scholarly journals Heat transfer and skin-friction in a nonequilibrium adverse pressure gradient

2021 ◽  
Vol 2039 (1) ◽  
pp. 012010
Author(s):  
N A Kiselev ◽  
Yu A Vinogradov ◽  
A G Zditovets
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Gradient Flow ◽  
Adverse Pressure Gradient ◽  
Opening Angle ◽  
Transfer Coefficients ◽  
Reynolds Analogy ◽  
Heat Transfer Coefficients ◽  
Gradient Parameter ◽  
Relative Friction

Abstract The paper presents the results of an experimental study of influence of a weak and moderate nonequilibrium adverse pressure gradient (APG) on the parameters of the dynamic and thermal boundary layers. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re **=5500. The section of the channel with APG was a slotted channel with an opening angle of the upper wall of 0-14°. The values of the relative (referred to the parameters in a zero pressure gradient flow at the same Re **) friction and heat transfer coefficients, as well as the Reynolds analogy factor depending on the longitudinal pressure gradient, are obtained. The values of the relative friction coefficient decreased to cf/cf0 =0.7 and those of the heat transfer to St/St0=0.9. A maximum value of the Reynolds analogy factor (St/St0)/(cf/cf0 )=1.16 was reached for the pressure gradient parameter β=2.9. The ratio of the heat transfer and drag coefficients of the dimpled to smooth surfaces remained approximately constant regardless of the presence or magnitude of a adverse pressure gradient.

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.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2003 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number (Rex≅900,000). An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy (2St/cf). Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

A Critical Assessment of Reynolds Analogy for Turbine Flows

2005 ◽  
Vol 127 (5) ◽  
pp. 472-485 ◽  
Author(s):  
J. Bons
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Adverse Pressure Gradient ◽  
Design Parameters ◽  
Freestream Turbulence ◽  
Reynolds Analogy ◽  
Pressure Drag

The application of Reynolds analogy 2St/cf≅1 for turbine flows is critically evaluated using experimental data collected in a low-speed wind tunnel. Independent measurements of St and cf over a wide variety of test conditions permit assessments of the variation of the Reynolds analogy factor (i.e., 2St/cf) with Reynolds number, freestream pressure gradient, surface roughness, and freestream turbulence. While the factor is fairly independent of Reynolds number, it increases with positive (adverse) pressure gradient and decreases with negative (favorable) pressure gradient. This variation can be traced directly to the governing equations for momentum and energy which dictate a more direct influence of pressure gradient on wall shear than on energy (heat) transfer. Surface roughness introduces a large pressure drag component to the net skin friction measurement without a corresponding mechanism for a comparable increase in heat transfer. Accordingly, the Reynolds analogy factor decreases dramatically with surface roughness (by as much as 50% as roughness elements become more prominent). Freestream turbulence has the opposite effect of increasing heat transfer more than skin friction, thus the Reynolds analogy factor increases with turbulence level (by up to 35% at a level of 11% freestream turbulence). Physical mechanisms responsible for the observed variations are offered in each case. Finally, synergies resulting from the combinations of pressure gradient and freestream turbulence with surface roughness are evaluated. With this added insight, the Reynolds analogy remains a useful tool for qualitative assessments of complex turbine flows where both heat load management and aerodynamic efficiency are critical design parameters.

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.

Effects of Surface Roughness on Heat Transfer and Aerodynamic Performance of Turbine Airfoils

1997 ◽  
Author(s):  
N. Abuaf ◽  
R. S. Bunker ◽  
C. P. Lee
Keyword(s):  
Heat Transfer ◽  
Surface Finish ◽  
Local Heat Transfer ◽  
Surface Finishing ◽  
Transfer Coefficients ◽  
Average Roughness ◽  
Reynolds Analogy ◽  
Local Skin ◽  
Heat Transfer Coefficients ◽  
Wide Range

Aerodynamic flow path losses and turbine airfoil gas side heat transfer are strongly affected by the gas side surface finish. For high aero efficiencies and reduced cooling requirements, airfoil designs dictate extensive surface finishing processes to produce smooth surfaces and enhance engine performance. The achievement of these requirements incurs additional manufacturing finishing costs over less strict requirements. The present work quantifies the heat transfer (and aero) performance differences of three cast airfoils with varying degrees of surface finish treatment. An airfoil which was grit blast and Codep coated produced an average roughness of 2.33 μm, one which was grit blast, tumbled, and Aluminide coated produced 1.03 μm roughness, and another which received further post coating polishing produced 0.81 μm roughness. Local heat transfer coefficients were experimentally measured with a transient technique in a linear cascade with a wide range of flow Reynolds numbers covering typical engine conditions. The measured heat transfer coefficients were used with a rough surface Reynolds Analogy to determine the local skin friction coefficients, from which the drag forces and aero efficiencies were calculated. Results show that tumbling and polishing reduce the average roughness and improve performance. The largest differences are observed from the rumbling process, with smaller improvements realized from polishing.

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.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2004 ◽  
Vol 126 (3) ◽  
pp. 385-394 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number Rex≅900,000. An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy 2St/cf. Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

scholarly journals Heat Transfer and Fluid Mechanics Measurements in Transitional Boundary Layer Flows

1985 ◽  
Vol 107 (4) ◽  
pp. 1007-1015 ◽  
Author(s):  
T. Wang ◽  
T. W. Simon ◽  
J. Buddhavarapu
Keyword(s):  
Heat Transfer ◽  
Turbulent Flows ◽  
Plate Boundary ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Shear Stresses ◽  
Boundary Layer Flows ◽  
Transfer Coefficients ◽  
Reynolds Analogy ◽  
Heat Transfer Coefficients

Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients, and profiles of velocity, temperature, and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68 percent and 2.0 percent free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.

Effects of Surface Roughness on Heat Transfer and Aerodynamic Performance of Turbine Airfoils

1998 ◽  
Vol 120 (3) ◽  
pp. 522-529 ◽  
Author(s):  
N. Abuaf ◽  
R. S. Bunker ◽  
C. P. Lee
Keyword(s):  
Heat Transfer ◽  
Surface Finish ◽  
Local Heat Transfer ◽  
Surface Finishing ◽  
Transfer Coefficients ◽  
Average Roughness ◽  
Reynolds Analogy ◽  
Local Skin ◽  
Heat Transfer Coefficients ◽  
Wide Range

Aerodynamic flow path losses and turbine airfoil gas side heat transfer are strongly affected by the gas side surface finish. For high aero efficiencies and reduced cooling requirements, airfoil designs dictate extensive surface finishing processes to produce smooth surfaces and enhance engine performance. The achievement of these requirements incurs additional manufacturing finishing costs over less strict requirements. The present work quantifies the heat transfer (and aero) performance differences of three cast airfoils with varying degrees of surface finish treatment. An airfoil, that was grit blast and Codep coated, produced an average roughness of 2.33 μm, one that was grit blast, tumbled, and aluminide coated produced 1.03 μm roughness, and another that received further postcoating polishing produced 0.81 μm roughness. Local heat transfer coefficients were experimentally measured with a transient technique in a linear cascade with a wide range of flow Reynolds numbers covering typical engine conditions. The measured heat transfer coefficients were used with a rough surface Reynolds analogy to determine the local skin friction coefficients, from which the drag forces and aero efficiencies were calculated. Results show that tumbling and polishing reduce the average roughness and improve performance. The largest differences are observed from the tumbling process, with smaller improvements realized from polishing.

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