Partially-Averaged Navier-Stokes Research Articles

Scale-resolving simulations of turbulent flows with coherent structures: Toward cut-off dependent data-driven closure modeling

Complex turbulent flows with large-scale instabilities and coherent structures pose challenges to both traditional and data-driven Reynolds-averaged Navier–Stokes methods. The difficulty arises due to the strong flow-dependence (the non-universality) of the unsteady coherent structures, which translates to poor generalizability of data-driven models. It is well-accepted that the dynamically active coherent structures reside in the larger scales, while the smaller scales of turbulence exhibit more “universal” (generalizable) characteristics. In such flows, it is prudent to separate the treatment of the flow-dependent aspects from the universal features of the turbulence field. Scale resolving simulations (SRS), such as the partially averaged Navier–Stokes (PANS) method, seek to resolve the flow-dependent coherent scales of motion and model only the universal stochastic features. Such an approach requires the development of scale-sensitive turbulence closures that not only allow for generalizability but also exhibit appropriate dependence on the cut-off length scale. The objectives of this work are to (i) establish the physical characteristics of cut-off dependent closures in stochastic turbulence; (ii) develop a procedure for subfilter stress neural network development at different cut-offs using high-fidelity data; and (iii) examine the optimal approach for the incorporation of the unsteady features in the network for consistent a posteriori use. The scale-dependent closure physics analysis is performed in the context of the PANS approach, but the technique can be extended to other SRS methods. The benchmark “flow past periodic hills” case is considered for proof of concept. The appropriate self-similarity parameters for incorporating unsteady features are identified. The study demonstrates that when the subfilter data are suitably normalized, the machine learning based SRS model is indeed insensitive to the cut-off scale.

Transonic buffet simulation using a partially-averaged Navier-Stokes approach

The present article assesses the capability of the partially averaged Navier-Stokes (PANS) method to reproduce accurately the self-sustained shock oscillations, also known as transonic buffet, occurring on airfoils and wings at transonic regime under certain conditions of Mach number and angle of attack. The test case under analysis is an OAT15A unswept wing at Mach number M∞=0.73 and Reynolds number Rec=3×106. The three-dimensional flow is studied by accounting for the wind tunnel walls adopted in the experiments of Jacquin et al. [1] in the simulations. The computations on a large-span, confined configuration reveal a strong three-dimensionality of the flow both before and after the buffet onset. Attention is paid to the comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results, to show the benefits of PANS in resolving flow unsteadiness at different flow resolutions, especially on affordable CFD grids, at limited additional cost. In this context, the role of the mesh metrics and the local turbulence level in the formulation of the model is described, as well as the relation of this latter with the spatiotemporal discretization used for the numerical simulations. The aim is to extend the use of PANS and obtain accurate predictions of flow cases involving shock-wave boundary layer interactions without expensive approaches.

Computational Fluid Dynamics Simulation Study on Aerodynamic Characteristics under Unfavorable Conditions during Flight Phase in Ski Jumping

Objective: The stability of the flight phase in ski jumping is crucial for athletes’ performance and safety. This study aims to investigate the influence of unfavorable conditions on aerodynamic characteristics and flight stability through computational fluid dynamics (CFD) numerical simulations. Methods: The ski jumper and the skis are considered a multi-body system. A detailed three-dimensional (3D) model of this multi-body system under a commonly observed posture during flight is established. The Partially Averaged Navier–Stokes (PANS) turbulence model is employed, and CFD simulations are conducted to predict the aerodynamic characteristics of the multi-body system under lateral environmental wind and asymmetric postures during the flight phase. The conditions of asymmetric postures include yaw rotation and roll rotation. Results: (1) Lateral environmental wind generated a yaw force, yaw moment, and roll moment, which influenced the lift, drag, and pitch moment of the athlete. These forces and moments were relatively small at lower wind speeds (less than 3 m/s) and became more significant at higher wind speeds (greater than 4.5 m/s). (2) Under the influence of yaw rotation or roll rotation, the multi-body system exhibited a noticeable yaw force, yaw moment, and roll moment, all showing a monotonic increasing trend. Moreover, they had a significant impact on the lift, drag, and pitch moment of the multi-body system. Conclusion: (1) The influence of unfavorable conditions was complex, resulting in a significant yaw force, yaw moment, and roll moment on the multi-body system. The adverse effects of roll rotation were generally greater than those of yaw rotation. (2) The multi-body system exhibited self-stabilizing tendencies in yaw and roll. This phenomenon can provide a solution to maintain flight stability by employing appropriate yaw or (and) roll rotation angles, effectively compensating for or even eliminating the adverse effects of lateral environmental wind. (3) Understanding the mechanisms of how unfavorable conditions affect aerodynamic characteristics and stability during flight in ski jumping can provide valuable assistance for real-time prediction and decision making during competitions, as well as scientific guidance for training athletes’ stable flight control and techniques for improving their sport performance.

