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The present study focuses on the experimental investigation and numerical study using Large Eddy Simulation (LES) for an air-impinging jet. The investigation is carried out for slot jet impingement on the heated cylinder with an adiabatic flat plate beneath the heated cylinder. The parametric investigation is conducted for parameters such as Reynolds number (Re), jet-to-cylinder spacing (h/S), surface curvature (S/D), and plate length (P/D). They are varied as Re = 10,000–25,000; h/S = 4–12, S/D = 0.072–0.108 and P/D = 0.5–2. The Nusselt number distribution over a cylinder is experimentally obtained, and to understand the impact of parameters such as Re, h/S, S/D, and P/D on it, the numerical results are extracted from LES. The Nusselt number improves with increasing Re and decreasing h/S however their impacts are different. The major influence of Re and h/S is noticeable from θ = 0°–180° and θ = 0°–90°; however, the impact of h/S is negligible from θ = 90°–180°. The Nusselt number gets enhanced with increasing S/D due to more air entrainment, which produces higher Reynolds stress and turbulence kinetic energy. The increasing plate length (P/D) shifts flow separation at a lower angular position (θ), thereby increasing the recirculation zone and reducing the attached flow region. The recirculation zone contributes to heat transfer improvement in that region. Hence, a longer plate length P/D = 2 is an ideal selection compared to P/D = 0.5 and 1 as it better facilitates the positioning of cylindrical food products with optimum heat transfer. Further, correlations are proposed for stagnation and average Nusselt numbers in terms of Re, h/S, S/D and P/D. [ABSTRACT FROM AUTHOR]

Experimental investigations of flow past two (one above other) horizontal cylinders have been presented in this paper. The experimental data captured over a rough-bed with double cylinders having three different diameters, were used for the analysis. Firstly, general characteristics such as streamwise velocity, Reynolds shear stress and turbulence intensity profiles have been elucidated at different downstream locations from cylinder position; then some advanced analysis such as length scales, turbulent kinetic energy (TKE) fluxes and budget have been investigated to exhibit their variations. Length scale profiles exhibit higher values in near bed; indicating comparatively larger eddies' downstream of both cylinders. TKE budget profiles indicate highly negative pressure energy diffusion rate together with a sufficient TKE production rate, stabilized by the amplified TKE diffusion and dissipation rates. To determine one of the most prime behaviors of turbulence characteristics, namely TKE dissipation rate more accurately, the concept of structure function has been employed. Primarily velocity gradient method elucidates TKE dissipation rate, then it has been verified by Kolmogorov's two-thirds law using second order structure function and Kolmogorov's − 5/3 law using the method of power spectra. [ABSTRACT FROM AUTHOR]

To provide computational fluid dynamics (CFD)–grade experimental data for studying stratification, measurements on the High-Resolution Jet (HiRJet) facility at the University of Michigan have been conducted with density differences of $1.5\% $ 1.5 % and $ - 1.5\% $ − 1.5 % , respectively. Fluid with a density different from the fluid initially present in the HiRJet tank was injected, and the propagation of the time-dependent density stratification was captured on a two-dimensional plane with the aid of the wire-mesh sensor technique for Reynolds numbers near 5000 and Richardson numbers near 0.29. Direct numerical simulations (DNSs) of the two cases have also been conducted to expand the multifidelity database. The novel experimental and DNS data were then used to assess the predictive capabilities of the Standard $k - \varepsilon $ k − ε (SKE) model and the Reynolds Stress Transport (RST) model. In particular, the propagation speed and thickness of the stratification fronts were assessed by comparing the CFD results against the experimental and DNS data. It was found that the general trends of the stratified density fronts were well predicted by the CFD simulations; however, slight overprediction of the thickness of the stratification layer was found with the SKE model while the RST model gave a larger overprediction of the mixing. Examination of the turbulent statistics showed that the turbulent viscosity was largely overpredicted by the RST model compared to the SKE model. [ABSTRACT FROM AUTHOR]

This study numerically investigates and compares the secondary currents, velocity dips, turbulence properties, and boundary shear stresses in supercritical narrow open channel flows (OCFs) and in narrow duct flows (DFs) using an updated Launder–Reece–Rodi Reynolds stress model in OpenFOAM, which was validated previously for supercritical flows using experimental data. Six steady state simulations were performed at a bulk velocity of 2.31 m/s covering Reynolds numbers from 3.08×105 to 6.16×105 and aspect ratios (width to flow depth) of 1.0. 1.25, and 2.0, which in combination with the observed Froude numbers from 1.65 to 2.33 for OCFs are comparable to sediment bypass tunnel flows. Although free surface produces greater maximum secondary flows, the top wall in DFs creates stronger bulging of the longitudinal velocity above the velocity dips, which generates marginally higher maximum longitudinal velocity and significantly higher velocity fluctuations compared to OCFs. Two pairs of corner vortices are observed in each half width for DFs. However, such vortices differ in OCFs, in which the reduction of aspect ratio develops intermediate vortices. Such differences in the secondary currents are interrelated to the observed variations in the distributions of longitudinal velocity and Reynolds stresses. Higher average bed and sidewall shear stresses are obtained for DFs than for OCFs. The bottom vortices undulate the bed shear stress distributions. Similarly, the sidewall corner vortices (for DFs) or intermediate vortices and inner secondary vortices (for OCFs) undulate the wall shear stress distributions. These undulations are further influenced by the aspect ratio. Moreover, the flow characteristics below the mid depth observed for OCFs are comparable to those obtained for DFs, especially for the square cross sections with aspect ratio of 1.0. [ABSTRACT FROM AUTHOR]

