Showing papers in "Numerical Heat Transfer Part A-applications in 1990"
TL;DR: In this paper, the effect of a centered, square, heat-conducting body on natural convection in a vertical square enclosure was examined numerically and the analysis revealed that the fluid flow and heat transfer processes are governed by the Rayleigh and Prandtl numbers, the dimensionless body size, and the ratio of the thermal conductivity of the body to that of the fluid.
Abstract: The effect of a centered, square, heat-conducting body on natural convection in a vertical square enclosure was examined numerically. The analysis reveals that the fluid flow and heat transfer processes are governed by the Rayleigh and Prandtl numbers, the dimensionless body size, and the ratio of the thermal conductivity of the body to that of the fluid. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of streamlines, isotherms, and the overall heat transfer across the enclosure as described by the Nusselt number. Heat transfer across the enclosure, in comparison to that in the absence of a body, may be enhanced (reduced) by a body with a thermal conductivity ratio less (greater) than unity. Furthermore, the heat transfer may attain a minimum as the body size is increased. These and other findings are justified through a careful examination of the local heat and fluid flow phenomena.
226 citations
TL;DR: In this article, the authors analyzed the performance of the simplified and full pressure-correction equations when the grid nonorthogonality becomes appreciable, and showed that the efficiency of the simple coupling algorithm is not affected by the nonorthographic grid, provided that no additional simplifications are introduced in the pressurecorrection equation.
Abstract: Extension of the SIMPLE pressure-velocity coupling algorithm to nonorthogonal grids results in a very complex pressure-correction equation (e.g., a 9-point computational molecule in a two-dimensional case, a 19-point.computational molecule in a three-dimensional case) The usual practice is therefore to further simplify this equation by neglecting the effect of nonorthogonality on the mass flux corrections, thus reducing the computational molecule to 5 or 7 points The paper analyzes the performance of the simplified and full pressure-correction equations when the grid nonorthogonality becomes appreciable. It is demonstrated here that the efficiency of the simple coupling algorithm is not affected by the grid nonorthogonality, provided that no additional simplifications are introduced in the pressure-correction equation. However, the algorithm with the simplified equation becomes inefficient when the angle between grid lines approaches 45° and it usually fails to converge for angles below 30°. The problem o...
107 citations
TL;DR: In this paper, a general formulation to treat mixed boundary conditions using the spline approximation has been presented, where numerical solutions have been obtained by solving the Navier-Stokes and energy equations.
Abstract: The present work is devoted to the numerical study of laminar natural convection flow from a heated horizontal cylinder under diverse surface boundary conditions using the spline fractional step method. A general formulation to treat mixed boundary conditions using the spline approximation has been presented. Numerical solutions have been obtained by solving the Navier-Stokes and energy equations. The results for the isothermal boundary condition as well as for the uniform heat flux are in good agreement with published experimental data and with other solutions presently available in the literature. Some new computations at very high Rayleigh numbers indicate the existence of attached separation vortices in the downstream plume region, the appearance of these vortices being dependent on the values of the Biot number. All results were computed on a personal computer using unequally spaced grids that provided good results with a minimum number of computational points. The numerical scheme presented here app...
103 citations
TL;DR: In this article, the authors investigated the structure of laminar wakes and heat transfer in the presence of thermal buoyancy art in a two-dimensional horizontal channel with a built-in square cylinder and showed that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone.
Abstract: Structures of laminar wakes and heat transfer in the presence of thermal buoyancy art investigated from the numerical solution of complete Navier-Stokes and energy equations in a two-dimensional horizontal channel with a built-in square cylinder. Results show that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone. For a given Reynolds number, the heating of the fluid in the channel is improved by mixed convection up to a certain Grashof number and deteriorates if the Grashof number is further increased.
75 citations
TL;DR: In this article, a finite difference method is proposed to remove the need for staggered grids in fluid dynamic computations, which can be applied to free convection in a square cavity, one-dimensional flow through an actuator disk and plane stagnation flow.
Abstract: A new finite difference method, which removes the need for staggered grids in fluid dynamic computations, is presented. Pressure checkerboarding is prevented through a differencing scheme that incorporates the influence of pressure on velocity gradients. The method is implemented in a SIMPLE-type algorithm, and applied to three test problems: one-dimensional flow through an actuator disk, plane stagnation flow, and free convection in a square cavity. Good agreement is obtained between the numerical solutions and the corresponding analytical or benchmark solutions
74 citations
TL;DR: In this paper, the buoyancy-driven flow in a tall rectangular cavity of 5:1 aspect ratio with a Rayleigh number of 4 ×1010 is calculated using finite volume methods.
