Tall Cavity Research Articles

Apron design for protecting double‐skin façade fires

SummaryAlthough double‐skin façade (DSF) is an environmental‐friendly architectural feature, its fire behaviour is a deep concern. The interior glass system including the glass pane, metal frame and associated accessories will be hotter than the exterior glass system as demonstrated by earlier studies. The glass pane above the fire room will be broken to spread flame into the upper compartment. Aprons are proposed to protect the air cavity of DSF in a way similar to those outside a single‐skin façade. In this paper, the effect of aprons in protecting against fire spread from an underlying compartment to the compartments above by preventing glass breakage of the inner glass pane was studied. Fire and smoke from a post‐flashover room fire adjacent to the DSF would be trapped in the air cavity between the two glass panes. Spreading of hot gases with different apron widths was studied by numerical simulations with CFD first. Fire environment with and without breaking the apron immediately above the fire room was studied. Full‐scale burning tests on part of an experimental DSF rig were then carried out to demonstrate the performance of horizontal apron in the DSF rig of 6 m tall and air cavity depth of 2 m with different apron widths. All demonstrated that providing apron is appropriate in protecting DSF fires. Copyright © 2014 John Wiley & Sons, Ltd.

Evaluation of Turbulent Models for Natural Convection of Compressible Air in a Tall Cavity

Numerical simulation of turbulent natural convection of compressible air in a tall cavity is carried out. In order to evaluate the accuracy of turbulent models, various turbulent models are applied to solve the natural convection in a tall cavity that has different temperatures imposed on two opposing vertical walls. For the large-eddy simulation (LES) model, Smagorinsky subgrid scale (SGS) and dynamic Smagorinsky SGS are also applied to the same cases in order to investigate the differences in temperature and velocity caused by different turbulent models. It is found that the k–ϵ model has a high accuracy of predicting velocity distribution at various sampled lines by comparing with experimental data at Rayleigh number of 2.03 × 1010 and 3.37 × 1010, while the LES model has good performance in predicting temperature distributions.

From catʼs eyes to multiple disjoint natural convection flow in tall tilted cavities: A direct primitive variables approach

Abstract Natural convection fluid flow in air-filled tall tilted cavities is studied numerically with a new direct projection method on the Boussinesq approximation in primitive variables. The study deals with “catʼs eyes” instabilities and multiple disjoint cells as the aspect ratio A and the angle of inclination ϕ of the cavity vary. The flows are validated with those reported before using the stream function-vorticity variables. New cases, A = 12 and 20 varying ϕ , lead to get more insight on the physical phenomenon.

Application of dynamic global-coefficient subgrid-scale models to turbulent natural convection in an enclosed tall cavity

Large-eddy simulations examining natural convection in an enclosed cavity with the simultaneous presence of laminar, transitional, and turbulent flow regimes were conducted. The Rayleigh number based on height of the cavity is 4.6 × 1010. Different dynamic global-coefficient procedures to compute the Vreman [A. W. Vreman, “An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications,” Phys. Fluids 16, 3670 (2004)] model coefficient were implemented for the subgrid-scale tensors in both the momentum and energy equations. Based on comparison with experimental and existing numerical data, it is shown that the dynamic model derived from the “global equilibrium” hypothesis gives favorable results in the mean flow and turbulence quantities. Nevertheless, because of higher subgrid-scale dissipation, transition to a turbulent flow is postponed when the Vreman model coefficient is either uniform or determined dynamically using the Germano identity approach. This suggests that much finer grid is desired when using these models in order to better capture the weak transitional boundary layer. Further, by exploring the instantaneous flow dynamics, it is demonstrated that characteristics of the coherent structures which resemble streaks in forced convection boundary layers are somewhat dissimilar in the different models.