Bioroughness plays an important role in modifying the velocity and sediment flux near the riverbed. It is therefore pertinent to study the influence of benthic fauna on the bed forms. To this end, large-eddy simulations are performed to investigate the influence of the arrays of mounds and their density on the turbulence characteristics in an open-channel flow. The simulated distributions of the time-averaged streamwise velocity and the turbulence intensity are in good agreement with the experimental data. Four numerical simulations are performed with varying streamwise spacings of mounds. Details of the time-averaged and instantaneous flow velocities are analyzed by multiple visualization methods, and the effects of the bioroughness density on the equivalent roughness height and the Darcy–Weisbach friction factor are quantified. The time-averaged flow in the wake of the mounds is characterized by a symmetric pair of vortices. The mounds behave like bluff bodies, increasing the riverbed roughness and heterogeneity in the flow environment. An increase in mound density is to promote the development of secondary currents and to increase the dispersive stress near the bed. The peaks of the Reynolds shear stress distributions decrease in both the streamwise and vertical directions for the high-density case due to a blockage effect. The instantaneous flow features, in the form of various turbulence structures, are generated near the top edge and the wake zone of mounds. The spacing between low-speed streaks decreases with an increase in equivalent roughness height. Multifrequency behavior that is observed is a result of shear layer roll-up from the edges of mounds and the flapping of wake. Finally, two formulas for equivalent roughness height and Darcy–Weisbach friction factor are proposed involving the bioroughness density and height. The findings demonstrate the effects of the bioroughness on the near-bed turbulence characteristics and sediment stability. Practical Applications: Bed forms produced by aquatic benthos are usually of small scale but with a large abundance. We performed a flume experiment as well as large-eddy simulations (a high-fidelity numerical simulation approach) to answer whether these microtopographies are important when studying flow and transport processes near the riverbeds. Four numerical simulations are performed with varying mound density. It was found that the microtopographies created by benthos indeed change the near-bed turbulence characteristics and sediment stability. Specifically at high abundances, benthos-induced bed forms could raise the bed roughness and the friction factor eightfold and threefold, respectively. This suggests the necessity of a modified roughness height formula and a friction coefficient formula based on the benthos abundance, which has been carried out in this study. Thus, engineers who are concerned with the flow and sediment transport in habitats of high-abundance benthos (e.g., wetlands and estuaries) may prefer to use these modified formulas and to develop a more accurate model of sediment transport. [ABSTRACT FROM AUTHOR]

The flapping characteristics of perforated flags with various porosities in different flow environments are studied using XFlow-Abaqus co-simulation. It is proved that flapping characteristics significantly correlate with flag porosity in different flow environments. Specifically, as the flag porosity increases, the flapping speed and vortex strength decrease monotonically. Further study of the influence of perforated flags on the flow structures surrounding a square cylinder revealed that different flag porosities lead to different levels of flow control. As the flag porosity increases, the flag's modulation weakens, the average drag on the square cylinder rises, and the influence of the Kármán vortex street becomes more significant. The flag-induced vortices can generate a high-pressure zone on the rear side of the square cylinder's top surface, leading to a decrease in the average lift on the square cylinder. It is notable that flags with different porosities generate vortices at different flapping states, which results in phase differences between the lift on the square cylinder and the flag. Finally, the study discusses the peaks of the Reynolds stress in the x- and y-directions, which delineate the boundary of the recirculation zone and reflect force fluctuations on the flag and the square cylinder, respectively. [ABSTRACT FROM AUTHOR]

The massive flow separation in the flow around a circular cylinder is challenging for the large-eddy simulation (LES) using the traditional equilibrium wall model (EQWM) for accurate prediction. To address this problem, a data-driven-non-equilibrium wall model (DNEQWM) was developed based on the result of the high-fidelity wall-resolved LES (WRLES) and the theoretical analysis. A hybrid modeling strategy was adopted in DNEQWM to deal with different flow regions. An empirical formula based on the analysis of the WRLES result was used to compute the wall shear stress in the attached region while the integration of the Navier–Stokes (N–S) equation was used in the separated region. Both EQWM and DNEQWM were applied to the LES of the flow around a circular cylinder at a classical Reynolds number of 3900 to evaluate the performance of the new model. It was found that DNEQWM was significantly superior to EQWM based on the analyses of the results of global flow quantities, surface pressure distributions, and flow details of mean and fluctuation velocities and the Reynolds stress in the wake. Flow visualizations indicated that DNEQWM can effectively reproduce the phenomenon of alternative periodic vortex shedding in the wake. The computational cost of DNEQWM was slightly lower than that of EQWM and significantly less than that of WRLES. This study presents a practical methodology for the wall model for the LES of the flow around the bluff body with smooth curved surfaces. [ABSTRACT FROM AUTHOR]

This paper presents an outer velocity scale and an inner scaling law of Reynolds shear stresses that are valid for the entire adverse pressure gradient (APG) region before separation, based on asymptotic expansions in turbulent boundary layers (TBLs). By reexamining the velocity defect and Reynolds shear stress in the outer region of TBLs, it is demonstrated that the pressure gradient effect can be included in asymptotic expansions. The mathematical requirements to be satisfied by the outer velocity scale are given. On this basis, we define a new outer velocity scale Uo, which is used in the mean momentum balance analysis over the entire APG region. The results show that there is a slowly evolving region of the Reynolds shear stress gradient in APG TBLs. We obtain a logarithmic decay law for the Reynolds stress gradient by asymptotic matching in this region, thus providing functional expressions for the total shear stress and total shear stress gradient in the inner region of TBLs. These expressions are valid for the entire APG region. Furthermore, we use the new velocity scale to determine three self-similar parameters in the momentum equation to discuss the conditions for approximate equilibrium. The changes in parameters point to changes in two physical properties of APG TBLs, the inertial force and turbulence production. [ABSTRACT FROM AUTHOR]

We apply the scale-relativity theory of turbulence to the turbulent boundary layer problem. On the basis of Kolmogorov's scaling, the time derivative of the Navier–Stokes equations can be integrated under the form of a macroscopic Schrödinger equation acting in velocity-space. In this equation, the potential coming from pressure gradients takes the form of a quantum harmonic oscillator (QHO) in a universal way. From the properties of QHOs, we can then derive the possible values of the ratio of turbulent intensities in the shear flow, R = σ u / σ v = 1.35 ± 0.05. We show that the Karman constant is theoretically predicted to be κ = 1 / R 3 , in good agreement with its typical value κ ≈ 0.4 and its observed possible variations. Then, we find a generic solution of our equations for the normal Reynolds stress pure profile, which closely fits the data from laboratory and numerical experiments. Its amplitude, μB, is the solution of an implicit equation that we solve numerically and analytically through power series, yielding to lowest order μ B − 1.35 ≈ − 2 (R − 1.35) , plus smaller contributions from other parameters. Consequently, the correlation coefficient of velocities is given by ρ ≈ 1 / R μ B 2 ≈ 1 / R 3 ≈ 0.4 and is therefore equal to the Karman constant to lowest order, in agreement with its universally measured value ≈ 0.4 for all shear flows. We also find a general similarity between turbulent round jets and boundary layers in their outer region. These results therefore apply to a wide set of turbulent flows, including jets, plane boundary layers, and, to some extent, channels and pipes. [ABSTRACT FROM AUTHOR]

