Numerical Analysis Of Natural Convection Research Articles

Numerical analysis of natural convection in sodium plenum below the grid plate of a fast reactor during a severe accident

Heat transfer characteristics of liquid sodium are quite different from that of normal liquids because of its very low Prandtl number. Empirical correlations for convective heat transfer in sodium are rather limited because of inherent difficulties in performing sodium experiments. In this paper, transient and steady natural convection developing inside a cylindrical enclosure heated from the top and cooled along the vertical side wall is studied by a numerical analysis. This problem is of relevance to the safety analysis of sodium cooled pool type fast reactor. The focus of the present investigation is to determine the effect of plate thickness on the natural convection heat transfer characteristics. For the case of a thick top plate, in the transient regime, heat transfer is conduction dominated and Nusselt number is found to be inversely proportional to square root of time as in the case of a thin plate. But the steady state heat transfer coefficient between the lower surface of thick hot plate and liquid sodium is less by about 25% than for a thin plate at the same temperature as the lower surface. The reason for this behaviour is traced to the weaker convective current developed in the case of a thick plate. Based on detailed parametric studies, a correlation for Nusselt number is derived with a correlation coefficient of 0.99, for use in the reactor safety analysis. The Nusselt number is found to be a function of Boussinesq number, thermal conductivity ratio between the wall material and liquid sodium and non-dimensional thickness of the plate. The validity of the correlation is further checked by applying it to different data sets not used for the derivation of the correlation.

PIV and numerical analysis of natural convection in tilted enclosures filled with air and with opposite active walls

In this paper an analysis of natural convection in an enclosure filled with air and with opposite heated and cooled walls is performed; four different tilts of the cavity are investigated: θ=0,π6,π3 and π2. A complete definition of the velocity field in the cavity is obtained through PIV (particle image velocimetry) and is shown in terms of velocity contour maps and streamlines; the same results are obtained through numerical analysis and compared with the experimental ones: a very good agreement is found. In addition the thermal field is calculated and the value of the Nusselt number (Nu) next to the how wall is reported. A brief overview on a new PIV aspect is also discussed: since very small velocity fields are investigated, the effect of heating by the pulsed laser light becomes relevant, thus introducing a disturb on the measuring field that has never been considered for PIV, since it is generally treated as a completely non-intrusive technique.

Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid

A numerical analysis of natural convection has been performed for a two-dimensional triangular enclosure with partially heated from below and cold inclined wall filled with nanofluid in presence of magnetic field. Governing equations are solved by finite volume method. Flow pattern, isotherms and average Nusselt number are presented for 0 < Ha<100, 104 < Ra<107,0<ϕ < 0.05 and six cases that are made by location of heat sources. The results show in presence of magnetic field flow field is suppressed and heat transfer decreases. Furthermore it is observed that maximum reduction of average Nusselt number in high value of Ha occurs at Ra = 106. It is found the nanoparticles are more effective at Ra = 104 where conduction is more pronounced.

Numerical Analysis of Natural Convection in a Cylindrical Envelope with an Internal Concentric Cylinder with Slots

Detailed numerical analysis is presented for natural convection heat transfer in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with QUICK scheme. The results show that the system can reach steady state and be symmetric when the Rayleigh number is below 4 × 105. When the Rayleigh number is greater than 6 × 105, an asymmetric periodical solution is obtained although the initial field and boundary conditions were symmetric. As the Rayleigh numbers increase further, a quasi-periodic solution of the system is achieved at Ra = 2 × 106, and the periodicity is lost at Ra = 6 × 106. It is ascertained that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.

Numerical Analysis of Natural Convection in a Rectangle Cavity With Discrete Heat Source on the Bottom Wall

Numerical Analysis of Natural Convection in a Rectangle Cavity With Discrete Heat Source on the Bottom Wall

Numerical analysis of natural convection in a prismatic enclosure

Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

Numerical analysis of natural convection in a prismatic enclosure

Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

Experimental and Numerical Analysis of Natural Convection in Geometrically Modeled Core Catcher of the Liquid-Metal-Cooled Fast Reactor