Abstract: The buoyancy-driven flow in a tall rectangular cavity of 5:1 aspect ratio with a Rayleigh number of 4 ×1010 is calculated using finite volume methods. The CELS solver is extended to be able to handle large density variations. CELS is compared with SIMPLEC, and it is shown to be up to more than 4 times as fast as SIMPLEC. A modified form of a low Reynolds number κ-e turbulence model is developed. This model is consistent in its near-wall behavior, and it allows simulation of the decay of grid turbulence. The model developed by Lam and Bremhorst [1] is also tested. Both turbulence models are shown to predict the transitional and relaminarization regions according to experiments.
67 citations
TL;DR: In this paper, a single-screw extruder with non-Newtonian fluid was studied numerically for thermal transport and the results indicated that the temperature variation in downstream direction has a small effect on the corresponding velocity field, which was determined mainly by the total volume flow rate.
Abstract: Thermal transport within the channel of a single-screw extruder has been studied numerically for non-Newtonian fluids, the computations art carried out for a given barrel temperature distribution and adiabatic screw. Numerical results are obtained using finite-difference techniques. The results indicate that the temperature variation in the downstream direction has a small effect on the corresponding velocity field, which is determined mainly by the total volume flow rate. It is also found that heat may be transferred from the flowing material to the barrel farther downstream under certain conditions. The residence time distribution is obtained numerically. Screw characteristics are presented in terms of bulk temperature rise versus screw speed
56 citations
TL;DR: In this paper, two different partition geometries are considered: one with a single partition located vertically at the center of the enclosure and the other with two identical partitions located at the top and bottom walls.
Abstract: Two-dimensional natural convection flows in square enclosures with partitions are analyzed for laminar flow. Side walls are assumed to be isothermal, while the top and bottom walls are adiabatic. Two different partition geometries are considered: one with a single partition located vertically at the center of the enclosure and the other with two identical partitions located at the top and bottom walls. Calculations are made for different Ray-leigh numbers, partition heights, and partition conductivities. Results show that the presence of partitions is relatively unimportant if the partitions do not cover more than half of the total height of the cavity. Overall heat transfer and thrvughflow respond only marginally to a change in partition conductivity except when the gap width is very small. Local results presented in the form of streamline and isotherm plots and variation of local Nusselt number over the hot wall provide valuable insight into the physical processes
53 citations
TL;DR: In this paper, the steady state natural convection for air bounded by two confocal horizontal elliptical cylinders was studied numerically for the case of inner hot and outer cold isothermal surfaces and the local and average Nusselt numbers were determined over the range of Raleigh numbers from 104 to 2 × 105 for different eccentricities of the inner surface.
Abstract: The steady-state natural convection for air bounded by two confocal horizontal elliptical cylinders has been studied numerically for the case of inner hot and outer cold isothermal surfaces. The local and average Nusselt numbers are determined over the range of Raleigh numbers from 104 to 2 × 105 for different eccentricities of the inner surface. Correlations are given for the average Nusselt number based on both the inner and the outer surfaces. Increasing the eccentricity of the inner surface increases the local Nusselt number over the entire inner surface and part of the outer surface.
47 citations
TL;DR: In this article, the authors considered thermocapillary convection in a rectangular cavity with a top 287 free surface and found the solutions that describe the thermocAPillary convections and interface shape of the free surface iteratively for both fixed heights and fixed angles of the contact between the free surfaces and the solid side walls.
Abstract: Thermocapillary convection in a rectangular cavity with a top 287free surface has been, considered. The top free surface of the cavity is subjected to inhomogeneous heating, which generates a bulk fluid motion. The Navier-Stokes equations and the energy equation have been solved by a finite-difference method with a boundary-fitted curvilinear coordinate system, which is generated numerically and always places the coordinate line coincident with the current boundary surfaces. The solutions that describe the thermocapillary convection and interface shape of the free surface are found iteratively for both fixed heights and fixed angles of the contact between the free surface and the solid side walls. The influence of the capillary, Reynolds, and Prandtl numbers on the flow field, the temperature distribution, and the free-surface deformation is considered. The results for a shallow cavity with small capillary, Reynolds, and Marangoni numbers are in qualitative and quantitative agreement with the previous asy...
