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Incipient wave breaking on a vertical circular pile is simulated with a Reynolds stress–$\\omega$ turbulence model. Comparison of results simulated with a stabilized two-equation turbulence model, as well as no turbulence model, demonstrates that the breaking point and the peak force on a vertical cylinder due to incipient breaking should not be affected by the turbulence closure model, provided that it is stable and the simulations are converged. Notably, the present results show that the build-up to peak force induced by incipient wave breaking can be accurately predicted without any turbulence closure model. However, for the prediction of the secondary load cycle (SLC), proper turbulence modelling is required, as this process involves both turbulence production and lee-side flow separation. The Reynolds stress–$\\omega$ model is demonstrated to predict the SLC more accurately than a stabilized two-equation $k$–$\\omega$ turbulence model, as the flow separation points and vorticity field are better predicted. Some existing studies indicate that the generation of the SLC does not necessarily result from flow separation, but is rather due to the suction force. The present work finds that the occurrence and point of flow separation significantly affect the magnitude of the suction force, which hence affects the SLC prediction significantly. For waves breaking on a vertical pile, proper turbulence modelling is therefore essential for accurate SLC predictions. (In the above, $k$ is the turbulent kinetic energy density and $\\omega$ is the specific dissipation rate.)

The physical mechanism of flow unsteadiness is one of the key problems in cavitating flow. Significant efforts have been exerted to explain the cavitation-vortex interaction mechanism. As well, the process of kinetic energy transport during the evolution of unsteady cavitating flow must be elucidated. In this work, 2D calculations of cavitating flow around a NACA66 hydrofoil were performed based on the open source software OpenFOAM. The modified shear stress transport k-ω turbulence model, which considers curvature and turbulent eddy viscosity corrections, was employed to close the governing equations. The Schnerr-Sauer cavitation model was adopted to capture the cavitation phase change process. Numerical results showed reasonable consistency with the results of the experiments conducted by Leroux et al. (2004). The results showed that cavitation promotes turbulence intensity and flow unsteadiness around the hydrofoil. During the attached sheet cavity growth stage, high-value regions of turbulent kinetic energy are located substantially at the interface of the cavity, particularly at the rear portion of the cavity region. During the cloud cavity shed-off stage, the cavity begins to break off and the maximum value of turbulent kinetic energy is observed inside the shed cavity. Finally, the influence of cavitation on the turbulence intensity is illustrated using the turbulent kinetic energy transport equation, which shows that the pressure diffusion and turbulent transport terms dominate as cavitation occurs. In addition, cavitation promotes turbulence production and increases dissipation with fluid viscosity and flow unsteadiness. The viscous transport term only acts in the cavitation shedding stage under large-scale vortex shedding. Overall, these findings are of considerable interest in engineering applications.

Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-ω model, the mixing length model, an equation-free νt and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.

The secondary motion caused by turbulence anisotropy is one of the crucial factors for determining the size of corner-flow separation in a side-wall interference flow field. Therefore, through a wall-resolved large-eddy simulation (LES) of a side-wall interference flow field, this study investigates the effects of the secondary motion on the corner-flow separation and explores the turbulence modelling that can reproduce the secondary flow motion. The momentum transport analysis using the LES results shows that the secondary vortex has twofold effects on delaying the corner-flow separation: the convective transport of the streamwise momentum towards the corner, and the enhanced production of turbulence by increasing the shear. Also, the vorticity transport analysis reconfirms that the secondary motion is caused primarily by turbulence anisotropy in the outer layer of the turbulent boundary layer. Furthermore, a quadratic constitutive relation (QCR) is proposed based on the analysis of the relationship between the Reynolds stress and velocity gradient. The proposed QCR consists of two quadratic terms and three constant parameters. The a priori analysis using the LES data shows that the proposed QCR represents the anisotropy of the Reynolds stress overall better than the existing QCR. Reynolds-averaged Navier–Stokes simulation using the proposed QCR with the Spalart–Allmaras turbulence model shows improvements in the prediction of the corner-flow separation compared to the results obtained by the existing QCR with the same turbulence model.

The present work focuses on the application of density-based topology optimization to the design of a surface cooler. This kind of device is used to cool down the oil circuit in aircraft engines thanks to the cold air in the bypass stream, and is subject to severe heat duty and pressure drop requirements. The optimization is carried out with an in-house implementation of the density method in OpenFOAM. A continuous adjoint strategy is employed to compute the sensitivities with respect to the design variables. Avoiding the so-called “frozen turbulence” assumption, the variations of the turbulent viscosity are taken into account in the computation of the sensitivity. The proposed model also considers the influence of the design variables on the wall distance function occurring in the formulation of the Spalart–Allmaras turbulence model. A simplified two-dimensional model is first employed to tune the optimization and the density model parameters. Then, the methodology is applied to a large-scale three-dimensional case, and the results are compared to a reference straight-fin geometry. The performance is finally evaluated with a reference solver, showing that the density model overestimates both the heat exchange and the total pressure loss, but that the methodology is still able to provide efficient designs in turbulent flow, starting from a very remote initialization.

