Partially Averaged Navier-Stokes Model Research Articles

Research on blade tip clearance cavitation and turbulent kinetic energy characteristics of axial flow pump based on the partially-averaged Navier-Stokes model

Research on blade tip clearance cavitation and turbulent kinetic energy characteristics of axial flow pump based on the partially-averaged Navier-Stokes model

Toward high-fidelity Numerical Wave Tank development: Scale resolving Partially-Averaged Navier–Stokes simulations of dam-break flow

Numerical Wave Tanks (NWTs) based on Navier–Stokes equations are emerging as valuable tools for simulating various ocean and coastal engineering flows. By capturing essential hydrodynamic non-linearities, including turbulent processes, these Navier–Stokes based NWTs can potentially provide high-accuracy data to complement traditional experimental wave basins for design and development applications. Many NWT approaches currently use the RANS (Reynolds Averaged Navier–Stokes) method. For many coastal resiliency and wave-energy converter applications, a higher fidelity turbulence treatment may be needed. In this work, we explore the applicability of the scale-resolving Partially-Averaged Navier–Stokes (PANS) technique for NWT computation. The PANS model is employed to study the dam-break benchmark case which is an important benchmark case for seawall and wave energy converter hydrodynamics analysis. Computations using RANS are also provided as a reference for accuracy and computational effort. The objectives are to: (i) investigate the effect of enhancing turbulence scale resolution on the pressure field, wave elevation and three-dimensional effects within the tank; and (ii) examine the influence of initial kinetic energy and grid resolution on the results. It is shown that, the early transient behavior is reasonably insensitive to scale resolution or initial turbulence level. Indeed, RANS and PANS of different scale resolutions yield similar results in the early stages as the flow physics is dominated by quasi-linear flow processes. The differences between RANS and PANS appear at later times. The so-called second pressure peak, standing wave amplitude and three-dimensional effects are better captured with increasing scale resolution for the same grid resolution. Overall, the results indicate that PANS is a viable model for NWT applications, with more detail being captured at a similar computational cost compared to RANS.

Numerical investigation of cavitating flow in centrifugal pump with improved partially-averaged Navier–Stokes method

ABSTRACT The objectives of this paper are to pursue an accurate numerical method of unsteady cavitating flow at a reasonable calculation cost and investigate the unsteady cavitating flow characteristics of a centrifugal pump. Firstly, the cavitating flow simulations of a centrifugal pump were performed using the partially-averaged Navier–Stokes (PANS) turbulence model and its improved model to evaluate the numerical methods based on experimental data. Compared with the experimental results, the improved PANS turbulence model can better predict the cavitating flows in the pump and has better applicability. Further, the unsteady cavitating flow characteristics of the centrifugal pump, such as the vapour volume fraction, the cavitation-vortex dynamics and the pressure and head fluctuations, were simulated by improved PANS model and discussed. The liquid flow vortex at the end of the cavitation in the impeller is an important reason for the periodic change of the cavitation shape. The periodic change of cavity volume has a certain impact on the pressure pulsation in the impeller and the pump head.

Scale-resolving simulations of the flow in a nuclear fuel bundle with a channel spacer grid using partially averaged Navier–Stokes and large-eddy simulation

The objective of this study is to evaluate the capabilities of the Partially Averaged Navier–Stokes (PANS) method in simulations of the flow through a rod bundle representative of a nuclear fuel assembly with a channel-type spacer grid. In the PANS bridging turbulence model, filters can be applied to obtain any level of resolution from Reynolds Averaged Navier–Stokes (RANS) to Direct Numerical Simulation (DNS). The closure model is sensitive to the length-scale cutoff by means of unresolved to total kinetic energy ratio (fk) and unresolved to total dissipation ratio (fε). Simulations are conducted to study the effect of the cutoff of length scale on the results obtained for flow statistics at selected locations in the domain. The results obtained with different PANS filters are compared with Unsteady RANS (URANS), Large Eddy Simulation (LES), and experiments. The mean and fluctuating flow components are computed at a representative plane located at the inter-channel between rods. Other flow quantities analyzed include the pressure drop upstream and downstream of the spacer grid, the turbulent kinetic energy, and the unresolved eddy viscosity. Additionally, we use the Lumley triangle to study turbulence anisotropy and to compare the nature of the energy content captured with LES and one of the PANS models. It is shown that the PANS model with fk=0.4, which resolves 60% of the turbulent kinetic energy content, captures the most relevant flow physics and is a suitable modeling approach for this application.

