Two-equation Heat Transfer Model Research Articles

Numerical Study of Low Pr Flow in a Bare 19-Rod Bundle Based on an Advanced Turbulent Heat Transfer Model

Compared to assuming a constant turbulent Prandtl number model, an advanced four-equation model has the potential to improve the numerical heat transfer calculation accuracy of low–Prandtl number (Pr) fluids. Generally, a four-equation model consists of a two-equation k−ε turbulence model and a two-equation kθ−εθ heat transfer model. It is essential to analyze the influence of dissimilar turbulence models on the overall calculation accuracy of the four-equation model. The present study aims to study the effect of using different turbulence models on the same kθ−εθ heat transfer model. First, based on the open-source computational fluid dynamics software OpenFOAM, an advanced two-equation kθ−εθ heat transfer model was introduced into the solver buoyant2eqnFoam, which was developed based on the self-solver buoyantSimpleFoam of OpenFOAM. In the solver buoyant2eqnFoam, various turbulence models built into OpenFOAM can be conveniently called to close the Reynolds stress and an advanced two-equation heat transfer model can be utilized to calculate the Reynolds heat flux of low-Pr fluids. Subsequently, the solver buoyant2eqnFoam was employed to study the fully developed flow heat transfer of low-Pr fluids in a bare 19-rod bundle. The numerical results were compared and analyzed with the experimental correlations and other simulation results to validate the effectiveness and feasibility of the solver buoyant2eqnFoam. Furthermore, the influence of combining different turbulence models with the same two-equation kθ−εθ heat transfer model was also presented in this study. The results show that the turbulence model has a considerable influence on the prediction of turbulent heat transfer in the high Peclet number range, suggesting that it should be prudent when picking a turbulence model in the simulations of low-Pr fluids.

Performance comparison of annular and flat-plate thermoelectric generators for cylindrical hot source

Utilizing the heat energy of exhaust gases is a promising application of thermoelectric generator (TEG), which can convert low grade thermal energy into electricity. The annular thermoelectric generator (ATEG) is thought to be much more feasible for cylindrical heat source compared to the flat-plate thermoelectric generator (FTEG) in reference to the compatibility. Nevertheless, the quantitative comparison is lacking to clarify the prevalent geometry of TEG for cylindrical heat source. In this work, the performances of ATEG and FTEG are compared in detail with varying inlet temperature, velocity and the convective heat transfer coefficient when cylindrical heat source is applied. The turbulent heat source is described by the standard κ-ɛ functions together with the two-equation heat transfer model, while the output power and conversion efficiency of the ATEG and FTEG are calculated by solving the coupled thermo-electric equations. Our results showed that the output powers and the conversion efficiencies of ATEG and FTEG both increase with the increase of the inlet velocity, temperature, and the convective heat transfer coefficient. The conversion efficiency of ATEG is always higher than that of FTEG. The conversion efficiency of ATEG becomes even larger than that of FTEG when inlet temperature and/or convective heat transfer coefficient are relatively larger. In contrast, the output power of ATEG has no obvious difference with that of FTEG. This study addressed the condition when the ATEG has obvious advantage compared to the FTEG with cylindrical heat source applied. Our results suggest the annular TEG is better choice for cylindrical hot source especially when the inlet temperature and/or convective heat transfer coefficient are relatively larger. It could be a helpful guide for choosing suitable geometry of TEGs for energy harvesting in complex condition.

CFD simulations of gas dispersion around high-rise building in non-isothermal boundary layer

Urban heat island phenomena and air pollution become serious problems in weak wind regions such as behind buildings and within street canyons, where buoyancy effect cannot be neglected. In order to apply CFD techniques for estimation of ventilation and thermal and pollutant dispersion in urban areas, it is important to assess the performance of turbulence models adopted to simulate these phenomena. As the first step of this study, we carried out wind tunnel experiments and CFD simulations of gas and thermal dispersion behind a high-rise building in an unstable non-isothermal turbulent flow. The standard k– ε model and a two-equation heat-transfer model as RANS models, and LES, were used for the CFD simulation. One of the important purposes of this study was to clarify the effect of inflow turbulence (both velocity and temperature) on flow field and gas/thermal dispersion for the LES calculation. Thus, LES calculations with/without inflow turbulence were conducted. The inflow turbulence was generated through a separate precursor simulation. The calculated results showed that both RANS models overestimated the size of the recirculation region behind the building and underestimated the lateral dispersion of the gas. Turbulent flow structures of LES with and without inflow turbulence were completely different. The LES result with inflow turbulence achieved better agreement with the experiment.