The impact of the swirl number on the flow field of a single-stage swirl combustor is investigated using the particle image velocimetry technology. The variations in recirculation zone size, pulsating region, turbulent distribution, vorticity, and Reynolds stress within the combustor are summarized through quantitative analysis of the flow field. Experimental results indicate the following: (1) Under the same air mass flow rate, the length of the recirculation zone in the combustion state is shorter than that in the cold state. (2) The length of the recirculation zone and the axial vortex spacing display a decreasing trend as the swirl number increases, while the width of the recirculation zone demonstrates an increasing trend. (3) For the single-stage swirl combustor, the primary pulsating region is at the swirling jet area at the exit of the swirl. As the swirl number increases, the standard deviation of radial velocity fluctuations and turbulent kinetic energy also increase. (4) The strong shear region of the single-stage swirl combustor can be divided into inner and outer shear layers based on the vorticity distribution and the Q criterion. The vortices in the inner and outer shear layers exhibit opposite orientations according to the vorticity distribution. Overall, the research results can provide basic experimental data for numerical simulation of swirl combustion. [ABSTRACT FROM AUTHOR]

Direct numerical simulations are performed to investigate the effect of the yaw angle (α) on the drag-reduction performance by riblets in a turbulent channel flow. The yaw angles of α = 0 ° and 90 ° correspond to the riblets parallel and perpendicular to the free-stream direction, respectively. It is well known that maximum drag reduction occurs at α = 0 ° , and the drag-reduction performance by riblets is degraded with increasing α. We obtain the critical yaw angle below which drag reduction can be achieved and investigate the corresponding mechanism. From a parametric study, drag reductions are achieved for α < 20 °. As α increases, the form drag increases more rapidly than the skin-friction drag decreases, resulting in the increase in the total drag. At drag reducing and increasing yaw angles, the mean velocity profiles in wall units shift upward and downward, respectively, and the latter profile suggests that the drag-increasing riblet is similar to a rough surface. With increasing α, the wall-normal and spanwise velocity fluctuations and Reynolds shear stress increase, and stronger near-wall vortices are generated. By applying a scaling analysis to the momentum equation in the riblet-perpendicular direction and the FIK (Fukagata–Iwamoto–Kasagi) identity [Fukagata et al., "Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows," Phys. Fluids 14, L73–L76 (2002); Peet and Sagaut, "Theoretical prediction of turbulent skin friction on geometrically complex surfaces," Phys. Fluids 21, 105105 (2009); Bannier et al., "Riblet flow model based on an extended FIK identity," Flow Turbul. Combust. 95, 351–376 (2015)] to the riblet-parallel direction, the total drag is expressed as a linear function of sin 2 α. [ABSTRACT FROM AUTHOR]

In this study, the particle-laden flow in the wake of a static and a rotating cylinder at Reynolds number of 140 000 was investigated using the Reynolds Averaged Navier–Stokes numerical approach. Three turbulence models such as k–ω shear stress transport, Reynolds stress model, and local-correlation transition model (LCTM) were selected to predict the flow topology. Lagrangian approach with one-way coupling was used to track solid spherical particles of different sizes (0.01, 0.1, 2.5, 10, and 50 μm). The study reveals that LCTM is the most accurate to predict the flow topology in both cases. Cylinder's rotation generates different effects on flow structure. It breaks the wake's symmetry and reduces its width, and increases the frequency of vortex shedding and the size of the recirculation zone. Particle transport analysis has revealed that particles' response to the flow depends on their Stokes number and wake flow topology. Particles of 0.01, 0.1, and 2.5 μm distribute in and around vortex cores, while particles of 10 and 50 μm do not penetrate vortex cores. Instead, 10 μm particles accumulate mainly around the periphery of vortices, while 50 μm particles skip the vortex street to the thin shear flow region between vortices to be transported by the mainstream flow. Finally, cylinder rotation reduces the particle spread in the vertical direction and shifts all particle distributions in the cylinder's rotation direction. Analysis of particle dispersion functions showed that cylinder's rotation reduces differences in dispersion extent depending on particle size. [ABSTRACT FROM AUTHOR]

The alteration of physical properties in cavitating flows due to phase transition presents challenges for accurately expressing turbulent viscosity in Reynolds-Averaged Navier–Stokes models. Addressing this issue is crucial for capturing cavitating flow characteristics effectively. This study introduces a modification to turbulent viscosity by considering the compressibility of the vapor–liquid mixture, applied within the k-omega Shear-Stress Transport (SST k − ω) model framework. Simulations of cavitating flow around the Clark-Y hydrofoil, National Advisory Committee for Aeronautics 66 hydrofoil, and wedge are conducted to validate the proposed method. Results indicate that the modified model can reproduce the cavity inception, development, cutoff, and shedding processes observed in the experiment. Notably, the modification model accurately reproduces distinct cavitating flow features such as U-shaped cavities, secondary shedding, and high-pressure phenomena resulting from collapse. Moreover, the predicted time-averaged velocity, time-averaged Reynolds stress component, and dominant frequencies of pressure and phase volume fraction surpass those of the original SST k − ω model, demonstrating improved performance. These findings highlight the enhanced accuracy and reliability of the proposed SST-multiphase compressibility modification k − ω model for simulating cavitating flows, thus contributing to improved understanding and prediction capabilities in relevant engineering applications. [ABSTRACT FROM AUTHOR]

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model. [ABSTRACT FROM AUTHOR]

The presentation and modeling of turbulence anisotropy are crucial for studying large-scale turbulence structures and constructing turbulence models. However, accurately capturing anisotropic Reynolds stresses often relies on expensive direct numerical simulations (DNS). Recently, a hot topic in data-driven turbulence modeling is how to acquire accurate Reynolds stresses by the Reynolds-averaged Navier-Stokes (RANS) simulation and a limited amount of data from DNS. Many existing studies use mean flow characteristics as the input features of machine learning models to predict high-fidelity Reynolds stresses, but these approaches still lack robust generalization capabilities. In this paper, a deep neural network (DNN) is employed to build a model, mapping from tensor invariants of RANS mean flow features to the anisotropy invariants of high-fidelity Reynolds stresses. From the aspects of tensor analysis and input-output feature design, we try to enhance the generalization of the model while preserving invariance. A functional framework of Reynolds stress anisotropy invariants is derived theoretically. Complete irreducible invariants are then constructed from a tensor group, serving as alternative input features for DNN. Additionally, we propose a feature selection method based on the Fourier transform of periodic flows. The results demonstrate that the data-driven model achieves a high level of accuracy in predicting turbulence anisotropy of flows over periodic hills and converging-diverging channels. Moreover, the well-trained model exhibits strong generalization capabilities concerning various shapes and higher Reynolds numbers. This approach can also provide valuable insights for feature selection and data generation for data-driven turbulence models. [ABSTRACT FROM AUTHOR]

