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.

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 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.

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Diameter Ratio ◽  
Wall Heat Transfer ◽  
Reattachment Point ◽  
Transfer Rates ◽  
Pipe Flows ◽  
Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

Experimental Investigation of Local Heat Transfer Distribution on Smooth and Roughened Surfaces Under an Array of Angled Impinging Jets

2001 ◽  
Author(s):  
Lamyaa A. El-Gabry ◽  
Deborah A. Kaminski
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Flow ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Local Heat ◽  
Impinging Jets ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Roughened Surface

Abstract Measurements of the local heat transfer distribution on smooth and roughened surfaces under an array of angled impinging jets are presented. The test rig is designed to simulate impingement with cross-flow in one direction which is a common method for cooling gas turbine components such as the combustion liner. Jet angle is varied between 30, 60, and 90 degrees as measured from the impingement surface, which is either smooth or randomly roughened. Liquid crystal video thermography is used to capture surface temperature data at five different jet Reynolds numbers ranging between 15,000 and 35,000. The effect of jet angle, Reynolds number, gap, and surface roughness on heat transfer efficiency and pressure loss is determined along with the various interactions among these parameters. Peak heat transfer coefficients for the range of Reynolds number from 15,000 to 35,000 are highest for orthogonal jets impinging on roughened surface; peak Nu values for this configuration ranged from 88 to 165 depending on Reynolds number. The ratio of peak to average Nu is lowest for 30-degree jets impinging on roughened surfaces. It is often desirable to minimize this ratio in order to decrease thermal gradients, which could lead to thermal fatigue. High thermal stress can significantly reduce the useful life of engineering components and machinery. Peak heat transfer coefficients decay in the cross-flow direction by close to 24% over a dimensionless length of 20. The decrease of spanwise average Nu in the crossflow direction is lowest for the case of 30-degree jets impinging on a roughened surface where the decrease was less than 3%. The decrease is greatest for 30-degree jet impingement on a smooth surface where the stagnation point Nu decreased by more than 23% for some Reynolds numbers.

Effects of a Realistically Rough Surface on Vane Heat Transfer Including the Influence of Turbulence Condition and Reynolds Number

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
E. L. Erickson ◽  
F. E. Ames ◽  
J. P. Bons
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rough Surface ◽  
Reynolds Numbers ◽  
Suction Surface ◽  
Average Roughness ◽  
Surface Distribution ◽  
Reynolds Analogy ◽  
Pressure Surface ◽  
Early Transition

Heat transfer distributions are experimentally acquired and reported for a vane with both a smooth and a realistically rough surface. Surface heat transfer is investigated over a range of turbulence levels (low (0.7%), grid (8.5%), aerocombustor (13.5%), and aerocombustor with decay (9.5%)) and a range of chord Reynolds numbers (ReC=500,000, 1,000,000, and 2,000,000). The realistically rough surface distribution was generated by Brigham Young University’s accelerated deposition facility. The surface is intended to represent a TBC surface that has accumulated 7500 h of operation with particulate deposition due to a mainstream concentration of 0.02 ppmw. The realistically rough surface was scaled by 11 times for consistency with the vane geometry and cast using a high thermal conductivity epoxy (k=2.1 W/m/K) to comply with the vane geometry. The surface was applied over the foil heater covering the vane pressure surface and about 10% of the suction surface. The 958×573 roughness array generated by Brigham Young on a 9.5×5.7 mm2 region was averaged to a 320×191 array for fabrication. The calculated surface roughness parameters of this scaled and averaged array included the maximum roughness, Rt=1.99 mm, the average roughness, Ra=0.25 mm, and the average forward facing angle, αf=3.974 deg. The peak to valley roughness, Rz, was determined to be 0.784 mm. The sand grain roughness of the surface (kS=0.466 mm) was estimated using a correlation offered by Bons (2005, “A Critical Assessment of Reynolds Analogy for Turbine Flows,” ASME J. Turbomach., 127, pp. 472–485). Based on estimates of skin friction coefficient using a turbulence correlation with the vane chord Reynolds numbers representative values for the surface’s roughness Reynolds number are 23, 43, and 80 for the three exit condition Reynolds numbers tested. Smooth vane heat transfer distributions exhibited significant laminar region augmentation with the elevated turbulence levels. Turbulence also caused early transition on the pressure surface for the higher Reynolds numbers. The rough surface had no significant effect on heat transfer in the laminar regions but caused early transition on the pressure surface in every case.

scholarly journals Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 13-23
Author(s):  
Zia Ullah ◽  
Muammad Ashraf ◽  
Saqib Zia ◽  
Ishtiaq Ali
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Surface Temperature ◽  
Skin Friction ◽  
Slip Velocity ◽  
Free Stream ◽  
Slip Flow ◽  
Stream Velocity ◽  
Velocity Oscillation