In the Prototype Fast Breeder Reactor, a core catcher is provided as an in-vessel core debris retention device to collect, support, and maintain in subcritical configuration the relocated core debris generated from fuel melting as a consequence of a severe accident scenario. It acts as a barrier to prevent settling of debris onto the main vessel and helps to maintain the main vessel temperature within acceptable creep range. In the Safety Engineering Division of the Indira Gandhi Center for Atomic Research, model experiments are carried out in water using a geometrically similar model to understand natural convective heat transfer and fluid flow in and around the core catcher below the grid plate. Influences of cylindrical and annular central openings (chimney) through the core catcher assembly are investigated to assess their relative thermal performances. Resistive heating elements are used as heat source to simulate debris decay heat on the core catcher. Series of experiments were carried out with both configurations. Temperatures were monitored at critical positions and compared with numerical evaluation. Flow fields and isotherms are analyzed with a computational model to understand the fluid flow and heat transfer characteristics inside the cavity along with experimental data for specified steady-state temperatures on the heat source plate. Numerical results are found to be in good agreement with those obtained from the experiments. The combined efforts of numerical and experimental work conclude that core catcher assembly with annular chimney is better in terms of natural convection heat removal capability.

Numerical Analysis of Natural Convection in Porous Cavities with Partial Convective Cooling Conditions

Numerical Analysis of Natural Convection in Porous Cavities with Partial Convective Cooling Conditions

Numerical analysis of natural convection in shed roofs with eave of buildings for cold climates

A numerical study has been carried out on partially heated triangular enclosures with eave. The eave and inclined wall has a cold temperature. The laminar, two-dimensional, steady governing equations of natural convection are solved in the streamfunction-vorticity form using a finite difference technique. Streamline, isotherm and Nusselt number are presented for different parameters such as aspect ratio A R = H / L from 0.25 to 1, ratio of eave length E = L / n where n changes from 3 to 7 and Rayleigh number from 10 3 to 10 6 . It is observed that the heat transfer decreases with increasing aspect ratio for small Rayleigh number but increases for higher Rayleigh number. Heat transfer also increases with decreasing eave length.

Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure ϕ, which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ s and the aspect ratio A. The side wall inclination parameter θ s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A = 0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle ϕ is more influential on heat transfer and flow strength than that of the side wall inclination angle θ s . It is also found that a Bénard regime occurs around ϕ = 90 ° , which depends on the inclination of the side wall, Rayleigh number and aspect ratio.

Numerical Analysis of General Trends in Single-Phase Natural Circulation in a 2D-Annular Loop

The aim of this paper is to address fluid flow behavior of natural circulation in a 2D-annular loop filled with water. A two-dimensional, numerical analysis of natural convection in a 2D-annular closed-loop thermosyphon has been performed for various radius ratios from 1.2 to 2.0, the loop being heated at a constant flux over the bottom half and cooled at a constant temperature over the top half. It has been numerically shown that natural convection in a 2D-annular closed-loop thermosyphon is capable of showing pseudoconductive regime at pitchfork bifurcation, stationary convective regimes without and with recirculating regions occurring at the entrance of the exchangers, oscillatory convection at Hopf bifurcation and Lorenz-like chaotic flow. The complexity of the dynamic properties experimentally encountered in toroidal or rectangular loops is thus also found here.

Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall

Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10≤Ra≤1000, aspect ratio parameter AR in the range 0.25≤AR≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25≤λ≤1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.

C224 粒子沈降を伴う懸濁液の自然対流の数値解析(混相流)

C224 粒子沈降を伴う懸濁液の自然対流の数値解析(混相流)

Numerical analysis of natural convection in parallel, convergent, and divergent open‐ended channels

PurposeTo investigate the natural convection in open‐ended parallel, convergent, and divergent channels using a fully elliptic procedure without extending the domain outside the channel for the application of the boundary conditions at the inlet and outlet of the channels.Design/methodology/approachThe model is two‐dimensional and fully elliptic in x and y directions, and the equations are solved only inside the channel by the finite volume method using a co‐located arrangement with a segregated procedure and boundary fitted coordinates. The pressure‐velocity coupling is solved by the PRIME algorithm.FindingsThe results are shown in terms of velocity vectors, streamlines, isotherms, and the local and the average Nusselt number for all fluids and configurations investigated. For high values of the Rayleigh number, a recirculation region in the outlet of all investigated configurations and Prandtl numbers was observed. Based on the results, a single correlation is proposed to evaluate the average Nusselt number for all fluids and configurations analyzed.Research limitations/implicationsThe shown results are based on the following hypothesis: steady‐state, two‐dimensional, laminar flow, and Boussinesq's aproximation. The results are presented in following range of parameters: 105&lt;(Smax/L)RaSmax&lt;108, where Smax denotes the maximum distance between the plates and Ra denotes the Rayleigh number; half angle of convergence or divergence (θ): 5° and 15°; and Prandtl numbers: 0.7, 5.0, and 88.Originality/valueLocal and average Nusselt numbers, for Prandtl numbers varying from 0.70 to 88, and a correlation for the average Nusselt number for all fluids and configurations are presented. The results presented in this paper are useful to engineers and researchers involved in thermal design and numerical methods.

