Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T07:51:46.299Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave formation and heat transfer at an ice-water interface in the presence of a turbulent flow

Published online by Cambridge University Press:  19 April 2006

R. R. Gilpin ,
T. Hirata  and
K. C. Cheng
R. R. Gilpin
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Canada
T. Hirata
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Canada Present address: Department of Mechanical Engineering, Shinshu University, Nagano, Japan.
K. C. Cheng
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Under some conditions of temperature and flow an ice-water interface in the presence of a turbulent stream has been observed to be unstable. In this paper the source and the conditions for the instability were investigated for a well-defined turbulent boundary-layer flow. It was found that the instability resulted from the interaction that occurs between a wavy surface and a turbulent flow over it. Such an interaction results in a heat transfer variation which is 90 to 180 degrees out of phase with the surface wave shape – a result which is consistent with the calculations of Thorsness & Hanratty (1979a, b).

The main factor controlling damping of the instability at an ice-water interface was found to be the rate at which heat is conducted away from the interface into the ice.

In the past it has been found that when an ice layer is melting, that is when the heat conduction in the ice is small, the ice surface is highly unstable. In the present study it was found that for a sufficiently large temperature ratio (Tf−Tw)/(T∞−Tf), a steady-state ice layer is also unstable. Furthermore it is predicted, from the present observations, that a growing ice layer with a ratio of ice-side to water-side heat fluxes of up to 2.3 could be unstable.

