V2F Model Research Articles

Assessment of performance of turbulence models in predicting supercritical pressure heat transfer in a vertical tube

Computational simulations of heat transfer to fluids at a supercritical pressure have been performed using an ‘in-house’ CFD code written for two-dimensional axisymmetric flow and heat transfer based on the Favre averaging approach. Results are compared with recently available direct numerical simulations (DNS) which provide a benchmark dataset ideal for model assessment. The objective of the present study is to evaluate the performance of low-Reynolds number turbulence models in predicting mixed convection heat transfer to fluids at supercritical pressure, especially paying attention to the features which enable them to respond to the modifications of the turbulence field due to influences of flow acceleration and buoyancy. It has been found that a group of turbulence models which were previously found closely reproducing mixed convection under conditions of constant properties do not perform well for flows considered in the present study due to an over-response to changes in the flow. Models which were less successful previously perform better. The V2F model performs the best among all models tested. For strong-buoyancy-influenced cases, most models are able to reproduce turbulence recovery reasonably well but not the improvement on heat transfer. This is attributed, at least partly, to the inability of turbulence models in reproducing turbulent heat flux using a constant turbulent Prandtl number. The influence of the lack of a suitable description of the axial turbulent heat flux has been shown to be insignificant except immediately after the commencement of heating.

Numerical Simulation of the Transitional and Unsteady Flow through a Low Pressure Turbine

A simulation strategy is developed for the computation of the time-accurate flow through low pressure turbines with periodically impinging wakes generated by moving cylinder rods. For the simulations, different time steps and turbulent inflow conditions and their impact on the laminar separation on the suction side are considered. A realizable cubic low-Reynolds numberk-ɛturbulence model and a linear V2F model are utilized to capture transitional effects, in particular the laminar separation bubble at the suction side. For comparison with experimental data, published in a companion paper, pressure distribution and boundary layer profiles of the mean and fluctuation RMS velocity are considered. While the periodically disturbed flow is predicted with a reasonable accuracy by each model, for the undisturbed flow, an additional realizability condition based on a turbulent time scale bound is incorporated into the cubic model in order to capture the reattachment of the flow.

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.

Conjugate Heat Transfer Analysis of a Cooled Turbine Vane Using the V2F Turbulence Model

The conjugate heat transfer methodology has been employed to predict the flow and thermal properties including the metal temperature of a NASA turbine vane at three operating conditions. The turbine vane was cooled internally by air flowing through ten round pipes. The conjugate heat transfer methodology allows a simultaneous solution of aerodynamics and heat transfer in the external hot gas and the internal cooling passages and conduction within the solid metal, eliminating the need for multiple/decoupled solutions in a typical industry design process. The model of about 3 million computational meshes includes the gas path and the internal cooling channels, comprising hexa cells, and the solid metal comprising hexa and prism cells. The predicted aerodynamic loadings were found to be in close agreement with the data for all the cases. The predicted metal temperature, external, and internal heat transfer distributions at the midspan compared well with the measurement. The differences in the heat transfer rates and metal temperature under different running conditions were also captured well. The V2F turbulence model has been compared with a low-Reynolds-number k-ε model and a nonlinear quadratic k-ε model. The V2F model is found to provide the closest agreement with the data, though it still has room for improvement in predicting the boundary layer transition and turbulent heat transfer, especially on the suction side. The overall results are quite encouraging and indicate that conjugate heat transfer simulation with proper turbulence closure has the potential to become a viable tool in turbine heat transfer analysis and cooling design.

The Role of Turbulence Models for Predicting a Thermal Stratification

A numerical study of the evaluation of turbulence models for predicting the thermal stratification phenomenon is presented. The tested models are the elliptic blending turbulence model (EBM), the two-layer model, the shear stress transport model (SST), and the elliptic relaxation model (V2-f). These four turbulence models are applied to the prediction of a thermal stratification in an upper plenum of a liquid metal reactor experimented at the Japan Nuclear Cooperation (JNC). The EBM and V2-f models predict properly the steep gradient of the temperature at the interface of the cold and hot regions that is observed in the experimental data, and the EBM and V2-f models have the capability of predicting the temporal oscillation of the temperature. The two-layer and SST models predict the diffusive temperature gradient at the interface of a thermal stratification and fail to predict a temporal oscillation of the temperature. In general, the EBM predicts best the thermal stratification phenomenon in the upper plenum of the liquid metal reactor.

