Partially-Averaged Navier-Stokes Research Articles

Partially averaged Navier-Stokes simulation of flow around an isolated building model with a 1:1:2 shape

This study analyzes the performance of a numerical model with partially averaged Navier–Stokes (PANS) equations for simulating the flow field around an isolated building model with a 1 (length): 1 (width): 2 (height) shape. The PANS model was based on the k−ωSST unsteady Reynolds-averaged Navier-Stokes equations (URANS) model, and three different values were imposed on the coefficient fk, which represents the proportion of modeled turbulence kinetic energy (TKE) in PANS. The simulation results were validated by experimental measurements and compared to those of large-eddy simulation (LES) and URANS. According to the results, it was found that the resolution ability of PANS can be adjusted between URANS and LES by tuning fk. When compared to URANS, PANS improved the performance in predicting the mean flow field around the target building and separation layers in the wake region. The prediction error in the reattachment length in the wake region was reduced by 88% compared to URANS. Because PANS can explicitly resolve more turbulence, the prediction accuracy of TKE against the experiment (FAC2: 0.85) is higher than that of URANS (FAC2: 0.45). Through power spectrum analysis, it was determined that PANS can reproduce the characteristic vortex shedding caused by the building with specific frequencies. When compared to LES, it resolved approximately 99% of turbulence fluctuations in the relatively low-frequency domain at the representative point in the wake region.

Improved scale-resolved predictions of flow and heat transfer past a bluff body using partially averaged Navier–Stokes and a high-order eddy viscosity closure

The partially averaged Navier–Stokes (PANS) methodology has emerged as a viable bridging method of turbulence computations. Partially averaged Navier–Stokes methodology allows the user to implicitly choose the filter cut-off seamlessly in the inertial sub-range of motion. In past, most PANS simulations have been performed using the linear eddy viscosity closure for the unclosed turbulent stresses. Recently, evaluation of the advantages of higher order eddy viscosity closures with the PANS methodology has also been initiated. With our motivation to make further progress in this direction, this study presents an evaluation of PANS methodology wherein the turbulent stresses are modelled involving closures up to the cubic products of the resolved strain-rate and the rotation-rate tensors. After appropriately adapting a popular Reynolds-averaged Navier Stokes cubic closure for the PANS paradigm, an extensive evaluation of the method is performed in the flow past a heated sphere at a Reynolds number of 10,000. Time-averaged PANS predictions of surface-related as well as wake-related quantities are compared against available experimental, direct numerical simulation as well as large eddy simulation results. Indeed, very significant improvements are demonstrated by the PANS methodology in conjunction with the cubic eddy viscosity closure when compared to the corresponding predictions of the PANS methodology using a linear or even a quadratic eddy viscosity closure. This study demonstrates the promising augmentative ability of the higher eddy-viscosity to the PANS framework in performing improved simulations of the separated flows.

Numerical investigation of the effect of the rectangle-type cavitating-bubble generator on the sheet/cloud cavitating flow around the NACA66 hydrofoil

The objective of this work is to present the effect mechanism of a passive control method using a spanwise rectangle-type cavitating-bubble generator (CG) on the unsteady partial cavitation based on the simulation. First of all, the numerical method using a Partially-averaged Navier–Stokes (PANS) turbulence model was validated and showed the good agreement with the experiment. Then the effects of CG on different cavitation stages were studied separately. It is found that the CG has a significant effect on the unsteady process of sheet cavity, and it can effectively mitigate or suppress the cavity shedding behavior, especially for the incipient cavitation stage with larger cavitation numbers. Correspondingly, the time-fluctuation amplitude of the wall-pressure, lift and drag for the hydrofoil with CG are reduced dramatically. In addition, the time-averaged lift-to-drag ratio of hydrofoil is improved desirably after using the CG. The conclusion of this work will be promising for the cavity dynamic controlling field.

