Tall Cavity Research Articles

Multi-cellular natural convection in the melt during convection-dominated melting

Convection-dominated melting in a rectangular cavity is analyzed numerically with particular attention to the multi-cellular flows in the melt. At the earlier stage of the melting, the melt region is quite similar to a cavity with high aspect ratio, where the multi-cellular natural convection appears. Numerical results show that the formation and evolution of the multiple flow cells in the melt region is approximately similar to that of a single-phase flow in a tall cavity with the same aspect ratio; however, the continuous change of the melt region due to the melting affects the detailed process. Also, numerical aspects for the prediction of the detailed flow structure in the melt are discussed.

Heat losses through building walls with closed, open and deformable cavities

This article reviews a recent body of work that documents the heat flow through walls with relatively complicated internal structure. The first part presents the fundamentals of natural convection heat transfer in two-dimensional enclosures filled with air. Numerical simulations for Rayleigh numbers in the range 6000–30000 and aspect ratio A=40 show that the air circulation is periodic (pulsating) and the core space is dominated by almost equidistant rolls. The heat transfer effected by such flows is documented, and the application to walls with tall cavities (hollow bricks) is discussed. The paper continues with a study of heat transfer through a ventilated wall heated by solar radiation from the side. The heated side is ventilated by an air channel opened at both ends. It is shown that the design of the air channel has a significant effect on the share of the radiative heat input intercepted by the air flow. The concluding part of the paper is a first-time review of new work on natural convection heat transfer across elongated vertical cavities with deformed side walls (e.g. air gaps in double-pane windows). It is shown that when the side walls are bent inward so that the cavity is narrower at mid-height than at its top and bottom ends, the total heat transfer rate through the system is increased significantly. The deformation of the walls also affects the intensity and structure of the buoyancy-driven flow in the air space. Overall, this article reviews some of the newest work on heat losses through complicated wall structures and projects it on the background provided by the existing literature. Copyright © 2002 John Wiley & Sons, Ltd.

PIV INVESTIGATION OF MULTICELLULAR LAMINAR NATURAL FLOW IN VERTICAL BENT CAVITIES

The objective of this article is to document the multicellular flow in a tall cavity with deformed heated side walls. The article describes an experimental study of natural convection in vertical plane and bent cavities with particle image velocimetry (PIV). One application is the double-glazed window submitted to extreme climate. The dynamic fields obtained from the measures are treated in two ways. The first one is a direct analysis of the instantaneous fields. The second one is the study of the coefficient of spatial auto-correlation. Results point out the presence of secondary cells in the cavities and a vertical displacement of these cells.

Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×106 and 1.43×106. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.

A direct numerical simulation of natural convection between two infinite vertical differentially heated walls scaling laws and wall functions

A direct numerical simulation has been performed for the case of a natural convection flow between two differentially heated vertical walls for a range of Rayleigh numbers (5.4×10 5< Ra<5.0×10 6). The simulation data are compared with experimental data of Dafa’Alla and Betts [Experimental study of turbulent natural convection in a tall cavity, Exp. Heat Transfer 9 (1996) 165–194] and the agreement is found to be acceptable. Given the numerical data we consider the scaling behaviour of the mean temperature, the mean velocity profile and of the profiles of various turbulence statistics. Point of departure is the approach proposed by George and Capp [A theory for natural convection turbulent boundary layers next to heated vertical surfaces, Int. J. Heat Mass Transfer 22 (1979) 813–826] who have formulated scaling relationships valid, respectively, in the near-wall inner layer and in the outer layer in the centre region of the channel. Matching of the scaling relationships in the overlap between the inner and outer region leads to explicit expressions which can be used as wall functions in computational procedures. The DNS data confirm the results of George and Capp for the scaling of the mean temperature profile. For the mean velocity profile our DNS data support another scaling in terms of a defect law for the velocity gradient in the inner layer. The scaling of George and Capp is also found to apply to the Reynolds stress, the temperature variance and the temperature fluxes. However, the velocity variances again seem to follow a different scaling.

Flow patterns of natural convection in an air-filled vertical cavity

Flow patterns of two-dimensional natural convection in a vertical air-filled tall cavity with differentially heated sidewalls are investigated. Numerical simulations based on a finite difference method are carried out for a wide range of Rayleigh numbers and aspect ratios from the onset of the steady multicellular flow, through the reverse transition to the unicellular pattern, to the unsteady multicellular flow. For aspect ratios (height/width) from 10 to 24, the various cellular structures characterized by the number of secondary cells are clarified from the simulations by means of gradually increasing Rayleigh number to 106. Unsteady multicellular solutions are found in some region of Rayleigh numbers less than those at which the reverse transition has occurred.

Heat and mass transfer across tall cavities filled with gas-vapour mixtures: the fully developed regime

Closed form expressions for the fully developed velocity, temperature and concentration profiles in a vertical channel are found by solving the equations for a cavity in the limit as the aspect ratio tends to infinity. We consider plane, steady, laminar, Boussinesq flow of an ideal gas-vapour mixture. The vertical walls are held at different constant temperatures and compositions, are impermeable to the gas and non-slip. The finite mass transfer effects of interfacial velocity and interdiffusion of enthalpy are included.