Low Reynolds-number effect on the turbulent natural convection in an enclosed 3D tall cavity

A numerical prediction of the natural convection of air in an enclosed tall differentially heated rectangular cavity of 0.076 × 2.18 × 0.52 m is detailed in this present paper. Two differential temperatures between the lateral plates are considered, of respectively, 19.6◦C and 39.9◦C, corresponding to low and high Rayleigh numbers, i.e., 0.86 × 10 6 and 1.43 × 10 6 . The mean equations for a three-dimensional compressible flow in Cartesian coordinates are deduced from the conservative mass, momentum and energy equations. The closure of the motion equations is achieved by means of two statistical turbulence models coupled with the wall functions: the standard k – ∈ model and its derived RNG one. The second model is used to improve the effect of low-Reynolds numbers, particularly in the viscous sublayer close to the wall. The numerical solution of the RANS equations is solved through a finite volume method based on a power-law discretisation scheme and a pressure–velocity SIMPLE algorithm, using a CFD code. The three-dimensional study allowed the detection of the toroidal secondary flow.

Stability characteristics of conjugate natural convection boundary layers

Flow in a differentially heated two dimensional rectangular cavity, partitioned in the centre by an infinitely conducting vertical wall, has been examined with numerical simulations over Rayleigh numbers around $10^{10}$ at Prandtl number $7.5$. The configuration is an idealised version of a flow which occurs commonly in engineering settings and is of fundamental importance. Heat is transferred between both sides of the cavity through the conducting wall with natural convection boundary layers forming on all vertical surfaces. We show for the first time that the flow becomes oscillatory above Rayleigh number $1.2\times 10^{10}$ for cavity height to width ratio of two, and above Rayleigh number $1.4\times 10^{10}$ for cavity height to width ratio of one. The results indicate that the instability is a convective boundary layer instability which becomes absolutely unstable as a result of the thermal coupling across the partition wall. References S. Paolucci and D. R. Chenoweth. Transition to chaos in a differentially heated vertical cavity. J. of Fluid Mech., 201:379--410, 1989. doi:10.1017/S0022112089000984 R. Anderson and A. Bejan. Heat transfer through single and double vertical walls in natural convection: Theory and experiment. Int. J. Heat Mass Transfer, 24(10):1611--1620, 1981. doi:10.1016/0017-9310(81)90069-7 Tatsuo Nishimura, Mitsuhiro Shiraishi, Fumio Nagasawa, and Yuji Kawamura. Natural convection heat transfer in enclosures with multiple vertical partitions. Int. J. Heat Mass Transfer, 31(8):1679--1686, 1988. doi:10.1016/0017-9310(88)90280-3 J. W. Elder. Turbulent free convection in a vertical slot. J. of Fluid Mech., 23:99--111, 1965. doi:10.1017/S0022112065001258 J. Patterson and J. Imberger. Unsteady natural convection in a rectangular cavity. J. of Fluid Mech., 100:65--86, 1980. doi:10.1017/S0022112080001012 G. N. Ivey. Experiments on transient natural convection in a cavity. J. of Fluid Mech., 144:389--401, 1984. doi:10.1017/S0022112084001658 J. C. Patterson and S. W. Armfield. Transient features of natural convection in a cavity. J. Fluid Mech., 219:469--497, 1990. doi:10.1017/S0022112090003032 P. Le Quere. Transition to unsteady natural convection in a tall water-filled cavity. Phys. Fluids A, 2(4):503--515, 1990. doi:10.1063/1.857750 S. W. Armfield and John C. Patterson. Wave properties of natural-convection boundary layers. J. Fluid Mech., 239:195--211, 1992. doi:10.1017/S0022112092004373 R. J. A. Janssen and R. A. W. M. Henkes. Influence of Prandtl number on instability mechanisms and transition in a differentially heated square cavity. J. of Fluid Mech., 290:319--344, 1995. doi:10.1017/S0022112095002539 S. Armfield and R. Janssen. A direct boundary-layer stability analysis of steady-state cavity convection flow. Int. J. Heat Fluid Flow, 17(6):539--546, 1996. doi:10.1016/S0142-727X(96)00065-3 J. C. Patterson, T. Graham, W. Schopf, and S. W. Armfield. Boundary layer development on a semi-infinite suddenly heated vertical plate. J. Fluid Mech., 453:39--55, 2002. doi:10.1017/S0022112001006553 R. A. W. M. Henkes. Turbulent natural convection boundary layers. PhD thesis, University of Delft, 1990. B. P. Leonard. A stable and accurate convective modelling procedure based on quadatic upstream interpolation. Comp. Meth. Appl. Eng., 19:59--98, 1979. doi:10.1016/0045-7825(79)90034-3 J. H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics. Springer, 2002. S. E. Norris. A Parallel Navier--Stokes Solver for Natural Convection and Free Surface Flow. PhD thesis, University of Sydney, 2000. R. Janssen and S. Armfield. Stability properties of the vertical boundary layers in differentially heated cavities. Int. J. Heat Fluid Flow, 17(6):547--556, 1996. doi:10.1016/S0142-727X(96)00077-X

