Low Reynolds Number Turbulence Model Research Articles

Comparison of Heat Transfer Characteristics between Supercritical N-Decane and Supercritical Carbon Dioxide in a Single Square Minichannel

Numerical investigations were conducted to analyze the heat transfer characteristics in a single square minichannel with supercritical C10H22 (sC10H22) and supercritical CO2 (sCO2). A single symmetric minichannel with a square cross-section of 1 mm × 1 mm and a length of 400 mm was selected, the top surface of which is applied with a uniform heat flux from 100 to 300 kW/m2. The inlet temperatures are varied from 20 to 150 °C and the inlet mass fluxes are ranged from 300 to 500 kg/(m2·s) in the physical model. The flow and heat transfer processes of the fluids were simulated in COMOSOL Multiphysics® software with RANS k-ω low-Reynolds number turbulence model. Results show that the heat removal capacity of sCO2 at 8 MPa is superior, which is 8 times that of sC10H22 at 3 MPa at the inlet temperature of 20 °C. When the inlet temperature and heat flux increase, the heat transfer performance of sCO2 drops sharply, while the overall performance of sC10H22 rises steadily. It suggests that sCO2 is more suitable for the heat transfer process with high-efficient cooling system at a lower inlet temperature, while sC10H22 is capable of a stable and long-time heat transfer process at a higher inlet temperature.

Heating and ventilation performance investigation of a novel linear slot diffuser with adaptive outlet area for near window applications

The linear slot diffuser has ideal cooling performance for near-window applications, and is used for ventilation by utilizing the coandă effect in some cases. However, it has insufficient throw distance due to buoyancy impact during heating periods. And airflow near window surfaces increases convection heat transfer, resulting in extra HVAC energy consumption. Our research focuses on a prototype linear slot diffuser with an adaptive outlet area. Two deflection panels are installed for adjusting the outlet area depending on temperature or usage scenarios. Supply air has a low velocity and wide diffusion range when the panels are open. It can utilize the coandă effect as well as keep convection heat transfer within an appropriate range. Closing the panels will halve the supply area and completely change airflow diffusion and turbulence characteristics. This is considered suitable for heating, but the mounting location needs to be re-evaluated. Therefore, this prototype's heating and ventilation performance is numerically investigated using a low-Reynolds number turbulence model with fine meshes. Temperature, airflow, tracer gas distribution in a typical office space, and the ADPI, DR, and age-of-air indexes are compared before and after outlet area adjustment. Diffuser mounting locations and exhaust methods are also altered to balance heating and ventilation efficiency. As a result, a proper installation location for this prototype is suggested. The adaptive supply area significantly improved this terminal's heating and ventilation performance. Temperature stratification was reduced to a maximum of one-tenth, and impinging jets or displacement ventilation were observed in some cases.

Heat transfer augmentation by plate motion in a wall jet flow over a heated plate: A conjugate heat transfer technique

The present study is an initiation to investigate the effect of plate movement on heat transfer characteristics in the solid plate and the fluid domain due to the turbulent wall jet flow over the plate in a quiescent surrounding. A conjugate technique is used to carry out the heat transfer solution that involves conduction in solid and convection in fluid coupled at the interface surface. The plate is heated continuously with a constant flux at its lower surface. A low-Reynolds number k − ε turbulence model developed by Yang and Shih (YS) is applied to simulate the turbulent flow. The parameters considered for the present study are the plate-jet velocity ratio ( 0 − 2 ) , the plate thickness ratio ( 0.5 − 1.5 ) , the conduction ratio ( 500 − 2000 ) , and the Reynolds number ( 7700 − 25 , 000 ) . The temperature distribution diagrams for various plate velocities, the interface temperature profile, and the averaged Nusselt number show a higher cooling rate at high plate-jet velocity ratios. The effect of plate thickness and conductivity ratios is visible in the temperature distribution diagrams. A better heat transfer is achieved at a higher Reynolds number, evident from the averaged and local Nusselt number distribution. A correlation is developed for average Nusselt number with the Reynolds number and plate-jet velocity ratios as the varying parameters.