Modeling, simulation and mixing time calculation of stirred tank for nanofluids using partially-averaged Navier–Stokes (PANS) k u − ϵ u turbulence model

Abstract The present study deals with the numerical simulation of stirred tank in the presence of nanofluids to see the effect of different volume fraction (ϕ) of nanoparticles on the behaviour of flow characteristics and for the calculation of mixing time in the entire tank. The flow is assumed to be steady, axisymmetric, two dimensional and incompressible. For the simulation of flow inside the vessel, partially-averaged Navier–Stokes (PANS) k u − ϵ u turbulence model is used. Control volume method has been taken to descretize the governing equation along with power-law schemes. Further, semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm and line-by-line tri-diagonal matrix algorithm (TDMA) have been taken to obtain the solution. The objective is to investigate the influence of ϕ on the characteristic flow variables and to calculate mixing time for different ϕ of nanofluids and for different values of f k , PANS model parameter. It is noted that with the increase in ϕ, mixing time has also been increased and it increases very fast for PANS k u − ϵ u model with the increase in filter width f k .

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.

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.

A nonlinear partially-averaged Navier–Stokes model with near-wall correction for separated turbulent flow

A nonlinear Partially-Averaged Navier–Stokes model with near-wall correction is developed for separated turbulent flow simulations. The periodic hills flow is simulated to validate the new model and the results are compared with the standard [Formula: see text] model, MPANS model, MSST PNAS model, standard [Formula: see text] PANS model, and experimental/LES results. It is found that the new model shows better performance in the prediction of both mean velocity and turbulent statistics compared to the other models. From the prediction of the near-wall friction coefficient of periodic hills flow, the new model shows good resolution in the near-wall region by considering the near-wall damping function to turbulent viscosity, gradient production term, and turbulence scale correction term for the near-wall region. From the analysis of anisotropy-invariant and sub-filtered stress (SFS), it can be found that the nonlinear term is necessary for prediction accuracy improvement in turbulent flow simulation with strong separation.

A formulation of PANS capable of mimicking IDDES

The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes fk which denotes the ratio of modeled to total kinetic energy. In RANS, fk=1 while in DNS it tends to zero. In the present study we propose an improved formulation for fk based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of fk is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.

Partially Averaged Navier-Stokes: A (k-ω)/(k-ε) Bridging Model

A new Partially Averaged Navier-Stokes (PANS) bridging model is derived from existing (k−ω) and (k−ε) PANS formulations. The model behaves like the PANS (k−ω) model near rigid walls and like the PANS (k−ε) model away from walls. The new model is tested using well-known benchmark problems; a backward-facing step representing wall-bounded flows, and a circular cylinder representing free shear flows. Our results are compared to existing experimental data and previous simulation results using PANS (k−ω) and PANS (k−ε). The comparisons show our model to be superior at predicting velocity profiles in both flows. In addition, Reynolds stress predictions are also shown to improve.

A novel Omega-driven dynamic PANS model

A novel Omega (Ω) -driven dynamic partially-averaged Navier-Stokes (PANS) model is proposed in this paper. The ratio of the modeled-to-total turbulent kinetic energies fk is dynamically adjusted by the rigid vorticity ratio (the ratio of the rigid vorticity to the total vorticity), the key parameter of the Ω vortex identification method. Three classical flow cases with rotation and curvature are used to test the model. The results show that the turbulent viscosity is effectively adjusted by the new dynamic fk and the LES-like mode is activated, which can help the revelation of more turbulence information and improve the prediction accuracy. The new PANS model does not contain any explicit dependency on the grid size and enjoys good adaptability to the flow fields, and can be used for efficient engineering computations of the turbulent flows in the hydraulic machinery.

A new formulation of f k for the PANS model

ABSTRACT The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji [Partially-averaged Navier-Stokes model for turbulence: a Reynolds-averaged Navier-Stokes to direct numerical simulation bridging method. ASME J Appl Mech. 2006;73(3):413–421], can be used to simulate turbulent flows either as a RANS, LES or DNS. The PANS model includes which denotes the ratio of modelled to total kinetic energy. In RANS, , and in DNS it goes to zero. In the present study we propose a new formulation for based on the H-equivalence introduced by Friess et al. [Toward an equivalence criterion for hybrid RANS/LES methods. Int J Heat Fluid Flow. 2015;122:233–246]. In this formulation the expression of is derived to mimic DES. This new formulation behaves very much like classic DES, even though the two formulations use different mechanisms to separate modelled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. Moreover, the new formulation exhibits similar robustness features as DES.

