Partially-Averaged Navier-Stokes Research Articles

Critical cavitation coefficient analysis of a space low specific centrifugal pump with micro gravity

Centrifugal pump was used in the loop as a baselined unit. The flow rate of the pump was very small, while the head was high. This space pump must work stable for a long time (more than a year), so the performance of the pump attracted public attention. The rotational speed of the impeller was limited for stability, so the pump belonged to low specific centrifugal pump. In this paper, a single-phase centrifugal pump, which was designed for single-phase fluid loops in satellites, was modeled for numerical simulation. The hydraulic region of the pump was discretized by structured mesh. Three dimensional (3-D) flow in the pump was studied by the use of computational fluid dynamics. Partially-Averaged Navier- Stokes (PANS) model based on RNG k-ε turbulence model was developed for the simulation of the unsteady flow. Velocity inlet and pressure outlet was used as the boundary conditions. Interface was used between the impeller and the casing, as well as the impeller and inlet pipe. Performances and pressure fluctuation of the pump were investigated. The dominant frequency of the pressure fluctuation is blade passing frequency at the region close to the tongue of the casing, while it is twice of blade passing frequency at the other region.

Numerical simulation of flow past a circular base on PANS methods

A nonlinear partially averaged Navier-Stokes (PANS) method based on RNG k-ε turbulence model is evaluated by a moderately high Reynolds number turbulence flow past a circular cylinder. The ratios of unresolved-to total kinetic energy (fk) and unresolved-to-total disspation (fε) for PANS method is sensitive to the simulation result. Simulation results based on different fk are compared with the experimental data. The quantities including mean streamline velocity, mean normal velocity, streamlines and et al. are analyzed. The computational result is reasonable when fk is less than 0.6. The PANS method can be used in the simulation of high Reynolds number turbulence flow.

Computational Vehicle Aerodynamics by Reference to DrivAer Model Configurations

The DrivAer model represents a generic, but realistic car configuration, created by merging the original geometries of two medium sized cars – the Audi A4 and the BMW 3 Series. Three down-scaled configurations differing in the rear-end shape are considered: fastback, notchback and estate-back. At the Technische Universitat Darmstadt, the performance of the so-called PANS (Partially-Averaged Navier-Stokes) computational method was analysed by reference to the DrivAer model. AUTHORS

Transient cavitating vortical flows around a hydrofoil using k-ω partially averaged Navier–Stokes model

For accurate simulations of wall-bounded turbulent cavitating flows, the present paper proposed a partially averaged Navier–Stokes (PANS) method derived from the [Formula: see text]-[Formula: see text] turbulence model. Transient cavitating vortical flows around a NACA66 hydrofoil were simulated by using the [Formula: see text]-[Formula: see text] PANS model with various filter parameters ([Formula: see text] and [Formula: see text], while [Formula: see text]) and a mass transfer cavitation model based on the Rayleigh–Plesset equation. Compared with the available experimental data, the [Formula: see text]-[Formula: see text] PANS model with [Formula: see text] can accurately reproduce the cavitation evolution with more complicated structures due to the reduction in the predicted eddy viscosity. Further analyses, using the vorticity transport equation, indicate that the transition of cavitation structure from two dimension to three dimension is associated with strong vortex–cavitation interaction, where vortex stretching and dilation may play a major role. Therefore, the [Formula: see text]-[Formula: see text] PANS model with the filter parameter of [Formula: see text] is an effective method to numerically predict the transient cavitating vortical flows around hydrofoils. The results obtained in this paper are helpful to provide a physical insight into the mechanisms of cavitation shedding dynamics.