CFD prediction of heat transfer at supercritical pressure with rough walls: Parametric analyses and comparison with experimental data

In this paper, a low-Reynolds number turbulence model developed by the authors in past activities for rough walls is used for predicting heat transfer at supercritical pressure in the presence of different degrees of surface finishing. The model, able to reproduce the typical trends of friction factors from classical data reported by Nikuradse and summarised in the Moody diagram, is based on a simple-minded description of the effect of wall protrusions through the boundary layer on turbulence production.Though prior validation of the model only on the basis of friction factor data did not assure any basis for achieving accuracy in heat transfer prediction, a sensitivity analysis is firstly presented in order to characterise the obtained predictions at variable values of the roughness parameter, in particular concerning the possible suppression of deteriorated heat transfer by roughened surfaces. These analyses are extended to different fluids, making use of a fluid-to-fluid similarity theory recently proposed by the authors in order to establish similar boundary conditions and predicted phenomena.The results obtained by these analyses can be considered interesting, especially in view of the design of supercritical water-cooled nuclear reactors; however, an assessment against experimental data was obviously necessary. Experimental carbon dioxide data published in a very recent archival paper were thus addressed and were found useful in this regard. Considering these data allowed to extend the above analysis to provide confirmation of the promising features of the model in comparison with wall temperature values obtained with different boundary conditions. The model here described appears promising not only for its capability to predict experimentally measured effects, but also for the perspective to be used in the study of the behaviour of purposely roughened surfaces reducing the probability of occurrence of deteriorated heat transfer.

Multi-objective optimization of non-uniform plate heat exchanger with dimples/protrusions for heat recovery of setting machines

The setting machine exhaust gas contains a large number of fiber particles and micro oil droplets, which are adhesive and flammable. This leads to difficulties in waste heat recovery of the exhaust gas. In this article, numerical and experimental studies of a non-uniform plate heat exchanger with dimples/protrusions for waste heat recovery of setting machines are carried out. Based on the three-dimensional fluid-thermal-structural coupling method, the regenerative process between gas and air are investigated numerically with low Reynolds number turbulence model. The effect of the structural parameters (protrusions diameters, protrusions spacing and plate spacing) and operation parameters (air inlet temperature, gas and air flow rate) on the heat transfer performance are discussed. The multi-objective optimization of the plate regenerator is conducted by Box-Behnken Design and Nondominated Sorting Genetic Algorithm II to maximize the thermal performance coefficient and minimize entransy dissipation number. It is found that when D1, H1 S1, D2, H2, S2 are 9 mm, 7 mm, 161 mm, 9 mm, 8 mm and 153 mm respectively, the heat exchanger has the best heat transfer performance. Compared with the original model, the heat transfer rate of the optimized heat exchanger is increased by 3.9%, the thermal performance coefficient of the air side and flue gas side is increased by 5.7% and 5.9% respectively, and the entransy dissipation number is reduced by 24.6%.

The effect of plate motion on heat transfer enhancement using turbulent offset jet flow: A conjugate approach

The present research is focused on computational analysis of conjugate heat transfer behavior of a turbulent offset jet flow over a moving flat plate in a quiescent environment. The plate of definite thickness and conductivity is subjected to isothermal condition at the plate bottom surface. The computation is carried out with a low-Reynolds number (LRN) turbulence model proposed by Yang and Shih which involves integration to wall (ITW) approach to capture the thin viscous sub-layer region within the boundary layer. The variation of offset ratio (ranging as 3, 7 and 11) and plate velocity (Up = 0 − 2) plays quite a major role in the distribution of interface temperature and Nusselt number. The conduction heat flow rate in solid depends upon the plate thickness ratio (S) which is varied as 0.5 − 1.5 and the conductivity ratio (K) ranging as 500 − 2000. The variation of average Nusselt number gives evidence of better cooling rate for smaller offset ratios and higher plate to jet velocity ratio.

