Hiroyuki Ozoe

Natural convection in an inclined rectangular channel at various aspect ratios and angles—experimental measurements

Abstract Rates of heat transfer were measured for laminar natural convection in silicone oil and air in a long rectangular channel. The aspect ratio (width/height) of the cross-section of the channel was varied over 1, 2, 3, 4·2, 8·4 and 15·5, and the Rayleigh number from 3 × 103 to 105. The channel was heated from below and cooled from above while the other two sides were insulated. The channel was then rotated about the long axis in steps through 180 degrees. The effect of inclination and of the aspect ratio on the rate of heat transfer was measured experimentally. A minimum and a maximum rate of heat transfer occurred as the angle of inclination was increased from 0 to 180 degrees. The angle of inclination at these critical conditions was found to be a strong function of the aspect ratio and a weak function of the Rayleigh number. A transition in the mode of circulation occurred at the angle corresponding to the minimum rate of heat transfer.

NATURAL CONVECTION PATTERNS IN A LONG INCLINED RECTANGULAR BOX HEATED FROM BELOW PART I. THREE-DIRECTIONAL PHOTOGRAPHY

Abstract The transient and steady flow patterns in glycerol in a slightly inclined, long box with a cross-sectional width-to-height ratio of 2.0 were photographed by the method of Krishnamurti. The box was rotated about the long dimension as an axis. The stable mode for very small angles of inclination was found to be a series of roll-cells with their axes running in the upslope. As the angle of inclination was increased to five or six degrees the circulation pattern changed to a series of oblique cells. Above seven degrees a single quasi-two-dimensional cell was observed with flow up the inclined heated plate and down the cooled plate. The rate of heat transfer was also measured. The average Nusselt number at first increased with angle of inclination, then decreased as the oblique cells appeared, and finally increased again as the quasi-two-dimensional cell was formed. Significant hysteresis was not observed in either the circulation pattern or the Nusselt number as the angle of inclination was decreased. The studies were carried out for a Rayleigh number of about 12000.

Long rolls generated by natural convection in an inclined, rectangular enclosure

The three-dimensional velocity and temperature fields, and in turn theaverage Nusselt number and representative streaklines were computed by a finite-difference method for a cellular element with a length-to-height ratio of 7 and several postulated width-to-height ratios near unity in a rectangular enclosure heated from below, perfectly insulated on the lateral surfaces, and inclined about the long dimension. Calculations were carried out for Ra = 4000, Pr = 10 and a single grid spacing (non-uniformin the longdimension)for cells with dragless lateral boundaries and for those with one dragless and one rigid. Computations such as these have previously been utilized to develop a simple, theoretically based method for the prediction of Nu in horizontal enclosures of arbitrary aspectratios. Further calculations are necessary to support such a method of prediction for inclined enclosures and to define its limits of applicability.

A Laboratory Experiment on the Dynamics of the Land and Sea Breeze

Abstract The land and sea breeze (LSB) circulation was simulated in a laboratory using a temperature controlled water tank. Flow visualization by tellurium and phenolphthalein and velocity measurement by laser-Doppler velocimeter were carried out in addition to temperature measurements. from similarity considerations, the simulated flow pattern was shown to have good correspondence with that in the atmosphere. It was shown that the overall features of the LSB flow pattern consist of a closed circulating motion caused by the periodically changing horizontal temperature difference between the land and the sea, and several kinds of small-scale motions induced by the periodic variation of the land surface temperature itself. The most important small-scale motion is the cellular convection which occurs all over the land surface due to unsteady heating from below in the morning calm. Other small-scale motions such as longitudinal vortex rows which are formed inland throughout the sea breeze layer, and gravity c...

