Computation of a turbulent natural convection in a rectangular cavity with the elliptic-blending second-moment closure

A numerical study of a turbulent natural convection in an enclosure with the elliptic-blending second-moment closure (EBM) is presented. The primary emphasis of the study is placed on an investigation of the accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent natural convection flow. The turbulent heat fluxes in this model are treated by the general gradient diffusion hypothesis (GGDH). The model is applied to the prediction of a natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for a validation of the turbulence models. The results are also compared with those by the two-layer model, the SST model, the V2-f model and the second-moment differential stress and flux model. It is shown that the elliptic blending model predicts as good as or better than the existing models for the mean velocity and turbulent quantities although this model employs a simpler GGDH for treating the turbulent heat fluxes.     

Treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for turbulent natural convection flows

In this paper a comparative study on the treatment of the turbulent heat fluxes with the elliptic-blending second-moment closure for natural convection flows is presented. Three different cases for treating the turbulent heat fluxes are considered. Those are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). These models are implemented in a computer code especially designed for an evaluation of turbulent models. Calculations are performed for turbulent natural convection flows in an 1:5 rectangular cavity (Ra = 4.3 × 10¹⁰) and in a square cavity with conducting top and bottom walls (Ra = 1.58 × 10⁹). The calculated results are compared with the available experimental data. The results show that the GGDH, AFM and DFM models produce sufficiently accurate solutions for the turbulent natural convection in an 1:5 rectangular cavity where the strength of the thermal stratification is weak in a central region of the cavity. However, the GGDH model produces very erroneous solutions for the turbulent natural convection in a square cavity with conducting walls where the Rayleigh number is relatively small and the thermally stratified region is dominant. The AFM and DFM produce very accurate solutions for both cases without invoking any numerical problems.     

Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method

A numerical study of a turbulent natural convection in a rectangular cavity with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural-convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds-averaged Navier-Stokes equation (RANS) method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction method to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.     

Computation of a turbulent Rayleigh–Benard convection with the elliptic-blending second-moment closure

This communication reports briefly on the computational results of a turbulent Rayleigh–Benard convection with the elliptic-blending second-moment closure (EBM). The primary emphasis of the study is placed on an investigation of accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent Rayleigh–Benard convection. The turbulent heat fluxes in this study are treated by the algebraic flux model where the molecular dissipation rate of turbulent heat flux is included. The model is applied to the prediction of the turbulent Rayleigh–Benard convection for Rayleigh numbers ranging from Ra = 2 × 10⁶ to Ra = 10⁹, and the computed results are compared with the previous experimental correlations, T-RANS and LES results. The predicted cell-averaged Nusselt number follows the correlation by Peng et al. [S.H. Peng, K. Hanjalic, L. Davidson, Large-eddy simulation and deduced scaling analysis of Rayleigh–Benard convection up to Ra = 10⁹, J. Turbulence 7 (2006) 1–29.] (Nu = 0.162Ra^0.286) in the ‘soft’ convective turbulence region (2 × 10⁶ ≤ Ra ≤ 4 × 10⁷) and it follows the experimental correlation by Niemela et al. [J.J. Niemela, L. Skrbek, K.R., Sreenivasan, R.J. Donnelly, Turbulent convection at very high Rayleigh numbers, Nature 404 (2000) 837–840.] (Nu = 0.124Ra^0.309) in the ‘hard’ convective turbulence region (10⁸ ≤ Ra ≤ 10⁹) within 5% accuracy. This result shows that the elliptic-blending second-moment closure with an algebraic flux model predicts very accurately the Rayleigh–Benard convection.     

