The Influence of Element Thermal Conductivity, Shape, and Density on Heat Transfer in a Rough Wall Turbulent Boundary Layer With Strong Pressure Gradients

2020 ◽  
Author(s):  
Christoph Gramespacher ◽  
Holger Albiez ◽  
Mattias Stripf ◽  
Hans-Jörg Bauer
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Reynolds Numbers ◽  
Formation Mechanisms ◽  
Pressure Gradients ◽  
Pressure Distributions ◽  
Roughness Elements ◽  
The Difference ◽  
Study Heat Transfer

Abstract Formation mechanisms for turbine roughness are manifold, including erosion, corrosion, deposition, and spallation or more recently additive manufacturing processes. Consequently, the resulting surfaces differ remarkably not only in roughness shape, height, and density, but also in element thermal conductivity. Because the roughness elements extend into the boundary layer, their temperature distribution has a direct influence on the thermal boundary layer and thus on the resulting convective heat transfer. In the current study, heat transfer distributions along a flat plate with more than 20 deterministic rough surface topographies that differ in element eccentricity, height and density are measured. For each surface roughness, measurements are conducted using two different element thermal conductivities (0.2 W/(mK) and 30 W/(mK)), two pressure distributions, four Reynolds numbers between 3 × 105 and 7.5 × 105 and various inlet turbulence intensities in the range of 1.5% to 8%. The pressure distributions resemble a typical suction and pressure side, respectively. Results show a heat transfer increase of up to 60% for the high thermal conductivity surfaces and up to 50% for the low conductivity ones. While heat transfer on the high conductivity surfaces is always higher than on the low conductivity ones, the difference becomes smaller with decreasing element density.

The Influence of Element Thermal Conductivity, Shape, and Density on Heat Transfer in a Rough Wall Turbulent Boundary Layer With Strong Pressure Gradients

2021 ◽  
Vol 143 (8) ◽  
Author(s):  
Christoph Gramespacher ◽  
Holger Albiez ◽  
Matthias Stripf ◽  
Hans-Jörg Bauer
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Reynolds Numbers ◽  
Formation Mechanisms ◽  
Pressure Gradients ◽  
Pressure Distributions ◽  
Roughness Elements ◽  
The Difference ◽  
Study Heat Transfer

Abstract Formation mechanisms for turbine roughness are manifold, including erosion, corrosion, deposition, and spallation or more recently additive manufacturing processes. Consequently, the resulting surfaces differ remarkably not only in roughness shape, height, and density but also in element thermal conductivity. Because the roughness elements extend into the boundary layer, their temperature distribution has a direct influence on the thermal boundary layer and thus on the resulting convective heat transfer. In the current study, heat transfer distributions along a flat plate with more than 20 deterministic rough surface topographies that differ in element eccentricity, height and density are measured. For each surface roughness, measurements are conducted using two different element thermal conductivities (0.2 W/(mK) and 30 W/(mK)), two pressure distributions, four Reynolds numbers between 3 × 105 and 7.5 × 105 and various inlet turbulence intensities in the range of 1.5 % to 8 %. The pressure distributions resemble a typical suction and pressure side, respectively. Results show a heat transfer increase of up to 60 % for the high thermal conductivity surfaces and up to 50 % for the low conductivity ones. While heat transfer on the high conductivity surfaces is always higher than on the low conductivity ones, the difference becomes smaller with decreasing element density.

Turbulent Convection From Deterministic Roughness Distributions With Varying Thermal Conductivities

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Steven R. Mart ◽  
Stephen T. McClain ◽  
Lesley M. Wright
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Wind Tunnel ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Infrared Camera ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Roughness Elements ◽  
Thermal Conductivities

Many flows of engineering interest are bounded by surfaces that exhibit roughness with thermal conductivities much lower than common metals and alloys. Depending on the local roughness element convection coefficients, the low thermal conductivities of the roughness elements may create situations where temperature changes along the heights of the elements are important and must be considered in predicting the overall surface convection coefficient. The discrete-element model (DEM) for flows over rough surfaces was recently adapted to include the effects of internal conduction along the heights of ordered roughness elements. While the adapted DEM provided encouraging agreement with the available data, more data are required to validate the model. To further investigate the effects of roughness element thermal conductivity on convective heat transfer and to acquire more experimental data for DEM validation, four wind tunnel test plates were made. The test plates were constructed using Plexiglas and Mylar film with a gold deposition layer creating a constant flux boundary condition with steady state wind tunnel measurements. The four test plates were constructed with hexagonal distributions of hemispheres or cones made of either aluminum or ABS plastic. The plates with hemispherical elements had element diameters of 9.53 mm and a spacing-to-diameter ratio of 2.099. The plates with conical elements had base element diameters of 9.53 mm and a spacing-to-base-diameter ratio of 1.574. An infrared camera was used to measure the temperature of the heated plates in the Baylor Subsonic Wind Tunnel for free stream velocities ranging from 2.5 m/s to 35 m/s (resulting in Reynolds number values ranging from 90,000 to 1,400,000 based on the distance from the knife-edge to the center of the infrared camera image) in turbulent flow. At lower Reynolds numbers, the thermal conductivity of the roughness elements is a primary factor in determining the heat transfer enhancement of roughness distributions. At the higher Reynolds numbers investigated, the hemispherical distribution, which contained more sparsely spaced elements, did not exhibit a statistically significant difference in enhancement for the different thermal conductivity elements used. The results of the study indicate that the packing density of the elements and the enhancement on the floor of the roughness distribution compete with the roughness element thermal conductivity in determining the overall convection enhancement of rough surfaces.

