Dr. Phil Ligrani:    p_ligrani@msn.com

• Heat transfer and flow characteristics
• Fundamental and applied investigations
• Heat transfer augmentation with minimal pressure drop penalties
• 3-D, unsteady, complex, elliptic flow fields
• Numerous applications including internal cooling of turbine airfoils used in gas turbine engines, heat exchangers, electronics cooling, biomedical devices
• Experimental results and numerical predictions of heat transfer and flow structure

Schematic diagrams of the experimental apparatus used for flow visualization and measurements of flow structure, the dimpled test surface, and the geometry details of deep, medium, and shallow dimples.

Flow structure over dimple surfaces with three different depths in a rectangular channel is experimentally studied for Reynolds number based on channel height from 2,100 to 20,000. The ratios of dimple depth to dimple print diameter d/D are 0.1, 0.2 and 0.3, respectively.

Flow Visualizations show substantial time varying behaviors of vortex pairs produced by dimples. For all three dimple depths, classic structure of the flow is observed: there is a primary vortex pair shedding at the central part of the dimple, and there are edge vortex pairs which advect downstream the edge of the dimples. Instantaneous flow visualization images show that the central primary vortex pairs are more convoluted, distorted, and the edge vortex seems to be bigger as the dimple depth becomes to be larger.

Surveys of time-averaged distributions of different components of local velocity, local total pressure, local static pressure, local streamwies vorticity provide consistent evidence of the existence and location of the primary vortex pair. There are larger deficits of total pressure and streamwise velocity with deeper dimples. As the dimple depth increases, higher magnitudes of streamwise vorticity, vortex circulation and Reynolds normal stress are obtained, which implies stronger vortices and increasing turbulence transport associated with the increase of the depth of dimples

Ensemble-averaged power spectral density profiles of longitudinal velocity fluctuations present additional information on the unsteadiness associated with the vortices shed from the dimples. Identified from these PSD profiles, primary vortex shedding frequencies ranges from 7 to 9 Hz, and edge vortex pair oscillation frequencies range from 5 to 7 Hz for Reynolds numbers based on channel height from 2,100 to 21,000.

Power Spectral Denstiy (PSD) Profiles

Ensemble-averaged power spectral density profiles of longitudinal velocity just downstream of the downstream edge of dimples in the 7 th row, for d/D=0.3, Re H =10,000, H/D=1.

Vortex Shedding Frequencies

Non-dimensional vortex shedding frequencies as dependent upon the Reynolds number for non-dimensional dimple depths d/D of 0.1, 0.2 and 0.3 at X/H=6.27, H=0.05.
(a) Z/H=0.0.
(b) Z/H=0.5.

Local Nusselt number ratio data from a channel with dimples and heating on one channel surface, for d/D=0.2, Re H =20,000, and H/D=1.

Local Nusselt number ratios, measured on a dimpled surface are shown in the above figure. These data are obtained using a dimple print diameter of 5.08 cm, a channel height of 5.08 cm, and a dimple depth of 1.016 cm, giving d/D=0.2. Here, these data are obtained with dimples placed only on the bottom surface of the channel. Heating is employed with a constant flux only on the bottom wall (with unheated side and top walls). Heat transfer coefficients and heat flux values (used to determine Nusselt numbers) are based on flat projected area.

The bulk flow direction in the above figure is from left to right in the direction of increasing X/D. Each d/D=0.2 dimple is located in the vicinity of each circular Nusselt number distribution. Notice that local Nusselt number ratio values are lowest in the upstream halves of the dimples. Each of these is positioned beneath a region of re-circulating flow, where advection velocities in the flow located adjacent to the surface are very low. Nusselt number ratios then increase progressively with streamwise distance along the dimpled surface. Values then become highest near the diagonal and downstream edges of the dimples, and on the flat surfaces just downstream of these locations. Here, local Nusselt number ratio augmentations are greater than 2.2, and are as high as 3.3 because of reattachment of the shear layer which forms across the top of each dimple, and because of the multiple vortex pairs which are periodically shed from each dimple. For the experimental conditions of these data, one relatively large vortex pair is shed from the central part of each dimple, and two smaller vortex pairs are shed from the spanwise edges of each dimple. These edge formed vortex pairs then strengthen as they advect downstream next to the edges of other dimples. This occurs because of the staggered arrangement of the dimples on the test surface, which causes each “edge” vortex pair to be located first on the right edge of a dimple, then on the left edge of another dimple, and so on. The result is interconnected regions of high local Nusselt number ratios, located diagonally between adjacent dimples, as shown in the above figure.