Partially-averaged Navier–Stokes simulations of turbulence within a high-order flux reconstruction framework

High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods and analyze the effects of high-order discretizations on hybrid turbulence models, particularly with respect the optimal model parameters and the relative accuracy benefits compared to approaches such as under-resolved direct numerical simulation (URDNS). We employ the Partially-averaged Navier–Stokes (PANS) approach using the flux reconstruction scheme on the flow around a periodic hill and the wake flow of a circular cylinder at a Reynolds number of 3900, the latter of which we provide direct numerical simulation results and novel statistical analysis. By increasing the order of the discretization while fixing the total degrees of freedom, it was observed that larger improvements in the prediction of the statistics and flow physics were generally seen with PANS than URDNS. Furthermore, less sensitivity to the resolution-control parameter was observed with a high-order discretization, indicating that high-order discretizations may be an effective approach for increasing the accuracy and reliability of hybrid turbulence models for scale-resolving simulations without a significant increase in computational effort.

The Development of a Partially Averaged Navier–Stokes KSKL Model

Abstract A new partially averaged Navier–Stokes (PANS) closure is derived based on the k−kL (KSKL) model. The aim of this new model is to incorporate the desirable features of the KSKL model, compared to the k−ω shear stress transport model, into the PANS framework. These features include reduced eddy-viscosity levels, a lower dependency on the cell height at the wall, well-defined boundary conditions, and improved iterative convergence. As well as the new model derivation, the paper demonstrates that these desirable features are indeed maintained, for a range of modeled-to-total turbulence kinetic energy ratios (fk), and even for multiphase flow.

Assessment of low- and high-fidelity turbulence models for heat transfer predictions in low-prandlt number flows

Linear eddy viscosity-based Reynolds-averaged Navier-Stokes (RANS), hybrid RANS/Large Eddy Simulation (LES), and LES models are applied for simulations of plane channel flow at Reynolds number Reτ = 150 and 640. Results are obtained for fluids with Prandtl number (Pr) of 0.025 and 0.71, for cases without buoyancy (Gr = 0) and for a vertical channel flow with buoyancy (Ri = 0.1–0.13). The objective is to evaluate the predictive capability of each class of model for low-Pr flow typical of liquid metal reactor cooling systems. For this purpose, RANS, partially-averaged Navier-Stokes (PANS) and LES computations are performed on grids which contain 0.67%, 2%, and 5% of the grid points used in the Direct Numerical Simulation (DNS), respectively, and the predictions of the mean and turbulent flow and thermal quantities are validated against DNS results. RANS results obtained using Kays variable turbulent Prandtl number (PrT) formulation were more accurate than those using constant PrT for low-Pr forced convective flows, but did not play a significant role for mixed convective flows. The variable PrT formulation likewise did not have significant effect for hybrid RANS/LES or LES computations, wherein > 90% turbulence was resolved. The RANS model performed reasonably well for flows without buoyancy, but for mixed convective flows, significantly under predicted the sharp pressure gradient around the mid-channel, and the limitations were identified due to over prediction of heat transfer by wall-normal fluctuations on the aiding side. Both PANS and dynamic Smagorinsky (DSM) showed similar predictions, and under predicted the mid-channel temperature gradient for the low-Pr vertical channel case and over predicted flow turbulence on the opposing flow side and thermal fluctuations on the aiding flow side. The Wall-Adapting Local Eddy-viscosity (WALE) model performed best among the LES subgrid stress models. The improved predictions by WALE over PANS and DSM were identified because of higher modeled dissipation predictions away from the wall. Future work will focus on investigation of non-linear RANS models and extend the validation for higher Re flows.

