Partially Averaged Navier-Stokes Model Research Articles

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field.

Evaluation of turbulence models for the numerical prediction of transient cavitation around a hydrofoil

The objective of this paper is to evaluate the predictive capability of three turbulence models for the simulation of unsteady cavitating flows around a 2D Clark-y hydrofoil. Three turbulence models were standard k-ε model, hybrid model of density correction model (DCM) and filter-based model (FBM) and an improved partially-averaged Navier-Stokes model (PANS) based on k-ε model. Using the above-mentioned turbulence models and a homogeneous cavitation model, the unsteady cloud cavitation flows around the hydrofoil were numerically simulated and the time evolutions of cavity shape and lift evolutions over time were obtained. The results with comparison to a tunnel experiment data show that the hybrid model and PANS model can accurately capture unsteady cavity shedding details, fluctuation frequency and amplitude of lift and drag. The k-ε model has a poor agreement with the real experimental visualizations and this is mainly attributed to an over prediction of the turbulent viscosity in the rear part of the cavity, which limits the reentrant jet fully reaching the leading edge. The adverse pressure gradient plays an important role in the progression of the reentrant jet. Both the shock wave generated by the collapse of the cloud cavity and the growth of attached sheet cavity contribute to the increase of adverse pressure gradient.

Effectiveness of cut‐off scales models for variable resolution methods

AbstractVariable resoltion methods can be divided in two groups, bridging and zonal methods. The bridging method is aimed to provide the best possible physical fidelity on any given numerical grid while varying seamlessly between Reynolds averaged Navier‐Stokes (RANS) model and Direct Numerical Simulations (DNS). Two of the most developed bridging methods are the partially integrated transport model (PITM) and partially averaged Navier‐Stokes (PANS) model. The PANS model was choosen here as the basic approach for the further theoretical extension but the conclusions derived in this work can be applied to the PITM model as well. It was shown in earlier studies that the implied cut‐off for the PANS method can be placed in any part of the spectrum including the dissipation range. This is done by varying the unresolved‐to‐total ratios of kinetic energy and dissipation. In the practice, the parameter which determines the unresolved‐to‐total kinetic energy ratio is defined by using the grid spacing and calculated integral length scale of turbulence. When the grid size is smaller, then more of the turbulent kinetic energy can be resolved. In the previous approach, the integral scale of turbulence is obtained by using resolved turbulence calculated as a difference between the instantaneous filtered velocity and the averaged velocity field. Such approach is impractical for cases with moving geometries or with transient boundaries. An alternative solution is to solve an additional equation for the resolved kinetic energy and then, the resolution parameter can be directly calculated as the equation for the unresolved kinetic energy is anyway solved. It must be only ensured that a modeled cut‐off length scale is larger than a numerical grid cell size. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B=10, Re=13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B=4, Re=20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.

Application of Modified PANS Model for Computation of Cloud Cavitation around a Clark-Y Hydrofoil

A density correction function was introduced to the Partially-Averaged Navier-Stokes Model (PANS) taking into account the local compressibility of two-phase mixture. The standard k-ε model, PANS model and the modified PANS model were used to simulate the unsteady cloud cavitation around a Clark-y hydrofoil and the evolutions of cavity shape, time-averaged turbulence viscosity distribution and lift coefficient variation were investigated. The results compared with experimental data show that the PANS model and the modified PANS model strongly reduce the turbulent viscosity and predict the cloud cavity shedding behavior observed in the experiment successfully, while the cavitation area and time-average lift coefficient predicted by the modified PANS model is closer to the experimental values than the original PANS model.

Instability Analysis of a Model Pump-Turbine with MGV Based on Nonlinear Partially Averaged Navier-Stokes Methods

Pump-turbines were always running at partial condition with the power grid changing. Flow separations and stall phenomena were obvious in the pump-turbine. Most of the RANS turbulence models solved the shear stress by linear difference scheme and isotropic models, so they could not capture all kinds of vortexes in the pump-turbine well. At present, partially-averaged Navier-Stokes (PANS) model has been found to be better than LES in simulating flow regions especially those with less discretized grid. In this paper, a new nonlinear PANS turbulence model was proposed, which was modified from RNG k-ε turbulence model and the shear stresses were solved by Ehrhardt's nonlinear methods. The nonlinear PANS model was used to study the instability of “S” region of a model pump-turbine with misaligned guide vanes (MGV). The opening of preopened guide vanes had great influence on the “S” characteristics. The optimal relative opening of the preopened guide vanes was 50% for the improvement of the “S” characteristics. Pressure fluctuations in the vaneless space were analyzed. It is found that the dominant frequency at the vaneless space was twice the blade passing frequency, while the second dominant frequency decreased as the preopening increased.