THE EFFECT OF VARIOUS PARAMETERS ON THERMOACOUSTIC CONVECTION

Thermoacoustic convection, that is, convection generated in a compressible fluid due to rapid heating of one of the enclosing walls, was studied numerically. Acoustic waves were found to be generated by sinusoidal heating of the wall as well as by a step function. In a finite layer of fluid the pressure wave is reflected back and forth until dissipated by viscosity. The fluctuating velocity generated by the pressure wave greatly enhances the rate of heat transfer over that for pure transient conduction. The same qualitative behavior but widely varying quantitative behavior was computed for different conditions. The simple theory of adiabatic waves, which neglects the diffusion of momentum and energy, accurately predicts the inter-relationship between the various dependent variables but neither the strength of the wave nor the rate of decay. Hence, these two approaches are complementary.

THREE-DIMENSIONAL NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A SPHERICAL ANNULUS

The three-dimensional equations of conservation in spherical coordinate were solved by a finite-difference method for natural convection in a spherical annulus. The vorticity-vector potential formulation and the alternating-direction-implicit method were utilized. Two sets of boundary conditions were considered. In the first the inner sphere was insulated, and a continuous sinusoidal temperature field was imposed on the outer sphere such that one vertical half was heated and the other cooled. In the second the inner sphere was cooled at uniform temperature, the same temperature distribution as before was imposed on the heated half of the outer sphere, and the previously cooled half was insulated. The computations were carried out for Ra = 500 and Pr = 1.0. The computed velocity and temperature fields are illustrated graphically. The streaklines were found to consist of pairs of double helices just as in rectangular and cylindrical enclosures.

Characteristics of air pollution in the presence of land and sea breeze—A numerical simulation

Abstract Characteristics of air pollution in the coastal region in the presence of the land and sea breeze were investigated numerically. First, two-dimensional primitive equations of momentum and heat were integrated to simulate the wind field of the land and sea breeze. Then, the motion of pollutant emitted into the land and sea breeze circulation, after its diurnal variation became completely cyclic, were traced for three days. Three cases with constant emission rate from line sources which are located aloft on the shoreline and on the sea surface, respectively, and from the surface source along the shore were examined. Characteristics of the diurnal pattern, including the apparent “background concentration” on the shore, as well as the daily variation of the pollutant concentration were discussed. From the analysis of long-period trajectories of neutrally-buoyant particles, general macroscopic motions of the pollutant were revealed.

Time‐dependent thermal convection in a stably stratified fluid layer heated from below

Time‐dependent thermal convection resulting when a stably stratified fluid layer is heated from below is analyzed as an initial‐value problem of a linear model. The effect of stratification on its development and structure is investigated. The convection is found to develop in three stages. Initially the given disturbance induces oscillatory motion with the corresponding Brunt–Vaisala frequency. In the second stage the stratification works to form secondary cells above the primary cell. This multiple cell pattern, however, changes slowly but periodically with time. Finally, the convection grows with an exponential growth rate, retaining a similar cell pattern. The vertical scale of the primary cell decreases with the stratification level, while the horizontal scale remains constant. The onset time of the manifest convection is predicted to be delayed as the stratification shifts from neutral to stable conditions. Attaining a maximum, it then becomes slightly earlier. Experimental results supporting the mo...

TECHNIQUE FOR RAPID CONVERGENCE OF THE PENALTY FINITE-ELEMENT METHOD WITH A MODIFIED GALERKIN SCHEME AND ITS APPLICATION TO NATURAL CONVECTION

This paper describes an efficient scheme for convergence of calculations using the penalty finite-element method. Sample calculations were carried out for laminar natural convection in a square channel and in a horizontal layer of fluid. The penalty parameter was initially set at a small value and then increased to larger values in discrete steps. This procedure decreased the computing time to 5% or less of that required for a single large value of the penalty parameter while producing less than 2% difference in the final value of the average Nusselt number. Extrapolation of the computed Nusselt numbers to zero element size resulted in a good agreement with prior experimental and numerical results.

The computation and dynamic display of three-dimensional streaklines for natural convection in enclosures

Abstract The rate of heat transfer in an inclined enclosure is critically dependent on the mode of circulation. The pattern of circulation in all finite enclosures is three dimensional. Streaklines are an effective means of displaying the mode and detailed pattern of such complex circulations. A computer program is presented for the calculation of the streaklines and another program for their dynamic display.