Research Papers: Techniques and Procedures

The Design and Validation of a Thermal Boundary Layer Wall Plate

[+] Author and Article Information
Drummond Biles

Department of Mechanical Engineering,
University of New Hampshire,
Durham, NH 03824
e-mail: dep42@wildcats.unh.edu

Alireza Ebadi

Department of Mechanical Engineering,
University of New Hampshire,
Durham NH 03824
e-mail: Alireza.Ebadi@unh.edu

Michael P. Allard

Department of Mechanical Engineering,
University of New Hampshire,
Durham, NH 03824
e-mail: mpw3@wildcats.unh.edu

Christopher M. White

Department of Mechanical Engineering,
University of New Hampshire,
Durham, NH 03824
e-mail: chris.white@unh.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 14, 2018; final manuscript received May 9, 2019; published online June 7, 2019. Assoc. Editor: Devesh Ranjan.

J. Fluids Eng 141(12), 121403 (Jun 07, 2019) (10 pages) Paper No: FE-18-1621; doi: 10.1115/1.4043773 History: Received September 14, 2018; Revised May 09, 2019

A feedback controlled thermal wall plate designed to investigate thermal boundary layer flows is described and validated. The unique capabilities of the design are the ability to modify the thermal boundary conditions in a variety of ways or to hold the wall-temperature fixed even when the flow above the wall is unsteady and strongly three-dimensional. These capabilities allow for the generation and study of thermal transport in nonequilibrium boundary layer flows driven by different perturbations and of varying complexity. The thermal wall plate and the experimental facility in which the thermal wall plate is installed are first described. The wall-plate is then validated in a zero-pressure-gradient (ZPG) boundary layer flow for conditions of a uniform wall temperature and a temperature step. It is then shown that the wall temperature can be held constant even when a hemisphere body is placed on the wall that produces large localized variations in the convective heat transfer coefficient. Last, since the thermal wall plate is intended to support the study of thermal transport in a variety of nonequilibrium boundary layer flow, several possible experimental configurations are presented and described.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Blasius, H. , 1908, “ Grenzschichten in Flüssig keiten mit kleiner Reibung,” Z. Math. Phys., 56, p. 37.
Kays, W. M. , and Crawford, M. E. , 1980, Convective Heat and Mass Transfer, 2nd ed., McGraw-Hill, New York.
Fox, R. W. , McDonald, A. T. , and Pritchard, P. J. , 2012, Introduction to Fluid Mechanics, 8th ed., Wiley, Hoboken, NJ.
Clauser, F. H. , 1956, “ The Turbulent Boundary Layer,” Adv. Appl. Mech., 4, pp. 1–51. [CrossRef]
Klewicki, J. C. , 2010, “ Reynolds Number Dependence, Scaling, and Dynamics of Turbulent Boundary Layers,” ASME J. Fluids Eng., 132(9), p. 094001. [CrossRef]
Sreenivasan, K. , and Antonia, R. , 1997, “ The Phenomenology of Small-Scale Turbulence,” Annu. Rev. Fluid Mech., 29(1), pp. 435–472. [CrossRef]
Sreenivasan, K. R. , 1999, “ Fluid Turbulence,” Rev. Mod. Phys., 71(2), pp. 383–395. [CrossRef]
Jimenez, J. , 2012, “ Cascades in Wall-Bounded Turbulence,” Annu. Rev. Fluid Mech., 44, pp. 27–45. [CrossRef]