A Compact Heat Exchanger has a large heat transfer area per unit volume, which is achieved by utilizing extremely high-density fins. A pin fin is one of the most frequently used fins because of its advantages such as minimal pressure drop and ease of fabrication by adjusting geometric parameters such as fin height (h), fin spacing (a), fin back pitch (b), and fin diameter (d). A numerical examination was carried out on a pin fin to develop a correlation between the Colburn-j factor and friction f factor. The study was conducted for a large range of Reynolds (Re) values, encompassing both laminar (Re 200–2000) and turbulent regions (Re 2500–15000). ANSYS Fluent was used to conduct the CFD-based numerical analysis, with air at 300 K as the working fluid. The Colburn j factor and friction f factor data were acquired in this numerical study for various Reynolds numbers, as well as non-dimensional geometrical characteristics such as the fin diameter-to-fin spacing ratio (d/a), fin diameter-to-fin back pitch ratio (d/b), and fin diameter-to-fin height ratio (d/h) values. These data were validated using available experimental data from open literature. The correlations of the Colburn j factor and friction f factor were determined over a wide range of Reynolds numbers as well as the geometric characteristics of the pin fins, spanning the complete operational range of Compact Heat Exchangers for Aerospace and other applications. [ABSTRACT FROM AUTHOR]

The objective of this study was to explore the higher-order turbulence statistics of flow and turbulent length scales around a complex pier (CP) and compare the results with those for a simple pier (SP). The velocity data were recorded in a laboratory flume using particle image velocimetry (PIV). The PIV data were analysed to estimate the velocity fluctuations of third order, turbulence production and dissipation rates, turbulent length scales and the contributions of burst–sweep events to the total Reynolds shear stress around the piers mounted on a rigid flat surface. The skewness and advection coefficients indicated a more asymmetric distribution of velocity fluctuations for the SP than for the CP. Ejection and sweep events illustrated the dominance of similar strengths for an extended period, downstream of the piers. The upstream turbulent kinetic energy production was similar for both piers, while the upstream dissipation rate was higher for the CP. The length scales were greater at the upstream for the case of the SP while, downstream, they were greater for the CP. The findings of this work demonstrate the importance of a pile cap in restricting downward-moving flow by showing a lower magnitude of scour-inducing turbulence parameters for the CP as compared with the SP. [ABSTRACT FROM AUTHOR]

In smooth prismatic open channels, the boundary shear stress is obtained from continuity and momentum equations. The shear stress is a function of gravity, secondary flow and gradient velocity. In this research, semi-analytical equations were developed to estimate the average boundary shear stress in smooth rectangular and trapezoidal open channels with side slopes of 0.5, 1.0, 1.5 and 2.0 using conformal mapping techniques. After dividing the channel cross-section into bed and wall sub-sections, a previously presented method was used to estimate the average shear stress of the bed and the wall in open channels. For the studied case, in the first estimate of shear stress, the secondary current and constant eddy viscosity were neglected. After determining correction factors for secondary currents and eddy viscosity, the second estimation provided a good match with experimental measurements of the average shear stress for all aspect ratios. [ABSTRACT FROM AUTHOR]

The present work investigates the combined effects of the upstream sediment mining pit and vegetation on the riverbank using emergent rigid vegetation beyond the toe on the flow structure and morphological changes due to fluvial erosion. A steep gradient of streamwise velocity and other turbulence parameters such as Reynolds shear stress (RSS), transverse RSS, and turbulent kinetic energy (TKE) at the interface of the vegetated and unvegetated part of the test segment was observed. The cross-sectional analysis showed that vegetation increased the velocity of the unvegetated main channel, and the sandpit increased even the near-bed velocity with a similar trend in its longitudinal variation at the center line of the main channel. The abrupt variation in RSS and transverse RSS at the location of the berm induces instability and erodes the berm present at the toe of the riverbank. The combination of the vegetation and sandpit led to increased TKE of the flow at the near-bed and berm locations. The morphological analysis showed complete riverbank erosion in both cases of the unvegetated riverbank, i.e., without or with an upstream pit. The installed stems of rigid vegetation on the riverbank helped decrease the fluvial erosion of the riverbank, and its profile observed minimal changes over the length of the test segment. However, the main channel erosion was amplified due to the vegetation (in no-pit case) at the beginning of the test segment, which eroded the bed of the main channel by about 67% of the bed thickness. Also, in the vegetated riverbank cases, the upstream pit caused an increase in erosion by 7.66% at the center of the main channel. The study helps establish the hypothesis of negating the effects of sediment mining on bank erosion by using the rigid vegetation on the riverbank beyond its toe location, which performed well by maintaining the riverbank profile. [ABSTRACT FROM AUTHOR]

Large-eddy simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) equations were used to study incompressible flow and heat transfer in a U-duct with a high-aspect-ratio trapezoidal cross section. For the LES, the WALE subgrid-scale model was employed, and its inflow boundary condition was provided by a concurrent LES of incompressible fully-developed flow in a straight duct with the same cross section and flow conditions as the U-duct. LES results are presented for turbulent kinetic energy, Reynolds stresses, pressure–strain rate, turbulent diffusion, turbulent transport, and velocity–temperature correlations, with a focus on how they are affected by the U-turn region of the U-duct. The LES results were also used to assess three commonly used RANS models: the realizable k-ε with the two-layer model in the near-wall region, the two-equation shear-stress transport model, and the seven-equation stress-omega Reynolds stress model. Results obtained show steady and unsteady RANS to incorrectly predict the effects of unsteady flow separation. The results obtained also identified the terms in the RANS models that need to be modified and suggested how turbulent diffusion should be modeled when there is unsteady flow separation. [ABSTRACT FROM AUTHOR]

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers M b = 0.3 and M b = 1.5 , with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6 × 10 − 5 , and 1.0 × 10 − 4 . Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at M b = 0.3 but has a diminished effect at M b = 1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface. [ABSTRACT FROM AUTHOR]

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows. [ABSTRACT FROM AUTHOR]

A method is presented for obtaining topology optimized designs for internally cooled high temperature applications, using a flexible geometry description, by means of a voxelization methodology and a novel boundary detection algorithm. A conjugate heat transfer approach is taken; the physics is described by a Stokes–Brinkman model for the flow, weakly coupled with a convection–diffusion model for the heat transfer. A practically relevant optimization formulation, consisting of a maximum temperature objective with a mass flow constraint, is used, and applied to an industrial-relevant non-trivial geometry resembling a guide vane in a gas turbine. Temperatures and velocities from the optimized design are compared with the response from a Stokes flow model with body-fitted mesh and a high-fidelity Reynolds-averaged Navier–Stokes model. A comparison of the performance from a mixed and a penalty approach for solving the flow problem is included. The voxelization approach shows good promise for handling complex design domains. [ABSTRACT FROM AUTHOR]