From catʼs eyes to disjoint multicellular natural convection flow in tall tilted cavities

Numerical results of two-dimensional natural convection problems, in air-filled tall cavities, are reported to study the change of the catʼs eyes flow as some parameters vary, the aspect ratio A and the angle of inclination ϕ of the cavity, with the Rayleigh number Ra mostly fixed; explicitly, the range of the variation is given by 12⩽A⩽20 and 0°⩽ϕ⩽270°; about Ra=1.1×104. A novelty contribution of this work is the transition from the catʼs eyes changes, as A varies, to a disjoint multicellular flow, as ϕ varies. These flows may be modeled by the unsteady Boussinesq approximation in stream function and vorticity variables which is solved with a fixed point iterative process applied to the nonlinear elliptic system that results after time discretization. The validation of the results relies on mesh size and time-step independence studies.

General expressions for the calculation of air flow and heat transfer rates in tall ventilation cavities

Solar heated tall ventilation cavities including solar chimneys are used to enhance natural ventilation of buildings. A validated CFD model was used to predict the buoyancy-driven air flow and heat transfer rates in vertical ventilation cavities with various combinations of heat distribution on two vertical walls ranging from symmetrical to fully asymmetrical heating. The natural ventilation rate and heat transfer rate have been found to vary with the total heat input, heat distribution on the cavity walls, cavity width and height and inlet opening position. General expressions for these variables have been obtained and presented in non-dimensional terms, Nusselt number, Reynolds number, Rayleigh number and aspect ratio (H/b), as Nu = f(Ra, H/b) and Nu = f(Ra, Re) or Re = f(Ra, Nu), for natural ventilation design.

Numerical Study of Natural Convection in a Differentially-Heated Rectangular Cavity Filled with TiO<sub>2</sub>-Water Nanofluid

In this study, the buoyancy-driven fluid flow and heat transfer in a differentially-heated rectangular cavity filled with the TiO2-water nanofluid is investigated numerically. The left and the top walls of the cavity are maintained at constant temperatures Thand Tc, respectively, with Th> Tc.The enclosure’s right and bottom walls are kept insulated. The governing equations are discretized using the finite volume method. A proper upwinding scheme is employed to obtain stabilized solutions for high Rayleigh numbers. Using the developed code, a parametric study is undertaken, and the effects of pertinent parameters, such as, the Rayleigh number, the aspect ratio of the cavity and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the cavity are investigated. It is observed from the results that by increasing the volume fraction of the nanoparticles, the mean Nusselt number of the hot wall increases for the shallow cavities; while, the reverse trend occurs for the tall cavities. Moreover, the heat transfer enhancement utilizing nanofluid is more effective at Ra = 103.

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.

