A modified PANS model for computations of unsteady turbulence cavitating flows

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.

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

The turbulence closure is significant to unsteady cavitating flow computations as the flow is frequently time-dependent accompanied with multiple scales of vortex. A turbulence bridging model named as PANS (Partially-averaged Navier-Stokes) purported for any filter-width is developed recently. The model filter width is controlled through two parameters: the unresolved-to-total ratios of kinetic energy fk and dissipation rate fω. In the present paper, the PANS method based on k-ω model is used to simulate unsteady cavitating flows over a Clark-y hydrofoil. The main objective of this work is to present the characteristics of PANS k-ω model and evaluate it depending on experimental data. The PANS k-ω model is implemented with various filter parameters (fk=0.2~1, fω =1/fk). The comparisons with the experimental data show that with the decrease of the filter parameter fk, the PANS model can reasonably predict the time evolution process of cavity shapes and lift force fluctuating in time. As the PANS model with smaller fk can overcome the over-prediction of turbulent kinetic energy with original k-ω model, the time-averaged eddy viscosity at the rear of attached cavity decreases and more levels of physical turbulent fluctuations are resolved. What's more, it is found that the value of ω in the free stream significantly affects the numerical results such as time-averaged cavity and fluctuations of the lift coefficient. With decreasing fk, the sensitivity of ω-equation on free stream becomes much weaker.

The present work deals with validation of the PANS (Partially-Averaged Navier-Stokes) computational methodology coupled with the \(\zeta -f\) RANS model of turbulence [10], formulated and implemented into the CFD software package AVL-FIRE by Basara et al. [2], in a broad range of wall-bounded flows featured by separation, swirling and tumbling motion. The configurations considered in the part I include a fully-developed flow in a plane channel (DNS by Moser et al. [14]) and flow separating from a continuous curved surface (reference database is provided by LES, [7] and [3]). The PANS approach, whose validation represents the prime objective of the present work, provides a seamless transition from the fully-modelled Unsteady RANS to the fully-resolved direct numerical solution (DNS) as the unresolved-to-total ratios of kinetic energy and its dissipation are appropriately varied. In addition, the complementary RANS (by using the \(\zeta -f\) model) computations of the flow configurations considered are also performed. The results obtained illustrate the PANS model capability to capture the turbulence unsteadiness leading consequently to a correct prediction of time-averaged flow quantities, unlike its RANS counterpart. The companion part II [4] is concerned with the PANS model application to more complex flow configurations including a tumbling vortex generation and compression and a swirling flow in a tube, the outlet of which is designed as an orifice with eccentric opening.

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.

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).

Vortex shedding behind a nonparallel pair of circular cylinders

The current industry design practice for addressing vortex shedding-induced vibration in thermowells is to use the ASME Power Test Code 19.3, Part 3 (PTC) [1], which essentially requires the vortex shedding frequency to be less than the first natural frequency of the thermowell by a reasonable design margin. The PTC also provides guidance for establishing the vortex shedding frequency and the natural frequency of the thermowell. In a 1996 paper presented at the ASME Pressure Vessel and Piping Conference, Blevins, et al [2] published test results for the natural frequencies and damping coefficients of several standard design thermowells. Also presented were the classic formulations for the calculation of the Von Karman vortex shedding and the thermowell natural frequency. The Blevins data indicated that for certain types of thermowells there was a discrepancy between the measured thermowell natural frequency and the frequency calculated using the PTC method. In this paper, the authors will review the basic calculations related to vortex shedding and thermowell natural frequency. This paper will also present Finite Element (FE) analyses of several thermowells from the Blevins paper and discuss the results of the FE analysis with respect to that paper’s test results. Discrepancies between the natural frequency calculated by the PTC methodology and the thermowell natural frequency test data presented by Blevins, and the results of the FE analyses will be discussed. The authors also introduce a design technique using fatigue analysis to assess the likelihood of thermowell failure. Use of the FE-derived natural frequency information and the fatigue analysis techniques will improve the safety of thermowell applications and may extend the service velocity in which a specific thermowell can be used.Copyright © 2002 by ASME

4 Modeling, simulation and mixing time calculation of stirred tank for nanofluids using partially-averaged Navier–Stokes (PANS) ku − ϵu turbulence model was published in Basic Sciences for Sustainable Development on page 85.