666 LRN型温度場2方程式モデルによるメゾスケール複雑乱流温度場の予測(OS2-2 乱流のモデリングとシミュレーション)

666 LRN型温度場2方程式モデルによるメゾスケール複雑乱流温度場の予測(OS2-2 乱流のモデリングとシミュレーション)

A TWO-EQUATION HEAT TRANSFER MODEL FOR WALL TURBULENT SHEAR FLOWS

A proposal for closing the Reynolds-averaged energy equation is presented at the twoequation level of turbulence modeling. The eddy diffusivity for heat is proposed as a function of the local energy of turbulence, k, and the local temperature time scale, t  , instead of using mixed time scale, m  . The proposed two-equation heat transfer model solves two differential equations, one for the temperature variance, t k , and the other for the temperature time scale, t  . The nearwall limiting behavior of turbulent quantities associated with heat transfer has been captured with the proposed model. Therefore, an additional term is included in the temperature variance equation to improve the prediction of nearwall behavior. Moreover, an exact and noval equation for the temperature time scale, t  , is introduced in this study. The proposed t t k  heat transfer model does not suffer from numerical stiffness problems since natural boundary conditions for the variables t k and t  are used ( t k = t  =0 at y=0). The proposed model is assessed by application to fullydeveloped turbulent channel flows under different wall thermal conditions with different values of Reynolds numbers. The results for all cases examined showed good agreement with those of the direct numerical simulation data.

Thermal analysis on metal-foam filled heat exchangers. Part II: Tube heat exchangers

The forced convection heat transfer characteristics in high porosity open-cell metal-foam filled tube heat exchangers are analysed in this paper. The Brinkman-extended Darcy momentum model and two-equation heat transfer model for porous media are employed for the analysis of the heat transfer performance. The morphological effects of metal foams on overall heat transfer are examined. The optimal foam-area ratio for a metal-foam filled counter-flow tube-in-tube heat exchanger is predicted. The study shows that the thermal performance of a metal-foam heat exchanger can be superior to that of conventional finned tube heat exchangers.

Thermal analysis on metal-foam filled heat exchangers. Part I: Metal-foam filled pipes

This paper presents an analytical study of the forced convection heat transfer characteristics in high porosity open-cell metal-foam filled pipes. The Brinkman-extended Darcy momentum model and two-equation heat transfer model for porous media were employed. Based on the analytical solutions, the velocity and temperature distributions in metal-foam filled pipes were obtained. The effects of the microstructure of metal foams on overall heat transfer were examined. The results show that the pore size and porosity of metal-foams play important roles on overall heat transfer performance. The use of metal-foam can dramatically enhance the heat transfer but at the expense of higher pressure drop.

Effect of Heat Flux Ratio on Two-Dimensional Horizontal Channel Flow

Numerical analysis is performed to investigate thermal fluid-flow transport phenomena in channel under asymmetrical heat flux from both side walls. Emphasis is placed on an effect of heat-flux ratio from both sides on the velocity and thermal fields. The low-Reynolds-number k-e turbulence model and the two-equation heat-transfer model are employed to determine turbulent viscosity and thermal eddy diffusivity, respectively. It is found that 1) under strong heating from both walls, laminarization, that is, a substantial deterioration in heat-transfer performance, occurs as in the circular tube flow case; 2) during the laminarization process, both the velocity and temperature gradients in the vicinity of the heated walls decrease along the flow, resulting in a substantial attenuation in both the turbulent kinetic energy and the temperature variance over the entire channel cross section; and 3) in contrast, laminarization is suppressed in the presence of one-side heating because turbulent kinetic energy is produced in the vicinity of the other insulated wall. Therefore, an occurrence of laminarization in the channel is affected by the ratio of heat flux from both side walls.