Numerical Simulation Research on Aerodynamic Characteristics during Take-Off Phase in Ski Jumping

In view of the inability to directly and accurately obtain an athlete’s aerodynamic force during the take-off phase through the wind tunnel test, the athlete’s aerodynamic force and surrounding flow field form under different take-off postures are obtained through numerical simulation research, and the effects of different take-off modes on the aerodynamic characteristics during take-off in ski jumping are discussed. The multi-body system composed of the athlete and skis was selected as the research object. By using a partially averaged Navier–Stokes (PANS) turbulence model and a 3D numerical simulation of computational fluid dynamics (CFD), the aerodynamic characteristics of the athlete under different take-off postures were predicted. The take-off modes include the knee-push-hip (KPH) mode and hip-drive-knee (HDK) mode, and the hip joint angle of the HDK mode is significantly greater than that of the KPH mode. First, the aerodynamic force ratio of the athlete’s torso and legs is obviously large. Although the aerodynamic forces of arms themselves are not obvious, they have a great impact on the overall aerodynamic characteristics of the athlete, so the posture of the arms cannot be ignored. The total drag and moment of the HDK mode are significantly higher than that of the KPH mode, and the lift-to-drag ratio of the HDK mode is significantly lower than that of the KPH mode. At first, the total lift of the HDK mode is higher than that of the KPH mode, but in the last attitude, the total lift of the HDK mode does not rise but fall, and finally, the total lift of the HDK mode is lower than that of the KPH mode. The aerodynamic characteristics change dramatically during the take-off phase, and the aerodynamic characteristics of the two take-off modes are quite different, and these changes and differences are difficult to observe during real training and at the competition site. The KPH mode has an obvious aerodynamic advantage over the HDK mode. During the take-off process, the athlete should increase the force generated by the knee joint extension and appropriately reduce the speed of the hip joint extension, control the using force order of the lower limb joints, and push the hip joint extension by the knee joint extension in order to avoid issues, such as the hip joint angle being too large, the hip joint extension angle being too fast, the center of gravity being too far back, and other problems. Studying the aerodynamic characteristics during the take-off phase provides valuable insights for athletes to achieve favorable flight postures after take-off, offering scientific guidance to improve their training strategies and enhance their competitive performance.

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

Influence of tip clearance on internal energy loss characteristics of axial flow pumps under different operating conditions

Axial flow pumps possess a unique structure where there must be clearances between the impeller and the piping wall, usually not exceeding 0.1% of the impeller diameter. Despite the small size of the clearance, the internal micro-vortex structures have a non-negligible impact on the main flow field of the impeller. Under the action of the pressure difference between the suction and pressure surfaces of blades, some fluids form high-energy jets in the tip clearance area, known as tip leakage vortices (TLVs). TLV interacts with the flow of the main flow field, exerting a significant impact on the internal flow state, energy loss, and hydraulic performance of the pump. To identify the influence of TLVs on the internal flow field and energy loss of axial flow pumps, this work uses a modified partially averaged Navier–Stokes (PANS) model to perform full flow field numerical calculations for a certain axial flow pump and conducts a comparative analysis of the internal flow field energy dissipation, unsteady vortex structures, energy loss, and other characteristics under three different tip clearances: 0.2 mm (0.05%D), 0.6 mm (0.15%D), and 1.0 mm (0.25%D) based on the energy transport theory. The results indicate that at optimal operating conditions, the internal energy distribution of the fluid in each flow passage is uniform, and the energy loss is primarily caused by axial backflow in the tip area; under critical rotating stall conditions, clearance size affects the distribution state of enstrophy in the guide vane flow passage, leading to average enstrophy being highest at the rim area and the most uneven distribution of enstrophy, inducing larger energy loss in the impeller; during deep stall conditions, the unevenness of internal energy distribution is stronger than that under critical stall conditions, but the overall energy loss within the impeller flow area is lower than that under critical stall conditions, while energy unevenness is mitigated as the tip clearance size increases.