28 citations
TL;DR: In this article, general two-and three-dimensional models were derived and solved numerically for the thermoacoustical convection that is generated in a compressible fluid by rapid heating of one of the vertical enclosing walls.
Abstract: General two- and three-dimensional models were derived and solved numerically for the thermoacoustical convection that is generated in a compressible fluid by rapid heating of one of the vertical enclosing walls. Various temperature profiles were imposed impulsively on the heated wall of a two-dimensional enclosure and found to be reflected in the immediately ensuing velocity vectors in the fluid. After sufficient time, say, 0.2 s for helium at atmospheric conditions with an imposed temperature difference of 273 K, the velocity field was also influenced by buoyant forces. Stable numerical solutions were developed for the initial and reflected three-dimensional field of velocity in a cubic enclosure.
TL;DR: In this article, a two-dimensional vertical cavity is considered, where the temperature of the porous media is initially maintained at the temperature in the hot wall, and the vertically opposite wall is abruptly cooled below the freezing temperature.
Abstract: Numerical investigations have been carried out to examine the characteristics of unsteady freezing heat transfer in water-saturated porous media. As a physical model, a two-dimensional vertical cavity is considered. The temperature of the porous media is initially maintained at the temperature of the hot wall. The vertically opposite wall is abruptly cooled below the freezing temperature. The equation of momentum includes Forchheimer's extension as the resistance to flow in the porous media. For the governing equations in the frozen and unfrozen porous layers, the transformations of variables are performed by the boundary fixing method, and the finite-difference equations are obtained by integrating the governing equations over the control volume. The successive overrelaxation method is utilized to solve the equations numerically. Modified Nusselt numbers are introduced to characterize the unsteady freezing heat transfer in water-saturated porous media. The flow patterns and the temperature distributions ...
TL;DR: In this article, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus the equation is solved for incremental pressure rather than density, and the turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model.
Abstract: Numerical investigation of transonic flows separated by streamline curvature and shock wave-boundary layer interaction is presented. The free-stream Much numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus the equation is solved for incremental pressure rather than density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free-stream Mach numbers considered whereas various k-e turbulence models fail to predict such a reversed flow region at low free-Stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave-turbulent boundary layer interaction as the free-stream Mach number is increased. These numerical results sho...
TL;DR: In this paper, the authors studied the transport phenomena of the extended Graetz problem with three different entrance boundary conditions and showed that the expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form.
Abstract: The transport phenomena of the extended Graetz problem with three different entrance boundary conditions are discussed. The expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form. The solution, assuming that the entrance boundary conditions for both temperature and energy flux (TFBC) are continuous, is the same as that for the problem in which the downstream region was considered infinite. Among all the procedures used, the computational procedures for TFBC are the simplest. The TFBC condition is recommended for use in analyzing the problem. Results show that temperature profiles and local Nussell number are influenced by Piclet number and different entrance boundary conditions. In addition, it is also shown that the asymptotic Nussell numbers for the three different conditions are the same.
TL;DR: In this paper, a numerical study was performed to analyze the steady natural convection heat transfer in a two-dimensional partially filled rectangular cavity with a uniform heat-generating saturated porous medium.
Abstract: A numerical study was performed to analyze the steady natural convection heat transfer in a two-dimensional partially filled rectangular cavity with a uniform heat-generating saturated porous medium. The boundary conditions were: two isothermal walls at different temperatures and two horizontal adiabatic walls. The study covered the range of 103 < Ra < 107 and 10-3 < Da < 10-8. The aspect ratio A was varied from 0.5 to 20, the filling factor F from 0.0 to 1.0, the dimensionless porous layer location Xp from 0.1 to 0.5 (symmetry line), and the asymmetric cooling θh from 0.0 to 0.5, It was found that the flow and temperature fields interact in different ways depending on various parameters (Ra, Da, A, Xp, θh and F).
TL;DR: In this paper, the effects of Planck number, optical thickness, Biot number, emissivity of the lower plate, and transmissivity of upper surface on the transition are analyzed for gray and nonscattering fluids.