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

Jet-to-Plate Distance Effect on Heat Transfer From a Flat Plate to an Impinging Jet at Various Reynolds Numbers

2012 ◽  
Author(s):  
Patricia Streufert ◽  
Terry X. Yan ◽  
Mahdi G. Baygloo
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Flat Plate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Air Jet ◽  
Plate Distance

Local turbulent convective heat transfer from a flat plate to a circular impinging air jet is numerically investigated. The jet-to-plate distance (L/D) effect on local heat transfer is the main focus of this study. The eddy viscosity V2F turbulence model is used with a nonuniform structured mesh. Reynolds-Averaged Navier-Stokes equations (RANS) and the energy equation are solved for axisymmetric, three-dimensional flow. The numerical solutions obtained are compared with published experimental data. Four jet-to-plate distances, (L/D = 2, 4, 6 and 10) and seven Reynolds numbers (Re = 7,000, 15,000, 23,000, 50,000, 70,000, 100,000 and 120,000) were parametrically studied. Local and average heat transfer results are analyzed and correlated with Reynolds number and the jet-to-plate distance. Results show that the numerical solutions matched experimental data best at low jet-to-plate distances and lower Reynolds numbers, decreasing in ability to accurately predict the heat transfer as jet-to-plate distance and Reynolds number was increased.

Heat transfer from a circular cylinder by acoustic streaming

1967 ◽  
Vol 30 (2) ◽  
pp. 337-355 ◽  
Author(s):  
Peter D. Richardson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Convection ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Acoustic Streaming ◽  
Mean Flow ◽  
Wide Range ◽  
Transverse Oscillations ◽  
Streaming Flow

An analysis is described for convection from a circular cylinder subjected to transverse oscillations relative to the fluid in which it is immersed. The analysis is based upon use of the acoustic streaming flow field. It is assumed that the frequency involved is sufficiently small that the acoustic wavelength in the fluid is much larger than the cylinder diameter, and that there is no externally imposed mean flow across or along the cylinder. Solutions are presented which are appropriate for a wide range of Prandtl number, and the cases of small and of large streaming Reynolds number are distinguished. The analysis compares favourably with experiments when the influence of natural convection is small.

Validation and Development of DNS Database for Low Prandtl Numbers in Rod Bundle

2019 ◽  
Author(s):  
Jonathan K. Lai ◽  
Elia Merzari ◽  
Yassin A. Hassan ◽  
Aleksandr Obabko
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Heat Transfer Characteristics ◽  
Reynolds Analogy ◽  
Transfer Characteristics ◽  
Rod Bundle ◽  
High Thermal Diffusivity ◽  
Prandtl Numbers

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Prt) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Prt. More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

Convective Heat Transfer From Heated Extended Surfaces With a Confined Slot Jet Impingement

2004 ◽  
Author(s):  
L. K. Liu ◽  
M. C. Wu ◽  
C. J. Fang ◽  
Y. H. Hung
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Mixed Convection ◽  
Average Nusselt Number ◽  
Jet Impingement ◽  
Separation Distance ◽  
Nusselt Numbers ◽  
Transfer Behavior ◽  
Extended Surfaces

A series of experimental investigations with stringent measurement methods on the studies related to mixed convection from the horizontally confined extended surfaces with a slot jet impingement have been successfully conducted. The relevant parameters influencing mixed convection performance due to jet impingement and buoyancy include the Grashof number, ratio of jet separation distance to nozzle width, ratio of extended surfaces height to nozzle width and jet Reynolds number. The range of these parameters studied are Grs = 3.77 × 105 – 1.84 × 106, H/W = 1–10, Hs/W = 0.74–3.40 and Re = 63–1383. In the study, the heat transfer behavior on the extended surfaces with confined slot jet impingement such as the temperature distribution, local and average Nusselt numbers on the extended surfaces has been systematically explored. The results manifest that the effect of steady-state Grashof number on heat transfer behavior such as stagnation, local and average Nusselt number is not significant; while the heat transfer performance increases with decreasing jet separation distance or with increasing extended surface height and jet Reynolds number. Besides, two new correlations of local and average Nusselt numbers in terms of H/W, Hs/W and Re are proposed for the cases of extended surfaces. A satisfactory agreement is achieved between the results predicted by these correlations and the experimental data. Finally, a complete composite correlation of steady-state average Nusselt number for mixed convection due to jet impingement and buoyancy is proposed. The comparison of the predictions evaluated by this correlation with all the present experimental data is made. The maximum and average deviations of the predictions from the experimental data are 7.46% and 2.87%, respectively.

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