A study of thermo-fluid characteristics of Czochralski melt using rotation and curvature corrected Partially-Averaged Navier-Stokes (PANS) turbulence models

A Czochralski melt flow encounters the effects of anisotropic body forces owing to the system rotation as well as significant streamline curvature due to inherent vortical structures and flow past curved surfaces. Two-equation eddy-viscosity models lack the ability to capture the flow anisotropy and curvature effects. Here we present the first study on the thermo-fluid characteristics of Czochralski melt using rotation and streamline curvature corrected Partially-Averaged Navier-Stokes (PANS) adaptations of the low-Re k-ε and SST k-ω models. The paper presents physical insights to the new PANS turbulence modelling approach highlighting improvements in the predicting capability of PANS models with the incorporation of rotation and curvature corrections. The PANS models showed good agreement with the results available in the literature (both experimental and computational). In addition for the PANS low-Re k-ε model it was observed that the prediction of the typical Czochralski melt flow structure in terms of shape, relative size and orientation of the characteristic cells improved with rotation and curvature corrections. Further thermal fluctuations and vortex cores also reduced in the melt in the case of the PANS low-Re k-ε model showing stabilization of flow. The corresponding rotation and curvature modification to the PANS SST k-ω model corrected the flow dynamics from a buoyancy dominated to rotationally driven along with an increase in the thermal fluctuations and vortex cores in the Czochralski melt resulting in a destabilization of the melt flow.

Evolution of incipient cavitation around two cylinders with different headforms

Incipient cavitating flows around two axisymmetric bodies with blunt and conical headforms respectively are investigated both experimentally and numerically. The Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) method are employed to investigate flow structures and the motion of incipient cavities. The partially averaged Navier–Stokes (PANS) method is evaluated by comparison with experimental data, and it is found that the PANS model with parameter fk = 0.2 (where fk is the ratio of unresolved to total kinetic energy) gives good predictions of the scale of the separation region and the time evolution of the morphology of incipient cavitation. The incipient cavities exhibit a hairpin-shaped structure, traveling arbitrarily and unattached to the body surface. During the evolution process, the incipient cavities move downstream, with some circumferential motion. The FTLE contours and the trajectories of tracer particles reveal significant circumferential flow in the detached vortex structures around the two cylinders. The greater the distance downstream from the cylinder head, the more pronounced is the circumferential motion. Furthermore, it is found that the motion of the incipient cavities is closely related to local flow behavior. The circumferential flow around the blunt-headed cylinder is stronger than that around the conical-headed cylinder. This provides a reasonable explanation for the more pronounced circumferential motion of incipient cavities around the blunt-headed cylinder.

Investigation of the effect of cavitation passive control on the dynamics of unsteady cloud cavitation

• We present a method to control various destructive effects of cloud cavitation such as vibration and high-pressure peaks. • Unsteady cloud cavitating flow around a hydrofoil was predicted using Partially-averaged Navier–Stokes (PANS) method. • Addition of the PANS Model in the OpenFOAM package. • Combination of the PANS method with Schnerr–Sauer cavitation model for obtaining the most accurate results. • Using a proper cavitation control a significant reduction in high wall-pressure peaks and vibration has been achieved. We present an efficient method to control the evolution of unsteady cloud cavitation around the CAV2003 benchmark hydrofoil using passive cavitation controllers so called cavitation-bubble generators (CGs). Cavitation control may be used in many engineering applications, particularly in the marine and turbo machinery field. We first simulated the unsteady cavitating flow around the hydrofoil without CGs using a Partially-averaged Navier–Stokes (PANS) method, and validated the acquired results against experimental data. We coupled the turbulence model with a mass transfer model and successfully implemented it in the open source toolbox OpenFOAM. Next, we studied the effect of different CGs on the qualitative parameters, such as the cavitation structure and the cavity shape. We varied size and location of the CGs to find the proper control of the cloud cavitation. We also analyzed in detail the effect of CGs on various destructive mechanisms of cavitation, such as highly unsteady cloud cavitation, turbulent velocity fluctuations , wall-pressure peaks, and degrading hydrodynamic performances . Our results revealed that CGs can substantially reduce instantaneous high-pressure pulsations on the hydrofoil surface. We observed that the cyclic behavior of unsteady cloud cavitation was suppressed, and the hydrodynamic efficiency of the hydrofoil was increased. The local boundary layer on the hydrofoil surface was altered, and the turbulent velocity fluctuation was reduced significantly, confirming that the vortex structures on the suction side and the wake region of the hydrofoil were changed remarkably.

Deciphering the flow structure of Czochralski melt using Partially Averaged Navier–Stokes (PANS) method

Czochralski melt flow is an outcome of complex interactions of centrifugal, buoyancy, coriolis and surface tension forces, which act at different length and time scales. As a consequence, the characteristic flow structures that develop in the melt are delineated in terms of recirculating flow cells typical of rotating Bénard–Marangoni convection. In the present study, Partially Averaged Navier–Stokes (PANS) method is used for the first time to study an idealized Czochralski crystal growth set-up. It is observed that with a reduction in the PANS filter width, more turbulent scales are resolved and the present PANS model is able to resolve almost all the characteristic flow structures in the Czochralski flow at a comparatively lower computational cost compared with more advanced turbulence modelling tools, such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES).