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On the transient response of the turbulent boundary layer inception in compressible flows

Published online by Cambridge University Press:  12 July 2018

J. Saavedra Open the ORCID record for J. Saavedra [Opens in a new window] ,
G. Paniagua  and
S. Lavagnoli
J. Saavedra*
Affiliation:
von Karman Institute for Fluid Dynamics, Rhode Saint Genese, 1640, Belgium Zucrow Laboratories, Purdue University, West Lafayette, IN 47907, USA
G. Paniagua
Affiliation:
von Karman Institute for Fluid Dynamics, Rhode Saint Genese, 1640, Belgium Zucrow Laboratories, Purdue University, West Lafayette, IN 47907, USA
S. Lavagnoli
Affiliation:
von Karman Institute for Fluid Dynamics, Rhode Saint Genese, 1640, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

The behavioural characteristics of thermal boundary layer inception dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the thermal boundary layer to be established is vital to optimize flow control strategies, as well as the thermal management of systems exposed to ephemeral phenomena, typically on the millisecond scale. This paper presents the time characterization of the momentum and thermal boundary layer development in transient turbulent compressible air flows. We present a new framework to perform such estimations based on detailed unsteady Reynolds averaged Navier–Stokes simulations that may be extended to higher fidelity simulations. First of all, the aerodynamic boundary layer initiation is described using adiabatic simulations. Additional numerical calculations were then performed by setting the isothermal wall condition to evaluate the additional time required by the thermal boundary layer to establish after the aerodynamic boundary layer reaches its steady state. Finally, full conjugate simulations were executed to compute the warm up effect of the solid during the blowdown of a hot fluid over a colder metallic test model. The transient performance of the turbulent thermal and momentum boundary layers is quantified through numerical simulations of air blowdown over a flat plate for different mainstream flow conditions. The effects of Reynolds number, free stream velocity, transient duration, test article length and free stream temperature were independently assessed, to then define a mathematical expression of the momentum boundary layer settlement. This paper presents a novel numerical correlation of the additional time required by the thermal boundary layer to be stablished after the settlement of the momentum boundary layer. The time scales of the aerodynamic and thermal boundary layers are presented as a function of relevant non-dimensional numbers, as well as the description of the response of the near wall flow to sudden free stream changes. The characterization of the boundary layer mechanisms discussed in this paper contribute to the establishment of an evidence-based foundation for advances in the field of flow control.

JFM classification

Boundary Layers: Boundary layer control Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 1117 - 1141
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Copyright
© 2018 Cambridge University Press 

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References

Blasius, H. 1908 Grenzschichten in flussigkeiten mit kleiner reibung. Zeitschrift fur Mathematik und Physik 56, 6–15.Google Scholar
Blasius, H. 1950 The boundary layers in fluids with little friction. NACA TM 1256.Google Scholar
Celik, I. B. 2008 Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. Trans. ASME J. Fluids Engng 130 (7), 078001.Google Scholar
Davies, R. W. & Bernstein, L. 1969 Heat transfer and transition to turbulence in the shock-induced boundary layer on a semi-infinite flat plate. J. Fluid Mech. 36 (1), 87–112.Google Scholar
Dorfman, A. S. 2009 Problems of Conjugate Heat Transfer. CRC Press.Google Scholar
Holden, M. S. 1971 Establishment time of laminar separated flows. AIAA J. 9 (11), 2296–2298.Google Scholar
Johnson, J., Clark, J. P. & Flanagan, M. J. 2007 RANS simulations of turbine vane heat transfer in short duration shock tunnel cascade experiments. In 43rd AIAA ASME SAE AASE Joint Propulsion Conference. AIAA Paper 2007-5000.Google Scholar
Kays, W. M. & Crawford, M. E. 1980 Convective Heat and Mass Transfer. McGraw-Hill.Google Scholar
Kermani, M. J., Gerber, A. G. & Stockie, J. M. 2003 Thermodynamically based moisture prediction using roes scheme. In 4th Conference of Iranian AeroSpace Society, pp. 27–29. Amir Kabir University of Technology.Google Scholar
Lee, J. Y. & Lewis, J. M. 1993 Numerical study of the flow establishment time in hypersonic shock tunnels. J. Spacecr. Rockets 30 (2), 152–163.Google Scholar
Li, H. & Nalim, M. R. 2008 Thermal-boundary layer response to convected far-field fluid temperature changes. Trans. ASME J. Heat transfer 130 (10), 101001.Google Scholar
Lighthill, J. 2001 Waves in Fluids. Cambridge University Press.Google Scholar
Luikov, A. V. 1973 Conjugate convective heat transfer problems. Intl J. Heat Mass Transfer 17, 257–265.Google Scholar
Luikov, A. V., Aleksashenko, V. A. & Aleksashenko, A. A. 1971 Analytical methods of conjugated problems in convective heat transfer. Intl J. Heat Mass Transfer 14, 1047–1056.Google Scholar
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598–1605.Google Scholar
Mirels, H. 1956 Boundary layer behind a shock or thin expansion wave moving into a stationary fluid. NACA TN 3712.Google Scholar
Moore, F. K. 1951 Unsteady laminar boundary-layer flow. NACA TN 24771.Google Scholar
Ostrach, S.1952 An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force. Tech. Rep., National Aeronautics and Space Administration Cleveland, OH, Lewis Research Center.Google Scholar
Perelman, T. L. 1961 On conjugate problems of heat transfer. Intl J. Heat Mass Transfer 3, 293–303.Google Scholar
Rayleigh, Lord 1911 Lxxxii. On the motion of solid bodies through viscous liquid. Lond. Edinb. Dublin Phil. Mag. J. Sci. 21 (126), 697–711.Google Scholar
Roe, P. L. 1986 Characteristic-based schemes for the Euler equations. Annu. Rev. Fluid Mech. 18, 337–365.Google Scholar
Schlichting, H. 2003 Boundary Layer Theory. Springer.Google Scholar
Smith, C. & Edward 1996 The starting process in a hypersonic nozzle. J. Fluid Mech. 24 (4), 625–640.Google Scholar
Stephan, K. & Laesecke, A. 1985 The thermal conductivity of fluid air. J. Phys. Chem. Ref. Data 14 (1), 227–234.Google Scholar
Stewartson, K. 1950 On the impulsive motion of a flat plate in viscous fluid. Q. J. Mech. Appl. Maths 4, 1–37.Google Scholar
Stewartson, K. 1960 The theory of unsteady laminar boundary layer. Adv. Appl. Mech. 6.Google Scholar
Toro, E. F. 2009 Riemann Solvers and Numerical Methods for Fluid Dynamics: The Equations of Fluid Dynamics. Springer.Google Scholar
Vigneron, D., Deliége, G. & Essers, J.-A. 2006 Low Mach number local preconditioning for unsteady viscous finite volumes simulations on 3D unstructured grids. In European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2006). TU Delft, The Netherlands.Google Scholar
Volchkov, E. P. & Levchenko, V. Y. 1965 Turbulent thermal boundary layer on a flat plate with a thermally insulated section. Inzhenerno Fizicheskii Zhurnal 8 (6), 479–482.Google Scholar
Watson, J. 1958 A solution of the Navier–Stokes equations illustrating the response of a laminar boundary layer to a given change in the external stream velocity. Q. J. Mech. Appl. Maths XI (3), 302–325.Google Scholar
Wen-Jei, Y. & Huang-Sen, H. 1968 Unsteady compressible laminar boundary-layer flow over a flat plate. AIAA J. 7, 100–105.Google Scholar