Abstract: In this paper the thermal instability of a fluid layer above a solid boundary induced by incident radiative heat to the upper free surface is studied numerically. Eddington approximation is adopted for the equation of transfer, and the pseudospectral method is used to solve the linearized perturbed equations. The effects of Planck number, optical thickness, Biot number, emissivity of the lower plate, and transmissivity of the upper surface on the transition are analyzed for gray and nonscattering fluids. In general, decreasing the temperature difference between the lower plate and the upper surface by increasing the Planck number and the optical thickness, and by decreasing the emissivity and the transmissivity at fixed Biot number, delays the onset of instability. Biot number plays a unique role for nonradiating fluids, and dual roles for radiating fluids on the occurrence of instability.
TL;DR: In this article, the results of numerical computations are presented for the free surface flow of a thin liquid film in the presence or absence of a gravitational body force, and the distributions of film height and friction coefficient were found to be strongly affected by the magnitude and orientation of the gravitational body forces.
Abstract: The results of numerical computations are presented for the free surface flow of a thin liquid film in the presence or absence of a gravitational body force. Three different flow systems were studied: a falling film down a vertical wall, plane and radial film flows under zero gravity, and plane and radial film flows along a horizontal plate in the presence of gravity. Computations were performed using a boundary-fitted coordinate system where the irregular free surface conformed to one of the flow boundaries. The distributions of film height and friction coefficient were found to be strongly affected by the magnitude and orientation of the gravitational body force. Besides the Reynolds number, the Froude number of the film, which characterizes the flow regime (i.e., supercritical or subcritical), is found to be an important parameter for horizontal flow in the presence of gravity.
TL;DR: In this article, a steady-state, two-dimensional model of heat transfer and fluid flow incorporating density variations was developed, and three different cases were studied: (1) no volume expansion, (2) volume expansion due to the density variation caused by superheating, and (3) volumetric volume expansion caused by both melting and super-heating.
Abstract: Natural convection and volume expansion can occur in a weld pool due to density variations caused by the heat input during welding. In the present study a steady-state, two-dimensional model of heat transfer and fluid flow incorporating density variations was developed, and three different cases were studied: (1) no volume expansion, (2) volume expansion due to the density variation caused by superheating, and (3) volume expansion due to the density variation caused by both melting and superheating. The effect of weld pool expansion on the resultant weld depth/width ratio was demonstrated, and a simple experiment was conducted using wax to provide evidence for volume expansion due to density variation caused by melting.
TL;DR: In this paper, the authors investigated the transient natural convection in a two-dimensional enclosure of which the upper and lower walls are adiabatic and used a penalty finite-element method with a Newton-Raphson iteration algorithm and a backward difference scheme dealing with the time term.
Abstract: The aim of this numerical study is to investigate the transient natural convection in a two-dimensional enclosure of which the upper and lower walls are adiabatic. Initially t = 0, the left wall is at a higher temperature than the right wall, and the fluid of the enclosure is at a steady flow state. At time t > 0, the temperature of the left wall descends to that of the right wall. This causes the flow of the fluid in the enclosure to change. As time increases, the flow decays. Finally, the flow ceases and the fluid becomes stationary. During the computing process, a penalty finite-element method with a Newton-Raphson iteration algorithm and a backward difference scheme dealing with the time term are adopted to solve the governing equations. A skyline method is used to reduce massive computer memory. The effect of Rayleigh number on the heat transfer mechanism during the transient process is examined by investigating the Ra = 104 case, in which conduction heat transfer is dominant, and the Ra = 106 case, ...
TL;DR: In this article, a numerical model for hyperbolic combustion within a four-stroke heat-barrier piston engine has been developed, with the fuel injector being colocated with a single valve, making possible an axisymmetric solution.
Abstract: A numerical model for hyperbolic combustion within a four-stroke heat-barrier piston engine has been developed. An idealized fuel injector simulates the type of injector used in current experimental hypergolic combustion research. Significant to the modeling of this injector is the need to overcome the problems posed by a unit Mach number boundary condition at the injector orifice opening. Overall, the model is used to simulate a compression stroke and fuel injection portion of a power stroke. An implicit finite-difference solution of the governing flow field equations is used. The engine is modeled with the fuel injector being colocated with a single valve, making possible an axisymmetric solution. Because of its physics, hypergolic combustion dictates an eddy dissipation combustion approach. In the final run a 20 × 26 mesh is used for the greater region, which is made up of the flow field and a thin portion of the adjacent cylinder linings and piston.
