Convection induced by the selective absorption of radiation for the Brinkman model

Convection induced by the selective absorption of radiation in a porous medium is studied analytically and numerically using the Brinkman model. Both linear instability analysis and nonlinear stability analysis are employed. The thresholds show excellent agreement so that the region of potential subcritical instabilities is very small, demonstrating that linear theory is accurate enough to predict the onset of convective motion. A surprising result shows that the critical Rayleigh number increases linearly as (Darcy number x Brinkman coefficient / dynamic viscosity of the fluid) increases.Received: 6 May 2003, Accepted: 26 May 2003     

Stability of double-diffusive convection induced by selective absorption of radiation in a fluid layer

Linear and nonlinear stability analyses were performed on a fluid layer with a concentration-based internal heat source. Clear bimodal behaviour in the neutral curve (with stationary and oscillatory modes) is observed in the region of the onset of oscillatory convection, which is a previously unobserved phenomenon in radiation-induced convection. The numerical results for the linear instability analysis suggest a critical value γ _c of γ, a measure for the strength of the internal heat source, for which oscillatory convection is inhibited when γ > γ _c . Linear instability analyses on the effect of varying the ratio of the salt concentrations at the upper and lower boundaries conclude that the ratio has a significant effect on the stability boundary. A nonlinear analysis using an energy approach confirms that the linear theory describes the stability boundary most accurately when γ is such that the linear theory predicts the onset of mostly stationary convection. Nevertheless, the agreement between the linear and nonlinear stability thresholds deteriorates for larger values of the solute Rayleigh number for any value of γ.     

Double-diffusive convection induced by selective absorption of radiation in a fluid overlying a porous layer

A linear instability analysis for the inception of double-diffusive convection with a concentration based internal heat source is presented. The system encompasses a layer of fluid which lies above a porous layer saturated with the same fluid. Detailed stability characteristics results are presented for key physical parameters including the solute Rayleigh number, depth ratio of the fluid to porous layer and strength of radiative heating.     

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.     

Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium

Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a linear instability analysis is performed. To establish conditional and unconditional nonlinear stability results, both the Darcy and Forchheimer models are employed to describe fluid flow. Due to the presence of significant regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear.Received: 6 May 2003, Accepted: 9 August 2003, Published online: 12 December 2003     

Three dimensional finite element analysis for Rayleight-Benard convection in rectangular enclosures

The pattern of Rayleigh-Benard convection of air in a rectangular box heated-from-below is studied by numerically solving the three-dimensional time-dependent Navier-Stokes equations under the Boussinesq approximation. Slightly supercritical Rayleigh number was adopted to track the evolutions of flow structure as a function of enclosure's aspect ratio (A=L/H). The flow will asymptotically evolve to different patterns, among which, two possible types of flow pattern are found. One consists of the pair of straight vortex rolls and the other appears as closed vortex rings. The transition between the flow patterns indicates that there exists a flow bifurcation with the variation of container's aspect ratio. In addition, both steady and oscillatory flows have been observed, corresponding to the pair of straight vortex rolls and the vortex ring, respectively. The complexity of flow structure tends to increase with the increasing aspect ratio of the rectangular enclosure. The project supported by the National Natural Science Foundation of China (19889210), the National Distinguished Young Fund (10125210), the Hundred Talents Program of CAS, and the Training Program for the Trans-Century Outstanding Young of MOE     

Taguchi design of three dimensional simulations for optimization of turbulent mixed convection in a cavity

This study discusses the application of Taguchi method in assessing maximum heat transfer rate for the turbulent mixed convection in an enclosure embedded with rotating isothermal cylinder. The simulations were planned based on Taguchi’s L16 orthogonal array with each trial performed under different conditions of position of the cylinder, Reynolds number (Re) and Rayleigh number (Ra). The thermal lattice Boltzmann based on D3Q19 methods without any turbulent submodels was purposed to simulate the flow and thermal fields. A relaxation time method with the stability constants is introduced to solve turbulent natural convection problems. Signal-to-noise ratios (S/N) analysis were carried out in order to determine the effects of process parameters and optimal factor settings. Finally, confirmation tests verified that Taguchi method achieved optimization of heat transfer rate with sufficient accuracy.     