F131 タービン翼前縁付け根部における熱流動場に関する研究(強制対流1)

When a turbulent boundary layer approaches a symmetric bluff-body, the body-generated adverse-pressure gradient precipitates a separation process that forces the impinging boundary layer vorticity to reorganize into a horseshoe vortex. Endwall heat transfer is influenced by the presence of horseshoe vortex. This paper shows the result of experimental and numerical study about the horseshoe vortex and heat transfer in the leading-edge endwall region. Naphthalene sublimation method was used to measure the detail local heat transfer coefficient distribution on the endwall. The v2f model resulted in good agreement of the local heat transfer coefficient distributions between experiments and numerical analysis.

Computational fluid dynamics and room air movement.

Computational Fluid Dynamics (CFD) and new developments of CFD in the indoor environment as well as quality considerations are important elements in the study of energy consumption, thermal comfort and indoor air quality in buildings. The paper discusses the quality level of Computational Fluid Dynamics and the involved schemes (first, second and third order schemes) by the use of the Smith and Hutton problem on the mass fraction transport equation. The importance of "false" or numerical diffusion is also addressed in connection with the simple description of a supply opening. The different aspects of boundary conditions in the indoor environment as, e.g., the simulation of Air Terminal Devices and the simulation of furnishings and occupants are discussed. The prediction of the flow in a room with a three-dimensional wall jet by the use of different turbulence models such as the k-epsilon model, the V2-f model and the Reynolds Stress model is addressed in the last chapter of the paper. The use of computational Fluid Dynamics as a practical design method for room air distribution is widespread. It is important to consider the quality of the predictions in order to obtain a sufficient level of accuracy. It is also important to work with a practical description of supply openings as well as with the right level of details in the occupied zone and the right turbulence model. All these aspects are addressed in the article.

Application of a k-ε model to heat transfer in impinging flows

Local heat transfer is predicted in turbulent axisymmetric jets, impinging onto a flat plate. A non-linear k-e model is used[1], in which both the constitutive law for the turbulent stresses and the transport equation for the turbulent dissipation rate e have an important contribution in the improved heat transfer predictions. The shape of the Nusselt number profiles, expressing dimensionless heat transfer, as well as the stagnation point value, are well predicted for different distances between the nozzle exit and the plate. Accurate flow field predictions are the basis for good heat transfer predictions. For a fixed Reynolds number, the influence of the nozzle-plate distance is well captured. For a fixed distance, the influence of the Reynolds number is correctly reproduced. Comparisons are made to a low-Reynolds standard k-e model[2] and the v2-f model[3]. A thorough discussion is found in [4]. Only a summary of those results is discussed here, while some new results are also presented.

Numerical Investigation of Impingement Cooling in Ribbed Ducts Due to Jet Arrays

A numerical investigation of impingement heat transfer and fluid flow in a rectangular two-pass duct was carried out. The impingement wall was smooth or with periodically mounted square ribs. A multiblock parallel CFD code was employed for the calculation. The turbulence modeling was treated by applying a low Reynolds number turbulence eddy viscosity model (LEVM) and a V2F model. First, the calculations were validated against available experimental data in a two-pass duct where the impingement wall was smooth. Then, jets impinging on ribbed walls were simulated. The distance from the nozzle to the impingement wall was fixed at four nozzle diameters (d). The square rib width was set as 0.5 d. The duct inlet Reynolds number was fixed at 10,000. Results show that the presence of ribs was favorable for the heat transfer enhancement on the impingement wall, but not for the side wall.