Rayeilgh number effect on the turbulent heat transfer within a parallelepiped cavity

This purpose is about a three dimensional study of natural convection within cavities. This problem is receiving more and more research interest due to its practical applications in the engineering and the astrophysical research The turbulent natural convection of air in an enclosed tall cavity with high aspect ratio (AR=H/W=28.6) is examined numerically. Two cases of differential temperature have been considered between the lateral cavity plates corresponding, respectively, to the low and high Rayleigh numbers: Ra=8.6?105 and Ra=1.43?106 [1]. For these two cases, the flow is characterized by a turbulent low Reynolds number. This led us to improve the flow characteristics using two one point closure low-Reynolds number turbulence models: RNG k-e model and SST k-w model, derived from standard k-e model and standard k-w model, respectively. Both turbulence models have provided an excellent agreement with the experimental data. In order to choose the best model, the average Nusselt number is compared to the experiment and other numerical results. The vorticity components surfaces confirm that the flow can be considered two-dimensional with stretched vortex in the cavity core. Finally, a correlation between Nusselt number and Rayleigh number is obtained to predict the heat transfer characteristics.

Investigation of natural circulation in cavities with uniform heat generation for different Prandtl number fluids

Natural convection in enclosures with uniform heat generation and isothermal side walls is studied here. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 106. For a horizontal square cavity, the flow becomes periodically oscillating at Ra=5×104 and chaotic at Ra=8×105. With a slight increase in the inclination angle, the oscillations die and for inclination angles greater than 150, the flow attain a steady state over a range of Ra. It is found that for tall cavities (aspect ratio>1), the steady-state solution is obtained for all values of Ra considered here. However, for wide cavities (aspect ratio<1), an oscillatory flow regime is observed. The maximum temperature within the cavity is calculated for the range of Ra, aspect ratio and Pr number. Correlations for the maximum cavity temperature is presented here. The values of critical Rayleigh number at which the convection sets in the rectangular cavity are also studied and two distinct criteria are determined to evaluate the critical Rayleigh number. Further, a three-dimensional simulation is performed for a cubic cavity. It is found that the steady state solutions are obtained for all Rayleigh number, except at Ra=106. This is in contrast to the predictions for a two-dimensional square cavity, which has an oscillatory zone from Ra=5×104 onwards.

Natural Convection in a Partially Heat Generating Rod Bundle Inside an Enclosure

Buoyancy induced flows in a partially heat generating rod bundle enclosed inside a tall cavity are investigated. First, a detailed experimental study is carried out, and the thermal hydraulics is analyzed at different power inputs and boundary cooling rates of the enclosure. Later, a generalized non-Darcy simulation is developed using a heat generating orthotropic porous media approach and is compared with the experimental results. The results of a numerical simulation for natural convection in enclosed partially heat generating rod bundles satisfactorily predict the temperature distribution within the rod bundle. Finally, a parametric study is carried out by varying the porosity (pitch to diameter ratio of the rod bundle) of the considered enclosure for the understanding of flow physics and heat transfer in such applications.

Development and Evaluation of a Prototype Solid Particle Receiver: On-Sun Testing and Model Validation

A prototype direct absorption central receiver, called the solid particle receiver (SPR), was built and evaluated on-sun at power levels up to 2.5 MWth at Sandia National Laboratories in Albuquerque, NM. The SPR consists of a 6 m tall cavity through which spherical sintered bauxite particles are dropped and directly heated with concentrated solar energy. In principle, the particles can be efficiently heated to a temperature in excess of 900°C, well beyond the stability limit of existing nitrate salt formulations. The heated particles may then be stored in a way analogous to nitrate salt systems, enabling a dispatchable thermal input to power or fuel production cycles. The focus of this current effort was to provide an experimental basis for the validation of computational models that have been created to support improved designs and further development of the solid particle receiver. In this paper, we present information on the design and construction of the solid particle receiver and discuss the development of a computational fluid dynamics model of the prototype. We also present experimental data and model comparisons for on-sun testing of the receiver over a range of input power levels from 1.58–2.51 MWth. Model validation is performed using a number of metrics including particle velocity, exit temperature, and receiver efficiency. In most cases, the difference between the model predictions and data is less than 10%.

Three-Dimensional Study of Heat and Mass Transfer in a Partially Porous Elongated Cavity

A 3D numerical analysis is carried out to investigate heat and mass transfer in a partly porous cavity of high aspect ratio. The goal is to determine the best physical and geometrical parameters that allow optimal heat and mass transfer rate in such domain used in a solar adsorption cooling system. The computational domain consists of a tall cavity heated on the left vertical wall and cooled on the opposing wall. The SIMPLE algorithm is used to handle the velocity pressure coupling. Simulation results allow determining the optimal configuration of the used porous substrate and plain fluid position in the cavity in order to optimize the performance of such solar adsorption cooling installation.