Numerical Investigation of Energy-Efficient Receiver for Solar Parabolic Trough Concentrator

In this paper, a thermal analysis of an energy-efficient receiver for solar parabolic trough concentrator is presented. Various porous receiver geometries are considered for the performance evaluation of a solar parabolic trough concentrator. Numerical models are proposed for a porous energy-efficient receiver for internal heat gain characteristics and heat loss due to natural convection. The internal flow and heat transfer analysis is carried out based on a RNG k-? turbulent model, whereas external heat losses are treated as a laminar natural convection model. The numerical models have been solved using the commercial engineering package, FLUENT. The thermal analysis of the receiver is carried out for various geometrical parameters, such as fin aspect ratio, thickness, and porosity, for different heat flux conditions. The inclusion of porous inserts in tubular receiver of solar trough concentrator enhanced the heat transfer about 17.5% with a pressure penalty of 2 kPa. The Nusselt number correlation is proposed based on the extensive numerical data for internal heat transfer inside the receiver. The proposed model is compared with more well-known natural convection models. A comparative study is carried out with different porous geometries to evolve an optimum configuration of energy-efficient receivers.     

非均匀热流下水平管内混合对流大涡模拟研究

针对以槽式太阳能集热器为背景的高密度、高度非均匀热流下水平管内的混合对流换热问题,采用大涡模拟方法,研究了热流密度非均匀性对水平管内混合对流瞬态涡结构、脉动强度、湍流热通量及局部平均壁温的影响;揭示了非均匀热流下自然对流对管内湍流特性的影响规律;提出了适用于不同热边界条件下管内混合对流换热的强化措施。结果表明:均匀热流时,自然对流会抑制管顶部的湍流脉动,使流动层流化,造成传热能力局部恶化;非均匀热流时,随着自然对流的增强,近壁面速度脉动强度先减小后增大,二次流逐渐增强,换热能力逐渐提高,故管内换热能力受湍流脉动与二次流协同影响;在自然对流影响下,均匀加热时管顶部可采用针对层流的强化换热措施,非均匀加热时需着重提高管底部高热流区域的湍流脉动与涡强度。     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

Modeling of heat transfer and differential diffusion in transported PDF methods

In order to model the conditional diffusive heat and mass fluxes in the joint probability density function (PDF) transport equation of the thermochemical variables, the diffusive fluxes are decomposed into their Favre mean and fluctuation. While the mean flux appears to be closed, the contributions of fluctuating fluxes are modeled with the interaction by exchange with the mean (IEM) model. Usually, the contribution of the Favre averaged diffusive fluxes is neglected at high Reynolds numbers. Here, however, this term is included to account for molecular mixing in regions, where turbulent mixing is negligible. This model approach is applied in steady state Reynolds Averaged Navier–Stokes (RANS)/transported PDF calculations to simulate the heat transfer of wall bounded flows as well as the stabilization of a hydrogen–air flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes. In wall bounded flows this is the case in the viscous sublayer. Heat transfer studies show, that “mixing models” based on the high Reynolds number assumption fail to compute correctly the temperature field and the heat flux close to the wall. A similar situation occurs at the flame root of the investigated turbulent hydrogen-air jet flame, where turbulent mixing is still too weak to achieve a fast mixing of reactants. In this area differential diffusion effects are observed in the experiment, i.e. superequilibrium temperatures and nonlinear relations between the elemental mixture fractions of hydrogen and oxygen. It will be shown, that the presented model can successfully reproduce these effects, which underlines the necessity to include Favre averaged molecular diffusive fluxes in transported PDF methods.     

SIMULTANEOUS ESTIMATION OF INLET TEMPERATURE AND WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW

An inverse heat convection problem is solved for simultaneous estimation of unknown inlet temperature and wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. Although we seek for two unknown functions, we formulate the inverse problem as one of parameter estimation through the representation of the unknown inlet temperature profile and the wall heat flux distribution by one-dimensional finite element interpolation. Nodal values of the inlet temperature and the wall heat flux at chosen positions are determined as unknown parameters through the Levenberg–Marquardt algorithm for minimization procedure. Numerical results for several testing cases with different magnitudes of measurement errors are examined by using simulated experimental data. The effects of the number and the locations of the temperature measurement points are discussed.     