A theoretical analysis of forced convection in a porous-saturated circular tube: Brinkman–Forchheimer model

Fully developed forced convection inside a circular tube filled with saturated porous medium and with uniform heat flux at the wall is investigated on the basis of a Brinkman–Forchheimer model. The matched asymptotic expansion method is applied at small Darcy numbers. For large Darcy numbers, the solution for the Brinkman–Forchheimer momentum equation is found in terms of an asymptotic expansion. Once the velocity distribution is determined, the energy equation is solved using the same asymptotic technique. The results for the two limiting cases of clear fluid and Darcy flow conditions show good agreement with those available in the literature.     

Thermocapillary convection mechanism due to the absorption of spatially periodic laser radiation

This paper deals with the problem of the occurrence of regular convection in a fluid layer with a single free surface following the absorption of a light wave with an intensity distribution spatially periodic in the plane of the layer due to the temperature dependence of the surface tension. The velocity and temperature profiles in the medium are determined. It is shown that, other things being equal, the response of the system to the light wave is greatest when the period of the interference intensity pattern is of the order of twice the thickness of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 5, pp. 47–50, September–October, 1985.The authors wish to thank N. T. Pashchenko, N. V. Tabiryan, and Yu. S. Chilingaryan for valuable discussions.     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convection. Received February 10, 2003 / Accepted February 10, 2003/ Published online May 9, 2003 / B. Straughan     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convectionReceived: 10 February 2003, Accepted: 11 March 2003, Published online: 12 September 2003     

Convection due to the selective absorption of radiation in a porous medium

Continuum Mech. Thermodyn. (2003) 15: 451-462 Digital Object Identifier (DOI) 10.1007/s00161-003-0125-5 Published online September 12, 2003-© Springer-Verlag 2003 Due to a technical error, the present contribution has been published twice in this journal. This article has already appeared in Volume 15 Number 3 (June 2003) and should be cited accordingly. Springer-Verlag wishes to apologize to its customers and readers for this mistake.Published online: 27 Oktober 2003     

Natural convection over a vertical flat plate due to absorption of thermal radiation

Heat transfer by simultaneous free convection and radiation in a participating fluid has received some attention during the past few years. However most of the previous work has been focussed on gases. The present work investigates the problem of combined radiation and natural convection in liquids. Analysis are given for an optically thick cold fluid layer adjacent to a non-emitting and non-reflecting radiation-transmitting plate. The external surface of the plate is subjected to heat loss to surroundings. The governing differential equations are transformed to a dimensionless form where the solution becomes dependent on the following parameters: the plate absorpitivity,α _p; the dimensionless distance along the plate,ζ; the fluid Prandtl number,Pr; and dimensionless heat loss coefficient to surrounding,N _c. A local non-similar technique is adopted to obtain solutions atPr=6.5 and at a wide range ofα _p,ζ, andN _c. The results showed that both velocity and temperature are non-similar and they are greatly affected by the value ofα _p whenζ is small. At large values of f the effect ofα _p diminishes and for a plate without heat loss the velocity becomes similar, i.e. independent of C The heat loss from the external surface of the plate causes the maximum temperature of the fluid to depart far from the plate. The results also showed that for plates without heat loss the local heat transfer coefficient from the plate depends on the local Grashof number to the power 0.185.     

The thick and thin limiting solutions for combined convection and radiation in the region of a two dimensional stagnation point

The low speed constant property flow of a gray absorbing and emitting gas is studied in the region of a two dimensional stagnation point. Two limiting cases are considered. These correspond to the case where the hydrodynamic boundary layer is either optically thin or optically thick. In the thin case, the errors in the total heat transfer are of the order of one percent for an optical thickness of 001. For the thick case, the three term Taylor series gives an excellent representation for the temperature profile and the best result for the convection heat transfer for an optical thickness of 1.0 and 10.0. The most accurate radiation heat transfer is found by using this profile in the exact numerical expression. The Rosseland expression gives the best representation for the total heat transfer.     