Numerical simulation of turbulent jet diffusion flames by means of two-equation heat transfer model

The present study deals with a numerical analysis of thermal transport phenomena in a turbulent jet diffusion flame of hydrogen spouting from a vertical circular nozzle. The k– ε turbulence and t 2 –ε t heat transfer models, and the eddy-dissipation model are employed to simulate thermal-fluid flow fields and combustion phenomena, respectively. The governing boundary-layer equations are discretized by means of a control volume finite-difference technique and are numerically solved. It is found that (i) the model employed here can be applied to combustion phenomena, and (ii) the presence of flame causes a substantial attenuation in the turbulent kinetic energy, resulting in the occurrence of laminarization.

A near-wall two-equation heat transfer model for wall turbulent flows

A proposed near-wall t 2 –ε t two-equation model for turbulent heat transport reproduces the correct near-wall behavior of temperature under various wall thermal boundary conditions. In this model, a mixing timescale is introduced to model the production term of ε t equation, and a more convenient boundary condition for ε t under the uniform wall heat flux is suggested. The present model is tested through application to turbulent heat transfer for channel flow. Predicted results are compared with direct numerical simulation (DNS) data. The near-wall t 2 –ε t two-equation model predicts reasonably well the distributions of the time-mean temperature, normal turbulent heat flux, temperature variance, dissipation rate and their near-wall budgets.

AN ANISOTROPIC TWO-EQUATION HEAT TRANSFER MODEL FOR TURBULENT HEAT TRANSPORT UNDER ARBITRARY WALL THERMAL CONDITIONS

An anisotropic near-wall t 2

RIGOROUS FORMULATION OF TWO-EQUATION HEAT TRANSFER MODEL OF TURBULENCE USING DIRECT SIMULATIONS

A rigorous two-equation heat transfer model has been constructed with the aid of the most up-to-date direct numerical simulation (DNS) data for wall turbulence with heat transfer. The DNS data indicate that the near-wall profile of the dissipation rate, ϵ1, for the temperature variance, kt (= t2¯ /2), is completely different from the existing model predictions. In this study, we performed a critical assessment of existing ϵ1 and ϵ1, equations for both two-equation and second-order closure models. Based on these assessments, we propose a new dissipation rate equation for temperature variance, taking into account all the budget terms in the exact ϵ1 equation. Also, the proposed ϵ1 equation is linked with a similarly refined kt equation to constitute a new two-equation heat transfer model. Comparisons of the present model predictions with the DNS data for a channel flow with heat transfer have shown excellent agreement for the profiles of kt and ϵ1 themselves and of the budget in the kt and ϵ1 equations. The model is also tested in turbulent boundary-layer flows with five different wall thermal conditions. Agreement with the experimental data is quite satisfactory.

Modeling the turbulent heat and momentum transfer in flows under different thermal conditions

Two-equation turbulence models for velocity and temperature (scalar) fields are developed to calculate wall shear flows under various flow conditions and related turbulent heat transfer under various wall thermal conditions. In the present models, we make the modified dissipation rates of both turbulent energy and temperature variance zero at a wall, though the wall limiting behavior of velocity and temperature fluctuations is reproduced exactly. Thus, the models assure computational expediency and convergence. Also, the present k- ε model is construted using a new type of expression for the Reynolds stress u iu j proposed by Abe et al. [Trans. JSME B 61 (1995) 1714–1721], whose essential feature lies in introducing the explicit algebraic stress model concept into the nonlinear k- ε formulation, and the present two-equation heat transfer model is constructed to properly take into account the effects of wall thermal conditions on the eddy diffusivity for heat. The models are tested with five typical velocity fields and four typical thermal fields. Agreement with experiment and direct simulation data is quite satisfactory.