COMPUTATIONAL STUDY OF HIGH-PRESSURE LIQUID INJECTION PROCESS BY MEANS OF LES AND PANS APPROACHES

For internal combustion engine, the determination of combustion characteristics and subsequent emissions formation relies heavily on the fuel injection process. With the increasing demand for enhanced fuel efficiency and reduced emissions, it becomes vital to develop fundamental understanding of physical process involved in the fuel injection process. In this study, an optimal numerical approach to predict high pressure liquid injection process in the context of industrial computations has been investigated. In particular, this study focuses on the respective performance of the Partially-Averaged Navier-Stokes and Large Eddy Simulation models to predict turbulent igniting sprays. Both approaches are coupled with widely used Lagrangian Discrete Droplet Method for spray modelling. The results are validated against well established ECN Spray A case in reactive and non reactive conditions. For reacting conditions, Flamelet Genrated Manifold (FGM) combustion model is employed in the present work. Comparative study and validation against experimental data showed that PANS turbulence model allows for coarser grids while still maintaining accurate results.

Tabulated Chemistry Combustion Model for Cost-Effective Numerical Simulation of Dual-Fuel Combustion Process

This study is dedicated to improving the efficiency of the flamelet-generated manifold (FGM) tabulated chemistry combustion modeling approach for predicting the combustion process in diesel-ignited internal combustion (IC) engines. The primary focus is on reducing table generation time and memory requirements. To accurately predict dual-fuel combustion processes, it is important to model both premixed and non-premixed combustion regimes. However, attempting to include both regimes in a single FGM lookup table leads to significant increases in the table size and generation time. In response, this work proposes a dual-table configuration, with each table dedicated to a specific regime. The solution is then interpolated from these tables based on the calculated combustion regime indicator during the computational fluid dynamics (CFD) simulation. This approach optimizes computational efficiency while ensuring an accurate representation of dual-fuel combustion. Additionally, to establish a cost-effective and accurate 3D CFD simulation workflow, the dual-table FGM methodology is coupled with the partially averaged Navier–Stokes (PANS) turbulence model. The feasibility of the proposed FGM methodology is tested utilizing six chemical kinetics mechanisms with different levels of detail. The results of this study demonstrated that the dual-table approach significantly accelerates table generation time and reduces memory requirements compared to a single table that includes both combustion regimes. Furthermore, 3D CFD simulation results of the dual-fuel combustion process are validated against available experimental data for three engine operating points. The in-cylinder pressure traces and rate of heat release obtained from the 3D CFD simulations employing the FGM PANS methodology show good agreement with experimental measurements, confirming the accuracy and reliability of this modeling approach.

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.

Flow over a step cylinder using partially-averaged Navier-Stokes equations with application towards dynamic subsea power cables

Understanding the flow characteristics of buoyancy sections in power cable and umbilical configurations is crucial for analyzing floating offshore wind turbine systems. Buoyancy sections decouple the motions from the floater and the destination point to ensure the integrity of the system. Using accurate drag coefficients in their design is essential, as they significantly impact the overall behavior of the configuration. Therefore, Computational Fluid Dynamic (CFD) analysis is performed in the present study on a single buoyancy module attached to a power cable represented by a step cylinder configuration. The Partially-Averaged Navier-Stokes (PANS) turbulence model is applied. Its accuracy is validated against experimental findings of a wall-mounted cantilever cylinder and an infinite cylinder. The numerical results reveal that the larger diameter cylinder (LDC) section reduces the drag experienced by the smaller diameter cylinder (SDC) section near the junction. The LDC has a sharp, chamfered, and filleted edge replicating the various shapes of buoyancy modules. The edge design of the LDC affects the drag forces and flow patterns. The SDC has an 8% lower drag coefficient in the fillet edge case than the sharp edge case. The drag coefficient is 3.5% lower for the LDC in the filleted edge case than the sharp edge case. The sharp edge causes a significant separation of the fluid upstream of the SDC. However, this separation is notably reduced when the LDC has a chamfered or filleted edge. Detailed drag coefficients for buoyancy section analysis of power cable configurations have been deduced from the presented results.