The effect of smaller turbulent motions on heat transfer in the annular gap flow of flywheel

The forced convective heat transfer in the gap of a flywheel is affects the safety of reactor coolant pump (RCP), such as the operation temperature limit of the bearing, therefore it is necessary to analyze the heat transfer in the annular gap flow of a flywheel. The current study provides evidence that the convective heat transfer depends on the flow structure. When the Taylor number of this flow is about 1E12, the flow structure has a special pattern likes Herringbone near the wall, and consists of many smaller Görtler vortices. Although the earliest experimental studies found the Görtler vortex with laser-induced fluorescence (LIF), these vortices are difficult to study by numerical analysis with direct numerical simulation (DNS) or the large eddy simulation (LES), and the Reynolds-averaged Navier–Stocks (RANS) cannot capture the smaller scale vortices in the wall boundary layers with overestimated eddy viscosity. In this paper, we adopt the partially-averaged Navier–Stokes (PANS) model to observe the smaller turbulent motions in the annular gap flow of a flywheel, and analyze the effect of Görtler vortices on convective heat transfer. Compared with k–ε, PANS simulation suggests that there are larger temperature gradients at the Görtler vortices region, and two temperature mixing processes occur at the boundaries of a pair of Taylor vortices.

Numerical evaluation of cavitation shedding structure around 3D Hydrofoil: Comparison of PANS, LES and RANS results with experiments

Results of cavitating turbulent flow simulation around a twisted hydrofoil were presented in the paper using the Partially-Averaged Navier-Stokes (PANS) method (Ji et al. 2013a), Large-Eddy Simulation (LES) (Ji et al. 2013b) and Reynolds-Averaged Navier-Stokes (RANS). The results are compared with available experimental data (Foeth 2008). The PANS and LES reasonably reproduce the cavitation shedding patterns around the twisted hydrofoil with primary and secondary shedding, while the RANS model fails to simulate the unsteady cavitation shedding phenomenon and yields an almost steady flow with a constant cavity shape and vapor volume. Besides, it is noted that the predicted shedding vapor cavity by PANS is more turbulent and the shedding vortex is stronger than that by LES, which is more consistent with experimental photos.

Turbulence simulations of flow past a circular cylinder based on a nonlinear partially averaged Navier–Stokes (PANS) method

A nonlinear partially averaged Navier–Stokes (PANS) method based on RNG [Formula: see text]–[Formula: see text] turbulence model is evaluated by a moderately high Reynolds number turbulence flow past a circular cylinder. The ratios of unresolved-to-total kinetic energy [Formula: see text] and unresolved-to-total dissipation [Formula: see text] for PANS method are sensitive to the simulation result. Simulation results based on different [Formula: see text] are compared with the experimental data. The quantities including mean streamline velocity, mean normal velocity, streamlines, etc. are analyzed. The computational result is reasonable when [Formula: see text] is less than 0.6. The PANS method can be used in the simulation of high Reynolds number turbulence flow.

Property assessment of PANS method for numerical simulation of flow around tandem cylinders

Partially averaged Navier-Stokes( PANS) method derived from the traditional Reynolds averaged Navier-Stokes( RANS) methods by introducing controlling parameter into original RANS equations to modify these equations,is one kind of hybrid methods which can effectively simulate the separated turbulent flows. Computational results of tandem cylinders using PANS method based on Menter shear stress transport( SST) turbulence model were presented in this investigation. The flow structures around tandem cylinders were analyzed and the accuracy and reliability of PANS method were also verified. Moreover,the influence of the model parameter on numerical results was investigated and the performance of different types of PANS methods was assessed. Studies show that the unresolved-to-total ratio of turbulence kinetic energy has significant effects on the numerical results,and taking this parameter as a constant value throughout the whole computational domain can hardly tackle the complex flow problem. Furthermore,the parameter is made to change along with flow physical information and the local grid scale. The variable fkPANS method agrees well with the results from SST detached-eddy simulation( DES) and the experimental measurements,suggesting strong adaptability to complex turbulence simulation.

Partially Averaged Navier Stokes simulation of turbulent heat transfer from a square cylinder

A variable resolution modeling approach, namely the Partially-Averaged Navier Stokes (PANS) approach, is used to study heat transfer in a separated turbulent flow field. The simulations are performed to assess the applicability and effectiveness of the PANS approach. Two types of grids are compared: a structured grid with full hexahedral elements with wall functions model (SM-WF) and an unstructured grid with hybrid tetrahedral-prismatic elements with wall resolve model (UM-WR). A heated square cylinder in cross air stream at Re=2.2×104 is considered and the simulations are performed using a finite volume based opensource software, OpenFOAM. It is observed that the PANS approach, with both the meshing strategies adopted, is able to predict the unsteady flow behavior around the cylinder and in the wake. But, only the wall resolve case reproduces the thermal and the Nusselt number behaviors around the cylinder as compared to experimental results. Further the wall resolve model is used to study the heat transfer phenomena at different faces of the cylinder over a complete vortex shedding cycle using the phase-averaged analysis of the shedding phenomenon. The turbulent heat fluxes are also studied to understand the effect of turbulence on convection.