PREDICTION OF TURBULENT BUOYANT FLOW USING AN RNG A-ϵ MODEL

Numerical predictions were carried out for turbulent natural convection in two tall air cavities. The standard and RNG k-e turbulence models were used for the predictions. The predicted results were compared with experimental data from the literature, and good agreement between prediction and measurement was obtained. Improved prediction was achieved using the RNG k-e model in comparison with the standard k-e model. The principal parameters for the improvement were investigated.

Numerical Study of Tall Masonry Cavity Walls Subjected to Eccentric Loads

This paper presents the results of the second phase of an ongoing investigation into the behavior of tall cavity masonry walls constructed with partially grouted and reinforced concrete block wythe and a burnt brick wythe tied together with semirigid shear connectors. In the first phase, a test program has been conducted on tall cavity walls under eccentric axial forces. In this phase a nonlinear finite-element analysis model is developed to simulate the database of existing test results. The model represents all components of the cavity wall, the reinforced concrete block backup wythe, the brick wythe, and the shear connectors. It accounts for the nonlinear material behavior of all components as well as the large displacement, small strain characteristics of the deformation. The numerical analysis results are successfully compared with a number of test results. The simulation offers insight into the mode of failure, in particular for walls with high eccentricity ratios. That same model is then used to numerically generate an extensive database to examine the effect of various wall parameters on wall stiffness and ultimate strength.

Tests of Tall Cavity Walls Subjected to Eccentric Loading

This paper presents a test program on full-scale reinforced slender shear connected cavity walls subjected to an eccentric compressive loading. A total of nine walls were tested. All specimens were constructed with a partially grouted and reinforced, 190-mm concrete masonry block wythe and a 90-mm burnt clay brick wythe. All had a slenderness ratio of height to backup wythe thickness of 27.8 and, except for one specimen, all walls had a 75-mm wide cavity. The primary variable, was the axial force eccentricity. The eccentricity varied both in magnitude from t/2 to t/3, and in direction, either towards or away from the brick wythe. Some walls were tested with a single curvature, others were tested in double curvature. The load-displacement response, failure mode, and ultimate load capacities are examined and reported along with the observation and discussion.

A comparative assessment of the second-moment differential and algebraic models in turbulent natural convection

Abstract Results of direct numerical simulation (DNS) of turbulent natural convection between two differentially heated infinite vertical plates for Ra=5.4 × 105 (Versteegh and Nieuwstadt 1996, Boudjemadi et al. 1996a) have been used to assess models of various terms in the transport equations for the turbulent heat-flux vector θ u i and the temperature variance θ 2 . The hypotheses used to truncate the differential model into algebraic forms have also been examined. We present some results of the computation of natural convection in the tall cavity, obtained with a fully differential and a four-equation ( k−e− θ 2 −e θθ ) algebraic model. Despite the unsatisfactory reproduction of individual terms in the equations, computations yielded acceptable agreement with available experimental and DNS data. Based on new evidence, possible improvements of the model are briefly discussed, aimed at ensuring a better term-by-term modelling of the transport equations for θu i and θ 2 .

Development of Multicellular Solutions in Natural Convection in an Air-Filled Vertical Cavity

Consideration is given to the multiple solutions of two-dimensional natural convection in a vertical air-filled tall cavity with differentially heated sidewalls. Numerical simulations are carried out for a wide range of Rayleigh numbers from the onset of the steady multicellular flow, through the reverse transition to the unicellular pattern, to the unsteady multicellular flow. The dependence of the flow structure on the initial condition is clarified from the simulations by means of starting from a motionless and isothermal state, and gradually increasing or decreasing the Rayleigh number.

EXPERIMENTAL STUDY OF TURBULENT NATURAL CONVECTION IN A TALL AIR CAVITY

Abstract This article describes an experimental study of turbulent natural convection in an air cavity with an aspect ratio of 28.6. The study provides data for the velocities and temperatures at a Rayleigh number based on cavity width of 0.83 × 106, which is useful in validating computational and theoretical results. A laser Doppler anemometer was used for velocity measurements, while fine thermocouples were used for temperature measurements. Heal transfer rates and heat losses from the cell are evaluated. Further, the experimental data in the central portion of the tall cavity have been averaged to simulate an antisymmetric, Boussinesq, fully developed flow in an infinitely tall air cavity. Causes of asymmetry of the data, including radiation absorption, are also assessed.

