Abstract
General two-dimensional models were derived and solved numerically for the thermoacoustical convection that is generated in a compressible fluid by rapid heating of one of the vertical enclosing walls. In the cases considered, the left wall temperature is raised rapidly (impulsively or gradually) while the right wall is held at a specified temperature. The top and the bottom walls of the considered enclosure are thermally insulated. The numerical solutions of the full Navier–Stokes equations were obtained by employing a highly accurate flux-corrected transport algorithm for the convection terms and by a central differencing scheme for the viscous and diffusive terms. It is numerically established that the magnitude of the power of pressure waves associated with the thermoacoustic effect, and the resulting flow pattern is strongly influenced by the difference in wall temperatures (values of overheating) and the speed of the wall heating process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. Trilling, ‘‘Acoustic wave induced flows and heat transfer in gases and supercritical fluids,’’ J. Acoust. Soc. Am. 27, 425–431 (1955).
L. W. Spradley and S. W. Churchill, ‘‘Pressure- and buoyancy-driven thermal convection in a rectangular enclosure,’’ J. Fluid Mech. 70, 705–720 (1975).
A. A. Gubaidullin, P. T. Zubkov, E. M. Sviridov, and E. N. Tarasova, ‘‘The effect of thermoacoustic waves on heat transfer in a layer of compressible medium,’’ High Temp. 44, 956–960 (2006).
L. Shen and P. Zhang, ‘‘An overview of heat transfer near the liquid-gas critical point under the influence of the piston effect: Phenomena and theory,’’ Int. J. Therm. Sci. 71, 1–19 (2013).
Y. Lin, B. Farouk, and E. S. Oran, ‘‘Flows induced by thermoacoustic waves in an enclosure: Effects of gravity,’’ J. Thermophys. Heat Transfer 20, 376–383 (2006).
B. Larkin, ‘‘Heat flow to a confined fluid in zero gravity,’’ Prog. Astro. Aeronaut. 20, 819–832 (1967).
H. Ozoe, N. Sato, and S. W. Churchill, ‘‘The effect of various parameters on thermoacoustic convection,’’ Chem. Eng. Commun. 5, 203–221 (2007).
H. Ozoe, N. Sato and S. W. Churchill, ‘‘Numerical analyses of two- and three-dimensional thermoacoustic convection generated by a transient step in the temperature of one wall,’’ Numer. Heat Transfer, Part A 18, 1–15 (1990).
M. A. Brown and S. W. Churchill, ‘‘Finite-difference computation of the wave motion generated in a gas by a rapid increase in the bounding temperature,’’ Comput. Chem. Eng. 23, 357–376 (1999).
B. Zappoli, S. Amiroudine, P. Carles, and J. Ouazzani, ‘‘Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid,’’ J. Fluid Mech. 316, 53–72 (1996).
H. Weller, H. Tabor, H. Jasak, and C. Fureby, ‘‘A tensorial approach to computational continuum mechanics using object-oriented techniques,’’ Comput. Phys. 12, 620–631 (1998).
I. V. Morenko, ‘‘Numerical simulation of laminar Taylor–Couette flow,’’ Lobachevskii J. Math. 41 (7), 1255–1260 (2020).
M. Kraposhin, M. Banholzer, M. Pfitzner, and K. Marchevsky, ‘‘A hybrid pressure-based solver for nonideal single-phase fluid flows at all speeds,’’ Int. J. Num. Meth. Fluids 88 (2), 79–99 (2018).
I. V. Morenko, ‘‘Numerical simulation of the propagation of pressure waves in water during the collapse of a spherical air cavity,’’ Ocean Eng. 215, 107905 (2020).
M. A. Brown and S. W. Churchill, ‘‘Experimental measurements of pressure waves generated by impulsive heating of a surface,’’ AIChE J. 22, 205–213 (1995).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by A. M. Elizarov)
Rights and permissions
About this article
Cite this article
Gubaidullin, D.A., Snigerev, B.A. Numerical Study of Thermoacoustic Waves in a Cavity under Rapid Wall Heating. Lobachevskii J Math 42, 2129–2134 (2021). https://doi.org/10.1134/S1995080221090122
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080221090122