Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
26
2
1999
On the Spherically Symmetric Phase Change Problem
110-145
J.
Riznic
Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
Gunol
Kojasoy
Department of Mechanical Engineering, University of Wisconsin-Milwaukee P.O. Box 784, Milwaukee, Wisconsin 53201
Novak
Zuber
Division of Reactor Safety Research, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, Washington, D.C. 20555, USA
Using the energy integral method, an analysis of the spherically symmetric phase change (moving boundary) problems is presented. The expression derived for the temperature gradient shows the effects of both the interfacial area change and the curvature. The results show that the thermal boundary layer from a growing sphere is thinner than that corresponding to a collapsing one.
The solution of the energy equation is then used to analyze the thermal diffusion-controlled bubble (or droplet) growth or collapse problem. The expression derived for the radial velocity takes into account the effects of (a) the Jakob number, (b) the interfacial area change and (c) the curvature. It is shown that (a) for large values of the Jakob number, the radius depends upon the first power of the Jakob number, (b) for small values of the Jakob number it is a function of the square root of this number, and (c) although widely used in the literature, an application of the "thin thermal boundary layer" model to cavitation, i.e., to collapsing bubbles, is incorrect, particularly at low Jakob numbers.
Finally, it is demonstrated that analyzes of bubble dynamics based on the energy integral method are in error because the assumed temperature profile was incorrect. It is shown that this erroneous temperature distribution can result in a 100% error when computing the temperature gradient at the interface.
Although the analysis presented in this paper is formulated by considering the thermal diffusion of energy, the same analysis and results with an appropriate redefinition of property terms can be applied to a spherically symmetric mass diffusion problem with a moving boundary.
Parametric Study of a Supersonic Unsteady Flow in a Nozzle for a Potential Lead Azide Laser
146-168
G.
Miron
The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
O.
Igra
The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
S.
Rosenwaks
Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, Israel
J.
Falcovitz
Institute of Mathematics, the Hebrew University, Jerusalem, Israel
A parametric numerical study is conducted for the flow in a converging-diverging nozzle suitable for a lead azide laser. The flow is generated by exploding a lead azide pellet at some standoff distance on the nozzle axis. It is shown that the nozzle presence significantly affects the explosion generated flow field. When the explosive products pass through the nozzle a very clear enhancement in the flow pressure, density and temperature is evident, in comparison with values obtained at the same locations in a similar free expansion flow (no nozzle). The enhancement in flow properties, especially in temperature, is desirable for melting all the small solid lead particles suspended in the explosion products gas flow. A suitable nozzle flow (i.e., a flow having a desirable pressure, density, temperature and velocity) can be obtained by the appropriate choice of the nozzle area ratio and its location (standoff distance) with respect to the explosion center. Changes in the pellet mass, its material density and/or the composition of the explosion products also affect the flow inside the nozzle as described in the text. The gasdynamics of the "nozzle-trapped" flow is performed by using a quasi-one-dimensional high-resolution scheme, including a special boundary condition at the nozzle inlet plane.
Experimental Study of Isothermal and Stably Stratified Wakes of a Circular Cylinder
169-188
P. M. V.
Subbarao
Department of Mechanical Engg., Indian Institute of Technology, New Delhi, 110016, INDIA
Krishnamurthy
Muralidhar
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Flow past a circular cylinder has been experimentally studied under isothermal and linearly stratified conditions. The characteristics of the wake depend on the Reynolds number Red and the Froude number through the Brunt-Vaisala frequency No. The ranges of values of these quantities considered in experiments are 300 < Red < 3000 and 0 < No < 3 s−1 (stable stratification). Time-averaged quantities that have been measured are mean velocity, variance of streamwise and vertical velocity fluctuations, Reynolds shear stress, mean temperature and variance of temperature fluctuation at various streamwise and vertical positions. Statistical measurements of spectra of velocity fluctuations have been carried out at selected streamwise positions. Engineering parameters such as coefficient of momentum loss and maximum velocity deficit have been calculated using the mean velocity profile in the nearwake. Turbulent kinetic energy, dissipation of turbulence, integral and microscales and the Kolmogorov scale have been calculated from the turbulence statistics. Isothermal experiments confirm many of the results obtained in earlier studies. The nearwake shows interesting features such as energy gradients above and below the midplane of the cylinder. These gradients determine the rate of decay of the velocity fluctuations. Stratification is seen to enhance the energy gradients, particularly those involving the vertical component of velocity. Stratification is also seen to diminish the velocity deficit, increase the vortex shedding frequency and reduce the transverse length scale, thus pointing towards a delay in the point of separation.
Towards a Unified Theory of Pool Boiling - the Case of Ideally Smooth Heated Wall
189-223
Yu. A.
Buyevich
CRSS, University of California, Santa Barbara, USA
The paper focuses on developing a unified model for nucleate and transition boiling for which purpose a number of complementary subproblems are considered in a more or less systematic way. These are: 1) activation of potential nucle-ation sites, 2) detachment of hydrodynamically interacting vapor bubbles that evolve at activated nucleation sites, 3) merging of neighboring bubbles with formation of vapor film patterns, and 4) the effect of constraints imposed on the boiling system by two-phase flow in the bulk. Transition pool boiling is interpreted as a natural continuation of the discrete bubble boiling regime into a parametric region where coalescence of bubbles is essential. As a result, the heated surface becomes covered with fluctuating intermittent vapor patches, and the mean surface-liquid contact area fraction decreases fast as surface superheat increases under otherwise identical conditions. Although this paper addresses an ideal case of boiling on a molecularly smooth wall where vapor nuclei may originate only at the molecular level in conformity with the Boltzman - Arrhenius kinetics, a way to generalize the model to boiling on real rough surfaces is straightforward.
An Influence of a Fractal-Like Mushy Region on Solidification Process
224-231
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
A. O.
Ivanov
Department of Mathematical Physics, Ural State University Ekaterinburg, Russia
M. E.
Komarovski
Department of Mathematical Physics, Urals State University, Ekaterinburg, Russia
The model of a unidirectional solidification in the presence of a fractal-like mushy region is suggested. The fractal structure of a mushy region is considered to be known and is approximated by the power dependence of the solid phase content on the spatial coordinate towards the solidification direction. The self-similar solution of the model is obtained. An influence of the mushy region fractal dimension on solidification velocity is revealed.
Methodical Notes on the Strong Solution of Some Well-Known Problems of Hydrodynamics
232-247
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
V. V.
Mansurov
Department of Mathematical Physics, Urals State University, Ekaterinburg, Russia
The present paper is concerned with the strong mathematical solutions of the well-known problems of hydrodynamics. An approach considered here may be used to solve more complicated problems and may help to the readers to form own point of view on the solution of problems. We tried to eliminate some methodical shortcomings met in recent books on hydrodynamics on the solution of the problems under consideration.
Emergence of a Mushy Region in Processes of Binary Melt Solidification
248-264
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
A. G.
Churbanov
NIKA Software; and Institute for Mathematical Modeling, Russian Academy of Sciences, Moscow, Russia
P. N.
Vabishchevich
Institute for Mathematical Modelling, RAS, Moscow, Russia
A formation of a mushy region (two-phase zone) for binary melt solidification is theoretically studied on the basis of numerical calculations. The velocity of solidification is determined in the form of a linear function of time for one-dimensional unidirectional solidification regime from a solid wall which is cooled gradually. Taking into account numerical calculations, we analytically determined the time of the emergence of a mushy region.