Polymer based additives with long chain of suspended particles in oil retain polarity effect in the presence of couple stresses. Further, at high speed of journal bearing, the oil film experiences substantial agitation due to pressure-viscosity interaction which evolve piezo-viscous dependency of the lubricant. The present article addresses the combined effects of piezo-viscous dependency and couple stresses of lubricant on the characteristics of multi-recessed hybrid journal bearing under misaligned operation. To govern the flow of piezo-viscous-polar lubricant in clearance space of the journal bearing, a piezo-polar function is used to obtain the modified form of Reynolds equation. Galerkin's technique is employed to obtain the finite element formulation in the form of algebraic equation, which is solved to determine the unknown pressure field in the bearing system. The present results reveal that the use of piezo-viscous-polar lubricant offers an enhancement in performance characteristics of bearing system, i.e., a significant hike of 13–36%, 27–30% and 7–10% in the values of S ¯ ij , C ¯ ij and ω ¯ th respectively vis-à-vis Newtonian lubricant. The numerically simulated non-dimensional results presented in the article may be useful to generate the bearing design data of the hybrid journal baring system functioning in realistic and stringent operating conditions. [ABSTRACT FROM AUTHOR]

In order to industrialize proton exchange membrane (PEM) fuel cells and balance of plant components, simulations are utilized to minimize costs during development and maximize performance. A key component in the anode path is the ejector, which is often optimized by 2D CFD to maximize the entrainment ratio. However, most turbulence models for 2D CFD simulations do not accurately predict the ejector's entrainment ratio across the entire operating range. This study involves validating various turbulence models using experimental data from two distinct ejectors. The optimal turbulence model, identified as the Reynolds Stress Model, achieves an average deviation of 6.1% in the entrainment ratio between simulation and experiment for both ejectors. This represents a significant improvement compared to traditional k-ε and k-ω turbulence models. The proposed turbulence model minimizes deviations in actual operation, thereby reducing testing and development costs, and contributing to the rapid industrialization of PEM fuel cell technology. • 2D CFD effectively predicts the entrainment ratio of ejectors for PEM fuel cells. • Two ejectors are validated over the entire operating range for the anode path. • Reynolds Stress Model (RSM) outperforms eddy viscosity models such as k-ε and k-ω. • RSM predicts shock waves more accurately due to anisotropy in Reynolds stresses. • The average deviation of 6.1% proves that simulation and experiment are valid. [ABSTRACT FROM AUTHOR]

The effect of uniform blowing on a spatially developing flat-plate turbulent boundary layer at Mach 2.25 is investigated using direct numerical simulations. Two values of the wall blowing ratio are considered, corresponding to low and high blowing rates. Uniform blowing is found to significantly reduce the near-wall turbulence anisotropy, although the turbulent kinetic energy still exhibits near-wall asymptotic behavior and the Reynolds analogy is relatively insensitive to changes in the blowing ratio. The pre-multiplied spectra of turbulent kinetic energy production demonstrate that increasing the blowing ratio significantly energizes the large-scale structures in the outer region, while suppressing the inner small-scale structures. An increase in the blowing ratio also has a strong influence on the behavior of the fluctuating wall pressure, amplifying the fluctuation intensity and reducing the dominant frequencies in the power spectrum. Two-point space–time correlations indicate that the characteristic length scale of the pressure fluctuations increases with increasing blowing ratio, whereas the convection velocity exhibits the opposite trend. Analysis of the reduced mean wall heat flux reveals that it is dominated by the relative balance between the work of the Reynolds stress and the turbulent transport of heat, but is insensitive to uniform blowing. Importantly, bidimensional empirical mode decomposition of the turbulent structures highlights the increasingly dominant contributions related to the significantly energized outer large-scale structures in the blowing region. [ABSTRACT FROM AUTHOR]

This study explores the generation of secondary flows of Prandtl's second kind in the actuator-disk simulation of wind-turbine wakes. Leveraging large-eddy simulation data and conducting an analysis of the mean streamwise vorticity budget, we uncover the physical mechanisms contributing to this phenomenon. Our investigations attribute the emergence of such flows to the spatial gradients of the Reynolds stresses in the wake downstream of the turbines, which are, in turn, influenced by ground effects. To further investigate the phenomenon, we specifically isolate the impact of secondary flows on the wake by employing a model recognized for its incapacity to capture such dynamics: a two-equation Reynolds-averaged Navier–Stokes (RANS) model founded on the linear eddy-viscosity hypothesis. By comparing the predictions of the RANS model with those of large-eddy simulations and wind-tunnel experiments, we highlight the effect of secondary flows on the wake structure and, in particular, the upward shift of the wake. Motivated by the obtained results, we then enhance the baseline RANS model by introducing a non-linear term within the Reynolds stress tensor. This modification leads to a more accurate representation of Reynolds stresses, enabling the RANS model to capture the secondary flows in the wake. Our analysis emphasizes the importance of employing advanced RANS models in the simulation of wind farms. [ABSTRACT FROM AUTHOR]

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361 ≤ R e τ ≤ 2000), corresponding to bulk velocity-based Reynolds numbers of 11 700 ≤ R e b ≤ 82 500 , using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for R e τ = 361 , followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the R e τ value rises, it becomes crucial for a grid to adhere to the condition of Δ x + ≤ 20 − 25 and Δ z + ≤ 10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer. [ABSTRACT FROM AUTHOR]

A direct numerical simulation (DNS) database for head-on quenching of premixed flames propagating across turbulent boundary layers representative of friction Reynolds numbers, R e τ , of 110 and 180 has been utilized to analyze the interrelation between Reynolds stresses and their dissipation rates during flame–wall interaction. The Reynolds stresses and their dissipation rates exhibit significant deviations from the corresponding non-reacting flow profiles within the flame brush and in the burned gas region. This behavior is prominent for the components in the wall-normal direction because the mean direction of flame normal acceleration due to thermal expansion aligns with the wall-normal direction in this configuration. The anisotropy of Reynolds stresses and their dissipation rate tensors have been found to be qualitatively similar, but the anisotropic behavior weakens with increasing R e τ . However, the components of the anisotropy tensors of Reynolds stresses and viscous dissipation rate are not related according to a linear scaling, and thus, the models based on this assumption do not successfully capture the viscous dissipation rate components obtained from the DNS data. By contrast, a model, which includes the invariants of the anisotropy tensor of Reynolds stresses and satisfies the limiting conditions, has been found to capture especially the diagonal components of the viscous dissipation rate tensor more successfully for both non-reacting and reacting cases considered in this work. However, the quantitative prediction of this model suffers for the components in the wall-normal direction for lower values of R e τ , but the performance of this model improves with an increase in R e τ . [ABSTRACT FROM AUTHOR]

