Interaction of von Karman vortices and intersecting main streams in staggered tube bundles

 Flow visualization, heat transfer and pressure drop characteristics in flow through staggered tube bundles have been regarded as classical, with results well-documented. However, the mechanism of producing such results has been left untouched. Applications of staggered tube bundles are abundant in industry, for example as heat exchange devices like the shell-and-tube type and fuel bundles in nuclear reactor cores. An experimental study is recorded in the present paper which investigates the interaction of von Karman vortices and intersecting main streams in staggered tube bundles. Flow visualization by means of the particle tracing method, laser Doppler velocimetry (LDV) and pressure drop measurements using a piezometer are conducted. A modified Reynolds number appropriate to flow through a staggered tube arrangement is defined together with a pressure drop coefficient. Auto-correlation and power spectrum analyses of signals obtained from LDV measurements yield an optimum spectrum frequency which is correlated against the Reynolds number. It is concluded that flow characteristics in staggered tube bundles are determined by the interaction between the von Karman vortex street and X-shaped interacting main streams. Received: 4 August 1997 / Accepted: 3 October 1998     

Flow boiling heat transfer on a heating element restricted by an interference sleeve

The flow boiling phenomenon over a heated tube restricted by an interference sleeve, which is a passive enhancement technique, has been analysed using a semi-empirical approach. The liquid boiled was water flowing through an annular cross-section. A model developed earlier for the case of pool boiling over porous surfaces has been adapted after modification to pool boiling with interference surfaces using equivalent geometrical parameters and a modified permeability factor. This was further extended to saturated flow boiling situation using an additive mechanism. The single phase heat transfer coefficient required for the additive mechanism is obtained from an experimental correlation developed in the present study. The suppression factors evaluated for the eight sleeve geometries used in the present investigation are expressed in terms of the single phase Reynolds number and the Martinelli parameter. Very good agreement was observed between the model predictions and experimental data validating the mechanisms postulated. Further, a purely empirical correlation based on the present experimental data has been proposed to estimate the two-phase heat transfer coefficient. While the empirical correlation shows a better fit with the experimental data, the additive model has a physical basis.     

Three-dimensional conical viscous incompressible fluid flows

New exact solutions of the Navier-Stokes equations are obtained for steady-state three-dimensional conical flows. In this class of flows the velocity decreases in inverse proportion to the distance from the source and the input equations reduce to two-dimensional ones. It is shown that in the spherical coordinate system the equations of motion reduce to a single nonlinear equation with respect to a scalar function which depends on the polar angles. The case in which this equation reduces to the integrable Liouville equation is discussed. This makes it possible to obtain a wide class of three-dimensional solutions in analytic form. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 144–148, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00063).     

Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz number is small and the Nahme number is non-zero and can be large. Thus the flows are fully-developed and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity. Gz Graetz number - h half-height of channel or disc - h ^* half-height of polymer melt region in channel or disc - L length of channel or pipe - m viscosity shear-rate exponent - Na _Q Nahme number based on flowrate - Na _P Nahme number based on pressure drop - Na _PL lower critical value of Nahme number based on pressure drop - Na _PU upper critical value of Nahme number based on pressure drop - Na _P Nahme number based on pressure gradient - p pressure - P pressure drop - Q volumetric flowrate - r radial coordinate in pipe or disc - R radius of pipe - Re Reynolds number - R _i inner radius of disc - R ₀ outer radius of disc - R ^* radius of polymer melt region in pipe - T temperature - T _m melting temperature of polymer - T ₀ reference temperature - T _w wall temperature - u axial velocity in pipe or channel or radial velocity in disc - w width of channel - x axial coordinate in channel - y transverse coordinate in channel or disc - z axial coordinate in pipe - thermal conductivity of molten polymer - thermal conductivity of frozen polymer - heat capacity of molten polymer - viscosity temperature exponent - dimensionless transverse coordinate in channel or disc - ^* dimensionless half-height of polymer melt region in channel or disc - dimensionless temperature - ^* dimensionless wall temperature - µ viscosity of molten polymer - µ ₀ consistency of molten polymer - dimensionless pressure drop - dimensionless pressure gradient - density of molten polymer - dimensionless radial coordinate in pipe or disc - _i dimensionless inner radius of disc - ^* dimensionless radius of polymer melt region in pipe - dimensionless velocity     

Optimal blunt-nosed figures of revolution in a gas of different rarefactions

Many studies have been made of the optimization of the shape of bodies in a gas stream. However, the majority of these have been made for supersonic and hypersonic flow in the limiting case of a continuum [1], and only a few studies have been made [1–3] for the case of flow over a body of a rarefied gas (mainly a free molecular stream). In the present paper, the problem of shape optimization is considered for hypersonic flow of a gas of different rarefactions over a body. Numerical methods are used to investigate the influence of the Reynolds number on the shape and drag of optimal figures of revolution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 158–161, May–June, 1980.     

Critical time for shock formation in radiative magnetogasdynamics

For the general case of magnetogasdynamics coupled to the radiation field, a differential scheme which is capable of dealing with variable optical depths, leads to a hyperbolic system of equations. To this system the standard techniques for evaluating the critical time of weak discontinuities is applied. In this paper the critical time for radiative magnetoacoustic waves propagating into a constant state is analyzed. Plane waves, spherical waves and cylindrical waves are studied.     

Free thermoconcentration convection above a localized heat source

Shadowgraph and probe techniques are used to investigate the free convective flow pattern above various localized heat sources (electrolytic cell — point source, short vertical cylinder, sphere) in an exponentially stratified fluid. The characteristic types of structure are classified with respect to the appearance of new forms of instability. The critical values of the global Rayleigh number, at which the flow pattern is restructured, are determined. The dependence of the height of the convection zone and the height of the individual cells on the governing parameters of the problem is investigated and the results are reduced to universal form. Laboratory experiments and oceanic observations are qualitatively compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–34, March–April, 1989.     

Nonlinear steady-state oscillations of an elastic plate floating on the surface of a liquid of finite depth

In addition to obtaining solutions by the perturbation method it is shown that in the case of nonlinear wave interaction given a certain relationship between the parameters of the interacting waves steady-state compound waves may exist.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 146–154, May–June, 1989.     

Approximating kinetic equation for weakly nonequilibrium states of polyatomic gases

The aim of the present paper is to construct an approximate kinetic equation that, first, takes into account correctly the possibility of excitation of both rotational and vibrational degrees of freedom of the molecules and, second, is valid for any law of intermolecular interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–187, March–April, 1982.We thank M, Ya. Alievskio for helpful consultations.