Predictions of External Heat Transfer for Turbine Vanes and Blades With Secondary Flowfields

Detailed heat transfer distributions on the endwall and along the vane/blade surface are essential for component mechanical integrity and life predictions. Due to secondary flows, high gradients in heat transfer are present at the endwall and at the vane or blade surface itself where the passage vortex influences the mainstream flow. This paper documents the benchmarking of three turbulence models: 1) k-ε realizable with wall functions, 2) k-ε realizable with two layer model, and 3) the V2F model for endwall and surface heat transfer and flowfield predictions. Benchmark experimental data from a scaled-up low speed rig for both a stator and rotor geometry are used for comparisons of heat transfer and flowfield. While the k-ε realizable turbulence models give a good prediction of the secondary flow pattern, the heat transfer at the endwall and at the surface is not well predicted due to the inadequate modeling of near wall turbulence. The V2F model gives better agreement with the experiments on the endwall and vane midspan heat transfer is also well predicted, although transition occurs too far upstream on the suction surface. The results from this study represent the feasibility of CFD utilization as a predictive tool for local heat transfer distributions on a vane/blade endwall.

Prediction of pressure loss and heat transfer in internal cooling passages.

This paper reports CFD-simulations of the turbulent flow, pressure loss and heat transfer occurring in ribbed passages. The channel section is rectangular, with an aspect ratio of 2.04. Ribs are square cross-section, their height is 10% of the channel height, and their inclination is varied from 90 degrees to 33 degrees. Reynolds number is 30,000. Three turbulence models (k-epsilon wall functions and 2-layer, V2F) are used and compared to the experimental data of Cho et al. All three models accurately predict the pressure losses due to the ribs and the qualitative heat transfer distribution on the ribbed wall. However, only the V2F model can accurately reproduce the absolute heat transfer levels, this at all inclination angles. The correlation developed by Han and co-workers for smaller rib-heights under-predicts the friction factor and wall heat transfer level on the current configuration. This shows the danger of using a correlation outside of its application range.

Predictions of Turbulent Heat Transfer in an Axisymmetric Jet Impinging on a Heated Pedestal

Cooling or heating of a flat plate by an impinging jet, due to its many applications, has been widely studied. Recent experimental data concerning more complex geometries has become available. In this study, the cooling of a heated pedestal mounted on a flat plate, a configuration which is closer to the one met in some engineering applications (e.g., cooling of electronic components), has been numerically simulated. The normal velocity relaxation turbulence model (V2F model) in an axisymmetric geometry has been adopted. Results have been obtained for a range of jet Reynolds numbers and jet-to-pedestal distances. Comparison of the predicted heat transfer coefficient with experiments has shown a very good agreement. For comparison, results have also been obtained with the widely used κ – ε turbulence model and the agreement with the data is poor.

Prediction of heat transfer in an axisymmetric turbulent jet impinging on a flat plate

The problem of cooling of a heated plate by an axisymmetric isothermal fully developed turbulent jet has been studied numerically. Computations were performed with the normal-velocity relaxation turbulence model (V2F model). Local heat transfer coefficient predictions are compared to the available experimental data. For comparison, computations have also been carried out with the widely used k- ε model. The V2F heat transfer predictions are in excellent agreement with the experiments, whereas the k- ε model does not properly resolve the flow features, greatly over-predicts the rate of heat transfer and yields physically unrealistic behaviors.

Computation of 3-D turbulent boundary layers using the V2F model

The V2F model makes use of the standard k–e model, but extends it by incorporating near-wall turbulence anisotropy and non-local pressure-strain effects, while retaining a linear eddy viscosity assumption. It has the attraction of fewer equations and more numerical robustness than Reynolds stress models. The model is presented in a form that is completely independent of distance to the wall. This formalism is well suited to complex, 3-D, multi-zone configurations. It has been applied to the computation of two complex 3-D turbulent flows: the infinitely swept bump and the appendage-body junction; some preliminary results for the flow in a U-bend are also presented. Despite the use of a linear, eddy viscosity formula, the V2F model is shown to provide excellent predictions of mean flow quantities. The appendage-body test case involves very complex features, such as a 3-D separation and a horseshoe vortex. The V2F simulations have been shown to successfully reproduce these features, both qualitatively and quantitatively. The calculation of the complex flow structure inside and downstream of the U-bend also shows very promising results.