Partially-averaged Navier-Stokes Simulations Research Articles

The application of laminar numerical wave tank for a heaving buoy hydrodynamics study in low-turbulence nonlinear waves

Numerical Wave Tanks (NWTs) allow for in-depth investigations into the hydrodynamics and wave responses of floating objects. Thus, they are widely used during the design phase of many offshore platforms and devices. Such problems often feature low turbulence, with wave propagation and wave-object interaction being the key features. In this paper, the merits of using a laminar flow model for a NWT with a free-to-heave buoy, subject to second order Stokes waves in a low sea state is investigated. The simulations are implemented using the interFoam solver, which is embedded in OpenFOAM. The time series of waves measured upstream and downstream of the buoy, and the buoy hydrodynamics are compared to analytical and experimental results for accuracy evaluations. It is shown that, due to the low turbulence level of the problem, the laminar approach can deliver more accurate results than turbulent models, such as Reynolds-averaged Navier-Stokes Simulation (RANS) or partially-averaged Navier-Stokes Simulation (PANS). Moreover, the simulation time of the laminar simulations is significantly shorter than to those of RANS and PANS.

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.

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.

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.

Numerical simulation of turbulent flow over a backward facing step using partially averaged Navier-Stokes method

This paper presents some key features of partially averaged Navier-Stokes (PANS) method in the simulation of turbulent flow over a backward facing step at Reh = 5100. Both fixed and spatially variable values for the unresolved-to-total ratio of kinetic energy (fk) are adopted in the present PANS simulations. Different model parameters relevant to PANS have been assessed. Detached eddy simulation (DES) is also adopted and the results from DES are compared in detail with PANS and the available experimental data. Variable fk PANS gives overall acceptable predictions but it is slightly less accurate than DES. The defects of PANS simulation with fixed fk throughout the entire computational domain are highlighted in this investigation. An improved step is to introduce variable fk to ensure the near-wall Reynolds averaged Navier-Stokes (RANS) solution. This paper provides encouraging results for PANS simulations of this wall-bounded flow involving separation.

Investigation of the near-wake flow topology of a simplified heavy vehicle using PANS simulations

The near-wake flow topology of a ground transportation system (GTS) is investigated using partially-averaged Navier–Stokes (PANS) simulations at Re=2.7×104. Recent numerical investigations for the GTS model using large eddy simulations (LES) showed an anti-symmetric flow topology (flow state II) in the vertical midplane compared to that observed in previous experimental studies (flow state I). The geometrical configuration of the GTS permits bi-stable behaviour, and the realisation of each of the two flow states, which are characterised by an asymmetrical flow topology, is achieved by varying the differencing scheme for the convective flux in the PANS simulations; AVL SMART schemes predict flow state I, while central differencing scheme (CDS) predicts flow state II. When the GTS model was placed away from the ground plane, the AVL SMART scheme fails to predict the flow asymmetry resulting in a pair of symmetrical vortices in the vertical midplane, while flow state II topology is observed when CDS is used. The switch from flow state I (II) to flow state II (I) is achieved by changing the numerical scheme from AVL SMART (CDS) to CDS (AVL SMART), with an intermediate transient-symmetric (TS) state being observed during the switching process. The numerical scheme in the PANS simulations thus plays a critical role in determining the initial flow topology in the near wake of the GTS.

Partially-averaged Navier–Stokes (PANS) simulations of flow separation over smooth curved surfaces

The objective of this study is to investigate flow separation in a channel with periodic hill-shaped constrictions using the Partially-averaged Navier–Stokes (PANS) methodology. Flow Reynolds numbers based on the bulk velocity above the crest of the hill and hill height are 10590 and 37000. Several PANS simulations are performed to study the effect of cut-off length scale and grid resolution. Turbulence statistics such as mean velocity and Reynolds stresses are compared against well documented experimental data and numerical results. Instantaneous and averaged flow structures as well as anisotropy-invariant maps are also presented in this paper.

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.

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.

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.

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.

Characterizing velocity fluctuations in partially resolved turbulence simulations

Many current turbulence model simulations follow the accuracy-on-demand paradigm to partially resolve the flow field for achieving optimal compromise between accuracy and computational effort. In many such approaches, the sub-grid viscosity is modeled using kinetic energy and dissipation of unresolved scales. It is of scientific value and practical utility to characterize the resolved velocity fluctuations of such flow fields to: (i) establish if the computed fields exhibit the self-similarity and scaling properties consistent with physical turbulence and (ii) demonstrate if the flow field tends to the limit of fully-resolved turbulence in a prescribed and controlled manner. Toward this end, we begin by characterizing partially-resolved flow computations as direct numerical simulations of non-Newtonian fluids. This paradigm permits the extension of the Kolmogorov and finite Reynolds number scaling to the computed fields. The statistical behavior of the intermediate and smallest computed scales is then postulated as a function of the degree of resolution. Then it is demonstrated that the flow field in partially-averaged Navier-Stokes simulations behaves in accordance with the adapted Kolmogorov hypotheses in isotropic turbulence computations. Further, the statistics of sub-Kolmogorov fluctuations are demonstrated to be self-similar over a range of resolutions.

Partially-Averaged Navier–Stokes Simulations of High-Speed Mixing Environment

Accurate simulation of the fuel-air mixing environment is crucial for high-fidelity scramjet calculations. We compute the velocity fields of jet into supersonic freestream flow and cavity flow typical of scramjet flame-holding applications at different scale resolutions using the partially-averaged Navier–Stokes (PANS) method. We present a sequence of variable resolution computations to demonstrate the potential of PANS method for high-speed mixing environment calculations.

Superiority of PANS compared to LES in predicting a rudimentary landing gear flow with affordable meshes

Results of simulations of the flow around a rudimentary landing gear are presented in the paper. A newly proposed improved Partially-Averaged Navier–Stokes (PANS) method using k−ε−ζ−f turbulence model is used for prediction of the flow. The results are compared with the experimental data but also with the results of two LES simulations performed using the PANS computational grids. PANS simulations predicted the flow in good agreement with the experimental data. LES predicted a non-physical creation of separation over the front wheels that does not exist in the PANS prediction and was not observed in the experimental oil film. PANS simulations showed low sensitivity to the grid refinement. They show clear advantage compared with the LES simulations when the computational grid is inadequate for resolution of the near-wall flow structures.

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.