Hara, T. , Ohya, Y. , Uchida, T. , and Ohba, R. , 2009, “ Wind-Tunnel and Numerical Simulations of the Coastal Thermal Internal Boundary Layer,” Boundary-Layer Meteorol., 130(3), pp. 365–381. [CrossRef]
Townsend, A. , 1957, “ The Structure of Turbulent Shear Flow,” The Mathematical Gazette, 41(337), p. 235.
Nagib, H. M. , and Chauhan, K. A. , 2008, “ Variations of Von Kármán Coefficient in Canonical Flows,” Phys. Fluids, 20, p. 101518. [CrossRef]
Kader, B. , and Yaglom, A. M. , 1972, “ Heat and Mass Transfer Laws for Fully Turbulent Wall Flows,” Int. J. Heat Mass Transfer, 15(12), pp. 2329–2351. [CrossRef]
Antonia, R. A. R. A. , Danh, Q. , and Prabhu, A. , 1977, “ Response of a Turbulent Boundary Layer to a Step Change in Surface Heat Flux,” J. Fluid Mech., 80(1), pp. 153–177. [CrossRef]
Bradshaw, P. , and Wong, F. Y. F. , 1972, “ The Reattachment and Relaxation of a Turbulent Shear Layer,” J. Fluid Mech., 52(1), pp. 113–135. [CrossRef]
Bandyopadhyay, P. R. , and Ahmed, A. , 1993, “ Turbulent Boundary Layers Subjected to Multiple Curvatures and Pressure Gradients,” J. Fluid Mech., 246(1), pp. 503–527. [CrossRef]
Castro, I. P. , and Epik, E. , 1998, “ Boundary Layer Development After a Separated Region,” J. Fluid Mech., 374, pp. 91–116. [CrossRef]
Blackwell, B. , Kays, W. M. , and Moffat, R. J. , 1972, “ The Turbulent Boundary Layer on a Porous Plate: An Experimental Study of the Heat Transfer Behavior With Adverse Pressure Gradients,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA-CR-130291.
Kader, B. , and Yaglom, A. , 1991, “ Spectra and Correlation Functions of Surface Layer Atmospheric Turbulence in Unstable Thermal Stratification,” Turbulence and Coherent Structures, Springer, Dordrecht, The Netherlands, pp. 387–398.
Bradshaw, P. , and Huang, G. , 1995, “ The Law of the Wall in Turbulent Flow,” Proc. Math. Phys. Sci., 451(1941), pp. 165–188. [CrossRef]
Kong, H. , Choi, H. , and Lee, J. S. , 2001, “ Dissimilarity Between the Velocity and Temperature Fields in a Perturbed Turbulent Thermal Boundary Layer,” Phys. Fluids, 13(5), pp. 1466–1480. [CrossRef]
Houra, T. , and Nagano, Y. , 2006, “ Effects of Adverse Pressure Gradient on Heat Transfer Mechanism in Thermal Boundary Layer,” Int. J. Heat Fluid Flow, 27(5), pp. 967–976. [CrossRef]
Wang, C. , 2008, “ Stagnation Flow Towards a Shrinking Sheet,” Int. J. Non-Linear Mech., 43(5), pp. 377–382. [CrossRef]
Durbin, P. , and Belcher, S. , 1992, “ Scaling of Adverse-Pressure-Gradient Turbulent Boundary Layers,” J. Fluid Mech., 238(1), pp. 699–722. [CrossRef]
George, W. K. , and Castillo, L. , 1993, “ Boundary Layers With Pressure Gradient: Another Look at the Equilibrium Boundary Layer,” Near-Wall Turbul. Flows, 1, pp. 901–910.
Cruz, D. O. A. , and Freire, A. P. S. , 1998, “ On Single Limits and the Asymptotic Behaviour of Separating Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 41(14), pp. 2097–2111. [CrossRef]
Cruz, D. O. A. , and Freire, A. P. S. , 2002, “ Note on a Thermal Law of the Wall for Separating and Recirculating Flows,” Int J. Heat Mass Transfer, 45(7), pp. 1459–1465. [CrossRef]
Cebeci, T. , Khattab, A. , and Schimke, S. , 1988, “ Separation and Reattachment Near the Leading Edge of a Thin Oscillating Airfoil,” J. Fluid Mech., 188(1), pp. 253–274. [CrossRef]
Launder, B. E. , 1988, “ On the Computation of Convective Heat Transfer in Complex Turbulent Flows,” ASME J. Heat Transfer, 110(4b), pp. 1112–1128. [CrossRef]