Pressure oscillations with ultra-low frequency induced by vortical flow inside Francis turbine draft tubes

The present paper aims to reveal the flow mechanism for the pressure oscillations with ultra-low frequency captured by the model test of Francis turbine operated at part-load condition. The experimental results indicate that the precessing vortex rope (PVR) induces the dominant pressure oscillation in the draft tube, and its frequency i.e. fPVR is one-fifth of runner rotation frequency (15.12 Hz). To investigate the PVR evolution in the turbine, numerical simulations based on the MSST PANS (modified SST based partially-averaged Navier-Stokes) model have been conducted, and the DMD (dynamic mode decomposition) method has been applied to analyze the modes for unstable flow inside the draft tube. To make out the effect of draft tube structure on the PVR and pressure oscillation, the conventional elbow-type draft tube i.e. EDT, and the conical draft tube i.e. CDT are treated for comparison. Under non-cavitation operation, both experiment and simulation capture two pressure oscillation components with ultra-low frequencies near fPVR/3 and 2fPVR/3. The analysis based on internal flow and DMD method depicts that the pressure oscillations with ultra-low frequency occur due to the strong interaction between the PVR and the backflow in the draft tube, and the elbow structure promotes the interaction and the swirling flow in the draft tube. It is also noted that the cavitation remarkably changes the dynamic characteristics of the precessing vortex rope in the draft tube. Further, cavitation alleviates the interaction between the PVR and backflow at the rear part of the PVR and suppresses the pressure oscillations with ultra-low frequency in the draft tube. Finally, it is confirmed that DMD analysis is helpful to depict the modal of the flow field and make out the important flow structure at various operations in the draft tube.

Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard [Formula: see text]–[Formula: see text] PANS model is also used. The results demonstrate that compared to [Formula: see text]–[Formula: see text] PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at [Formula: see text] and [Formula: see text], it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

Modeling and simulation of transitional Rayleigh–Taylor flow with partially averaged Navier–Stokes equations

The partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters fϕ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity ϕ of the turbulent closure, fϕ. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations' fidelity.

Partially averaged Navier-Stokes closure modeling for variable-density turbulent flow

This work extends the framework of the partially-averaged Navier-Stokes (PANS) equations to variable-density flow, \text{i.e.}, multi-material and/or compressible mixing problems with density variations and production of turbulence kinetic energy by both shear and buoyancy mechanisms. The proposed methodology is utilized to derive the PANS BHR-LEVM closure. This includes \textit{a-priori} testing to analyze and develop guidelines toward the efficient selection of the parameters controlling the physical resolution and, consequently, the range of resolved scales of PANS. Two archetypal test-cases involving transient turbulence, hydrodynamic instabilities, and coherent structures are used to illustrate the accuracy and potential of the method: the Taylor-Green vortex (TGV) at Reynolds number $\mathrm{Re}=3000$, and the Rayleigh-Taylor (RT) flow at Atwood number $0.5$ and $(\mathrm{Re})_{\max}\approx 500$. These representative problems, for which turbulence is generated by shear and buoyancy processes, constitute the initial validation space of the new model, and their results are comprehensively discussed in two subsequent studies. The computations indicate that PANS can accurately predict the selected flow problems, resolving only a fraction of the scales of large eddy simulation and direct numerical simulation strategies. The results also reiterate that the physical resolution of the PANS model must guarantee that the key instabilities and coherent structures of the flow are resolved. The remaining scales can be modeled through an adequate turbulence scale-dependent closure.

An improved partially-averaged Navier-Stokes model for secondary flows

In the present study, the modified formulations of the partially-averaged Navier-Stokes (PANS) model were suggested for accurate prediction of the secondary flow by resolving the anisotropy of turbulence. The main characteristics of the modified PANS (mPANS) models were to resolve the wide range of turbulent length scale by decreasing fk value in the region where the anisotropic behavior of turbulence dominates. The information on the region, where there is highly anisotropic turbulence, was procured by using the budget analysis and the anisotropy invariant map. The level of how much fk should be reduced was determined by model factors, which were set to be able to resolve the secondary flow in a square duct and around a prolate spheroid. To identify the reliability of the model factors, the mPANS models were applied to the flow around the KRISO very large crude oil carrier at Froude number of 0.142. The mPANS models showed improved predictions of the hook-shape pattern of the streamwise component of velocity and secondary vortex on the propeller plane compared to the original PANS (oPANS) results by decreasing the modeled turbulent kinetic energy.