The turbulent jet plays an important role in fluid mechanics since it is a prototype of free turbulent flow which presents many unsolved problems, among which the absence of closure of the governing equations. Despite the chaotic nature of turbulence, it is characterized by the existence of many universal structures, in particular dimensionless invariants such as its opening angle or the correlation coefficient of velocities. After having given new exact solutions of the Reynolds Averaged Navier–Stokes equations (RANS), we suggest a solution to this puzzle in the scale-relativity framework. In this theory, the time derivative of the Navier–Stokes equations is integrated in terms of a macroscopic Schrödinger equation acting in velocity-space. This equation involves a constant ℏ v which can be identified with the energy dissipation rate, while the pressure gradient manifests itself as a quantum harmonic oscillator (QHO) potential. The squared modulus of its solutions yields the probability density function (PDF) of velocities. The Reynolds stresses can then be derived from this PDF, so that the closure problem is solved in this case. This allows us to obtain a theoretical prediction for the turbulent intensity radial profile (and therefore for the pressure) which agrees with the experimental data. The ratio of axial over radial velocity fluctuations is found to be R = 1.3 – 1.4 from QHO properties, in good agreement with its experimental values; we theoretically predict a jet opening angle α = 1 / 2 R 3 accounting for its universal value ≈ 1 / 5 ; the mean ratio of turbulent intensity amplitudes over jet centerline axial velocity is predicted to be X = 19 / 80 , in good agreement with its universally measured value ≈ 1 / 4 ; from these parameters we derive possible values of the radial turbulent intensity amplitude μ = 0.19 – 0.22 consistent with experiments; finally, we find a correlation coefficient of velocities ρ = 1 / R 3 = 2 α , suggesting an explanation for the universal value ≈ 0.4 observed for the turbulent jet and for all free shear flows. [ABSTRACT FROM AUTHOR]

The separated flow past a 6:1:1 spheroid is numerically investigated by means of the scale-adaptive simulation technique. The Reynolds number based on the free-stream velocity and the diameter at middle-section of the spheroid is located in the subcritical regime, i.e., Re = 3900. In comparison with the circular cylinder at the same Reynolds number, about 35% drag reduction is acquired by the spheroid, and the fluctuations of lift and drag are suppressed effectively. According to the detailed comparison, the satisfactory drag reduction and suppression of fluctuating force obtained by the spheroid are closely associated with the higher base-pressure and lower turbulent fluctuations in the near wake. Abundant contrasts of the different spanwise sections are presented to reveal the mechanism of constrained flow and apex effect of the spheroid. In addition, in order to provide reliable data for testing and developing turbulence models, a large number of turbulence statistics are computed and compared with previous data of the circular cylinder and sphere at comparable Reynolds numbers. Lower Reynolds stress peaks and less vigorous coherent structures indicate that the three-dimensional force and constrained flow caused by the spheroid can lead to the formation of steady shear layer and vortex separation. Furthermore, proper orthogonal decomposition and dynamic mode decomposition are employed to understand the large-scale wake flow structures behind the spheroid. The modal analysis results confirm that the wake of the spheroid is more stable than the circular cylinder, reconfirming the effective flow control. [ABSTRACT FROM AUTHOR]

We propose a model that integrates a drift flux model with a vegetation source term and the k − ω shear stress transport with improved delayed detached eddy simulation turbulence model to simulate sediment-laden vegetated flows. The numerical model was validated using experimental data from Lu ["Experimental study on suspended sediment distribution in flow with rigid vegetation," Ph.D. thesis (Hohai University, Nanjing, Jiangsu, China, 2008)] and Wang and Qian ["Velocity profiles of sediment-laden flow," Int. J. Sediment Res. 7, 27–58 (1992)]. We analyzed the vertical profile characteristics and spatial distribution features of sediment-laden vegetated flows at different vegetation densities. A detailed analysis was conducted on the correlations between variables that could affect the suspended sediment distribution, including vorticity, vertical velocity, Reynolds stress, and turbulent kinetic energy (TKE) fields. It was found that the vorticity field is primarily correlated with the suspended sediment concentration (SSC) field at the vegetation canopy, while the vertical velocity field above the canopy has a positive correlation with the SSC field. Both the Reynolds stress and TKE fields above the canopy exhibit positive correlations with the sediment concentration field. However, below the canopy, both fields show negative correlations with the sediment concentration. The TKE field is closely related to the suspended sediment distribution near the bottom, whereas the Reynolds stress field influences the suspended sediment distribution near the surface. The overall correlation between Reynolds stress and TKE with sediment concentration is negative, with their correlation significantly higher than that of vorticity and vertical velocity, indicating a closer connection with the movement of suspended sediments than the other variables. [ABSTRACT FROM AUTHOR]

We employ spectral-space and real-space quantities to characterize large-scale motions (LSMs) and very-large-scale motions (VLSMs) in open-channel flows (OCFs). The obtained data on velocity auto- and co-spectra, spectral correlation coefficient, and structure functions of the second and third orders are consistent with the hypothesis that VLSMs are a special type of coherent structure rather than an alignment of LSMs, even if active interactions between LSMs and VLSMs most likely take place. The Letter is concluded with a conceptual velocity spectrum for OCFs and an explanation of the mechanism of VLSMs' contribution to the Reynolds shear stress. [ABSTRACT FROM AUTHOR]

Rotor hubs are predominantly responsible for the parasitic drag encountered by high-speed rotorcraft. To gain a deeper understanding of the fluid dynamics around rotor hubs, simulations of counter-rotating coaxial rotor-hub flows were conducted, which was subsequently followed by a corroborative experiment at Pennsylvania State University. The simulation process employed a computational fluid dynamics framework termed "Mercury," which utilizes an unstructured/Cartesian multimesh paradigm. This process incorporated Spalart-Allmaras delayed detached eddy simulation turbulence modeling for an accurate representation of the flow. The investigation into the coaxial hub flow physics was conducted at two different advance ratios: 0.25 and 0.6, constructed by building up the hub components. The interaction between the hub and fairing components led to an increase in the average hub drag and caused unsteady harmonics in the hub and fairing drags. Furthermore, it was noted that different advance ratios affected the drag and wake structures. The complete hub model was then simulated in a water tunnel with an advance ratio of 0.25. Predictions of mean and unsteady drag, as well as mean wake velocity fields, were compared with the experimental results. Overall, the mean wake velocity field from the simulation qualitatively aligned with the experimental results, especially in the near-wake region. Additionally, the buildup model analysis significantly aided in understanding the intricate wake structures surrounding the hub. [ABSTRACT FROM AUTHOR]