Numerical Analysis of Natural Convection in Porous Media: The Influence of Non-Darcian Terms and Thermal Dispersion

Numerical Analysis of Natural Convection in Porous Media: The Influence of Non-Darcian Terms and Thermal Dispersion

Experimental and numerical analysis of natural convection for Al–5.5% Cu alloy

Numerical and experimental investigations have been made for aluminum–5.5% copper (Al–5.5% Cu) binary alloy. During these investigations the effect of natural convection on the solidification process and the alloy structure are studied. No slip condition (stationary liquid metal) is proved to be the applicable condition at top boundaries of liquid metals exposed directly to the ambient (room temperature). Experimental and numerical results show good agreement. The results present, as the temperature increases the temperature gradient increases and so the natural convection currents. Natural convection flow is quantified and proved to work as a stirrer for temperatures higher or equal to 1100 K, i.e., eddy currents of the metal flow are strong enough to break the weak nuclei. So coarse grains are obtained in the solidified structure.

GDQ METHOD FOR NATURAL CONVECTION IN A SQUARE CAVITY USING VELOCITY–VORTICITY FORMULATION

ABSTRACT This article describes a compact numerical algorithm based on the generalized differential quadrature (GDQ) method for the numerical analysis of natural convection in a differentially heated square cavity. The velocity–vorticity form of the Navier–Stokes equations and energy equation are used to represent the mass, momentum, and energy conservations of the fluid medium in the cavity. The GDQ form of the governing equations and the vorticity definition at the boundaries are solved by a coupled solution algorithm using a global matrix scheme for all the field variables. The vorticity values at the boundary are correctly imposed using the GDQ method, which approximates a given space derivative with higher-order accuracy compared to the existing schemes based on Taylor's series expansion. This has assured a divergence-free solution for the flow field by satisfying the continuity constraint, though the pressure term is not used directly in the present formulation. The proposed algorithm is validated for a lid-driven cavity flow for Reynolds number Re = 100, 400, and 1,000, and the predicted velocity profiles are in excellent agreement with the benchmark solutions. The algorithm is then used to compute the average Nusselt number and flow parameters for natural convection in a square cavity for Rayleigh number Ra = 103, 104, 105, and 106. These results are in better agreement with the benchmark solutions than the results obtained by other numerical schemes, which used much finer grids compared to the present scheme.

Numerical analysis of natural convection in air in a vertical convergent channel with uniformly heated conductive walls

Natural convection in air in a convergent channel with the two principal flat plates at uniform heat flux with finite thickness and thermal conductivity was numerically investigated. Laminar, two-dimensional steady-state conditions were assumed. An extended computational domain was adopted, which allows to take into account the diffusion by both momentum and energy outside the channel. A comparison with experimental data was carried out. Stream function and temperature fields are presented. Average Nusselt numbers were evaluated and presented. Temperature profiles are strongly affected by the convergence angle at low Rayleigh numbers. At the lower minimum gap, streamlines and isotherms show a low pressure region in the channel due to a choked flow in its upper end. Numerical values of the Nusselt number are in good agreement with experimental results.

Numerical Analysis of Natural Convection and Mixing in Two-Fluid Stratified Pools With Internal Heat Sources

Abstract The heat transport in two-layer fluid systems has been investigated numerically for slice-type semicircular pools with internal heat sources. The fixed interface model has been applied to study natural convection in the system of the immiscible fluids. The double-diffusion model has been employed to describe the heat transfer and mixing for the miscible fluids. The numerical results are compared to data measured in the SIMECO experiments. Based on the numerical simulations, the effect of the ratio of the fluid properties has been quantified. The results are of interest for the corium melt coolability in a postulated severe accident scenario in a light water reactor.