Partially-Averaged Navier–Stokes simulations of flows around two different Ahmed bodies

The paper reports a study about the prediction of flows around simplified vehicles using Partially-Averaged Navier–Stokes (PANS). Numerical simulations are performed for two simplified vehicles: a slanted-back Ahmed body at Re=30,000 and a squared-back Ahmed body at Re=300,000. A comparison of the resolved and modeled physical flow scales is made with corresponding LES and experimental data for a better understanding of the performance of the PANS model. The PANS model is compared for coarse and fine grid resolutions and it is indicated that even a coarse-grid PANS simulation is able to produce fairly close flow predictions to those from a well-resolved LES simulation. The results indicate the possibility of improvement of the predictions by employing a finer grid resolution.

Numerical simulation of cavitation shedding flow around a hydrofoil using Partially-Averaged Navier-Stokes model

Purpose – The purpose of this paper is to predict the unstable cavitation shedding flow around a 2D Clark-y hydrofoil. Design/methodology/approach – The paper studies Partially Averaged Navier-Stokes (PANS) model which was employed in the two-phase flow with a homogeneous cavitation model. Findings – Maximum density ratio affects the mass transfer rate between the liquid and the vapor significantly. The cavitating flow predicted by PANS model can resolve more turbulent scales by decreasing the parameter fk. Originality/value – The accuracy of numerical prediction is improved by increasing the maximum density ratio and decreasing fk.

Partially-averaged Navier–Stokes method for turbulent thermal plume

In this paper, the partially-averaged Navier–Stokes (PANS) simulation is performed for a turbulent thermal plume. The aim of the paper is to assess the PANS method for modeling buoyancy-driven flows at a reasonable computational cost. PANS is a turbulence closure model which is developed to be used as a bridging model ranging from the direct numerical simulation to the Reynolds-averaged Navier–Stokes simulation by varying the level of resolution. The PANS computations are performed for various values of the filter-width to evaluate the sensitivity of the filter-widths to the computed flow statistics. The present simulations have been carried out employing a source code buoyantPimpleFOAM based on the OpenFOAM platform. In order to capture the effect of buoyancy on turbulence, the generalized gradient diffusion hypothesis is employed to model the production of turbulence due to buoyancy. A detailed comparison of the time-averaged and turbulent statistics obtained from the PANS simulations with the experimental data and LES results reported in the literature has been presented. The present results have also been compared with the results of the unsteady Reynolds-averaged Navier–Stokes solutions. The PANS model is shown to enhance the computing capability significantly in predicting buoyancy-driven flows compared with those of URANS model. Finally, various important unsteady flow structures of turbulent thermal plume have been visualized from the instantaneous flow statistics obtained using the PANS simulations.

Unsteady Numerical Simulation of Flow in Draft Tube of a Hydroturbine Operating Under Various Conditions Using a Partially Averaged Navier–Stokes Model