How many secondary flows are in 'Leonard's vertical slot'?

The preconditioned TFQMR algorithm of the Krylov subspace method is implemented into SIMPLER as the inner-iteration method. In order to compare with Leonard and Drummond's results, QUICK and PWL schemes are applied respectively to solve the two-dimensional natural convection in a vertical tall cavity. From simulation results at very fine grids, it is found that although there are only minor difference in the Nusselt numbers, the numbers of secondary flows in that tall slot is not definite, being 11 or 12 depending on the computational conditions.

On the appearance of Moffatt eddies in viscous cavity flow as the aspect ratio varies

Two-dimensional Stokes flow in a rectangular driven cavity is studied. Flow in very tall or shallow cavities has many counter-rotating eddies lying along the cavity centerline. This structure is investigated by constructing asymptotic approximations to the flow based on the assumptions A⪡1 and A⪢1, where A is the cavity’s aspect ratio. We show that the number of eddies increases as A tends to infinity or zero and derive asymptotic formulas for the values of the aspect ratio at which the streamline topology bifurcates and a new eddy appears. We concentrate particularly on flow driven by translation of the top and bottom cavity walls with equal and opposite velocities. For this benchmark problem our asymptotics are able to connect existing computations (performed in the approximate range of 10−1≤A≤101) with Moffatt’s 1964 theory for an infinite channel (i.e., A=0 or ∞). We show that tall cavities have sequences of eddies which match the infinite channel flow, as observed in the previous computations. In contrast, shallow cavities have only half the number of eddies and a more complicated streamline topology. In both cases our asymptotic approximations give analytic formulas for the number of eddies and the shape of the streamlines. Other flows, corresponding to different driving at the boundaries, are also discussed and can be treated by the asymptotic methods we derive.

Effect of the magnetic field and heat generation on the free convection flow in a tall cavity filled with a porous medium

An analytical study of the steady magnetohydrodynamics (MHD) free convection in an tall cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. It is considered that the Darcy law model is used. It is assumed that a uniform magnetic field normal to the walls of the cavity is externally imposed. The values of the governing parameters are as follows: Hartmann number \(\operatorname{Ha}=0, 10\) and \(50\), Rayleigh number \(\operatorname{Ra} = 10^{3}\), and the aspect ratio \(a=0.01\). The velocity and temperature profile are determined. These profiles are presented graphically at the center line of the cavity. It is found that the analytical solution is in very good agreement with the numerical solution which is obtained by solving partial differential equations using a finite-difference method.

Effect of the surface thermal radiation on turbulent natural convection in tall cavities of façade elements

The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified numerically. The parameters considered were: the Rayleigh number 109–1012, the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total heat transfer has a maximum value of 15.19% (Ra = 109, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 1012, A = 80) with e* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity were observed. Two different temperature patterns were observed a conductive regime Ra = 109 and a boundary layer regime Ra = 1012.

Numerical Experiments in Turbulent Natural Convection Using Two-Equation Eddy-Viscosity Models

This work is focused on the simulation and prediction of turbulent natural convection flows by means of two-equation eddy-viscosity models. In order to show the generality, precision, and numerical issues related to these models under natural convection, three different buoyancy-driven cavities have been simulated: a tall cavity with a 30:1 aspect ratio, a cavity with a 5:1 aspect ratio, and, finally, a 4:1 aspect ratio cavity. All cases are solved under moderate and∕or transitional Rayleigh numbers (2.43×1010, 5×1010, and 1×1010, respectively) and all simulations are compared to experimental and∕or direct numerical simulation data available in literature. These different situations allow to check the applicability of two-equation eddy-viscosity models in buoyancy-driven flows, giving criteria on computational effort∕precision and their physical behavior.