Toru Fusegi

A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure

A high-resolution, finite difference numerical study is reported on three-dimensional steady-state natural convection of air, for the Rayleigh number range 103 ⩽ Ra ⩽ 106, in a cubical enclosure, which is heated differentially at two vertical side walls. The details of the three-dimensional flow and thermal characteristics are described. Extensive use is made of state-of-the-art numerical flow visualizations. The existence of the transverse z-component velocity, although small in magnitude, is clearly shown. Comparison of the present three-dimensional results with the two-dimensional solutions is conducted. The three-dimensional data demonstrate reasonable agreement with the experimental measurements.

Laminar and turbulent natural convection. Radiation interactions in a square enclosure filled with a nongray gas

A numerical investigation of interactions oflaminar and turbulent natural convection and radiation in a differentially heated square enclosure was performed. Songray gas radiation was analyzed with the P^-approximation method for the radiative transfer equation and the weighted sum of gray gases model, A desirable compatibility was achieved in the resultant formulation for radiative transfer with the governing equations for natural convection flows. The Favre-averaged formulation was employed for analyzing turbulent flows together with a k-e model. In the analysis, a two-dimensional enclosure filled with carbon dioxide gas was considered. Solutions were obtained for a range of Grashof numbers and Prandtl numbers varying from 104 to 1010 Characteristics of flow and temperature fields were compared with predictions in the literature and were found to be in good agreement in general.

Numerical study of thermoacoustic waves in an enclosure

The behavior of thermoacoustic waves in a nitrogen-filled two-dimensional cavity is numerically studied in order to investigate how these waves may be used as an effective heat removal mechanism. The compressible, unsteady Navier–Stokes equations were solved for a series of initial conditions by combining a flux-corrected transport algorithm for convection with models for temperature-dependent viscosity and thermal conduction. By considering a one-dimensional test problem and comparing the results to existing data, the accuracy of the present numerical method is verified. In the problems considered, the vertical walls of a cavity were heated or cooled to generate the thermoacoustic waves. Both impulsive and gradual changes of the wall temperatures were considered. When the vertical wall was heated impulsively and nonuniformly, the waves induced two-dimensional flows within the enclosure. The observed thermoacoustic waves oscillate and eventually decay due to viscous and heat dissipation.

Three-dimensional numerical simulation of periodic natural convection in a differentially heated cubical enclosure

A high-resolution, finite-difference numerical study is carried out of three-dimensional unsteady periodic natural convection of air in a cubical enclosure at the Rayleigh number of 8.5×106. The enclosure is subjected to differential heating at the two vertical side walls. The other vertical walls are insulated. A linear temperature profile is specified at the thermally-conducting horizontal walls. Flow details in the three-dimensional field are captured by elaborate post-processing of the computational results, for which the state-of-the-art numerical visualization techniques are utilized. The three-dimensionality of the mean flow fields is observed to be confined into narrow regions near the end walls. The time-dependent solutions clearly indicate the periodic nature of the flow. The oscillation frequency is in close agreement with the previous experimental measurements reported in the literature.

NATURAL CONVECTION-RADIATION INTERACTIONS IN A CUBE FILLED WITH A NONGRAY GAS

A three-dimensional numerical study was performed on interactions of natural convection and radiation in a cubical enclosure filled with carbon dioxide gas. The enclosure was heated differentially by two opposing vertical walls. Gas radiation was analyzed by the P1 differential approximation method and the weighted sum of gray gas model. Computations were carried out over a range of the Rayleigh number, Ra, between 105 and 109. The Prandtl number and the overheat ratio were held fixed at 0·68 and 1·0, respectively. Unsteady transitional flows were computed by a direct simulation method, without using any explicit turbulence models. From the predictions, a mean heat transfer correlation has been proposed as Nu = 0·323 Ra0·342 in the surface/gas radiation mode, where Nu is the time and spatially averaged Nusselt number at the isothermal walls.

Predictions of fluid flow and heat transfer problems by the vorticity-velocity formulation of the Navier-Stokes equations

Abstract A relatively novel formulation of the Navier-Stokes equations is evaluated for obtaining solutions of 2-dimensional incompressible fluid flow and convective heat transfer problems. A vorticity transport equation along with two Poisson equations for the velocity components and the energy equation are solved by a finite difference scheme. A direct solution procedure is used for solving simultaneously the dependent variables along a grid line, using a block tridiagonal matrix algorithm. As test problems, laminar flow motion and heat transfer in a square cavity and in a horizontal concentric annulus induced by various strength of buoyancy and external shear forces are investigated. The formulation is found to be stable for high Reynolds and Grashof numbers and has features that may be desirable for solving a wide variety of flow and heat transfer problems.

Natural convection of a variable property gas in asymmetrically heated square cavities

Convective flows in an asymmetrically-heated square enclosure are presently studied for the case of the variable property gas, air, where the cavity has a centrally-located heated section on its bottom plate and a cooling element on its side wall. For a range of density difference parameters lower than 2, the intensity of convection was reduced as the parameter value increased; the thermal and velocity boundary layers thicken on the enclosure surfaces, and the maximum values of the stream function decrease and shift their location toward the cavity center. 13 references.

NUMERICAL STUDY OF NATURAL CONVECTION IN A DIFFERENTIALLY HEATED SQUARE CAVITY WITH INTERNAL HEAT GENERATION

A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical side-walls of the cavity are differentially heated, and a uniform internal heat generation is also present. Comprehensive computations have been performed over a range of the two principal parameters, i.e ., the internal Rayleigh number, Ra I , which represents the strength of the internal heat generation, covers 10 9 ≤ Ra I ≤ 10 10 ; and, the external Rayleigh number, Ra E , which denotes the effect due to the differential sidewall-heating, is set at Ra E = 5 × 10 7 for most computations. The impetus is placed on delineating the flow and heat transfer characteristics when the Rayleigh numbers are substantially high. The patterns of the global flow field illustrate qualitative changes as Ra I is varied. As the relative strength of the internal heat generation increases, the flows near the top portion of the heated side wall is directed downward. When the effect of the internal heat generation is dominant, the heat transfer properties across the heated side wall are of special interest. Over the top portion of the heated wall, the thermal energy leaves from the system to the surroundings. Only in the bottom part of the heated wall, the heat transfer is directed into the system. These numerical solutions are in qualitative agreement with the available experimental measurements.

Three-Dimensional Natural Convection-Radiation Interactions in a Differentially Heated Cube Filled with Gas-Soot Mixtures

A high-resolution, three-dimensional finite difference numerical study was performed on interactions of natural convection and surface/gas/soot radiation in a differentially heated cubical enclosure over the Rayleigh number of 105 ≤ Ra ≤ 109. A robust gas/soot radiation model used in the analysis was based on the P1-differential approximation method and the weighted sum of gray gas model. The three-dimensional characteristics of the thermal and flow fields were examined in detail by the state-of-the-art three-dimensional numerical visualization techniques. The effects of each mode of radiation were described. Overall, radiation was found to enhance the three-dimensionalities of the fields.