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence. [ABSTRACT FROM AUTHOR]

The inflow of a rotating centrifugal impeller is normally perturbed by an upstream stationary component; therefore, the development of turbulent flow is different from the case with steady and uniform inflow. In this work, we performed a large-eddy simulation on turbulent flow in a centrifugal impeller, considering perturbation from the inflow and emphasizing the development of perturbation and its influence on flow in the impeller. The inflow perturbation is applied for the streamwise (w-) velocity and is time-varying as generated by a random number generator. A normal-distributed pattern of perturbation is always assumed with the intensity of perturbation, defined as the ratio between the perturbation amplitude and the mean velocity, set as fv = 0%, 5%, 10%, and 20%, where fv denotes the perturbation intensity. The inflow perturbation notably affects the passage flow. The velocity fluctuation and secondary flow increase in intensity as the perturbation intensity increases from fv = 0% to 10%, while a further increase to fv = 20% slightly weakens the velocity fluctuation. Although this phenomenon is less obvious in terms of the time-averaged characteristics of velocity, the Reynolds stress terms CtCa and CrCa under time-averaging still reflect a clear variation trend, and the Reynolds stresses are observed significantly on the blade suction surface. [ABSTRACT FROM AUTHOR]

The rotation of the solar corona is not a fully resolved issue. Coronal holes (CHs) reveal sometimes more rigid, but in other cases more differential rotation profiles. We used two datasets of coronal bright points (CBPs), one within CHs, and one outside of CHs. We analyzed rotation profiles in the two datasets of CBPs and compared them to check if there is any difference between rotation profiles for CBPs within CHs and those outside of CHs. The reported rigidity of the CHs rotational profiles implies that Reynolds stresses, which are considered to be the main drivers of the solar differential profile, should also be different between the two datasets. Therefore, we analyzed the horizontal Reynolds stress for the two datasets as well. We also compared the meridional motion of the two datasets. In all cases the results between the two datasets were the same within the observational error. In both datasets the solar rotation profile is significantly differential and similar to the photospheric profile. [ABSTRACT FROM AUTHOR]

The effects of Reynolds number, coflow stream and surface roughness on a steady two-dimensional wall jet were examined experimentally in an atmospheric boundary layer wind tunnel using a Cobra probe. Five Reynolds numbers in the range 56,500 < Re < 134,000 and five values of coflow velocity/jet velocity ratio ranging from 0.11 to 0.23 were considered. In addition, a 40-grit sheet was used as the rough surface to investigate the effect of surface roughness. The results demonstrate that the Reynolds stress increases with the decrease of slot Reynolds number, and the effects of a higher Reynolds number on the spread of the half-height and the decay of maximum velocity are less pronounced. The coflow and surface roughness have a clear effects on the streamwise development of the half-height and the maximum mean velocity. The coflow significantly decreases the spread rate and the decay of maximum velocity compared with those without coflow, while the surface roughness increases those parameters relative to those on a smooth surface. [ABSTRACT FROM AUTHOR]

The turbulence intensity and yaw angle of crosswinds exert a substantial impact on the aerodynamic characteristics of trains traveling in windy regions. It is urgent to study how the yaw angle and turbulence intensity of incoming flow jointly affect the aerodynamic characteristics of the train and the corresponding flow field under turbulent crosswind. A high-speed train scaled at a ratio of 1/8 of its actual size at different yaw angles was investigated. Three inflow conditions were adopted, including uniform inflow, Iu = 0.05 inflow, and Iu = 0.2 inflow (Iu is turbulence intensity). The turbulent inflow was generated by the synthetic eddy method. The instantaneous and time averaged characteristics of aerodynamic loads and pressure loads of the train were analyzed. The vortex structures, vorticity, swirling strength, mean velocity, reverse flow, and Reynolds stresses are analyzed to explore the flow pattern and flow evolution. The results found that the fluctuation of the aerodynamic loads, the average side fore, and the average rolling moment of the train are remarkably enhanced under turbulent inflow. These results stem from the alterations in the flow field around the train induced by turbulent inflow, consequently leading to variations in surface pressure on the train. As the turbulence intensity of the inflow increases, the stability of the vortex structures decreases, and the position of the large-scale vortex structure has been changed. Moreover, the yaw angle (β) exerts a more significant influence on the vortex structure's flow pattern on the leeward side compared to the inflow turbulence intensity. [ABSTRACT FROM AUTHOR]

When axial flow pumps-as-turbines (PATs) operate under off-design conditions, unstable and unsteady flow structures appear in the internal flow field, resulting in suboptimal functioning. These operating conditions not only decrease the efficiency of the hydraulic machines but also affect their mechanical reliability. This study establishes relative streamline coordinates, based on the blade's mean camber line, to investigate flow instabilities in axial flow PATs from a new perspective. Numerical simulations on an axial flow PAT were performed and validated using experimental data. The results show that flow separation is more likely to occur due to the more curved profile at the blade's suction surface, leading to considerable fluctuations in velocity along the flow direction and enstrophy amplitude near both the hub and impeller shroud. Moreover, the poor matching of the relative inflow angle of the impeller with the blade inlet angle leads to impingement losses near their leading edge, generating unstable flows and significant pressure pulsations, which induces hydraulic instability within the impeller. In addition to rotor-stator interference effects, the curvature of the blade suction surface profile and the bend structure of inlet conduit are significant factors that influence the pressure pulsation distribution of the PAT. An analysis of the enstrophy transport equation indicates that the relative vortex generation and the Reynolds stress dissipation terms play a key role in both vortex generation and dissipation, whereas the viscous term has a lower influence. These findings can serve as a reference for the optimization and efficient design of axial flow PATs. [ABSTRACT FROM AUTHOR]

This work introduces an ensemble variational method with adaptive covariance inflation for learning nonlinear eddy viscosity turbulence models where the Reynolds stress anisotropy is represented with tensor-basis neural networks. The ensemble-based method has emerged as an important alternative to data-driven turbulence modeling due to its merit of non-derivativeness. However, the training accuracy of the ensemble method can be affected by the linearization assumption and sample collapse issue. Given these difficulties, we introduce the hybrid ensemble variational method, which inherits the merits of the ensemble method in non-derivativeness and the variational method in nonlinear analysis. Moreover, a covariance inflation scheme is proposed based on convergence states to alleviate the detrimental effects of sample collapse. The capability of the ensemble variational method in model learning is tested for flows in a square duct, flows over periodic hills, and flows around the S809 airfoil, with increasing complexity in the training data from direct observation to sparse indirect observation. Our results show that the ensemble variational method can learn relatively accurate neural network-based turbulence models in scenarios of small ensemble size and sample variances, compared to the ensemble Kalman method. It highlights the superiority of the ensemble variational method in practical applications, since small ensemble sizes can reduce computational costs, and small sample variance can ensure the training robustness by avoiding nonphysical samples of Reynolds stresses. [ABSTRACT FROM AUTHOR]