TL;DR: In this paper, the effect of Reynolds number (Re) on forced convection over a heated cylinder for both incompressible and compressible flows is studied nondimensionally and numerically.
Abstract: The flow and thermal fields in forced convection over a heated cylinder for both incompressible and compressible flows are studied nondimensionally and numerically. The governing system includes fully two-dimensional Navier-Stokes momentum, energy, and continuity equations in body-fitted coordinates. The effect of Reynolds number (Re) is investigated. In the incompressible case, Re is a function of free-stream velocity. The predicted results are in good agreement with those obtained by the other numerical methods and experimental measurements. In the compressible case, Re is governed by cylinder surface temperature. The characteristics of fluid flow and heat transfer when surface temperature is increased are found to be simitar to those obtained by decreasing incoming flow velocity in the incompressible case.
TL;DR: In this paper, a Galerkin mixed finite element method was used to predict the effect of fluid elasticity, temperature-dependent fluid properties, shear dependent fluid properties and viscous dissipation on the overall rate of heat transfer between a polymer melt and a sphere.
Abstract: A Galerkin mixed finite-element method was used to predict the effect of fluid elasticity, temperature-dependent fluid properties, shear-dependent fluid properties, and viscous dissipation on the overall rate of heat transfer between a polymer melt and a sphere. A correlation is developed for the Nusselt number that accounts for changes in Peclet number, viscous dissipation, and a temperature-dependent viscosity function
TL;DR: In this article, a numerical study has been conducted to examine the influence of free surface curvature, due to the presence of various contact angles, on thermocapillary convection within a cavity.
Abstract: A numerical study has been conducted to examine the influence of free surface curvature, due to the presence of various contact angles, on thermocapillary convection within a cavity. The results indicate that the system hydrodynamics are changed by a combination of surface temperature gradient modification due to the presence of the adiabatic meniscus and variation in the length of the free surface, as well as viscous force dependence on the wetting angle. Local and overall heat transfer rates are, in turn, altered. Wetting liquids exhibit decreased surface fluid velocities and convective heat transfer rates, while non-wetting liquids are characterized by more complicated behavior with local increases and decreases in surface fluid velocities and an increase in local heat transfer near the free surface.
TL;DR: In this paper, a laminar, mixed convection flow in a horizontal, parallel plate channel heated uniformly at the top and bottom plates was considered, and calculations were performed for Pr = 0.7, 0 < Ra∗ < 2.5 × 104, and values of a nondimensional conductance ratio in the range 10−5 < γ < 103.
Abstract: Calculations were performed for fully developed, laminar, mixed convection flow in a horizontal, parallel plate channel heated uniformly at the top and bottom plates. Spanwise conduction within the plates was considered, and calculations were performed for Pr = 0.7, 0 < Ra∗ < 2.5 × 104, and values of a nondimensional conductance ratio in the range 10−5 < γ < 103. It is shown that mixed convection heat transfer enhancement is restricted to the lower surface and that the attendant secondary flow induces large spanwise surface temperature variations for which the maximum temperature exceeds values associated with the upper surface. Increased conduction within the bottom plate weakens the secondary flow and decreases spanwise temperature variations. Results of the calculations have important implications in situations for which there is interest in maintaining reduced temperatures, as well as large heat transfer enhancement, at the bottom plate.
TL;DR: In this paper, the effect of thermal radiation and mixed convection on the thermal entrance region of a horizontal isothermally heated rectangular channel is numerically investigated and the effects of radiation and convection are examined.
Abstract: The interaction of thermal radiation with laminar mixed convection for a gray fluid in the thermal entrance region of a horizontal isothermally heated rectangular channel is numerically investigated. The vorticity-velocity formulation of the Navier-Stokes equation and the integral formulation for radiation solved by finite-element nodal approximation are employed. The effects of radiation and convection on local Nusselt number, the development of bulk temperature, and the friction factor are examined. Secondary flow induced by the buoyancy effects leads to a significant enhancement in heat transfer in the entrance region. The result shows that the existence of secondary flow causes fluctuations in local Nusselt number and this phenomenon is reduced by the effect of thermal radiation and a large aspect ratio.