Why you should not use ‘Hybrid’, ‘Power‐Law’ or related exponential schemes for convective modelling—there are much better alternatives

AbstractIn many areas of computational fluid dynamics, especially numerical convective heat and mass transfer, the ‘Hybrid’ and ‘Power‐Law’ schemes have been widely used for many years. The popularity of these methods for steady‐state computations is based on a combination of algorithmic simplicity, fast convergence, and plausible looking results. By contrast, classical (second‐order central) methods often involve convergence problems and may lead to obviously unphysical solutions exhibiting spurious numerical oscillations. Hybrid, Power‐Law, and the exponential‐difference scheme on which they are based give reasonably accurate solutions for steady, quasi‐one‐dimensional flow (when the grid is aligned with the main flow direction). However, they are often also used, out of context, for flows oblique or skew to the grid, in which case, inherent artificial viscosity (or diffusivity) seriously degrades the solution. This is particularly trouble‐some in the case of recirculating flows, sometimes leading to qualitatively incorrect results—since the effective artificial numerical Reynolds (or Péclet) number may then be orders of magnitude less than the correct physical value. This is demonstrated in the case of thermally driven flow in tall cavities, where experimentally observed recirculation cells are not predicted by the exponential‐based schemes. Higher‐order methods correctly predict the onset of recirculation cells. In the past, higher‐order methods have not been popular because of convergence difficulties and a tendency to generate unphysical overshoots near (what should be) sharp, monotonic transitions. However, recent developments using robust deferred‐correction solution methods and simple flux‐limiter techniques have eliminated all of these difficulties. Highly accurate, physically correct solutions can now be obtained aptimum computational efficiency.

Thermally driven tall cavity flows in porous media: the convective régime

Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy-Rayleigh number, A , and the cavity aspect ratio, h (height / width). Steady motion is generated by maintaining the vertical sidewalls at different constant temperatures and the horizontal boundaries are assumed to be thermally insulating. The present study is concerned with the limit of large aspect ratio, h → ∞. and Darcy-Rayleigh numbers A of order h , such that convection is important throughout the cavity. The main properties of the flow and heat transfer are obtained by considering a vertical boundary-layer approximation to the motion in the main body of the cavity. This leads, in particular, to the prediction of a position of minimum heat transfer across the cavity, of interest in the thermal insulation of buildings and other areas of technology.

Numerical study of thermal convection in tall laterally heated cavities

Two-dimensional convective flows in tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical sidewalls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. By using a Dufort-Frankel-Multigrid method, numerical results for the relevant end-zone problems in the limit of large aspect ratio are obtained for a range of Rayleigh numbers from A = 500 to 70000 and for different Prandtl numbers σ. The flow patterns show that the parallel flow in the core region is destroyed at A c ≈ 7880σ , in good agreement with stability analysis. Nusselt number predictions are compared with those of previous numerical and experimental studies of the overall cavity flow.

Transient oscillatory conjugate natural convection in a tall water cavity

A two-dimensional numerical simulation was conducted to investigate the effects of the heat capacity of the heated wall on the transient oscillatory convection in a tall cavity. Results were particularly obtained for water (Pr=6) in a tall cavity (A=6) with constant-heat-flux heating on one side and isothermal cooling on the opposing side. Significant wall heat capacity effects were found. Specifically, a heated wall of finite heat capacity can slow down the flow evolution process to steady state at low Rayleigh number and damp the flow oscillation during the initial developing period at high Rayleigh number. In periodic flow atRa* H =4.4×1010 the wall heat capacity significantly reduces the amplitude of the temperature oscillation. A quasi-periodic flow atRa* H =4.8×1010 was found to become periodic when the wall heat capacity was included. The wall heat capacity does not shown noticeable effect when the flow is chaotic forRa* H =6.0×1010.

Thermally driven tall cavity flows in porous media

Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy–Rayleigh number A and the cavity aspect ratio h (height/length). Steady motion is generated by maintaining the vertical sidewalls at different constant temperatures and the present study is concerned with the limit of large aspect ratio, h –&gt; ∞, where nonlinear convective flow occurs near each end of the cavity. This flow is analysed by asymptotic methods for small and large values of A and is computed numerically for other values of A . Predictions of the heat transfer across the cavity are obtained and are compared with the results of full numerical simulations.

A Note on Multiple and Unsteady Solutions in Two-Dimensional Convection in a Tall Cavity

Two-dimensional natural convection in a vertical differentially heated air-filled cavity is investigated numerically from the onset of the multicellular flow structure to the return of the unicellular pattern. Several branches of solutions characterized by different numbers of cells in the flow structure are found. The return to the unicellular flow structure occurs through a gradual decrease in the number of cells and each change in the number of cells is characterized by hysteresis. Also, unsteady solutions are found.

Transition to unsteady natural convection in a tall water-filled cavity

The transition to unsteady natural convection in a water-filled differentially heated cavity of vertical aspect ratio 10 is studied numerically by integrating two-dimensional Navier–Stokes equations in the Boussinesq approximation. The numerical algorithm combines a pseudospectral Chebyshev space discretization with a third-order time-stepping scheme. The top and bottom horizontal walls are considered to be either insulated or perfectly conducting. The critical Rayleigh number for adiabatic walls is found to be more than 30 times larger than that corresponding to perfectly conducting walls. In both cases, however, examination of the space-time structure of the temperature and velocity fluctuations shows that the onset of unsteadiness corresponds to boundary layer instability. In the case of perfectly conducting end walls, the transition to unsteady solutions possesses the characteristic features of a supercritical Hopf bifurcation. This is used to accurately determine the critical value. The dependence of the basic oscillation period in the vicinity of the critical Rayleigh number is given. Finally, the influence of unsteadiness on the local heat transfer coefficient is shown.