Another result is a highly elliptic flow field in which flow events in one dimple communicate with flow events in other dimples. Similar communications between different flow events are observed in other types of flows with vortex structures and high levels of unsteadiness that enhance mixing. For example, channels interrupted by quadrangular elements and channels with rectangular grooves also produce periodic, unsteady vortex ejections and interactions, as well as self-sustained flow oscillations, which also result in enhanced surface heat transfer levels. Similar events occur in the present dimpled channel. Here, local Nusselt numbers are augmented beneath the vortex pairs because of the action of their secondary flows in advecting heat over different length scales, and in spreading shear gradients over larger flow volumes. This latter effect increases turbulence production, and three-dimensional turbulence transport.

RECENT PUBLICATIONS:

• Local Heat Transfer and Flow Structure On and Above a Dimpled Surface in a Channel (G. I. Mahmood, M. L. Hill, D. L. Nelson, P. M. Ligrani, H.-K. Moon, and B. Glezer), ASME Transactions-Journal of Turbomachinery, Vol. 123, No. 1, pp. 115-123, January 2001.
• Heat Transfer in a Channel With Dimples and Protrusions on Opposite Walls, (G. I. Mahmood, M. Z. Sabbagh, and P. M. Ligrani), AIAA Journal of Thermophysics and Heat Transfer, Vol. 15, No. 3, pp. 275-283, July-September 2001.
• Flow Structure Due to Dimple Depressions on a Channel Surface, (P. M. Ligrani, J. L. Harrison, G. I. Mahmood, and M. L. Hill), Physics of Fluids, Vol. 13, No. 11, pp. 3442-3451, November 2001.
• Flow Structure and Local Nusselt Number Variations in a Channel With Dimples and Protrusions on Opposite Walls, (P. M. Ligrani, G. I. Mahmood, J. L. Harrison, C. M. Clayton, and D. L. Nelson), International Journal of Heat and Mass Transfer, Vol. 44, No. 23, pp. 4413-4425, December 2001.
• Heat Transfer in a Dimpled Channel:  Combined Influences of Aspect Ratio, Temperature Ratio, Reynolds Number, and Flow Structure, (G. I. Mahmood, and P. M. Ligrani), International Journal of Heat and Mass Transfer, Vol. 45, No. 10, pp. 2011-2020, May 2002.
• Numerical Simulation of Flow and Heat Transfer Inside a Micro-Channel With One Dimpled Surface, (X. J. Wei, Y. K. Joshi, P. M. Ligrani), Paper IMECE2002-21633, 2002 International Mechanical Engineering Congress and Exhibition (IMECE), New Orleans, Louisiana, November 17-22, 2002.
• Nusselt Number Behavior on Deep Dimpled Surfaces Within a Channel, (N. K. Burgess, M. M. Oliveira, and P. M. Ligrani), ASME Transactions-Journal of Heat Transfer, Vol. 125, No. 1, pp. 11-18, February 2003.
• Discussion of: “Heat Transfer in Rotating Rectangular Cooling Channels (AR=4) With Dimples“, (P. M. Ligrani), ASME Transactions-Journal of Turbomachinery, Vol. 125, No. 3, p. 564, July 2003.
• Numerical Predictions of Flow Structure Above a Dimpled Surface in a Channel, (J. Park, P. R. Desam, and P. M. Ligrani), Numerical Heat Transfer, Part A: Applications, Volume 45, Number 1, pp. 1-20, January 2004.