Test of turbulence models for natural convection in an open cubic tilted cavity

A comparison was made between six turbulence models and experimental temperature profiles for the turbulent natural convection in a tilted open cubic cavity. The experimental setup consists of a cubic cavity of 1 m by side with one vertical wall receiving a constant and uniform heat flux, whereas the remaining walls are thermally insulated. The thermal fluid is air and the aperture is facing the heated wall. The temperature profiles were obtained at different heights and depths and each one consists of 10 positions inside the cavity. A commercial computational fluid dynamic software was used for the simulation and different turbulence models of k-ε_t and k-ω families were evaluated against experimental data. The lowest absolute average percentage difference for the experimental and numerical temperature profiles was for the rk-ε_t model and the highest was for the sk-ω model.     

NUMERICAL STUDY OF TURBULENT NATURAL CONVECTION IN A SIDE-HEATED SQUARE CAVITYAT VARIOUS ANGLES OF INCLINATION

Turbulent natural convection at a moderately high Rayleigh number (4.9 2 10 10 ) in a two-dimensional side-heated square cavity at various angles of inclination is studied numerically. Initially, the performance of the low Reynolds number k - y model of Wilcox (1994) and the low Reynolds number k m l turbulence model of Lam and Bremhorst (1981), in predicting buoyancy-driven flow in a noninclined enclosure, is evaluated against experimental measurements. The evaluation is focused on the prediction of the flow patterns and convective heat transfer in the boundary layer and corner regions. The performance of the Wilcox k m y model is found to be superior in capturing the flow physics such as the strong streamline curvature in the corner regions. The Lam and Bremhorst k m l model is not capable of predicting these features but provides reasonable predictions away from the corners. None of these models, however, is capable of predicting the boundary-layer transition from laminar to turbulent. In order to study the effect of the inclination of the square cavity on the heat transfer and flow patterns, computations are then performed using the Wilcox k m y model for a range of inclination angles from 0° through 90°, keeping other parameters fixed. The computed flow patterns, isotherms, convection strengths, variation of the local Nusselt numbers along the heated walls, and the average Nusselt number for various inclination angles of the square cavity are reported. It is noticed that the flow fields and heat transfer characteristics become significantly different for inclinations greater than45°. The computational procedure is based on finite-volume collocated mesh. The pressure-velocity coupling in the governing equations is achieved using the well-known SIMPLE method for numerical computation. The linear algebraic system of equations is solved sequentially using the strongly implicit procedure (SIP).     

Convective heat transfer on leeward building walls in an urban environment: Measurements in an outdoor scale model

Convection over the building envelope is a critical determinant of building cooling load, but parameterization of convection in building energy models and urban computational fluid dynamics models is challenging. An experimental investigation intended to clarify the heat transfer mechanism of a convective wall boundary layer (WBL) on a leeward, vertical building wall was conducted at the Comprehensive Outdoor Scale Model (COSMO) facility for urban atmospheric research. Comparison of mean and turbulent temperature fluctuation intensity profiles showed that the dominant regime of the WBL flow was turbulent natural convection. Implications for parameterization of convective heat fluxes in urban areas are discussed.     

A one-fluid,two-dimensional flow simulation model for a kettle reboiler

A one-fluid, or algebraic slip, model has been developed to simulate two-dimensional, two-phase flow in a kettle reboiler. The model uses boundary conditions that allow for a change in flow pattern from bubbly to intermittent flow at a critical superficial gas velocity, as has been observed experimentally. The model is based on established correlations for void fraction and for the force on the fluid by the tubes. It is validated against pressure drop measurements taken over a range of heat fluxes from a kettle reboiler boiling R113 and n-pentane at atmospheric pressure.The model predicts that the flow pattern transition causes a reduction in vertical mass flux, and that the reduction is larger when the transition occurs at a lower level. Before transition, the frequently-used, one-dimensional model and the one-fluid model are shown to predict similar heat-transfer rates because similar magnitudes of mass flux are predicted. After transition, the one-dimensional model significantly over-predicts the mass fluxes. The average heat-transfer coefficient predicted by the one-fluid model is consequently about 10% lower. The one-fluid model shows that tube dryout can be expected at much lower heat fluxes than previously thought and that the fluid kinetic energy available to induce tube vibrations is significantly smaller.     

