

In this paper, the authors demonstrate the application of a modified Ru(phen)-based temperature-sensitive paint which was originally developed for the evaluation of unsteady aero-thermodynamic phenomena in high Mach number but short duration experiments. In the present work, the modified TSP with a temperature sensitivity of up to −5.6%/K was applied in a low Mach number long-duration test case in a low-pressure environment. For the demonstration of the paint’s performance, a flat plate with a mounted cylinder was set up in the High-Speed Cascade Wind Tunnel (HGK). The test case was designed to generate vortex shedding frequencies up to 4300 Hz which were sampled using a high-speed camera at 40 kHz frame rate to resolve unsteady surface temperature fields for potential heat-transfer estimations. The experiments were carried out at reduced ambient pressure of p∞ = 13.8 kPa for three inflow Mach numbers being Ma∞=[0.3;0.5;0.7]. In order to enable the resolution of very low temperature fluctuations down to the noise floor of 10−5 K with high spatial and temporal resolution, the flat plate model was equipped with a sprayable carbon nanotube (CNT) heating layer. This constellation, together with the thermal sensors incorporated in the model, allowed for the calculation of a quasi-heat-transfer coefficient from the surface temperature fields. Besides the results of the experiments, the paper highlights the properties of the modified TSP as well as the methodology.

Turbine Blade Tip Heat Transfer in Low Speed and High Speed Flows

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Andrew P. S. Wheeler ◽  
Nicholas R. Atkins ◽  
Li He
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Coefficient ◽  
Mach Number ◽  
Transfer Coefficient ◽  
High Speed ◽  
Low Speed ◽  
Blade Tip ◽  
The Heat Transfer Coefficient ◽  
Recovery Temperature

In this paper, high and low speed tip flows are investigated for a high-pressure turbine blade. Previous experimental data are used to validate a computational fluid dynamics (CFD) code, which is then used to study the tip heat transfer in high and low speed cascades. The results show that at engine representative Mach numbers, the tip flow is predominantly transonic. Thus, compared with the low speed tip flow, the heat transfer is affected by reductions in both the heat-transfer coefficient and the recovery temperature. The high Mach numbers in the tip region (M>1.5) lead to large local variations in recovery temperature. Significant changes in the heat-transfer coefficient are also observed. These are due to changes in the structure of the tip flow at high speed. At high speeds, the pressure side corner separation bubble reattachment occurs through supersonic acceleration, which halves the length of the bubble when the tip-gap exit Mach number is increased from 0.1 to 1.0. In addition, shock/boundary-layer interactions within the tip gap lead to large changes in the tip boundary-layer thickness. These effects give rise to significant differences in the heat-transfer coefficient within the tip region compared with the low speed tip flow. Compared with the low speed tip flow, the high speed tip flow is much less dominated by turbulent dissipation and is thus less sensitive to the choice of turbulence model. These results clearly demonstrate that blade tip heat transfer is a strong function of Mach number, an important implication when considering the use of low speed experimental testing and associated CFD validation in engine blade tip design.

scholarly journals Skin Friction in the Laminar Boundary Layer in Compressible Flow

1949 ◽  
Vol 1 (2) ◽  
pp. 137-164 ◽  
Author(s):  
A. D. Young
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Compressible Flow ◽  
Laminar Boundary Layer ◽  
Momentum Equation ◽  
Forward Movement ◽  
Semi Empirical

SummaryFrom an analysis of the work of Crocco and others, semi-empirical formulae are derived for the skin friction on a flat plate at zero incidence with a laminar boundary layer. These formulae arefor the general case of heat transfer, andwhen there is no heat transfer.The problem of heat transfer and the effect of radiation are discussed in the light of these formula;. The second formula is then utilised in the development of an approximate method for solving the momentum equation of the boundary layer on a cylinder without heat transfer. The method indicates that with increase of Mach number there is a marked forward movement of separation from a flat plate in the presence of a constant adverse velocity gradient.

scholarly journals Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

2014 ◽  
Vol 17 (1) ◽  
pp. 189-212 ◽  
Author(s):  
Xian Liang ◽  
Xinliang Li
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Flat Plate ◽  
Wall Temperature ◽  
Wall Region ◽  
Mean Velocity ◽  
Reynolds Analogy

AbstractIn this paper, direct numerical simulation (DNS) is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate atMa∞= 2.25,5,6,8. WhenMa∞= 8, two cases with the ratio of wall-to-reference temperatureTω/T∞= 1.9 and 10.03 are considered respectively. The wall temperature approaches recovery temperatures for other cases. The characteristics of compressible turbulent boundary layer (CTBL) affected by freestream Mach number and wall temperature are investigated. It focuses on assessing compressibility effects and the validity of Morkovin's hypothesis through computing and analyzing the mean velocity profile, turbulent intensity, the strong Reynolds analogy (SRA) and possibility density function of dilatation term. The results show that, when the wall temperature approaches recovery temperature, the effects of Mach number on compressibility is insignificant. As a result, the compressibility effect is very weak and the Morkovin's hypothesis is still valid for Mach number even up to 8. However, when Mach number equal to 8, the wall temperature effect on the compressibility is sensitive. In this case, whenTω/T∞= 1.9, the Morkovin's hypothesis is not fully valid. The validity of classical SRA depends on wall temperature directly. A new modified SRA is proposed to eliminate such negative factor in near wall region. Finally the effects of Mach number and wall temperature on streaks are also studied.

Turbine Blade Tip Heat Transfer in Low Speed and High Speed Flows

2009 ◽  
Author(s):  
Andrew P. S. Wheeler ◽  
Nicholas R. Atkins ◽  
Li He
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Coefficient ◽  
Mach Number ◽  
Transfer Coefficient ◽  
High Speed ◽  
Low Speed ◽  
Blade Tip ◽  
The Heat Transfer Coefficient ◽  
Recovery Temperature

In this paper, high and low speed tip flows are investigated for a high-pressure turbine blade. Previous experimental data are used to validate a CFD code, which is then used to study the tip heat transfer in high and low speed cascades. The results show that at engine representative Mach numbers the tip flow is predominantly transonic. Thus, compared to the low speed tip flow, the heat transfer is affected by reductions in both the heat transfer coefficient and the recovery temperature. The high Mach numbers in the tip region (M>1.5) lead to large local variations in recovery temperature. Significant changes in the heat transfer coefficient are also observed. These are due to changes in the structure of the tip flow at high speed. At high speeds, the pressure side corner separation bubble reattachment occurs through supersonic acceleration which halves the length of the bubble when the tip gap exit Mach number is increased from 0.1 to 1.0. In addition, shock/boundary-layer interactions within the tip gap lead to large changes in the tip boundary-layer thickness. These effects give rise to significant differences in the heat-transfer coefficient within the tip region compared to the low-speed tip flow. Compared to the low speed tip flow, the high speed tip flow is much less dominated by turbulent dissipation and is thus less sensitive to the choice of turbulence model. These results clearly demonstrate that blade tip heat transfer is a strong function of Mach number, an important implication when considering the use of low speed experimental testing and associated CFD validation in engine blade tip design.

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