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.

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.

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.

Heat transfer across rough surfaces

1963 ◽  
Vol 15 (3) ◽  
pp. 321-334 ◽  
Author(s):  
P. R. Owen ◽  
W. R. Thomson
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Skin Friction ◽  
Functional Form ◽  
Reynolds Analogy ◽  
Roughened Surface ◽  
Order Of Magnitude ◽  
The Individual

It is argued that the heat transfer between a roughened surface and a stream of incompressible fluid flowing over it is dependent on both the viscosity and thermal conductivity of the fluid even when the roughness is large enough for viscosity to have ceased to affect the skin friction.Concentrating on closely spaced roughness, sufficiently large for the skin friction to be independent of Reynolds number, a simple model is constructed of the flow near the surface. It consists of horseshoe eddies which wrap themselves round the individual excrescences and trail unsteadily downstream; the eddies are imagined to scour the surface and thereby to transport heat between the surface and the more vigorous flow in the neighbourhood of the roughness crests. Taken in conjunction with Reynolds analogy between temperature and velocity distributions in the fluid away from the surface, the model leads to an expression for the rate of heat transfer which contains a function of the roughness Reynolds number and the Prandtl number of the fluid whose detailed form is found by appeal to the limited experimental data available. An order-of-magnitude argument suggests that the functional form established empirically is consistent with the assumed model of the flow close to the surface.The object of the work is to establish a basis for the analysis of experimental data and for their extrapolation with respect to Reynolds number and Prandtl number.

scholarly journals Roughness effects in turbulent forced convection

2018 ◽  
Vol 861 ◽  
pp. 138-162 ◽  
Author(s):  
M. MacDonald ◽  
N. Hutchins ◽  
D. Chung
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Forced Convection ◽  
Temperature Difference ◽  
Skin Friction Coefficient ◽  
Stanton Number ◽  
Reynolds Analogy ◽  
Momentum And Heat Transfer

We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$, appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$, where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.

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.

Skin Friction Measurements of Transition in High Reynolds Number, Adverse Pressure Gradient Flow

2018 ◽  
Author(s):  
Brian M. Holley ◽  
Larry W. Hardin ◽  
Gregory Tillman ◽  
Ray-Sing Lin ◽  
Jongwook Joo
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Data Set ◽  
High Reynolds

A combined experimental and analytical modeling effort has been carried out to measure the skin friction response of the boundary layer in high Reynolds number adverse pressure gradient flow. The experiment was conducted in the United Technologies Research Center (UTRC) Acoustic Research Tunnel, an ultra-low freestream turbulence facility capable of laminar boundary layer research. Boundary layer computational fluid dynamics and stability modeling were used to provide pre-test predictions, as well as to aid in interpretation of measured results. Measurements were carried out at chord Reynolds numbers 2–3 × 106, with the model set at multiple incidence angles to establish a range of relevant leading edge pressure gradients. The combination of pressure gradient and flight Reynolds number testing on a thin airfoil has produced a unique data set relevant to propulsion system turbomachinery.

Skin Friction Measurements of Transition in High Reynolds Number, Adverse Pressure Gradient Flow

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Brian M. Holley ◽  
Larry W. Hardin ◽  
Gregory Tillman ◽  
Ray-Sing Lin ◽  
Jongwook Joo
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Data Set ◽  
High Reynolds

Abstract A combined experimental and analytical modeling effort has been carried out to measure the skin friction response of the boundary layer in high Reynolds number adverse pressure gradient flow. The experiment was conducted in the United Technologies Research Center (UTRC) Acoustic Research Tunnel, an ultra-low freestream turbulence facility capable of laminar boundary layer research. Boundary layer computational fluid dynamics and stability modeling were used to provide pre-test predictions, as well as to aid in interpretation of measured results. Measurements were carried out at chord Reynolds numbers 2–3 × 106, with the model set at multiple incidence angles to establish a range of relevant leading edge pressure gradients. The combination of pressure gradient and flight Reynolds number testing on a thin airfoil has produced a unique data set relevant to propulsion system turbomachinery.

Measurements in adverse-pressure-gradient turbulent boundary layers with a step change in surface roughness

1975 ◽  
Vol 70 (3) ◽  
pp. 573-593 ◽  
Author(s):  
W. H. Schofield
Keyword(s):  
Surface Roughness ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Step Change ◽  
Internal Layer ◽  
Mean Velocity ◽  
Law Of The Wall

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

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