Under sufficiently unstable conditions waves on the ice surface grow to an amplitude at which flow separations occur near the wave crests. This results in a ‘rippled’ ice surface pattern very similar to the patterns observed on mobile bed surfaces (Kennedy 1969) or surfaces which are being dissolved into a flowing stream (Allen 1971). The development of a ‘rippled’ ice surface results in a very substantial increase in the mean heat-transfer rate which would have an important influence on predictions of ice formation in the presence of a turbulent stream.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 619 - 640
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. R. L. 1971 Bed forms due to mass transfer in turbulent flows: a kaleidoscope of phenomena. J. Fluid Mech. 49, 49–63.Google Scholar
Ashton, G. D. 1972 Turbulent heat transfer to wavy boundaries. Proc. 1972 Heat Transfer Fluid Mech. Inst., pp. 200–213.
Ashton, G. D. & Kennedy, J. F. 1972 Ripples on underside of river ice covers. Proc. A.S.C.E. 98 (HY9), 1603–1624.Google Scholar
Bathelt, A. G., Viskanta, R. & Leidenfrost, W. 1979 An experimental investigation of natural convection in the melted region around a heated horizontal cylinder. J. Fluid Mech. 90, 227–239.Google Scholar
Beaubouef, R. T. & Chapman, A. J. 1967 Freezing of fluids in forced flow. Int. J. Heat Mass Transfer 10, 1581–1587.Google Scholar
Blumberg, P. N. & Curl, R. L. 1974 Experimental and theoretical studies of dissolution roughness. J. Fluid Mech. 65, 735–751.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARD no. 169.Google Scholar
Carey, K. L. 1966 Observed configuration and computed roughness of the underside of river ice, St. Croix River, Wisconsin. U.S. Geol. Surv. Prof. Paper 550-B, B192-198.Google Scholar
Cheng, K. C. & Wong, S. L. 1977 Liquid solidification in a convectively cooled parallel-plate channel. Can. J. Chem. Engng 55, 149–155.Google Scholar
Edling, W. H. & Ostrach, S. 1970 An experimental study of melting wave behaviour. Heat Transfer 1970, vol. 1, Cu 2.3. Elsevier.
Genther, K. 1969 Freezing of liquids in pipes with turbulent flow. Int. Inst. of Refrig. Bull., pp. 397–412.
Gilpin, R. R. 1979 The morphology of ice in a pipe at or near transition Reynolds numbers. Heat Transfer - San Diego 1979, A.I.Ch.E. Symposium Series 189, vol. 75, pp. 89–94.
Gilpin, R. R. & Lipsett, A. W. 1978 Impingement melting: Experiment and numerical simulation. Proc. 6th Int. Heat Transfer Conf., vol. 3, pp. 43–47. Hemisphere, Washington, D.C.
Hirata, T., Gilpin, R. R., Cheng, K. C. & Gates, E. M. 1979 The steady state ice layer profile on a constant temperature plate in a forced convection flow: I. The laminar regime. Int. J. Heat Mass Transfer 22, 1425–1433.Google Scholar
Hirata, T., Gilpin, R. R. & Cheng, K. C. 1979 The steady state ice layer profile on a constant temperature plate in a forced convection flow: II. The transition and turbulent regimes. Int. J. Heat Mass Transfer 22, 1435–1443.Google Scholar
Hsu, K. 1973 Spectral evolution of ice ripples. Ph.D. thesis, Dept of Mechanics and Hydraulics, University of Iowa, Iowa City.
Jahn, A. & Klapa, M. 1968 On the origin of ablation hollows (polygons) on snow. J. Glaciology 7, 299–312.Google Scholar
Kendall, J. M. 1970 The turbulent boundary layer over a wall with progressive surface waves. J. Fluid Mech. 41, 259–281.Google Scholar
Kennedy, J. F. 1969 The formation of sediment ripples, dunes, and antidunes. Ann. Rev. Fluid Mech. 1, 147–168.Google Scholar
Kroegen, D. G. & Ostrach, S. 1974 The solution of a two-dimensional freezing problem including convection effects in the liquid region. Int. J. Heat Mass Transfer 17, 1191–1207.Google Scholar
Lapadula, C. & Mueller, W. K. 1966 Heat conduction with solidification and a convective boundary condition at the freezing front. Int. J. Heat Mass Transfer 9, 702–704.Google Scholar
Larsen, P. A. 1969 Heat losses caused by an ice cover on open channels. J. Boston Soc. Civ. Eng. 56, 45–67.Google Scholar
Larsen, P. A. 1973 Hydraulic roughness of ice covers. Proc. A.S.C.E. 99, 111–119.Google Scholar
Libby, P. A. & Chen, S. 1965 The growth of a deposited layer on a cold surface. Int. J. Heat Mass Transfer 8, 395–402.Google Scholar
Mark, H. J. 1954 The influence of melting and anomalous expansion on the thermal convection in laminar boundary layers. Appl. Sci. Res. 4, 435–452.Google Scholar
Nachtsheim, P. R. & Hagen, J. R. 1972 Observations of crosshatched wave patterns in liquid films. A.I.A.A. J. 10, 1637–1640.Google Scholar
Özisik, M. N. & Mulligan, J. C. 1969 Transient freezing of liquids in forced flow inside circular tubes. J. Heat Transfer 91, 385–389.Google Scholar
Pozvonkov, F. M., Shurgalskii, E. F. & Akselrod, L. S. 1970 Heat transfer at a melting flat surface under conditions of forced convection and laminar boundary layer. Int. J. Heat Mass Transfer 13, 957–962.Google Scholar
Savino, J. M. & Siegel, R. 1969 An analytical solution for solidification of a moving warm liquid onto an isothermal cold wall. Int. J. Heat Mass Transfer 12, 803–809.Google Scholar
Savino, J. M., Zumdieck, J. F. & Siegel, R. 1970 Experimental study of freezing and melting of flowing warm water at a stagnation point on a cold plate. Heat Transfer 1970, vol. 1, Cu 2.10. Elsevier.
Shibani, A. A. & Özisik, M. N. 1977a A solution of freezing of liquids of low Prandtl number in turbulent flow between parallel plates. J. Heat Transfer 99, 20–24.Google Scholar
Shibani, A. A. & Özisik, M. N. 1977b Freezing of liquids in turbulent flow inside tubes. Can. J. Chem. Engng 55, 672–677.Google Scholar
Siegel, R. & Savino, J. M. 1966 An analysis of the transient solidification of a flowing warm liquid on a convectively cooled wall. Proc. 3rd Heat Transfer Conf. 4, A.S.M.E., pp. 141–151.
Sparrow, E. M., Patanka, S. V. & Ramadhyani, S. 1977 Analysis of melting in the presence of natural convection in the melt region. J. Heat Transfer 99, 520–526.Google Scholar
Stephan, K. 1969 Influence of heat transfer on melting and solidification in forced flow. Int. J. Heat Mass Transfer 12, 199–214.Google Scholar
Thomason, S. B., Mulligan, J. C. & Everhart, J. 1978 The effect of internal solidification on turbulent flow heat transfer and pressure drop in a horizontal tube. J. Heat Transfer 100, 387–394.Google Scholar
Thorsness, C. B. & Hanratty, T. J. 1979a Mass transfer between a flowing fluid and a solid wavy surface. A.I.Ch.E. J. 25, 686–697.Google Scholar
Thorsness, C. B. & Hanratty, T. J. 1979b Stability of dissolving or depositing surfaces. A.I.Ch.E. J. 25, 697–701.Google Scholar
Yen, Y. C. & Tien, C. 1963 Laminar heat transfer over a melting plate, the modified Leveque problem. J. Geophys. Res. 68, 3673–3678.Google Scholar
Zerkle, R. D. & Sunderland, J. E. 1968 The effect of liquid solidification in a tube upon laminar-flow heat transfer and pressure drop. J. Heat Transfer 90, 183–190.Google Scholar
Zilker, D. P., Cook, G. W. & Hanratty, T. J. 1977 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech. 82, 29–51.Google Scholar
Zilker, D. P. & Hanratty, T. J. 1979 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flow. J. Fluid Mech. 90, 257–271.Google Scholar