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.

We investigated the three-dimensional characteristics in the unsteady cavitating flow over an axisymmetric body with a blunt headform. A high-speed video camera was used to visualize the cavitating flow structures. A modified PANS (Partially-averaged Navier-Stokes) turbulence model coupled with Kubota cavitation model was used to simulate the time-evolution process of the unsteady cavitating flows. The finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures (LCS) methods are applied to investigate the three-dimensional flow patterns. The results show that the numerical method is capable of simulating the unsteady cavitating flow for capturing the attached cavity with maximum-length, the cavity break-off and U-type shedding, in accordance with the qualitative features observed in the experiment. Three-dimensional characteristics are extremely impressive in the unsteady cavitating flows. The re-entrant flows originate from different circumferential positions at the closure region of the attached cavity, and move upstream at different speeds. Moreover, substantial circumferential motions in the unsteady cavitating flow are found based on Lagrangian trajectories, and it is reasonably deduced that the U-type shedding cavity is primarily induced by the effect of re-entrant flow motions consisting of moving upstream and circumferential flows as well.

Physical Modalities of Therapy in Pediatric Rheumatic Diseases

During the development of high by-pass aircraft engine fans, stall flutter often becomes a major issue because it restricts their part-speed operability at near-stall conditions. Stall flutter is usually experienced on the first flexure mode, where a few nodal diameters are dominant. However, our recent tests showed strong non-synchronous excitation for the second flexure (2F) mode containing multiple nodal diameters, which is a distinguishing characteristic from well-known stall flutter. This paper aims to understand the mechanism of the observed 2F excitation. Aerodynamic damping is evaluated by nonlinear transient CFD simulations across a range of fan massflow near stall. The aerodynamic damping turns negative when vortex shedding near the blade tip spills upstream and interacts with the leading edge of the neighbouring blade. Also, the vortex shedding behaviour and resulting aerodynamic damping clearly depend on the blade amplitude. The vortex shedding has broadband spectra for both frequency and circumferential modes under low amplitude, and they lock on the blades’ motion under large amplitude. From these observations, it is concluded that the observed 2F excitation can be categorized into non-synchronous vibrations found in recent literature. The coincidence of blade vibration and vortex shedding is also discussed from unsteady signal processing.

Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

High-fidelity numerical simulations based on wall-resolved large-eddy simulations (LESs) are used to investigate the vortex shedding dynamics in a linear turbine cascade. The profile geometry is the well-documented LS59 highly loaded rotor blade. The simulation campaign covered several outlet Mach numbers (subsonic and transonic) and several experimental configurations to shed light on the relations between vortex shedding frequency, the laminar or turbulent states of boundary layers, and the resulting cascade losses. A first major result concerned experiments for transonic outlet Mach number. LES without inlet turbulence and LES without tripping the suction-side boundary layer are unable to match the experimental flow field. In the untripped case, the recirculation bubble is shorter leading to a vortex shedding Strouhal number of 0.17, whereas in simulations with trip wire or inlet turbulence, the bubble was longer, with a Strouhal of 0.24. A second finding is that the inlet turbulence intensity is able to drive the switching between two regimes for subsonic outlet Mach numbers: the so-called detached vortex shedding (long bubble, St∼0.24) or a “transonic vortex shedding” (short bubble, St∼0.19). The appearance of shock waves and very coherent rolls in the wake for the “transonic” regime can lead to a doubling of the cascade losses due to the drastic pressure drop near the trailing edge. Such a change in the flow regime, due solely to an increase in freestream turbulence, has not been reported earlier.