Cubical Enclosure Research Articles

Effects of a Heated Strip Arrangement on Heat Transfer Rate in Cubical Enclosures

Effects of a Heated Strip Arrangement on Heat Transfer Rate in Cubical Enclosures

Mathematical simulation of nonstationary regimes of natural convection in a cubical enclosure with finite-thickness heat-conducting walls

Nonstationary regimes of conjugate thermal-gravitational convection in a cubical enclosure in the conditions of horizontal temperature difference is numerically analyzed. The external surfaces of two opposite walls were at constant different temperatures, the rest external edges were considered adiabatic. The mathematical model based on Oberbeck-Bussinesq equations is formulated in dimensionless natural velocity-pressure variables. Typical temperature and velocity fields, which represent the effect of the nonstationarity factor, Prandtl number, and thermophysical characteristics of the enclosure solid walls on the flow and heat transfer, are obtained.

Numerical and Experimental Study of Rayleigh–Bénard–Kelvin Convection

We performed experimental and numerical studies of combined effects of thermal buoyancy and magnetization force applied on a cubical enclosure of a paramagnetic fluid heated from below and cooled from top. The temperature difference between the hot and cold wall was kept constant. After considering neutral situation (i.e. a pure natural convection case), magnetic fields of different intensity were imposed. The magnetization force produced significant changes in flow (transition from laminar to turbulent regimes), wall-heat transfer (enhancement) and turbulence (turbulence structures reorganization). The strong magnetic field and its gradients were generated by a superconducting magnet which can generate magnetic field up to 10 T and where gradients of the magnetic induction can reach up to 900 T2/m. A good agreement between experiments and numerical simulations was obtained in predicting the integral wall heat transfer over entire range of considered working parameters. Numerical simulations provided a detailed insights into changes of the local wall-heat transfer and long-term time averaged first and second moments for different strengths of the imposed magnetic induction.

On the suitability of steady RANS CFD for forced mixing ventilation at transitional slot Reynolds numbers

Accurate prediction of ventilation flow is of primary importance for designing a healthy, comfortable, and energy-efficient indoor environment. Since the 1970s, the use of computational fluid dynamics (CFD) has increased tremendously, and nowadays, it is one of the primary methods to assess ventilation flow in buildings. The most commonly used numerical approach consists of solving the steady Reynolds-averaged Navier-Stokes (RANS) equations with a turbulence model to provide closure. This article presents a detailed validation study of steady RANS for isothermal forced mixing ventilation of a cubical enclosure driven by a transitional wall jet. The validation is performed using particle image velocimetry (PIV) measurements for slot Reynolds numbers of 1000 and 2500. Results obtained with the renormalization group (RNG) k-ε model, a low-Reynolds k-ε model, the shear stress transport (SST) k-ω model, and a Reynolds stress model (RSM) are compared with detailed experimental data. In general, the RNG k-ε model shows the weakest performance, whereas the low-Re k-ε model shows the best agreement with the measurements. In addition, the influence of the turbulence model on the predicted air exchange efficiency in the cubical enclosure is analyzed, indicating differences up to 44% for this particular case. This article presents a detailed numerical study of isothermal forced mixing ventilation driven by a low-velocity (transitional) wall jet using steady computational fluid dynamics (CFD) simulations. It is shown that the numerically obtained room airflow patterns are highly dependent on the chosen turbulence model and large differences with experimentally obtained velocity fields can be present. The renormalization group (RNG) k-ε model, which is commonly used for room airflow modeling, shows the largest deviations from the measured velocities, indicating the care that must be taken when selecting a turbulence model for room airflow prediction. As a result of the different predictions of the flow pattern in the room, large differences are present between the predicted air exchange efficiency obtained with the four tested turbulence models, which can be as high as 44%.

An analysis of unsteady thermal convection of paramagnetic fluid in cubical enclosure under strong magnetic field gradient

The experimental studies of the flow and heat transfer of a paramagnetic fluid inside a cubical enclosure in a configuration heated from below and subjected to various strong non-uniform magnetic field gradients are presented. In contrast to the previously reported studies in literature, which observed solely laminar flow regimes, the appearance and sustenance of the periodic- and fully transient – flow motions for the very first time were investigated. This was consequence of using significantly stronger magnetic field gradient (up to 900 T2/m) than those used in previous studies (up to 200 T2/m). The fluid flow was studied at two Rayleigh numbers: 7.89·105 and 1.86·106. Non-monotonic behaviour of flow with increase of imposed magnetic field gradients was observed for both cases. Detailed analysis (Fast Fourier Transform) of temperature time series has been reported.

Performance of DOM and IDA with different angular discretization methods in 3-D absorbing–emitting–scattering media

Predicted accuracy and computationally efficiency of Discrete Ordinates Method (DOM) and Improved Differential Approximation (IDA) were evaluated by applying both methods to cubical enclosure problems containing purely isotropically/linearly anisotropically scattering/absorbing–emitting–isotropically scattering medium and comparing their predictions with benchmark solutions available in the literature. Performances of DOM and IDA with S8, S10 and T4 quadratures were assessed by comparing their predictions against benchmark solutions. DOM with S8 and IDA with T4 were found to provide more accurate and efficient solutions compared to other discretization schemes. However, overall comparisons reveal that DOM S8 produces higher accuracy and computational efficiency than IDA T4 on all test problems under consideration.

