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Temperature response of a single blow regenerator using axially dispersive thermal wave of finite propagation velocity – analysis and experiment

International Journal of Heat and Fluid Flow
Publication Date
DOI: 10.1016/s0142-727x(99)00061-2


Abstract Transient behaviour of the regenerator bed is analysed using a hyperbolic dispersion model. Flow maldistribution and backmixing in fluids are taken into account by introducing an axial dispersion term in the energy equation which is assumed to follow Chester’s hyperbolic conduction law. Danckwerts' type boundary condition is extended for the present analysis by introducing the finite propagation velocity of the dispersion wave which is assumed to originate at the entry of the bed (see, e.g. Danckwerts, P.V., 1953. Chemical Engineering science, Genie Chimique, vol. 2, pp. 1–14). The governing equations are solved using Laplace transformation technique. The inverse Laplace transformation is carried out by using a fast Fourier transform technique proposed by Crump (cf. Crump, K.S., 1976. J. Assoc. Comput Mach. 23, 89–96). Analysis shows that at a lower dispersive Peclet number which indicates higher rate of maldistribution and backmixing, the effect of propagation velocity of the dispersive wave plays a significant role in the transient response of the bed. Results reveal that the present approach is a more general one which at higher dispersion wave propagation velocity and lower dispersion coefficient approaches Schumann’s classical model (cf. Schumann, T.E.W., 1929. J. Franklin Institute 208, 405–416). The present model is subsequently validated by conducting an experiment with a packed bed of stainless steel wire mesh subject to a sudden rise in the inlet fluid temperature. The results indicate a strong hyperbolic effect and the experimental technique developed can be used for determination of the dispersion coefficient and its propagation velocity.

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