Unsteady Cavitating Flow around a Hydrofoil Simulated Using the Partially-Averaged Navier—Stokes Model

Numerical simulations of unsteady cavitating flow around a NACA66-mod hydrofoil were performed using the partially-averaged Navier—Stokes method with different values of the resolution control parameters (fk = 1.0−0.2, f∊ = 1). With decreasing fk, the predicted cavitating flow becomes unsteady as the time-averaged turbulent viscosity at the rear part of the attached cavity is gradually reduced. For fk = 0.9 and 0.8, the cavity becomes unstable and its length dramatically expands and shrinks, but the calculation fails to predict the vapor cloud shedding behavior observed experimentally. With smaller fk less than 0.7, the cloud shedding behavior is simulated numerically and the predicted cavity shedding frequency increases. With fk = 0.2, the whole cavitating flow evolution can be reasonably reproduced including the cavity growth/destabilization observed previously. The reentrant flow along the suction surface of the hydrofoil is the main trigger to cause the vapor cloud shedding. The wall pressure along the hydrofoil surface oscillates greatly due to the dynamic cavity shedding. Comparing the simulations and experiments, it is confirmed that for the PANS method, resolution control parameters of fk = 0.2 and f∊ = 1 are recommended for numerical simulations of unsteady cavitating flows. Thus, the present study shows that the PANS method is an effective approach for predicting unsteady cavitating flow over hydrofoils.

A Partially-Averaged Navier-Stokes model for hill and curved duct flow

Turbulent flows past hill and curved ducts exist in many engineering applications. Simulations of the turbulent flow are carried out based on a newly developed technique, the Partially-Averaged Navier-Stokes (PANS) model, including separation, recirculation, reattachment, turbulent vortex mechanism. The focus is on how to accurately predict typical separating, reattaching and secondary motion at a reasonable computational expense. The effect of the parameter, the unresolved-to-total ratio of kinetic energy ( f k ), is examined with a given unresolved-to-total ratio of dissipation ( f ɛ ) for the hill flow with a much coarser grid system than required by the LES. An optimal value of f k can be obtained to predict the separation and reattachment locations and for more accurate simulation of the resolved turbulence. In addition, the turbulent secondary motions are captured by a smaller f k as compared with the RANS method with the same grid.

A low Reynolds number variant of partially-averaged Navier–Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier–Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k– ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results – at a reduced CPU time – as compared to the Dynamic Smagorinsky model.

Partially Averaged Navier-Stokes method for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state, and the flow is frequently unsteady and turbulent. The Reynolds-Averaged Navier-Stokes (RANS) approach has been popular for turbulent flow computations. The most widely used ones, such as the standard k − ɛ model, have well-recognized deficiencies when treating time dependent flow field. To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures, conditional averaging is adopted for the Navier-Stokes equation, and one more parameter, based on the filter size, is introduced into the k − ɛ model. In the Partially Averaged Navier-Stokes (PANS) model, the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy f 1 . This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil. From the experimental validations regarding the forces, frequencies, cavity visualizations and velocity distributions, the PANS model is shown to improve the predictive capability considerably, in comparison to the standard k − ɛ model, and also, it is observed the value of f 1 in the PANS model has substantial influence on the predicting result. As the filter width f 1 is decreased, the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity, and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.

Numerical simulation of flow past a square cylinder using Partially-Averaged Navier–Stokes model

In this study, we carry out a two-stage partially averaged Navier–Stokes (PANS) simulation past a square cylinder to examine the effect of a grid system on the predicted results. The important focus in PANS is how the control parameter which is the ratio of unresolved-to-total turbulent kinetic energy is determined in the flow field. In this work, the parameter is evaluated by using an equation that we propose. The model equation utilizes the turbulent length scale, the Kolmogorov length scale and the cut-off grid length. We first perform RANS simulation to approximately evaluate the turbulent length scale and the Kolmogorov length scale. Then we construct five different grid systems based on these length scales and perform PANS simulation in which the length scales to determine control parameter are also updated as the simulation proceeds. Simulation results are compared with experimental data and the other LES and DES results. The comparison suggests that PANS approach is very effective in simulating separated turbulent flows in the sense that accurate predictions can be obtained by using a much coarser grid system than is required for LES. We then suggest the grid spacing requirements for a proper PANS simulation.

Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method

A turbulence bridging method purported for any filter-width or scale resolution—fully averaged to completely resolved—is developed. The method is given the name partially averaged Navier-Stokes (PANS) method. In PANS, the model filter width (extent of partial averaging) is controlled through two parameters: the unresolved-to-total ratios of kinetic energy (fk) and dissipation (fε). The PANS closure model is derived formally from the Reynolds-averaged Navier-Stokes (RANS) model equations by addressing the following question: if RANS represents the closure for fully averaged statistics, what is the corresponding closure for partially averaged statistics? The PANS equations vary smoothly from RANS equations to Navier-Stokes (direct numerical simulation) equations, depending on the values of the filter-width control parameters. Preliminary results are very encouraging.