Oscillatory states in thermal convection of a paramagnetic fluid in a cubical enclosure subjected to a magnetic field gradient

We report experimental and numerical studies of combined natural and magnetic convection of a paramagnetic fluid inside a cubical enclosure heated from below and cooled from above and subjected to a magnetic field gradient. Values of the magnetic field gradient are in the range 9≤|grad|b(0)|(2)|≤900 T(2)/m for imposed magnetic field strengths in the center of the superconducting magnet bore of 1≤|b(0)|(max)≤10 T. Very good agreement between experiments and simulation is obtained in predicting the integral heat transfer over the entire range of working parameters (i.e., thermal Rayleigh number 1.15×10(5)≤Ra(T)≤8×10(6), Prandtl number 5≤Pr≤700, and magnetization number 0≤γ≤58.5). We present a stability diagram containing three characteristic states: steady, oscillatory (periodic), and turbulent regimes. The oscillatory states are identified for intermediate values of Pr (40≤Pr≤70) and low magnetic field (|b(0)|(max)≤2 T). Turbulent states are generated from initially stable flow and heat transfer regimes in the range of 70≤Pr≤500 for sufficiently strong magnetic field (|b(0)|(max)≥4 T).

Lattice Boltzmann Analysis of the Heat Transfer in Cubical Enclosures

The purpose of this work is to study hydrodynamic and thermal characteristics of air contended into a differentially heated cubic cavity. Due to their importance in the characterization of heat transfer in this kind of configuration, the effect of some parameters is analyzed. It consists in the Rayleigh number and the aspect ratio. In order to resolve the governing equations, the Lattice-Boltzmann method coupled with finite difference method is used.

Transients and turbulence pockets in thermal convection of paramagnetic fluid subjected to strong magnetic field gradients

We performed combined experimental and numerical studies of the flow and heat transfer of a paramagnetic fluid inside a differentially heated cubical enclosure subjected to various strong non-uniform magnetic field gradients. Two different heating scenarios are considered: unstable (heated from below) and stable (heated from above) initial thermal stratification. In contrast to the previously reported studies in literature, which observed solely laminar flow regimes, we investigated also appearance and sustenance of the periodic- and fully transient-flow motions for the very first time. This was consequence of using significantly stronger magnetic field strength (up to 10 T experimentally, and up to 15 T numerically) than those used in previous studies (up to 5 T). Detailed comparison between experiments and numerical simulations are performed and generally very good agreements were obtained.

A numerical simulation of double-diffusive conjugate natural convection in an enclosure

Transient thermosolutal convection in a cubical enclosure having finite thickness walls filled with air, submitted to temperature and concentration gradients, is studied numerically. In the first series of numerical simulations, the influence of Rayleigh number on fluid motion and heat and mass transfer ( N = 1, Ra = 10 4–10 5) is analyzed. The second series deals with the effect of the dimensionless time ( N = 1, Ra = 5 × 10 4, τ = 1–100). In the third series the influence of the conductivity ratio on heat and mass transfer ( N = 1, Ra = 10 5, k fs = 0.037, 0.0037) is investigated. The fourth series deals with the effect of the mass source sizes on the heat and mass transfer regimes. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.

Natural Convection Flow in a Cubical Enclosure with a Heated Strip

DOI: 10.2514/1.36648 Natural convection flow in a cubical enclosure with a heated strip is solved numerically using the finite element method. The heated strip simulates an array of electronic chips. The heated strip is attached to the front wall and maintained at high temperature, and the entire opposite wall is maintained at low temperature. The Rayleigh numbers of 10 4 ,1 0 5 , and 10 6 are considered in the analysis and the heated strip is either vertically or horizontally attachedtothewall.Theresultsindicatethattheheattransferstronglydependsontheorientationandpositionofthe heated strip. The maximum Nusselt number for the horizontal heated-strip configuration can be achieved if the heater is placed at the lower half of the wall, whereas for the vertical heated-strip case, the maximum Nusselt occurs whenthe heated stripis placed inthe middle of the wall. Increasing the Rayleigh number significantlyincreases heat transfer in the enclosure for the examined case studies.

Dissolution of a solid sphere in a multicomponent liquid in a cubic enclosure

In this paper we present a numerical investigation of the dissolution process of a solid spherical particle in a cubical enclosure. The numerical setup is inspired by the experimental observation of the dissolution of Al2O3 particles in a CaO–Al2O3–SiO2 containing liquid at elevated temperatures by confocal scanning laser microscopy. To gain insight into the dissolution behavior, a systematic numerical study has been undertaken of several parameters influencing the dissolution process. The presented results can directly be used to estimate the time to complete dissolution or the diffusion coefficient in a dissolution experiment.

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

AbstractA parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Reτ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 106 is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.