Assessment of RANS turbulence models on predicting supercritical heat transfer in highly buoyant horizontal flows

This paper rigorously validates the RANS models against the DNS on predicting turbulent flow and heat transfer of highly buoyant horizontal supercritical fluids. The low-Reynolds number turbulence models of RNG, AKN, V2F and ( k − ω ) SST that are recommended in literature are selected. Also, the LS model demonstrating good performance in some in-house CFD codes has been reimplemented via User-Defined Functions (UDFs) and examined for supercritical simulations, in particular with strong buoyancy effects. The results indicated that the AKN model works best among the tested models on the reproductions of some bulk parameters that are of interest (such as wall temperature, Nusselt number and skin friction coefficient) and the distortions of the turbulent velocity profile caused by the strong buoyancy, closely followed by the V2F model. The UDFs implemented LS model exhibits much better performances than the originally incorporated version in FLUENT, which is attributed to the more proper model implementation that leads to better treatments on the fluid flow and heat transfer, especially in the near-wall regions. Regarding the reproductions on the turbulence kinetic energy generations under the studied conditions, the RANS models are unable to give satisfactory results, the simulated suppression in the top half is more drastic. Similar to the vertical supercritical fluids, with quite high-strength buoyancy, the heat transfer recovers around the horizontal pipe top wall but the RANS models' response to the “recovery” is poor. The model performance on reproducing the turbulent statistics is closely related to the implementation of the vital structural parameters.

Numerical and Experimental Investigation of Three-Dimensional Flow in Combined Protective Canister Filters

This work deals with the numerical and experimental investigation of flow in the protective filters which combine fibrous pleats and the absorbent cartridge. The flow through the complete 3D geometry of all parts of the filters, including complex geometry of the pleats, is numerically modeled using high-quality computational grids. The sorbent filling, textile dividers as well as the material of filtration pleats are modeled as the porous media with the coefficients of the quadratic Forchheimer equation derived from the experiments in the laboratory located at the SIGMA Research and Development Institute. A comprehensive CFD analysis has been carried out using the ANSYS CFX package with the SST turbulence model, which combines advantages of both the high- and the low-Reynolds number turbulence models. The fully parametric description of the pleats enables the generation of high-quality structured computational grids for a wide range of pleat heights and widths and to use numerical shape optimization process. The numerical simulations show very good agreement of calculated and measured pressure drop for all variants of the complex geometry of the combined filter. To simulate a real application of the protective filter, the unsteady simulations which follow the human breathing pattern have been performed with the flow rate corresponding to the increased human activity.

Turbulent heat transfer of highly buoyant supercritical CO2 flow in various horizontal pipes

Supercritical CO2 (sCO2) is considered as an ideal heat transfer fluid for power cycles adapted to a wide range of heat sources. This paper employs computational approach based on Reynolds-Averaged Navier-Stokes (RNAS) modelling to study highly buoyant turbulent sCO2 flow and heat transfer heated in various horizontal tubes with diameter of 4.57 mm, 13.39 mm, and 22.14 mm. The conditions with relatively high ratio of heat flux q to mass flux G are simulated. The chosen AKN k − ε low-Reynolds number turbulence model is rigorously validated against experiments and DNS covering a wide range of operation conditions and exhibits quite satisfactory consistencies on the strong buoyancy reproductions of horizontal supercritical flows. With sCO2 heat transfer data presented, details about the coupled turbulent flow characteristics have been discussed. It has been observed that in various size horizontal geometries, not only the local sCO2 heat transfer along the tube top surface, but also the overall performance within the liquid-like region near Tpc is greatly degraded by the strong buoyancy, and the deterioration regime expands with decreasing pipe diameter. For the highly buoyant horizontal sCO2 flows, a backflow vortex appears near the top wall then a second velocity peak forms which locates further into the core flow section for larger diameter pipes; The radial velocity profile of the top wall has been flattened even distorted into “half-M” shape that the turbulence statistics decline remarkably then the turbulent activities and thermal advection are attenuated. With sCO2 heated into the gas-like regime, the heat transfer recovers because of the reduced buoyancy effects.