96/06792 A two-equation heat transfer model reflecting second-moment closures for wall and free turbulent flows

96/06792 A two-equation heat transfer model reflecting second-moment closures for wall and free turbulent flows

A two-equation heat transfer model reflecting second-moment closures for wall and free turbulent flows

A new two-equation heat transfer model which incorporates some essential features of second-order modeling is proposed. The present model is applicable to heat transfer problems in both wall and free turbulent flows not unusually deviating from the equilibrium state. Furthermore, by introducing the Kolmogorov velocity scale, the model can appropriately express the low Reynolds number effects in the near-wall region and is also applicable to complex heat transfer fields with flow separation and reattachment. It is shown that the proposed model predicts quite successfully heat transfer in both wall and free turbulent flows; i.e., a homogeneous isotropic decaying flow, a homogeneous shear flow, a boundary-layer flow heated from the origin, and a boundary-layer flow subjected to a sudden change in the wall-heating condition; whereas, such predictions have been almost impossible with existing two-equation heat transfer models.

A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows—II. Thermal field calculations

A new turbulence model to calculate complex turbulent heat transfer in separating and reattaching flows is proposed. This new model is a modified version of the latest low-Reynolds-number two-equation heat-transfer model, in which the main improvement is achieved by introducing the Kolmogorov velocity scale, u ε ≡ (νε) 1 4 , instead of the friction velocity u τ , to account for the near-wall and low-Reynolds-number effects in both attached and detached flows. After investigating the characteristics of various time scales for the heat-transfer model, we adopted a composite time scale which gives weight to a shorter scale among the velocity- and temperature-field time scales. It is validated that the present model predicts quite accurately the turbulent heat transfer in separating and reattaching flows downstream of a backward-facing step, which involve most of the essential physics of complex turbulent heat transfer, under various conditions of flow Reynolds number and upstream boundary-layer thickness. In addition, the computational results have revealed several new mechanistic features of the turbulent heat transfer in separating and reattaching flows.

A Two-Equation Heat-Transfer Model Reflecting Second-Moment Closures for Wall and Free Turbulent Flows.

Abstract A new two-equation heat transfer model which incorporates some essential features of second-order modeling is proposed. The present model is applicable to heat transfer problems in both wall and free turbulent flows not unusually deviating from the equilibrium state. Furthermore, by introducing the Kolmogorov velocity scale, the model can appropriately express the low Reynolds number effects in the near-wall region and is also applicable to complex heat transfer fields with flow separation and reattachment. It is shown that the proposed model predicts quite successfully heat transfer in both wall and free turbulent flows; i.e., a homogeneous isotropic decaying flow, a homogeneous shear flow, a boundary-layer flow heated from the origin, and a boundary-layer flow subjected to a sudden change in the wall-heating condition; whereas, such predictions have been almost impossible with existing two-equation heat transfer models.

Rigorous Modelling of Two-Equation Heat-Transfer Model Using Direct Simulations. 1st Report. Assessment and Reconstruction of Dissipation-Rate Equations for Temperature Variance.

A rigorous two-equation heat-transfer model has been constructed with the aid of the most up-to-date direct numerical simulation (DNS) data for wall turbulence with heat transfer. The DNS -data indicate that the near-wall profile of the dissipation rate, εt, for temperature variance, t2, is completely different from the existing model predictions. In the 1st report, we have performed a critical assessment of existing εt-and εt-equations for both two-equation and second-order closure models. Based on these assessments, we propose a new dissipation-rate equation for temperature variance, taking into account all the budget terms in the exact εt-equation. Comparisons of the present model predictions with the DNS data for a channel flow with heat transfer show an excellent agreement for the profiles of εt itself and the budget in the εt-equation.

Development of Two-Equation Heat Transfer Model Based on Direct Simulations of Turbulent Flows with Different Prandtl Numbers.

A low-Reynolds-number two-equation kt-et model has been constructed with the aid of direct numericai simulation (DNS) data bases on turbulent flows with different Prandtl numbers. The model adopts new length and time scales to represent various sizes of eddies in a thermal field. The predicted results for thermal fields at different Prandtl numbers were compared with the relevant DNS and experimental data. These comparisons indicate that the proposed model has sufficient capability to reproduce the DNS data, to perform highly stable computations and to analyze the heat transfer in various Prandtl number fluids.

Two-Equation Heat-Transfer Model for Turbulent Flows with Separation and Reattachment.

Two-Equation Heat-Transfer Model for Turbulent Flows with Separation and Reattachment.