TL;DR: In this article, a numerical procedure for solving radiative heat transfer problems within an absorbing-emitting-scattering media using variable nodal placement is presented based on the discrete exchange factor method, in which exchange factors are calculated from point to point (eliminating the need for multiple integrations).
Abstract: A numerical procedure for solving radiative heat transfer problems within an absorbing-emitting-scattering media using variable nodal placement is presented Based on the discrete exchange factor method, in which exchange factors are calculated from point to point (eliminating the need for multiple integrations), the procedure is shown to display good accuracy and great flexibility Examples for irregular geometries illustrate the compatibility of the method with finite-element mesh generators We show how local mesh refinement can be used to enhance the solution resolution in predetermined regions, which is especially important where high gradients exist In addition, we discuss the versatility of the procedure for calculating combined-mode (ie, radiation in the presence of conduction and/or convection) problems
TL;DR: In this article, a rigorous method based on variable substitution is described to circumvent numerical problems associated with phase disappearance/appearance, and test calculations show that selection of primary variables for the Newton iteration has a profound effect on the number of nonlinear iterations required for convergence.
Abstract: Numerical techniques are described for modeling two-phase (liquid and gas), two-component (water and air) nonisotkermal flow in fractured porous media. Interphase mass transfer, latent heat, conduction, convection, gravity, and capillary effects are included. A rigorous method based on variable substitution is described to circumvent numerical problems associated with phase disappearance/appearance. Test calculations show that selection of primary variables for the Newton iteration has a profound effect on the number of nonlinear iterations required for convergence. Comparisons with previously reported compulations indicate that the method used here is very efficient. For a fractured waste canister problem, a previously unreported pressure pulse phenomenon is predicted. Comparisons of one- and two-dimensional simulations show that one-dimensional results can be misleading.
TL;DR: In this paper, a computational methodology for simulating mixed convection melting of a pure substance is presented, which employs a stream function-vorticity-temperature formulation in conjunction with a time-variant mesh.
Abstract: A computational methodology for simulating mixed convection melting of a pure substance is presented. The mathematical model employs a stream function-vorticity-tem-perature formulation in conjunction with a time-variant mesh. Unlike most transformed grid techniques, the position of the phase front is determined implicitly on application of the Stefan condition. The model is then applied to the melting of a pure metal, gallium, for forced to free convection-dominated heat transfer. Results indicate that according to the relative intensity of buoyancy and inertia forces, the movement and the shape of the solid-liquid interface are considerably perturbed.
TL;DR: In this paper, a finite-difference scheme for solving the boundary layer equations governing laminar mixed convection heat transfer from a rotating sphere that is maintained at uniform surface heat flux and subjected to a uniform stream in the direction of its axis of rotation is presented.
Abstract: This paper presents a finite-difference scheme for solving the boundary layer equations governing laminar mixed (forced and free) convection heat transfer from a rotating sphere that is maintained at uniform surface heat flux and subjected to a uniform stream in the direction of its axis of rotation. Numerical results are presented to show the effect of a superimposed aiding or opposing free convection on the meridional and azimuthal velocities, wall shear stress components, separation angle, local Nusselt number, and wall temperature. As compared with power series studies available in the literature, the present scheme is capable of obtaining solutions for considerably larger values of the parameter Ta/Re2.
TL;DR: In this article, a multidimensional numerical solution is developed that predicts axisym-metric two-dimensional in-cylinder flows on the boundaries of curved wall cylinder heads, and three types of cylinder heads are considered: deep hemisphere, flat hemisphere, and flat plate.
Abstract: An algorithm for a multidimensional numerical solution is developed that predicts axisym-metric two-dimensional in-cylinder flows on the boundaries of curved wall cylinder heads. Three types of cylinder heads are considered: “deep hemisphere,” “flat hemisphere,” and “flat plate.” The time-dependent strong conservative law forms of the governing equations are written in axisymmetric nonorthogonal curvilinear coordinates. A fully staggered grid system is used for all variables, so that no explicit description of the pressure boundary conditions is necessary. An algebraic grid generation technique is used to map the complex fluid domain onto a rectangle for every time step. Hence the metric of the coordinate transformation can be determined by direct analytic differentiation. The discretized conservation equations are derived from a control volume approach and are solved by using a modification of the simple calculation procedure. The effects of the shapes of cylinder head on the velocity distribution are in...