Prediction of heat transfer from a circular cylinder in a cross-flow at a low sub-critical Reynolds number with the Partially-Averaged Navier-Stokes method

The prediction of turbulent heat transfer at a reasonable computational cost is a topical issue in computational fluid dynamics. This study addresses the numerical simulation of heat transfer from a circular cylinder in a cross-flow. Simulations were performed at a low sub-critical Reynolds number (Re = 3900) using the Partially-Averaged Navier-Stokes (PANS). Seven ratios of unresolved to total turbulent kinetic energy fk ranging from 0.15 to 0.7 were considered in order to reveal the influence of physical resolution on the flow and heat transfer statistics. Further, a low Reynolds number approach fε = fk was evaluated for fk ≥ 0.5. Additionally, simulations using the Large Eddy Simulation (LES) method were conducted on the same computational grids. The low physical resolution (fk > 0.5) in the PANS simulation at the coarse spatial resolution led to the earlier transition and later separation of the boundary layer which resulted in the overprediction of heat transfer at the rear stagnation point. The low Re approach (fε = fk) provided similar results as the low physical resolution case (fk = 0.7, fε = 1) and spatial refinement did not influence the predicted results. The results of our study indicated the suitability of the PANS for applications involving heat transfer from a bluff body provided an adequate physical resolution level is set.

Assessment of Turbulence Models for Low Reynolds Number Flows and Their Computational Costs, Part 1: Staggered Tube Bank

Abstract This study investigates the accuracy of computational fluid dynamics (CFD) models to predict heat transfer in turbulent separated flows at low Reynolds numbers. This article will focus on flow in a staggered tube bank, while its companion articular will focus on a square prism (cylinder) in cross flow. Experimental data for both local heat transfer and velocity profiles are available for these cases and have been used extensively in the literature to evaluate various CFD methods. Six unsteady models were used and the results show that the unsteady shear stress transport (SST) model provided good overall accuracy relative to the mean Nusselt number for both cases. However, the SST model failed to accurately predict local variations. The partially averaged Navier–Stokes (PANS) variant of the SST model did show a marked improvement over the baseline SST model. The dynamic Smagorinsky large eddy simulation (LES) showed a much-improved fidelity to the local Nusselt number but unpredicted the actual values. The computational cost for the LES model was significant and it was found that the computationally expensive models with higher degrees of resolved turbulence did not necessarily return better results. Finally, the pressure drop results for the six models were scaled to predict the mean Nusselt number with the generalized Leveque method and were found to be very accurate. This method should prove useful to predict heat transfer performance with computationally less expensive cold flow results.

Assessment of Turbulence Models for Low Reynolds Number Flows and Their Computational Costs, Part 2: Square Prism in Cross Flow

AbstractThe accuracy of six turbulent flow modeling techniques in an unsteady solution is evaluated against experimental data for a square prism in cross flow. The selected models, shear stress transport (SST), SST-SAS, Reynolds stress model (RSM), partially averaged Navier–Stokes (PANS)-SST, detached eddy simulation (DES), and large eddy simulations (LES), models are the same as those presented in Part 1 of this study, which focused on flow in a staggered tube bank. For this geometry, the SST model proved to be effective at capturing the averaged Nusselt values per side of the square with relatively low computational costs. The SST model, however, showed poorer fidelity to the local Nusselt number profile compared to the experimental data. The LES approach provided a more accurate representation of the local Nusselt number but the computational cost was significantly higher. The PANS modification to the SST model did provide a noticeable improvement in accuracy at a reasonable cost while the SAS modification did not see the same improvement. These conclusions are generally consistent with those found for the staggered tube bank in Part 1 of this study. This study can be used as a guide for the industrial user to select a turbulence model for a similar problem with a low Reynolds number and significant flow separation.