Turbulent Convection From Deterministic Roughness Distributions With Varying Thermal Conductivities

2011 ◽  
Author(s):  
Steven R. Mart ◽  
Stephen T. McClain ◽  
Lesley M. Wright
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Wind Tunnel ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Infrared Camera ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Roughness Elements ◽  
Thermal Conductivities

Many flows of engineering interest are bounded by surfaces that exhibit roughness with thermal conductivities much lower than common metals and alloys. Depending on the local roughness element convection coefficients, the low thermal conductivities of the roughness elements may create situations where temperature changes along the heights of the elements are important and must be considered in predicting the overall surface convection coefficient. The discrete-element model (DEM) for flows over rough surfaces was recently adapted to include the effects of internal conduction along the heights of ordered roughness elements. While the adapted DEM provided encouraging agreement with the available data, more data are required to validate the model. To further investigate the effects of roughness element thermal conductivity on convective heat transfer and to acquire more experimental data for DEM validation, four wind tunnel test plates were made. The test plates were constructed using Plexiglas and Mylar film with a gold deposition layer creating a constant flux boundary condition with steady state wind tunnel measurements. The four test plates were constructed with hexagonal distributions of hemispheres or cones made of either aluminum or ABS plastic. The plates with hemispherical elements had element diameters of 9.53 mm and a spacing-to-diameter ratio of 2.099. The plates with conical elements had base element diameters of 9.53 mm and a spacing-to-base-diameter ratio of 1.574. An infrared camera was used to measure the temperature of the heated plates in the Baylor Subsonic Wind Tunnel for free stream velocities ranging from 2.5 m/s to 35 m/s (resulting in Reynolds number values ranging from 90,000 to 1,400,000 based on the distance from the knife-edge to the center of the infrared camera image) in turbulent flow. At lower Reynolds numbers, the thermal conductivity of the roughness elements is a primary factor in determining the heat transfer enhancement of roughness distributions. At the higher Reynolds numbers investigated, the hemispherical distribution, which contained more sparsely spaced elements, did not exhibit a statistically significant difference in enhancement for the different thermal conductivity elements used. The results of the study indicate that the packing density of the elements and the enhancement on the floor of the roughness distribution compete with the roughness element thermal conductivity in determining the overall convection enhancement of rough surfaces.

scholarly journals ON CORRECTION TO TEMPERATURE FIELD DUE TO VARIABLE THERMAL CONDUCTIVITY IN CASE OF BOUNDARY LAYER FLOW PAST A MOVING CYLINDER WITH SUCTION

2014 ◽  
Vol 44 (4) ◽  
pp. 351-354
Author(s):  
R. R. RANGI ◽  
N. AHMAD
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Viscous Incompressible Fluid ◽  
Liquid Metals ◽  
Variable Thermal Conductivity ◽  
Moving Cylinder ◽  
Layer Flow ◽  
Study Heat Transfer

The boundary layer flow of viscous incompressible fluid over a moving cylinder with suction has been considered to study heat transfer with variable thermal conductivity. The heat transfer is affected by thermal conductivity for the liquid metals within 0ºF to 400ºF range. In this case, we observe that the transfer of heat behaves differently in two different regions: 0  1 and  >1. Hence, we solve the two boundary value problems to draw out recommendations. The results have been discussed graphically.

Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface

2015 ◽  
Vol 93 (7) ◽  
pp. 725-733 ◽  
Author(s):  
M. Ghalambaz ◽  
E. Izadpanahi ◽  
A. Noghrehabadi ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Transfer Enhancement ◽  
Base Fluid ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Enhancement Ratio ◽  
Transfer Enhancement

The boundary layer heat and mass transfer of nanofluids over an isothermal stretching sheet is analyzed using a drift-flux model. The relative slip velocity between the nanoparticles and the base fluid is taken into account. The nanoparticles’ volume fractions at the surface of the sheet are considered to be adjusted passively. The thermal conductivity and the dynamic viscosity of the nanofluid are considered as functions of the local volume fraction of the nanoparticles. A non-dimensional parameter, heat transfer enhancement ratio, is introduced, which shows the alteration of the thermal convective coefficient of the nanofluid compared to the base fluid. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using the fourth-order Runge–Kutta and Newton–Raphson methods along with the shooting technique. The effects of six non-dimensional parameters, namely, the Prandtl number of the base fluid Prbf, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, variable thermal conductivity parameter Nc and the variable viscosity parameter Nv, on the velocity, temperature, and concentration profiles as well as the reduced Nusselt number and the enhancement ratio are investigated. Finally, case studies for Al2O3 and Cu nanoparticles dispersed in water are performed. It is found that increases in the ambient values of the nanoparticles volume fraction cause decreases in both the dimensionless shear stress f″(0) and the reduced Nusselt number Nur. Furthermore, an augmentation of the ambient value of the volume fraction of nanoparticles results in an increase the heat transfer enhancement ratio hnf/hbf. Therefore, using nanoparticles produces heat transfer enhancement from the sheet.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

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.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

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