Effect of an External Magnetic Field on the 3-D Unsteady Natural Convection in a Cubical Enclosure

A numerical study of natural convection in a differentially heated cubic cavity for Pr = 0.054 and in the presence of an external magnetic field orthogonal to the isothermal walls is carried out. The effect of this field on the three-dimensional spiraling transverse flow is analyzed. In addition to the damping and laminarization effects of the external magnetic field, an organization of the central three-dimensional motion is observed. Also, a depiction of the merging phenomena of the two central vortices is shown.

Lattice Boltzmann method for double-diffusive natural convection

A lattice Boltzmann method for double-diffusive natural convection is presented. The model combines a multicomponent lattice Boltzmann scheme with a finite-difference solution of the energy equation to simulate natural convection caused by gradients in temperature and concentration. The model is validated both in two and three dimensions, and the agreement with literature data is satisfactory. A case study of thermosolutal convection of air in a cubical enclosure with horizontal thermal and solutal gradients is presented, exhibiting a rich variety of flow structures.

Heat transfer enhancement in cubical enclosures with vertical fins

Natural convection of air in a cubical enclosure with a thick partition fitted vertically on the hot wall is numerically investigated for Rayleigh numbers of 10 3–10 6. A three dimensional convective circulation is generated, in which the cold flow sweeps the fin faces and the hot wall, with low flow blockage. The combined contributions of these faces cause heat transfer enhancements over 40% at high Rayleigh numbers and thermal conductivity ratios ( R k ). These enhancements significantly exceed the ones obtained with horizontal fins. Even low R k values cause heat transfer enhancements, except at Ra = 10 4.

Three-dimensional natural convection in finned cubical enclosures

Three-dimensional natural convection of air in a cubical enclosure with a fin on the hot wall is numerically investigated for Rayleigh numbers of 10 3–10 6. The fin, with a thickness of 1/10 of the cavity side, is placed horizontally on the hot wall. The solid to fluid thermal conductivity ratio ( R k ) and the fin width are varied. Because the fin is shorter than the cavity side, the cold flow sweeps the lower fin face and the hot wall at the clearances between the fin sides and the lateral walls, where high vertical velocities are reached. The fin inhibits the frontal and lateral access of fluid to the upper fin face, especially at low Rayleigh numbers. Low values of R k cause heat transfer reductions. The contribution of the fin faces increases at high R k causing heat transfer enhancements above 20%, which exceed the ones obtained in most two-dimensional studies. In the range of Ra from 10 5 to 10 6, maximum heat transfer rates are found for dimensionless fin widths of 0.6 and 0.8 respectively. It is concluded that for 10 5 ⩽ Ra ⩽ 10 6 a fin of partial width is more effective in promoting heat transfer than a fin of full width.

Indoor Deposition and Forced Re-suspension of Respirable Particles

The rate at which particles deposit and re-suspend from indoor surfaces is an essential parameter in determining human exposure to aerosol particles. In this study, we investigate experimentally particle deposition and forced re-suspension in a cubical enclosure for three particle sizes (0.7, 1.5 and 4 m). For particle deposition, the results are presented in terms of particle deposition velocity. It was observed that the particle deposition velocity is particularly significant for the floor surface. Deposition on vertical and ceiling surfaces becomes important only when these surfaces are electrically charged. Air humidity did not influence the particle deposition apart from when it was close to saturation. Re-suspension of particles from the floor surface due to household activities was also studied. It was observed that small particles are more difficult to detach from the floor than bigger ones. Besides, there is a pressure above which re-suspension is very likely to occur (minimum re-suspension pressure). This minimum pressure is dependent on the particle size.

Experimental and numerical analyses of magnetic convection of paramagnetic fluid in a cube heated and cooled from opposing verticals walls

The effect of a strong magnetic field on the natural convection of paramagnetic fluid in a cubical enclosure was examined. The enclosure was heated from one vertical copper wall with electric wire and cooled from the opposite wall with water pumped from a thermostating bath. The temperatures of the cooled and heated walls were measured with six thermocouples. The working fluid consisted of 80% mass glycerol aqueous solution containing 0.8 [mol⋅(kg of solution) −1] of gadolinium nitrate hexahydrate to make it paramagnetic. A thermochromic liquid crystal slurry was added to the working fluid in order to visualize the temperature field in the illuminated cross-section. Numerical computations were carried out for a system corresponding to the experimental one, and computed Nusselt numbers agreed well with those obtained experimentally.

Buoyant convection in a cubical enclosure under time-periodic magnetizing force

A numerical investigation is made of buoyant convection of a paramagnetic fluid in a cubical enclosure under constant gravity g 0. Conventional buoyant convection arises by maintaining different temperatures at two opposite vertical sidewalls. The other walls are thermally insulated. To this basic layout, an electric wire is placed below the bottom horizontal wall to produce a magnetic field. The magnetizing force is induced, which modifies the convective flow and heat transfer characteristics. Comprehensive numerical solutions have been acquired to the governing equations. Of interest are the cases when the strength of the magnetizing force is time-periodic. The computed results reveal the presence of resonance, which is characterized by maximal amplification of the fluctuations of heat transport in the interior. The flow is shown to resonate to the basic mode of internal gravity oscillations. The study points to the feasibility of using the time-periodic magnetizing force as an effective regulator of the convective fluid system.