Influence of various aspects of low-Reynolds number turbulence models on predicting flow characteristics and transport variables in a horizontal direct-chill casting

Computational Fluid Dynamics (CFD) was used to simulate the solidification in a horizontal direct-chill (HDC) casting using five low-Re k-ɛ turbulence model: including the v2¯−f model of Durbin (V2F), Yang-Shih (YS), Chang-Hsieh-Chen (CHC), Abid (AB), and Abe-Kondoh-Nagano (AKN). The model incorporated turbulence energy production due to buoyancy in the k and ɛ equations to predict flow pattern, eddy viscosity ratio, turbulence intensity, turbulence velocity, turbulence energy production due to buoyancy, solid fraction, and temperature. Three sets of grids were systematically chosen in such a way that the grid refinement factor was above 1.3. The results obtained indicate that the solution was independent of grid size. The flow pattern predicted using the turbulence models are generally similar, but the V2F indicated additional minor counter-clockwise recirculating cells toward the bottom mold. Further, the solutions indicate that turbulence energy production due to buoyancy contributes to the strong turbulence levels predicted towards the top mold region. The predicted velocity of the mean flow for the V2F model in the flow domain is higher, followed by the YS model and least for the CHC, AB, and AKN models. The eddy viscosity ratio is highest with a value of 144 at y+<100 for the CHC model, followed by AKN and AB with eddy viscosity ratios of 144 and 137 respectively. Then, the YS has a maximum eddy viscosity ratio of 114 at y+<50, V2F has the least maximum eddy viscosity ratio of 78 at y+<150. The turbulence intensity, the turbulence velocity, and the turbulence energy production due to buoyancy were highest towards the top mold for the CHC, AB, and AKN than the YS and V2F models. The V2F and YS predicted lower temperature curves and higher solid fraction curves towards the mid-section of the profiles than the CHC, AB, and AKN models.

Numerical simulation of photocatalytic oxidation of gaseous pollutants using low Reynolds number turbulence models

Introduction: Photocatalytic oxidation of gaseous pollutants in differential reactors is simulated using computational fluid dynamics. Materials and methods: The momentum equation and pollutant transport are solved by using ANSYS Fluent. The SIMPLE algorithm is used to treat the pressure-velocity coupling. The laminar flow and low Reynolds k−ε models are used to describe turbulence. Results: Velocity field distribution and degradation efficiency of different models at various flow rates were obtained and compared with the experimental data. The simulation results of degradation efficiency under different models are basically consistent. Conclusion: Although low Reynolds k-ε models have better simulation results for high inlet flow rates, in terms of computation complexity, laminar flow is recommended for simulation.

Numerical study on turbulent characteristics of wall jet in a quiescent environment over a plate in motion

The present article reports the numerical analysis of a two dimensional turbulent wall jet flow over a horizontal moving plate in a quiescent environment. The simulation is done using the low-Reynolds number turbulence model proposed by Yang and Shih [21]. The turbulent characteristics are observed for various velocity ratio of plate with respect to jet (Up ) from keeping Reynolds number at jet inlet to be constant at 15000. The Reynolds averaged Navier Stokes (RANS) equations are discretized using the finite volume method and solved in steady state condition. The pressure correction technique applied to couple the velocity and pressure terms is SIMPLEC (semi-implicit pressure linked equation-consistent). The variation of jet half-width and the decaying local maximum velocity (Umax ) for the bottom plate moving with high velocity (Up > 1) shows dominancy of plate motion over the jet stream in the flow field. The velocity contour diagram shows the velocity distribution in the flow field. The Reynolds stresses induced in the wall proximate regions are directly proportional to the relative motion of the flow field but the magnitude of Reynolds stress away from wall decreases by increasing the plate velocity. The plate motion significantly affects the turbulence characteristics and the flow field in the viscous laminar zone of the wall region.