Interpretation of simple and cloud-resolving simulations of moist convection–radiation interaction with a mock-Walker circulation

An idealized two-dimensional mock-Walker circulation in the tropical atmosphere forced by prescribed horizontal gradients in sea-surface temperature (SST) is discussed. This model problem includes feedbacks between cumulus convection and tropical large-scale circulations that have proved challenging for global climate models to predict accurately. Three-dimensional cloud-resolving model (CRM) simulations that explicitly simulate turbulent circulations within individual cloud systems across 4,096 and 1,024 km-wide Walker circulations are compared with a simple theoretical model, the Simplified Quasiequilibrium Tropical Circulation Model (SQTCM). This theoretical model combines the weak-temperature-gradient approximation with a unimodal truncation of tropospheric vertical structure coupled to highly simplified formulations of moist precipitating cumulus convection and its cloud-radiative feedbacks. The rainfall, cloud and humidity distribution, circulation strength, energy fluxes and scaling properties are compared between the models. The CRM-simulated horizontal distribution of rainfall and energy fluxes are adequately predicted by the SQTCM. However, the humidity distribution (drier subsidence regions and high-humidity boundary layers in the CRM), vertical structure and domain-size scaling of the circulation differ significantly between the models. For the SQTCM, the concept of gross moist stability – related to advection of moist static energy (MSE) out of tropospheric columns by the mean divergent circulation – is used to explain the width and intensity of the rainy region. Column MSE budgets averaged across the ascent branch of the simulated Walker circulation provide similar insight into the cloud-resolving simulations after consideration of the more complex horizontal and vertical circulation structure and the role of transient eddies. A nondimensional ascent-region moist stability ratio α, analogous to the SQTCM gross moist stability, is developed. One term of α is related to the vertical profiles of ascent-region mean vertical motion and ascent-region edge MSE; a second term is proportional to eddy export from the ascent region. Smaller α induces a narrower, rainier ascent region. The sensitivity of the SQTCM and CRM to a uniform 2 K increase in SST is compared, and the rainy upward branch of the circulation narrows in both models. MSE budget arguments are used to explain this behavior. In the simple model, the gross moist stability is a decreasing function of tropospheric temperature. Hence gross moist stability reduces and the ascent region narrows as the SST increases. In the CRM, increased atmospheric radiative cooling due to the warmer and moister troposphere destabilizes the MSE profile and decreases α, inducing a narrower ascent region. In the CRM, and to a lesser extent in the SQTCM, intensified shortwave cloud forcing in the warmer climate causes a negative radiative feedback on the SST change.Funding for this work from NSF grant DMS-0139794 is gratefully appreciated     

Three dimensional movement measurement for the wing of a flying airplane

The movement parameters of a wing of a flying airplane are important for its design, analysis and life-estimation, while the three dimensional (3D) measurement of these parameters is a difficult task. A measurement setup is proposed as well as its corresponding calibration methods for the camera system on both ground condition and air condition, image processing algorithms and a new method of locating 3D straight lines through plane-plane intersection are developed. The test results show that the 3D measurement accuracy in the condition of flying in the air can be better than 1 mm.     

Prediction of natural convection flow using network model and numerical simulations inside enclosure with distributed solid blocks

Steady state natural convection of a fluid with Pr ≈ 1 within a square enclosure containing uniformly distributed, conducting square solid blocks is investigated. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The natural convection flow is predicted employing the nondimensional volumetric flow rate (Q_max^* Q_{\max }^{*} ) by using a network model and also using numerical simulations. For identical solid and fluid thermal conductivities (i.e. k _s  = k _f ), a parametric study of the effect of number of blocks (N ²), gap size (δ) and enclosure Rayleigh number (Ra) on Q_max^* Q_{\max }^{*} is performed using the two approaches. Network model predictions are observed to agree well with that from the simulations until Raδ³ ~ 12. Considering the enclosure with blocks as a porous medium, for a fixed enclosure Ra number, increasing the number of blocks for a fixed volumetric porosity leads to a decrease in enclosure permeability, which in turn reduces the flow rate. When the number of blocks is fixed, and for a given Ra number, the flow rate increases as the porosity increases by widening the gap between the blocks.