Numerical prediction of film cooling effectiveness over flat plate using variable turbulent prandtl number closures

Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensional discrete-hole film cooling arrangement.The effects of basic geometrical characteristics of the holes,i.e.diameter D,length L and pitch S/D were studied.Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered.The variabiUty of the turbulent Prandtl number Pr_t in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford,or employing the Abe,Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance kg and its destruction rate ε_θ.The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology.All implemented models for turbulent heat transfer performed sufficiently well for the considered case.It was confirmed,however,that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.     

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–? 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.     

Direct and inverse mixed convections in an enclosure with ventilation ports

The numerical study presented in this work describes the direct and inverse mixed convection problems in a slot-ventilated enclosure subjected to an unknown heat flux on one side. Particularly, the interaction of internal natural convection with the cold ventilated flow leads to various flow fields depending on the Richardson number, Reynolds number, and the functional form of the imposed boundary heat flux. Fluid and heat transport structures across the enclosure are visualized by the streamlines and heatlines, respectively. Subsequently, an iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined for a domain of arbitrary geometries. In this approach, no a priori information is needed about the unknown boundary heat fluxes to be determined. The accuracy of the heat flux profile solutions is shown to depend strongly on the values of Reynolds number and flux functional forms. Effects of measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the natural convection and forced convection.     

Heat transfer by mixed convection in a vertical flow undergoing transition

Heat transfer, for aiding mixed convection from vertical, uniform flux surfaces and for small forced convection effects, is considered here. Simple relations have been proposed to correlate the new experimental data which were obtained in a flow undergoing transition from a laminar regime toward turbulence. Experiments were performed in air at pressures ranging from 4.4 to about 8 bar. The correlation based on experimental data for laminar flow for Pr = 0.7 has been extended to other Prandtl numbers through numerical integration of the transport equations. It is shown that, for both laminar and turbulent mixed convection, the Nusselt number may be successfully correlated, employing suitable combinations of the corresponding heat transfer correlations for forced and for natural convection. The parameter characterizing the mixed convection effect was found to be different in laminar and turbulent flow. However, in each of these regions, the relevant parameter is proportional to the ratio of the applicable characteristic forced and natural convection velocity scales.     

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.     

Fouling in a Steam Cracker Convection Section Part 2: Coupled Tube Bank Simulation using an Improved Hybrid CFD-1D Model

Abstract

Performing an adequate fouling study for the heat exchangers in the convection section of a steam cracker requires reliable data on circumferential tube wall temperature profiles. A hybrid Computational Fluid Dynamics (CFD)-1D convection section model, developed to perform coupled flue gas/process gas side simulations of convection sections, is improved by the implementation of flue gas radiation modeling and extended to include typical tube banks. A complete naphtha cracker convection section is simulated with the improved hybrid CFD-1D model. All tubes show distinct maximum heat fluxes on the tube walls due to the high flue gas velocity. Based on the calculated circumferential heat flux profiles, the maximum heat flux value is calculated to be 1.8 times the average tube heat flux value. As computational costs associated with a hybrid CFD-1D simulation are high, a convective heat flux profile reconstruction scheme is developed. Using the scheme, circumferential heat flux profiles are reconstructed, based on the heat fluxes calculated when performing a fully 1D coupled convection section simulation. The heat flux reconstruction profile scheme enables fast retrieval of circumferential heat flux profiles and, thus, tube wall temperature profiles. Optimization and/or design of a steam cracker convection section becomes less computationally demanding.