Numerical Investigation of Turbulent Offset Jet Flow Over a Moving Flat Plate Using Low-Reynolds Number Turbulence Model

Abstract The present study reports the numerical simulation of turbulent plane offset jet flow over a moving plate. The effect of plate velocity on various flow characteristics is discussed in detail including the special case of a stationary plate. For turbulence closure, the low-Reynolds number (LRN) turbulence model proposed by Yang and Shih (YS) is applied because it is computationally robust and reported to work quite effectively in several complex flow situations. The computations have been carried out with a Reynolds number of 15,000 for various offset ratios (OR = 3, 7, and 11) and different velocity ratios (Uplate) of the plate in the range 0–2. The finite volume method (FVM) with a staggered grid arrangement has been used to solve the transport equations. The application of the LRN model along with the integration to wall (ITW) approach enables us to capture one closed loop of the Moffatt vortex near the left corner of the wall for the stationary plate case. The spreading of the jet has been found to reduce by increasing the velocity of the plate. The jet half-width lies very close to the wall for the plate to jet velocity 1.5 and 2. For two extreme limits of plate velocity, i.e., Uplate = 0 and 2, the nearly self-similar profiles are observed at different axial locations in the wall jet region. Also, the flow is observed to exhibit nearly self-similar behavior when velocity profiles are plotted for various offset ratios at a given axial location in the wall jet region for Uplate = 0 and 2. It has been found that the flow characteristics are significantly influenced by the plate velocity.

Numerical Simulation of Solar Radiation and Conjugate Heat Transfer through Cabin Seat Textile

Abstract The solar radiation and the conjugate heat transfer through the cabin seat fabric were investigated numerically with a focus on a comparative analysis of various fabric solar reflectance or reflectivity (SR) and inlet cooling air velocity. For this purpose, 3D compressible Reynolds-averaged Navier–Stokes equations with the low Reynolds number turbulence model were utilized to simulate the airflow in the cabin. The discrete ordinate radiation model was adopted to describe the solar radiation. The conjugate heat transfer between the airflow and the fabric seats was included. The airflow temperature, radiative heat flux, and radiative heat transfer through the fabrics in a fixed cross section were studied. The results demonstrate that the increase in fabric SR leads to the increase in energy reflected to the atmosphere, which will bring about a lower temperature on the seat fabric. The decrease in emissivity and the energy absorbed results in the lower heat transfer and heat radiation and leads to the improvement of the cabin thermal environment. The high-temperature gradient near the seat causes the forced air circulation and is beneficial for the improvement of the thermal comfort. However, the cooling effect is not so obvious near the cabin seats when the inflow speed is increased.

Laminarization of turbulent flow in a heated vertical finned tube

Laminarization of the turbulent flow of Helium in a heated vertical finned tube was studied using a low-Reynolds number turbulence model. The study was carried out for an inlet Reynolds number of 6000, a non-dimensional wall heat flux value of 0.003, the number of fins ranging from 8 to 24, and non-dimensional fin height ranging from 0.1 to 0.3. Reductions in turbulent kinetic energy production and low-velocity regions in the inter-fin region are observed which promoted laminarization. Also, for low Reynolds number turbulent flow with large heat fluxes, the finned tubes are found to offer comparatively lower heat transfer enhancement at the expense of a larger pressure drop penalty.

Research on improvements of low Reynolds number turbulence model based on flow around automobiles

This article proposes two new turbulence models for steady-state and transient-state solutions. For the steady-state solution, by introducing the streamline curvature factor and response threshold value into the low Reynolds number (LRN) k-ε model, a modified LRN k-ε model is obtained, which is applied to simulate an automobile flow-field by Fluent solver. The comparisons among the results obtained by the modified model, realizable k-ε model, original LRN k-ε model, and HD-2 wind tunnel test show the modified model can simulate the flow separation, the wake flow-field, aerodynamic force most accurately. For the transient-state solution, by combining the constrained-large-eddy simulation (CLES) idea with the modified model method to modify the RANS/LES model, a transition LRN CLES model is proposed. The comparisons of the transition model, scale-adaptive simulation (SAS) model, and the actual road test results for aerodynamic noise show that the transition LRN CLES model has the better simulation ability.

