The Effect of Element Thermal Conductivity on Turbulent Convective Heat Transfer From Rough Surfaces

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Stephen T. McClain ◽  
B. Keith Hodge ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Convective Heat Transfer ◽  
Rough Surfaces ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Experimental Measurements ◽  
Fin Efficiency ◽  
Roughness Elements

The discrete-element model for flows over rough surfaces considers the heat transferred from a rough surface to be the sum of the heat convected from the flat surface and the heat convected from the individual roughness elements to the fluid. In previous discrete-element model developments, heat transfer experiments were performed using metallic or high-thermal conductivity roughness elements. Many engineering applications, however, exhibit roughness with low thermal conductivities. In the present study, the discrete-element model is adapted to consider the effects of finite thermal conductivity of roughness elements on turbulent convective heat transfer. Initially, the boundary-layer equations are solved while the fin equation is simultaneously integrated so that the full conjugate heat transfer problem is solved. However, a simpler approach using a fin efficiency is also investigated. The results of the conjugate analysis and the simpler fin efficiency analysis are compared to experimental measurements for turbulent flows over ordered cone surfaces. Possibilities for extending the fin efficiency method to randomly rough surfaces and the experimental measurements required are discussed.

The Effect of Element Thermal Conductivity on Turbulent Convective Heat Transfer From Rough Surfaces

2009 ◽  
Author(s):  
Stephen T. McClain ◽  
B. Keith Hodge ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Convective Heat Transfer ◽  
Rough Surfaces ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Experimental Measurements ◽  
Fin Efficiency ◽  
Roughness Elements

The discrete-element model for flows over rough surfaces considers the heat transferred from a rough surface to be the sum of the heat convected from the flat surface and the heat convected from the individual roughness elements to the fluid. In previous discrete-element model development, heat transfer experiments were performed using metallic or high-thermal conductivity roughness elements. Many engineering applications, however, exhibit roughness with low thermal conductivities. In the present study, the discrete element model is adapted to consider the effects of finite thermal conductivity of roughness elements on turbulent convective heat transfer. Initially, the boundary-layer equations are solved while the fin equation is simultaneously integrated so that the full conjugate heat transfer problem is solved. However, a simpler approach using a fin-efficiency is also investigated. The results of the conjugate analysis and the simpler fin-efficiency analysis are compared to experimental measurements for turbulent flows over ordered cone surfaces. Possibilities for extending the fin-efficiency method to randomly-rough surfaces and the experimental measurements required are discussed.

A Comparison of Approximate Versus Exact Geometrical Representations of Roughness for CFD Calculations of cf and St

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
J. P. Bons ◽  
S. T. McClain ◽  
Z. J. Wang ◽  
X. Chi ◽  
T. I. Shih
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Rough Surface ◽  
Turbulence Model ◽  
Rough Surfaces ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Flat Part ◽  
Roughness Elements

Skin friction (cf) and heat transfer (St) predictions were made for a turbulent boundary layer over randomly rough surfaces at Reynolds number of 1×106. The rough surfaces are scaled models of actual gas turbine blade surfaces that have experienced degradation after service. Two different approximations are used to characterize the roughness in the computational model: the discrete element model and full 3D discretization of the surface. The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection on the flat part of the surface and the convection from each of the roughness elements. Correlations are used to model the roughness element drag and heat transfer, thus avoiding the complexity of gridding the irregular rough surface. The discrete element roughness representation was incorporated into a two-dimensional, finite difference boundary layer code with a mixing length turbulence model. The second prediction method employs a viscous adaptive Cartesian grid approach to fully resolve the three-dimensional roughness geometry. This significantly reduces the grid requirement compared to a structured grid. The flow prediction is made using a finite-volume Navier-Stokes solver capable of handling arbitrary grids with the Spalart-Allmaras (S‐A) turbulence model. Comparisons are made to experimentally measured values of cf and St for two unique roughness characterizations. The two methods predict cf to within ±8% and St within ±17%, the RANS code yielding slightly better agreement. In both cases, agreement with the experimental data is less favorable for the surface with larger roughness features. The RANS simulation requires a two to three order of magnitude increase in computational time compared to the DEM method and is not as readily adapted to a wide variety of roughness characterizations. The RANS simulation is capable of analyzing surfaces composed primarily of roughness valleys (rather than peaks), a feature that DEM does not have in its present formulation. Several basic assumptions employed by the discrete element model are evaluated using the 3D RANS flow predictions, namely: establishment of the midheight for application of the smooth wall boundary condition; cD and Nu relations employed for roughness elements; and flow three dimensionality over and around roughness elements.

A Comparison of Approximate vs. Exact Geometrical Representations of Roughness for CFD Calculations of CF and ST

2005 ◽  
Author(s):  
J. P. Bons ◽  
S. T. McClain ◽  
Z. J. Wang ◽  
X. Chi ◽  
T. I. Shih
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Rough Surface ◽  
Turbulence Model ◽  
Rough Surfaces ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Flat Part ◽  
Roughness Elements

Skin friction (cf) and heat transfer (St) predictions were made for a turbulent boundary layer over randomly rough surfaces at Reynolds number of 1 × 106. The rough surfaces are scaled models of actual gas turbine blade surfaces that have experienced degradation after service. Two different approximations are used to characterize the roughness in the computational model: the discrete element model and full 3-D discretization of the surface. The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection on the flat part of the surface and the convection from each of the roughness elements. Correlations are used to model the roughness element drag and heat transfer thus avoiding the complexity of gridding the irregular rough surface. The discrete element roughness representation was incorporated into a two-dimensional, finite difference boundary layer code with a mixing length turbulence model. The second prediction method employs a viscous adaptive Cartesian grid approach to fully resolve the three-dimensional roughness geometry. This significantly reduces the grid requirement compared to a structured grid. The flow prediction is made using a finite-volume Navier-Stokes solver capable of handling arbitrary grids with the Spalart-Allmaras (S-A) turbulence model. Comparisons are made to experimentally measured values of cf and St for two unique roughness characterizations. The two methods predict cf to within ±8% and St within ±17%, the RANS code yielding slightly better agreement. In both cases, agreement with the experimental data is less favorable for the surface with larger roughness features. The RANS simulation requires a two to three order of magnitude increase in computational time compared to the DEM method and is not as readily adapted to a wide variety of roughness characterizations. The RANS simulation is capable of analyzing surfaces composed primarily of roughness valleys (rather than peaks), a feature that DEM does not have in its present formulation. Several basic assumptions employed by the discrete element model are evaluated using the 3D RANS flow predictions, namely: establishment of the mid-height for application of the smooth wall boundary condition, cD and Nu relations employed for roughness elements, and flow three-dimensionality over and around roughness elements.

Reduced Rough-Surface Parametrization for Use With the Discrete-Element Model

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Stephen T. McClain ◽  
Jason M. Brown
Keyword(s):  
Heat Transfer ◽  
Rough Surface ◽  
Surface Characterization ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Diameter Distribution ◽  
Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly rough surface. The requirement for a roughness-element diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

Reduced Rough-Surface Parameterization for Use With the Discrete-Element Model

2007 ◽  
Author(s):  
Stephen T. McClain ◽  
Jason M. Brown
Keyword(s):  
Heat Transfer ◽  
Rough Surface ◽  
Surface Characterization ◽  
Rough Surfaces ◽  
Roughness Element ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Diameter Distribution ◽  
Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly-rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly-rough surface. The requirement for a roughness element-diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly-rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly-rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

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.

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