Stirred tank simulation using Partially-Averaged Navier-Stokes k_u-epsilon _u turbulence model

In the present study, simulation of a stirred tank using axial flow impeller has been studied numerically to see the behaviour of flow variables in the entire vessel. It is assumed that the flow is steady state, two dimensional, incompressible and axisymmetric. For simulation, Partially-Averaged Navier-Stokes (PANS) k_u-epsilon _u turbulence model has been taken into account. For discretization, control volume method along with upwind and power-law schemes have been taken. The solutions are obtained by using the SIMPLE algorithm. The boundary conditions for impeller are given by using the experimental data. The main objective is to investigate the influence of different filters width f_k of the PANS k_u-epsilon _u model parameter on the characteristic flow variables. The predicted results of the PANS k_u-epsilon _u model for different f_k have been compared with the experimental data at different axial levels of the stirred tank. It has been observed that the power-law scheme gives better agreement with the experimental data. Further, near the impeller region, PANS predicted results are better for smaller f_k. Also, Reynolds-Averaged Navier-Stokes Shear Stress Transport (SST) k-omega turbulence model has been tested for comparative study.

Numerical investigation on the formation mechanism of ventilated cavitation with gas jet cavitator

The complexity of the formation mechanism of ventilated cavities makes it difficult to be explored experimentally. In this study, the formation mechanism of cavity regimes around a gas jet cavitator were first numerically predicted using the partially averaged Navier–Stokes (PANS) and homogeneous free surface models. The numerical framework was validated by comparing the numerical predictions with available experimental data. The numerical results showed that the cavity evolves across four different regimes with increasing ventilation rate, that is, bubbly flow, stable cavity, unstable cavity, and jet cavity. Moreover, the gas jet length in the front of the nozzle continues to increase, and the vortex structure in the cavity transitions from a streamwise vortex to a vortex filament. Furthermore, the correlation between the adverse pressure gradients and the characteristics of the cavity was analyzed, and the results demonstrated that the adverse pressure gradient leads to stagnation of the gas jet and cavity closure.

Effect of the flow upstream the impeller inlet on flow instability of a centrifugal pump

Under part-load conditions, flow instability phenomena in a hydraulic machinery could lead to strong pressure fluctuations and vibrations, posing a great threat to the safety of the units. This paper analysed unsteady flow in a centrifugal pump (specific speed of 39 min−1·m3s− 1·m) with different inlet geometries under part-load conditions. An advanced turbulence model, PANS (partially averaged Navier-Stokes), acting as a bridge from RANS to DNS, is applied for numerical simulations. The results indicated the pump with a straight inlet pipe reached higher values of pump head and efficiency near the design point than the test pump with a non-straight inlet pipe. According to the characteristic curves, hump phenomenon was observed at 0.75ϕbep for the pump having a straight inlet pipe, while it occurred at 0.5ϕbep for the test pump. Under the condition of a low flow rate i.e. ϕ=0.5ϕbep, there is strong pre-swirling flow upstream impeller inlet for the test pump, which contributes to the propagation of rotating stall cells; But energy loss in the impeller inlet of the pump with straight inlet pipe is slightly higher than that in the test pump due to the presence of the stationary stall cells, which causes large energy loss in the impeller and the passage upstream impeller inlet. Further, rotating stall cells are captured in the impeller in both pumps under the condition of ϕ=0.75ϕbep.