Soft abrasive flow (SAF) finishing has advantages in precise processing for the workpieces with tiny scale or irregular geometric surfaces. However, current SAF finishing methods have surface quality problem caused by uneven flow field profile. To resolve the problem, a novel double-inlet SAF finishing method is proposed based on the fluid collision theory. Taking two constrained processing apparatuses (single-inlet and double-inlet) as the objectives, in combination with the shear stress transport (SST) k-ω turbulence model, the fluid mechanic models for the two apparatuses are set up, and the preliminary abrasive flow field characteristics are acquired. Referring to the collision conservation principles, the profiles of dynamical pressure and turbulence intensity in double-inlet constrained passage are obtained. The simulated results show that the flow field distribution of single-inlet passage is in a steady state and non-uniform, a periodic oscillation phenomenon appears in double-inlet passage, and it can enhance the turbulence intensity and movement randomness of abrasive flow. The processing experiments show that the proposed SAF finishing method can make the roughness on parallel flowing direction less than 50 nm and can improve the finishing uniformity and efficiency.

We numerically investigate stalling flow around a static airfoil at high Reynolds numbers using the Reynolds-averaged Navier–Stokes equations (RANS) closed with the Spalart–Allmaras turbulence model. An arclength continuation method allows to identify three branches of steady solutions, which form a characteristic inverted S-shaped curve as the angle of attack is varied. Global stability analyses of these steady solutions reveal the existence of two unstable modes: a low-frequency mode, which is unstable for angles of attack in the stall region, and a high-frequency vortex shedding mode, which is unstable at larger angles of attack. The low-frequency stall mode bifurcates several times along the three steady solutions: there are two Hopf bifurcations, two solutions with a two-fold degenerate eigenvalue and two saddle-node bifurcations. This low-frequency mode induces a cyclic flow separation and reattachment along the airfoil. Unsteady simulations of the RANS equations confirm the existence of large-amplitude low-frequency periodic solutions that oscillate around the three steady solutions in phase space. An analysis of the periodic solutions in the phase space shows that, when decreasing the angle of attack, the low-frequency periodic solution collides with the unstable steady middle-branch solution and thus disappears via a homoclinic bifurcation of periodic orbits. Finally, a one-equation nonlinear stall model is introduced to reveal that the disappearance of the limit cycle, when increasing the angle of attack, is due to a saddle-node bifurcation of periodic orbits.

The implementation of the wind turbine is a major issue in the wind engineering sector. However, the presence of wind turbines in the lower part of the atmospheric boundary layer (ABL) requires an appropriate study for the simulation of turbulent airflow in the wind farm situated on hilly terrain. The use of precise Computational Fluid Dynamics (CFD) simulations for the ABL flow is vital for numerous applications, such as wind energy, building, urban planning, etc. To achieve accurate results, it is imperative that the inlet boundary conditions produce vertical profiles that keep a uniform horizontal distribution (with no streamwise gradients) in the upstream region of the computational domain for all important parameters. A development approach is proposed herein, focused on the imposition of two different inlet profiles when used in combination with the rough z0-type scalable wall function. The horizontal homogeneity of these profiles has been verified by 2D Reynolds averaged Navier-Stokes (RANS) through the examination of a neutral ABL in an empty computational domain using the k-ε turbulence model. The findings indicate that the use of this modeling approach can yield relatively consistent homogeneity of neutral ABL for both inlet boundary conditions. Subsequently, sensitivity analyses were performed on the inflow profiles to forecast the evolution of the bottom half of an idealized truly-neutral ABL and to accurately capture the complex dynamics of atmospheric flows over hilly terrain. This study compares the results with the CRIACIV (Inter-University Research Centre on Building Aerodynamics and Wind Engineering) boundary layer wind tunnel experimental data, showing that the inflow profiles and the presence of topographic complex have a significant impact on air velocity, turbulent kinetic energy and turbulence intensity in the x-direction. The results obtained are in good correlation with published experimental data in the presence of the hill surface.

In this study, a computational thermo-fluid dynamics simulation of a wide-slot jet impingement heating process is performed. The present configuration consists of a turbulent incompressible air jet impinging orthogonally on an isothermal cold plate at a Reynolds number of around 11,000. The two-dimensional mean turbulent flow field is numerically predicted by solving Reynolds-averaged Navier–Stokes (RANS) equations, where the two-equation eddy viscosity k-ω model is utilized for turbulence closure. As the commonly used shear stress transport variant overpredicts heat transfer at the plate due to excessive turbulent diffusion, the recently developed generalized k-ω (GEKO) model is considered for the present analysis, where the primary model coefficients are suitably tuned. Through a comparative analysis of the various solutions against one another, in addition to reference experimental and numerical data, the effectiveness of the generalized procedure in predicting both the jet flow characteristics and the heat transfer at the plate is thoroughly evaluated, while determining the optimal set of model parameters. By improving accuracy within the RANS framework, the importance of model adaptability and parameter tuning for this specific fluid engineering application is demonstrated. This study offers valuable insights for improving predictive capability in turbulent jet simulations with broad engineering implications, particularly for industrial heating or cooling systems relying on wide-slot jet impingement.

The flexibility of the FMHL+ pumped storage power plants can be improved by extending the hydraulic short-circuit operating mode. CFD simulations of the flow in three bifurcations are performed to calculate the head losses and to investigate the flow topology in the pipes. A specific attention is paid to the influence of the curvature correction that has been developed for two-equation RANS turbulence models. For the T-junction considered, the activation of the curvature correction influences the head losses whereas for the two Y-junctions computed, no effect is observed. By comparing with the Y-junctions, the T-junction leads to higher head losses and helicity in the pipes downstream of the bifurcation. Compared to the current the intragroup hydraulic short circuit operation permitted, the intergroup and interplant hydraulic short circuit mode should provide better performances with possible gains until of −55% in head losses and −94% in helicity upstream of the turbines.