Numerical study on jet-wake flow and its evolution in a centrifugal pump with alternating stall

Stall and jet-wake flow are two typical forms of unstable flow phenomena in centrifugal pumps, significantly affecting their stability. This paper investigates the interaction mechanisms between stall and jet-wake flow in a centrifugal impeller under different working conditions. The unsteady numerical study utilizes the partially averaged Navier–Stokes (PANS) model with a new dynamic fk expression derived from the rotation-corrected energy spectrum. The results reveal four stages in the flow field evolution of the centrifugal pump under different working conditions. In stage I, no stall vortices are present, and the jet-wake flow occurs. The velocity distribution at the impeller outlet depends on the pressure difference distribution between the pressure and suction sides within the flow passage. As the flow rate decreases, the pressure difference between the two sides increases, intensifying the jet-wake phenomenon. Under part-load conditions (stages II, III, and IV), the presence of stall vortices becomes the main factor affecting the jet-wake flow. These stall vortices influence the local and downstream flow fields, thus altering the distribution of the jet-wake. When the stall vortex is on the pressure side, it reduces the velocity near the pressure side, weakening the intensity of the jet-wake. On the other hand, when the stall vortex is on the suction side, it reduces the velocity near the suction side, enhancing the intensity of the jet-wake.

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.

Numerical study on unsteady cavitation flow and vortex dynamics characteristics around the Delft Twist 11 hydrofoil

The objective of this study is to explore the unsteady cavitation characteristics and the mechanism of cavitation-vortex interaction around a twist hydrofoil. The cavitation conditions were simulated using the Partially-Averaged Navier-Stokes (PANS) method in conjunction with a homogeneous flow cavitation model. The numerical method employed in this study successfully captures the intricate shedding process of cavitation on the hydrofoil surface. Furthermore, the cavity morphology obtained at various time instants exhibits a remarkable agreement with the experimental results. The simulation results of the unsteady characteristics of cavitation shedding on the hydrofoil surface revealed that the shedding process could be divided into primary and secondary shedding phases. The primary shedding happened as a result of the re-entrant jet flow generated by the adverse pressure gradient at the cavitation tail. Notably, the secondary shedding was predominantly caused by the combined effects of the re-entrant jet and the side re-entrant jet flow. During the primary shedding process, the cavitation experienced disturbances from the side re-entrant jets, causing it to roll and be drawn upwards into a U-shape cavity structure. Subsequently, as the secondary shedding happened, the side re-entrant jets contributed to the formation of a secondary U-shape cavity at the cavitation tail. The investigation on the cavitation-vortex interaction around the hydrofoil showed a strong consistency between the distribution of vortices and cavitation. The foot of the primary U-shape vortex was attached to the hydrofoil surface, while the shedding vortex tail on both sides exhibited secondary U-shape vortex structures. The primary U-shape vortex formation resulted from the combined effects of suction and rotation generated by the side re-entrant jets and re-entrant jets on both sides of the hydrofoil. The secondary U-shape vortex was induced by secondary shedding cavitation which produced by rotational effects at the stable cavitation tail.

Evaluation of the PANS method for the prediction of the fluid flow in a cyclone separator

The simulation of the cyclone separation efficiency can rapidly become very expensive in time of calculation, which is not suitable for industrial application. The prediction of the complex turbulent gas flow inside a cyclone is necessary to estimate its pressure drop, its characteristics and finally its separation efficiency. Even though classic models such as RSM and LES can effectively predict such type of flow, the quality of the results and the computation cost can be discussed. In this work, Partially Averaged Navier–Stokes (PANS) method is proposed to simulate the fluid flow inside a gas cyclone. Compared to experimental and numerical results of a literature review, this model predicts reasonably the time-averaged tangential and axial velocity fields, and more accurately the pressure drop across the cyclone in shorter CPU times. The sensitivity of the PANS approach to the unresolved to total kinetic energy ratio f k was also evaluated with two different definitions. The first one was the standard definition developed by Girimaji et al. [1] and the second one was based on a statistical equivalence between the DES and PITM. The proposed model offers a better cost to quality ratio compared to the classic RANS approach.