Perry, A. E. , Bell, J. , and Joubert, P. , 1966, “ Velocity and Temperature Profiles in Adverse Pressure Gradient Turbulent Boundary Layers,” J. Fluid Mech., 25(2), pp. 299–320. [CrossRef]
Araya, G. , and Castillo, L. , 2012, “ DNS of Turbulent Thermal Boundary Layers Up to Reθ = 2300,” Int. J. Heat Mass Transfer, 55(15–16), pp. 4003–4019. [CrossRef]
Narasimha, R. , and Prasad, S. N. , 1994, “ Leading Edge Shape for Flat Plate Boundary Layer Studies,” Exp. Fluids, 17(5), pp. 358–360. [CrossRef]
Shakerin, S. , and Miller, P. L. , 1995, “ Experimental Study of Vortex Diffusers,” National Renewable Energy Laboratory, Washington, DC, Report No. NREL/TP-472-7331.
Peters, M. , Hirschberg, A. , Reijnen, A. , and Wijnands, A. , 1993, “ Damping and Reflection Coefficient Measurements for an Open Pipe at Low Mach and Low Helmholtz Numbers,” J. Fluid Mech., 256(1), pp. 499–534. [CrossRef]
Weng, C. , Boij, S. , and Hanif, A. , 2016, “ Numerical and Theoretical Investigation of Pulsatile Turbulent Channel Flows,” J. Fluid Mech, 792, pp. 98–133. [CrossRef]
Al-Asmi, K. , and Castro, I. P. , 1993, “ Production of Oscillatory Flow in Wind Tunnels,” Exp. Fluids, 15(1), pp. 33–41. [CrossRef]
Shea, P. R. , Berger, Z. P. , Berry, M. G. , and Glauser, M. N. , 2014, “ Low-Dimensional Modeling of a Mach 0.6 Axisymmetric Jet,” AIAA SciTech Forum, 1(52), pp. 1–12.
Mehdi, F. , and White, C. M. , 2011, “ Integral Form of the Skin Friction Coefficient Suitable for Experimental Data,” Exp. Fluids, 50(1), pp. 43–51. [CrossRef]
Hoffmann, P. H. , and Perry, A. E. , 1979, “ The Development of Turbulent Thermal Layers on Flat Plates,” Int J. Heat Mass Transfer, 22(1), pp. 39–46. [CrossRef]
Moretti, P. M. , and Kays, W. M. , 1965, “ Heat Transfer to a Turbulent Boundary Layer With Varying Freestream Velocity and Varying Surface Temperature—An Experimental Study,” Int. J. Heat Mass Transfer, 8(9), pp. 1187–1202. [CrossRef]
Reynolds, W. C. , Kays, W. M. , and Kline, J. , 1958, “ Heat Transfer in the Turbulent Incompressible Boundary Layer—Part II: Step Wall-Temperature Distribution,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA-MEMO-12-2-58W/PT2.
Simpson, R. L. , 2001, “ Junction Flows,” Annu. Rev. Fluid Mech., 33(1), pp. 415–443. [CrossRef]
Savory, E. , and Toy, N. , 1986, “ Hemisphere and Hemisphere-Cylinders in Turbulent Boundary Layers,” J. Wind Eng. Ind. Aerodyn., 23, pp. 345–364. [CrossRef]
Hansen, A. C. , and Cermak, J. E. , 1975, “ Vortex Containing Wakes of Surface Obstacles,” Ph.D. thesis, Colorado State University, Fort Collins, CO.
Chyu, M. K. , and Natarajan, V. , 1996, “ Heat Transfer on the Base Surface of Three-Dimensional Protruding Elements,” Int. J. Heat Mass Transfer, 39(14), pp. 2925–2935.
Wu, X. , and Moin, P. , 2010, “ Transitional and Turbulent Boundary Layer With Heat Transfer,” Phys. Fluids, 22(8), p. 085105. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic of the experimental facility. Air enters the facility from right-to-left. The primary components include as follows: (1) freestream heaters, (2) seeding manifold, (3) turbulence management section, (4) contraction, (5) thermal wall-plate located on the bottom wall of the test-section, (6) rotor-stator assembly, (7) diffuser, and (8) centrifugal fan.