The variable energy demand requires a great flexibility in operating a hydroturbine, which forces the machine to be operated far from its design point. One of the main components of a hydroturbine where undesirable flow phenomena occur under off-design conditions is the draft tube. Using computational fluid dynamics (CFD), the present paper studies the flow in the draft tube of a Francis turbine operating under various conditions. Specifically, four operating points with the same head and different flow rates corresponding to 70%, 91%, 99%, and 110% of the flow rate at the best efficiency point (BEP) are considered. Unsteady numerical simulations are performed using a recently developed partially averaged Navier–Stokes (PANS) turbulence model, and the results are compared to the available experimental data, as well as the numerical results of the traditionally used Reynolds-Averaged Navier–Stokes (RANS) models. Several parameters including the pressure recovery coefficient, mean velocity, and time-averaged and fluctuating wall pressure are investigated. It is shown that RANS and PANS both can predict the flow behavior close to the BEP operating condition. However, RANS results deviate considerably from the experimental data as the operating condition moves away from the BEP. The pressure recovery factor predicted by the RANS model shows more than 13% and 58% overprediction when the flow rate decreases to 91% and 70% of the flow rate at BEP, respectively. Predictions can be improved significantly using the present unsteady PANS simulations. Specifically, the pressure recovery factor is predicted by less than 4% and 6% deviation for these two operating conditions. A similar conclusion is reached from the analysis of the mean velocity and wall pressure data. Using unsteady PANS simulations, several transient features of the draft tube flow including the vortex rope and associated pressure fluctuations are successfully modeled. The formation of the vortex rope in partial load conditions results in severe pressure fluctuations exerting oscillatory forces on the draft tube. These pressure fluctuations are studied for several locations in the draft tube and the critical region with highest fluctuation amplitude is found to be the inner side of the elbow.

Three-dimensional unsteady cavitating flows around an axisymmetric body with a blunt headform

We investigated the three-dimensional characteristics in the unsteady cavitating flow over an axisymmetric body with a blunt headform. A high-speed video camera was used to visualize the cavitating flow structures. A modified PANS (Partially-averaged Navier-Stokes) turbulence model coupled with Kubota cavitation model was used to simulate the time-evolution process of the unsteady cavitating flows. The finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures (LCS) methods are applied to investigate the three-dimensional flow patterns. The results show that the numerical method is capable of simulating the unsteady cavitating flow for capturing the attached cavity with maximum-length, the cavity break-off and U-type shedding, in accordance with the qualitative features observed in the experiment. Three-dimensional characteristics are extremely impressive in the unsteady cavitating flows. The re-entrant flows originate from different circumferential positions at the closure region of the attached cavity, and move upstream at different speeds. Moreover, substantial circumferential motions in the unsteady cavitating flow are found based on Lagrangian trajectories, and it is reasonably deduced that the U-type shedding cavity is primarily induced by the effect of re-entrant flow motions consisting of moving upstream and circumferential flows as well.

Partially Averaged Navier-Stokes method based on k-ω model for simulating unsteady cavitating flows

The turbulence closure is significant to unsteady cavitating flow computations as the flow is frequently time-dependent accompanied with multiple scales of vortex. A turbulence bridging model named as PANS (Partially-averaged Navier-Stokes) purported for any filter-width is developed recently. The model filter width is controlled through two parameters: the unresolved-to-total ratios of kinetic energy fk and dissipation rate fω. In the present paper, the PANS method based on k-ω model is used to simulate unsteady cavitating flows over a Clark-y hydrofoil. The main objective of this work is to present the characteristics of PANS k-ω model and evaluate it depending on experimental data. The PANS k-ω model is implemented with various filter parameters (fk=0.2~1, fω =1/fk). The comparisons with the experimental data show that with the decrease of the filter parameter fk, the PANS model can reasonably predict the time evolution process of cavity shapes and lift force fluctuating in time. As the PANS model with smaller fk can overcome the over-prediction of turbulent kinetic energy with original k-ω model, the time-averaged eddy viscosity at the rear of attached cavity decreases and more levels of physical turbulent fluctuations are resolved. What's more, it is found that the value of ω in the free stream significantly affects the numerical results such as time-averaged cavity and fluctuations of the lift coefficient. With decreasing fk, the sensitivity of ω-equation on free stream becomes much weaker.

Numerical prediction of cavitating flow around a hydrofoil using pans and improved shear stress transport k-omega model

The prediction accuracies of partially-averaged Navier-Stokes model and improved shear stress transport k-? turbulence model for simulating the unsteady cavitating flow around the hydrofoil were discussed in this paper. Numerical results show that the two turbulence models can effectively reproduce the cavitation evolution process. The numerical prediction for the cycle time of cavitation inception, development, detachment, and collapse agrees well with the experimental data. It is found that the vortex pair induced by the interaction between the re-entrant jet and mainstream is responsible for the instability of the cavitation shedding flow.