• Numerical Predictions of Flow Structure and Local Nusselt Number Ratios Along and Above Dimpled Surfaces with Different Dimple Depths in a Channel, (S. Y. Won, and P. M. Ligrani), Numerical Heat Transfer, Part A: Applications, Vol. 46, No. 6, pp. 549-570, October 2004.
• Numerical Predictions of Heat Transfer and Fluid Flow Characteristics For Seven Different Dimpled Surfaces in a Channel, (J. Park, and P. M. Ligrani), Numerical Heat Transfer, Part A: Applications, Vol. 47, No. 3, pp. 209-232, February 2005.
• Nusselt Numbers and Flow Structure On and Above a Shallow Dimpled Surface Within a Channel Including Effects of Inlet Turbulence Intensity Level, (P. M. Ligrani, N. K. Burgess, and S. Y. Won), ASME Transactions-Journal of Turbomachinery, Vol. 127, No. 2, pp. 321-330, April 2005.
• Comparisons of Flow Structure Above Dimpled Surfaces With Different 2004.Dimple Depths in a Channel, (S. Y. Won, Q. Zhang, and P. M. Ligrani), Physics of Fluids, Vol. 17, No. 4, pp. 045105-1 to 045105-9, April 2005.
• Effects of Dimple Depth on Channel Nusselt Numbers and Friction Factors, (N. K. Burgess, and P. M. Ligrani), ASME Transactions-Journal of Heat Transfer, Special Issue – Gas Turbine Heat Transfer, Vol. 127, No. 8, pp. 839-847, August 2005.
• Effects of Exterior Surface Dimples on Heat Transfer and Friction Factors for a Cross-Flow Heat Exchanger, (L. D. Sherrow, P. M. Ligrani, Y. Chudnovsky, and A. Kozlov), Journal of Enhanced Heat Transfer, Vol. 13, No. 1, pp. 1-16, 2006.
• Dimple Array Effects on Turbulent Heat Transfer and Flow Structure (P. M. Ligrani), Turbulence, Heat and Mass Transfer 5 (Editors: K. Hanjalic, Y. Nagano, S. Jakirlic), Begell House Inc., New York, Wallingford (UK), pp. 59-78, 2006.
• Numerical Simulation of Laminar Flow and Heat Transfer Inside a Micro-Channel With One Dimpled Surface, (X. J. Wei, Y. K. Joshi, P. M. Ligrani), ASME Transactions-Journal of Electronic Packaging, Vol. 129, No. 1, pp. 63-70, March 2007.
• Numerical Predictions of Heat Transfer and Flow Characteristics of Heat Sinks With Ribbed and Dimpled Surfaces in Laminar Flow (H. Wee, Q. Zhang, P. M. Ligrani, and S. Narasimhan), Numerical Heat Transfer, Part A: Applications, Vol. 53, No. 11, pp. 1156-1175, November 2008.
• Thermal Performance of Dimpled Surfaces in Laminar Flows (N. Xiao, Q. Zhang, P. M. Ligrani, and R. Mongia), International Journal of Heat and Mass Transfer, Vol. 52, Nos. 7-8, pp. 2009-2017, March 2009.
• Numerical Predictions of Heat Transfer and Flow Structure in a Square Cross-Section Channel With Various Non-Spherical Indentation Dimples (G. Xie, J. Liu, P. M. Ligrani, and W. Zhang), Numerical Heat Transfer, Part A: Applications, Vol. 64, No. 3, pp. 187-215, August 2013.
• Numerical Analysis of Flow Structure and Heat Transfer Characteristics in Square Channels With Different Internal-Protruded Dimple Geometrics (G. Xie, J. Liu, P. M. Ligrani, and W. Zhang), International Journal of Heat and Mass Transfer, Vol. 67, pp. 81-97, December 2013.
• Numerical Analysis of Flow Structure and Heat Transfer Characteristics in Dimpled Channels with Secondary Protrusions (Y. Xie, Z. Shen, D. Zhang, and P. M. Ligrani), ASME Transactions-Journal of Heat Transfer, Vol. 138, No. 3, pp. 031901-1 to 031901-6, March 2016.