Grahic Jump Location
Fig. 2

(a) Probability density function (PDF) of freestream temperature measured in the wind tunnel over a 2 h period. The vertical green line represents the setpoint temperature and the vertical red line represents the measured mean temperature with a confidence interval of 99% and (b) Schematic of the seeding manifold used for particle image velocimetry (PIV).

Grahic Jump Location
Fig. 3

(a) Solid model schematic of the thermal wall-plate and (b) detailed schematic of a section of the thermal wall-plate: right tilted 45 deg lines denotes the heated wall plate, left tilted 45 deg lines shows the surrounding layer of calcium silicate insulation and the hash marked section represents the copolymer acetal frame which positions all components. Three evenly spaced embedded thermocouples are located along line AA.

Grahic Jump Location
Fig. 4

A diagram detailing the wall plate heater controller circuit. (1) designates the embedded thermocouples, which are fed to an amplifier (2), whose signal is then fed to a LabVIEW program (3), which determines if the heaters should be in an off or on position and sends a final signal to an SCR circuit (4), which communicates to the thermal wallplate heaters.

Grahic Jump Location
Fig. 5

Schematic of rotor-stator design, left shows the rotor, shown in the middle is the stator, and the right plot depicts a freestream velocity time series taken with a pitot-static tube for a quarter revolution of the rotor-stator mechanism

Grahic Jump Location
Fig. 6

(a) Representative ensemble-averaged IR image of plate #5 for Tset = 40 °C and (b) spanwise profile of streamwise averaged temperature from figure (a)

Grahic Jump Location
Fig. 7

Wall-normal profiles of mean streamwise velocity at Reθ = 1527 with thermal wall plate on (×) and off (◁) plotted in (a) outer-coordinates and (b) inner-coordinates. The solid lines denote the data from Ref. [45] at a similar Re.

Grahic Jump Location
Fig. 8

Wall-normal profiles of mean temperature plotted in (a) outer-coordinates and (b) inner-coordinates. Shading denotes a ±5% variance in computed uτ value. The dotted line denotes the data from Araya and Castillo [30] at Reθ = 2290.

Grahic Jump Location
Fig. 13

Spanwise temperature profiles taken from the center of the IR images at a downstream position where the number of controller is detailed within the figure legend. For clarity of identification of profiles, data points are plotted for every respective fifth data point within the spanwise profile of the IR image. Shaded region denotes a 95% confidence interval for each profile.

Grahic Jump Location
Fig. 12

Two plane view of cartoon depiction for resulting flow field from hemisphere perturbation. The XZ-plane provides a birds eye view of the developing vortex wake, and the YZ-plane provides a view of vortex wake downstream of the hemisphere and the resulting wall temperature.

Grahic Jump Location
Fig. 11

Spatial temperature distributions located downstream of a hemisphere for four values of ReD. The streamwise and spanwise positions have been normalized by the hemisphere diameter D =3 cm.

Grahic Jump Location
Fig. 10

Wall-normal profiles of mean temperature after thermal step. Respective plates heated for each profiles is detailed within the legend of Fig. 10(a). Plotted in (a) inner-coordinates using St (Eq. (4)), and (b) modified inner-coordinates using StT (Eq. (5)), subsequent profiles are offset by Θ+ = 6 for visual clarity. The dotted line denotes the data from Araya and Castillo [30] at Reθ = 2290.

Grahic Jump Location
Fig. 9

(a) Representative ensemble-averaged IR image of temperature step. The top-plate is unheated where T =25 °C and the bottom plate is set to T =40 °C. The flow is from top-to-bottom and (b) The streamwise profile of spanwise averaged temperature.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In