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.

Numerical study of thermal mixing phenomenon using partially averaged Navier-Stokes

Thermal mixing between cold and hot streams of fluids in a T-junction may lead to high-cycle thermal fatigue in nuclear power plant piping material. Temperature fluctuations near the wall surface are the main reason for this degradation. Computational Fluid Dynamics (CFD) using space and energy-resolving turbulence modeling paradigms can predict this transient behavior. In this study Partially averaged Navier-Stokes (PANS) turbulence method is used to simulate the Vattenfall T-junction test case. Two different values for the filter control parameter fk = 0.5 and fk = 0.25 are used. Calculations results for velocity and temperature fields are compared with Large Eddy Simulations (LES) and available experimental data. For fk = 0.5, time-averaged and root mean square (RMS) temperatures show lower values than the LES and experimental data. For fk = 0.25 both time-averaged and RMS temperature results are close to the LES and experimental values. The Power Spectral Density (PSD) of the temperature signal shows peaks in the case of both PANS-0.25 and LES in the range of 3 to 4 Hz, which is in line with the experimental results. It can be concluded that the PANS method has the capability to resolve temperature and velocity fields for thermal mixing phenomenon in T-junction pipes and can be used for the assessment of high-cycle thermal fatigue.

Validation of PANS and effects of ground and wheel motion on the aerodynamic behaviours of a square-back van

This paper presents a numerical investigation of the effects of the moving ground and rotating wheels on the turbulent flow around a 1/10 scaled square-back van model. A comprehensive comparison among the partially averaged Navier–Stokes (PANS), large eddy simulation (LES) and particle image velocimetry (PIV) involving the aerodynamic drag, the wake topology, the velocity and the Reynolds stress profiles in the wake region is conducted. The proper orthogonal decomposition (POD) and fast Fourier transform (FFT) are applied to the shear layers shedding from the trailing edges to comment on the coherent structures and their frequency content. The Reynolds number for both simulations and experiments is set to Re = 2.5 × 105 based on the inlet velocity ${U_{inf}} = 9\;\textrm{m}\;{\textrm{s}^{ - 1}}$ and the width of the model W = 0.17 m. The results show that PANS accurately predicts the flow field measured in experiments and predicted by a resolved LES, even with a low-resolution grid. The superiority of the PANS approach could provide good guidance for industrial research in predicting the turbulent flow around the square-back van model with affordable computational grids. The ground and wheel motion mechanism on the aerodynamic forces has been revealed by analysing the surface pressure distribution, the wheels’ surrounding flow, the underbody flow characteristics and the turbulent wake structures. The effects of the ground and wheel motion on the frequency, evolution and development characteristics of the wake shear layers are analysed, thus providing relevant insights for future experimental investigations of square-back van models.

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.

An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows

Characterization of unsteady loads is critical for the development of control systems for next-generation air vehicles. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) methods are prohibitively expensive, and existing Reynolds-Averaged Navier-Stokes (RANS) approaches have been shown to be inadequate in predicting both mean and unsteady loads. In recent years, scale-resolving methods, such as Partially Averaged Navier-Stokes (PANS) and Detached Eddy Simulation (DES), have been gaining acceptance and filling the gap between RANS and LES. In this study, we focus on a new variant of the PANS method, namely blended PANS or BPANS, which was shown to perform well in the incompressible regime for both wall-bounded and free shear flows. In this paper, we extend BPANS to compressible supersonic flows by adding a compressibility correction, leading to a new model called BPANS CC. The new model is tested using a well-known supersonic mixing layer case, and the results show good agreement with experimental data. The model is then used on a complex supersonic retropropulsion case and the results are in good agreement with experimental data.

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 .