Research on wind buffeting noise characteristics of a vehicle based on ILRN and DES-ILRN methods

In view of the unsatisfactory calculation accuracy of common turbulence models, two improved models, called improved low-Reynolds number (ILRN) k− ε and Detached EddySimulation (DES)-ILRN are proposed. Basing on the low-Reynolds number (LRN k− ε) turbulence model in this paper, revised concepts include the introduction of turbulence time scale, eddy viscosity coefficient limitation concept and separation perception model. Otherwise, the DES model is improved by introducing the ILRN model. The accuracy of the two models is validated through wind tunnel test. Then, the wind buffeting noise from rear windows is received by ILRN and DES-ILRN turbulence models, and the obtained results are compared with the road test. The accuracy of ILRN and DES-ILRN turbulence models in calculating wind buffeting noise of a real vehicle is validated by experiment. ILRN and DES-ILRN models are applied to research the wind buffeting noise, and good calculation results are obtained. They are promising methods to solve wind buffeting noise problems.

Improved Discrete Random Walk Stochastic Model for Simulating Particle Dispersion and Deposition in Inhomogeneous Turbulent Flows

Abstract The performance of different versions of the discrete random walk models in turbulent flows with nonuniform normal root-mean-square (RMS) velocity fluctuations and turbulence time scales were carefully investigated. The OpenFOAM v2−f low Reynolds number turbulence model was used for evaluating the fully developed streamwise velocity and the wall-normal RMS velocity fluctuations profiles in a turbulent channel flow. The results were then used in an in-house matlab particle tracking code, including the drag and Brownian forces, and the trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm were evaluated under the one-way coupling assumption. The distributions and deposition velocities of fluid-tracer and finite-size particles were evaluated using the conventional-discrete random walk (DRW) model, the modified-DRW model including the velocity gradient drift correction, and the new improved-DRW model including the velocity and time gradient drift terms. It was shown that the conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The concentration profiles of tracer particles obtained by using the modified-DRW model still are not uniform. However, it was shown that the new improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size heavy particles. In addition, good agreement was found between the estimated deposition velocities of different size particles by the new improved-DRW model with the available data.

Consistent surface roughness extension for wall functions

An approach to extend the near-wall treatment approach of RANS turbulence models using wall functions for rough surfaces is proposed. The formulation is consistent with the low-Reynolds number turbulence model roughness extension, leading to reduced near-wall grid spacing dependence and accurate predictions for a large range of ks+/y+ values. The formulation is further extended to the temperature wall functions and heat transfer prediction is assessed. The drawbacks of using the Reynolds analogy assumption are highlighted and three thermal corrections to improve these drawbacks are also examined. In particular, the correction term by Aupoix (2015), which accounts for the effect of the wetted surface area, is incorporated in the wall function formulation. This correction term significantly improves predictions as compared to the other two thermal correction terms at the expense of adding an additional physical parameter.

Discussion on improved method of turbulence model for supercritical water flow and heat transfer

The turbulence model fails in supercritical fluid-flow and heat transfer simulation, owing to the drastic change of thermal properties. The inappropriate buoyancy effect model and the improper turbulent Prandtl number model are several of these factors lead to the original low-Reynolds number turbulence model unable to predict the wall temperature for vertically heated tubes under the deteriorate heat transfer conditions. This paper proposed a simplified improved method to modify the turbulence model, using the generalized gradient diffusion hypothesis approximation model for the production term of the turbulent kinetic energy due to the buoyancy effect, using a turbulence Prandtl number model for the turbulent thermal diffusivity instead of the constant number. A better agreement was accomplished by the improved turbulence model compared with the experimental data. The main reason for the over-predicted wall temperature by the original turbulence model is the misuse of the buoyancy effect model. In the improved model, the production term of the turbulent kinetic energy is much higher than the results calculated by the original turbulence model, especially in the boundary-layer. A more accurate model for the production term of the turbulent kinetic energy is the main direction of further modification for the low Reynolds number turbulence model.