Effects of different droplet dispersion modeling methods on diesel spray simulation in Eulerian-Lagrangian framework

The realistic prediction of spray dynamics and dispersion is one of the main tasks of the combustion simulations in diesel engines. Usually, droplet dispersion modeling accuracy can be improved by the development of turbulence models and stochastic dispersion models. Although droplet dispersion due to turbulence is an important phenomenon in high-velocity fuel sprays, studies on the effect of these models are relatively few. Among these studies, the influence of a common used stochastic dispersion model on spray dynamics is not well understood and the application of hybrid turbulence models to fuel spray simulation in the Eulerian-Lagrangian framework with two-way coupling is still at starting stage. In the present study, a better understanding of the effect of the stochastic model on spray dynamics can be obtained by using a statistical analysis of stochastic dispersion time and velocity of dispersed droplets. In order to assess the ability of the hybrid model to improve the radial spread and the inhomogenous distribution of small droplets produced by a high-pressure injector, a partially averaged Navier-Stokes (PANS) model is implemented in an open-source code OpenFOAM and is compared with an unsteady Reynolds averaged Navier-Stokes (RANS) model and a large eddy simulation (LES) model. The results show the importance of resolving large-scale turbulent structures on droplet dispersion modeling in high-velocity fuel spray simulation. The common stochastic dispersion model used in RANS developed for homogenous, isotropic turbulent flows leads to the non-physical dynamics and distribution of droplets and hence is not applicable to the droplet dispersion which is dominated by the non-stochastic motion of large-scale structures in free shear layers. Using PANS instead of RANS should improve the droplet dispersion modeling accuracy of high-velocity fuel sprays in the development of diesel engines with an advanced injection system.

Partially-averaged Navier–Stokes simulations of turbulent flow past a square cylinder: Comparative assessment of statistics and coherent structures at different resolutions

Scale-resolving simulations of the turbulent wake behind a square cylinder are performed at Re = 22 000 using the partially averaged Navier–Stokes (PANS) k-ω closure model at different degrees of resolution (cut-off scales) corresponding to the unresolved-to-total kinetic energy ratio fk ∈ [0.10, 0.50]. The two principle objectives of the study are to (i) establish the degree of resolution required for an accurate computation of different quantities of interest ranging from flow statistics to coherent structures and (ii) develop a protocol for a quantitative assessment and comparison of the large-scale coherent structures simulated at different degrees of resolution. Straightforward use of proper orthogonal decomposition (POD) to assess and compare large-scale coherence at different resolution levels can prove difficult as small-scale features can affect the POD mode shape and amplitude. To overcome this difficulty, two methods of quantifying coherent structures in the wake are proposed. These methods are based upon the incorporation of Fourier and Chebyshev decompositions with spectral proper orthogonal decomposition, respectively. We examine the first-mode energy spectra and the corresponding streamwise mode shapes using the results generated from PANS simulations at different degrees of resolution. It is demonstrated that increasingly finer resolutions are needed for integral quantities, one-point statistics, frequency spectra, and coherent structures, in that order. The underlying physics is explicated.

Characterization of coherent structures in turbulent wake of a sphere using partially averaged Navier–Stokes (PANS) simulations

The large-scale coherent structures in the wake of a sphere at subcritical Reynolds number (Re = 3700) are examined at different degrees of resolution (filter size) using scale-resolving simulations (SRS) of turbulence. The Partially averaged Navier–Stokes (PANS)-SRS method is employed to compute the wake flow at four levels of resolution marked by unresolved-to-total kinetic energy ratios: fk = 0.5, 0.3, 0.2, 0.1. The results from the four simulations are used to compute one-point statistics, frequency spectra, and spatio-temporal POD (proper orthogonal decomposition) modes. One-point statistics are reasonably well reproduced (in comparison with existing data) at all degrees of resolution. However, the frequency spectra and POD modes exhibit some degree of dependence on the level of resolution. It is demonstrated that accurate depiction of coherent structures is contingent upon adequately resolving key underlying instabilities. The finest resolution PANS simulation (fk = 0.1) is then used to characterize the large-scale coherent structures in the near-wake of the sphere. The main features of this wake, specifically azimuthal mode shapes, modal energy, and frequency content, are compared with experiments and numerical simulations of wakes of other axisymmetric bodies resulting in good agreement. Overall, the study demonstrates that PANS-SRS can capture key one-point statistics and coherent structure features of complex flows in a cost-efficient manner.