A New PANS Model for Unsteady Separated Flow Simulations

A new Partially Averaged Navier-Stokes (PANS) model is proposed with the aim of simulating unsteady separated flows at reasonable computational expense. The unresolved-to-total ratio of kinetic energy (fk) related to PANS method is taken as a spatially varying and dynamically updating parameter in the computations. Turbulent flow past a backward-facing step is chosen as a test case in an effort to evaluate the model performance. PANS computations are compared to the experimental data and the traditional Detached Eddy Simulations (DES), showing their excellent capability of resolving turbulent fluctuations. Boundary layer shielding technique is also introduced into the PANS approach and effectively improves the computational results.

Computational study of supersonic turbulent-separated flows using partially averaged Navier-stokes method

Separation commonly exists in the flows around flight vehicles and also in the internal combustor flows. Simulation of high-speed turbulent-separated flows using a reliable computational design tool is crucial for the development of supersonic and hypersonic vehicles. In this paper, we present the computational results of supersonic base and ramped-cavity flows at high Reynolds numbers using the partially averaged Navier-Stokes (PANS) method. The current PANS models are based on the Menter SST turbulence model and also the Wilcox k-ω model. Results from PANS simulations are compared in detail with the available experimental data. The effect of the resolution control parameter fk (the ratio of unresolved-to-total kinetic energy) relevant to the PANS method is investigated. More turbulent flow structures are resolved as expected with decreasing fk, but it does not mean better results can be obtained. Spatially varying and dynamically updated fk in PANS simulations has been performed. Results from variable fk PANS simulations show good agreement with the experiment and great improvement when compared to Reynolds averaged Navier-Stokes (RANS) computation and constant fk PANS simulations.

Fluid flow and conjugate heat transfer in a matrix of surface-mounted cubes: A PANS study

The Partially-Averaged Navier–Stokes (PANS) method is intended to provide the optimum fidelity on any given numerical grid while varying seamlessly between the Reynolds-Averaged Navier–Stokes (RANS) model and direct numerical simulation (DNS). This method belongs to so called bridging or seamless methods. The PANS method has been more often used in the research community but also in the industry in last years. This is probably due to its simplicity, robustness and recent theoretical extensions as well as due to the detailed validations on the number of complex cases presented in many publications. As for any relatively new modeling approach, the list of validation cases should be further extended. Therefore, an additional test case is included in this paper. The PANS method is validated here for the fluid flow and heat transfer in a matrix of surface-mounted cubes. The ζ-f variant of PANS was used and compared with its RANS counterpart. The calculation procedure, which now includes the energy equation as well, is explained. A brief description of on-going developments and possible next improvements is also given in this paper.

A partially-averaged Navier–Stokes model for the simulation of turbulent swirling flow with vortex breakdown

This paper presents the development and validation of a new partially-averaged Navier–Stokes (PANS) model which can successfully predict turbulent swirling flow with vortex breakdown. The proposed PANS model uses an extended low Reynolds number k–ε model as the baseline model. Furthermore, a new formulation for the unresolved-to-total turbulent kinetic energy ratio fk is developed using partial integration of the complete turbulence energy spectrum. Therefore, the present formulation of fk is believed to be superior to the previously used constant or computed values. The newly developed PANS model is used in unsteady numerical simulations of two turbulent swirling flows containing vortex breakdown, namely swirling flow through an abrupt expansion and flow in a draft tube of a hydraulic turbine operating under partial load. The present PANS model accurately predicts time-averaged and root-mean-square (rms) velocities in the case of the abrupt expansion, while it is shown to be superior to the Delayed Detached Eddy Simulation (DDES) and Shear Stress Transport (SST) k–ω models. Predictions of the reattachment length using the present model shows at least 14% and 23% improvements compared to the DDES and the SST k–ω models respectively. Also, transient features of the flow, e.g. vortex rope formation and precession, is well captured in the case of the complex draft tube flow. The frequency of the vortex rope precession, which causes severe fluctuations and vibrations, is well predicted by only 7% deviations from the experimental data.