Experiments were conducted to systematically investigate the nearly homogeneous turbulence generated by multiple oscillating grids. Altogether 54 runs were completed by employing five different grids. For each run, four to nine layers of grids were installed, which were operated with different frequencies, strokes and grid spacings. The particle image velocimetry was used to obtain flow velocity characteristics. Instantaneous flow measurements reveal that the flow structure varies depending on the grid configuration. For regular grids, turbulent wakes of nearly uniform size were generally observed. In comparison, for double-scale grids, the size of wakes varied with the bar width. In the near-grid region, the horizontal distributions of Reynolds stresses are strongly influenced by the grid geometry, showing obvious inhomogeneity especially for wide bars. The inhomogeneity reduces as the distance from the grid increases. At the midplane between two neighboring grids, the flow characteristics appear similar for all grid configurations. The size of the region where the turbulence appears nearly homogeneous is affected by the grid spacing and stroke. Generally, the double-scale grid can produce a greater homogeneous region than the regular grid. This study shows that the decay law of turbulence intensity developed for a single oscillating grid can be successfully extended to multiple oscillating grids. In addition, a theoretical interpretation of the decay law is presented by considering the variation in the velocity and size of wakes when evolving away from the grid. [ABSTRACT FROM AUTHOR]

A long-standing question in the Reynolds-averaged modeling of turbulent flow is how to predict accurately flows with temporal or spatial unsteadiness. In this paper, we present a "return to equilibrium" approach to modeling the unsteady Reynolds stress anisotropy bij in terms of differential transport equations, the solutions to which are constrained by algebraic closures for bij in flows at equilibrium and by the corresponding rapid-distortion-theory solutions for flows far from equilibrium. When coupled with scale equations for the turbulent kinetic energy and the dissipation rate, these anisotropy evolution equations comprise a complete closure scheme for which no additional model coefficients are required. Evaluations of this closure scheme, in which two different existing equilibrium algebraic models for bij were employed, were carried out for homogeneous turbulence in flows with a step imposition of shear, with continuously oscillatory shear at different frequencies and with a prescribed time-dependent plane-strain rate. Good agreement was achieved between model predictions and experimental/simulation target data in all test cases, with either Girimaji's bij model or a structure-based bij model used as the equilibrium algebraic closure. [ABSTRACT FROM AUTHOR]

In order to improve the cyclone anti-erosion design and performance, the research on the influences of erosion spiral angle on cyclone flow field and separation performance was conducted by numerical simulations using computational fluid dynamics technique with the aid of the Ansys-Fluent 19.2 software and experiments. Based on numerical simulations, Reynolds stress model was used to describe the variation of airflow field, and Oka erosion model was utilized to make predictions about the cyclone wall erosion. The models were verified by the experimental data, ensuring the accuracy of results in this work. The results reveal that the erosion of fine particles on the cyclone wall is caused by the random interaction, and as the particle size increases, the location of collision between the particle and cyclone wall is closer to the air inlet. The cyclone cylinder in inlet channel front and the bottom of the cone is prone to the structural size deformation by the cyclone wall erosion. The cyclone wall erosion enhances the synergistic effect of the secondary flow inside the cyclone separation space, and the cyclone flow field stability further decreases as the increase in the erosion spiral angle at the cone bottom, resulting in a sharp decline in the cyclone performance. Compared with the cyclone without erosion, as the erosion spiral angle is 30°, the size of completely separated particles increases from 4 to 8 μm, the cut size increases from 1.33 to 1.6 μm, and the pressure drop is 420.73 Pa with a decrease in about 35.44%. [ABSTRACT FROM AUTHOR]

Water scarcity is a global concern, with irrigation of food crops contributing significantly to freshwater depletion. Drip irrigation technology reduces water consumption but faces issues like clogging in narrow discharge sections, diminishing efficiency, and increasing costs. Accurate prediction of flow characteristics and understanding parameters affecting biofilm growth and particle deposition is crucial for effective anti-clogging strategies. Computational fluid dynamics (CFD) using turbulence models can be a valuable tool. This study evaluated the accuracy and efficiency of different turbulence models (standard k-ε , Reynolds Stress Model, and Large Eddy Simulation) in predicting the flow characteristics of a commercial emitter in a drip irrigation system. Results showed the standard k-ε model as a preferred choice for simulating mean flow characteristics and emitter discharge due to its balance between accuracy and computational efficiency. However, the Large Eddy Simulation model provided the most accurate results, considering the emitter discharge, unsteady flow behavior, wall shear stress distribution, and oscillatory index, despite requiring more computational resources. This model is valuable for understanding hydrodynamic effects on emitter clogging. The study also investigated the impact of velocity fluctuations, wall shear stress, and oscillatory shear index on biofilm growth and deposition in the emitter. Low shear stress in inlet and return zones reduced self-cleaning ability, leading to particle and microorganism attachment. Maintaining appropriate wall shear stress values in other regions proved crucial for improving anti-clogging ability. High oscillatory shear index values enhanced mass transfer, nutrient mixing, diffusion within the biofilm, and self-cleaning capacity. In summary, this study greatly enhances our understanding of how flow dynamics and biofilm management impact drip irrigation systems. It provides practical insights for engineers and practitioners, aiding in the creation of more efficient and clog-resistant systems. By optimizing these dynamics and strategies, this research promotes sustainable water use in agriculture, while also minimizing maintenance costs and maximizing crop yields. • Large eddy simulation accurately predicts hydrodynamic impact on emitter clogging. • K-ε balances emitter discharge prediction's accuracy and computational efficiency. • Spectral analysis of velocity evolution showed anisotropy in energy dissipation. • Velocity fluctuation and OSI could affect biofilm growth and sediment accumulation. • Wall shear stress is crucial to the self-cleaning ability. [ABSTRACT FROM AUTHOR]

The EnFlo stratified-flow wind tunnel is described, and the parameterization of stable atmospheric boundary layers in the context of wind turbines and stability classification is given, as are the scaling constraints for stratified-flow wind tunnel experiments. Wake measurements of mean velocity, Reynolds stresses, and turbulent heat flux were made for three mild stable states, including overlying inversion, and the neutral state. The depth of the atmospheric boundary layer was kept constant, and so the results show the effect of change in stability alone, without the change in scale that would also arise in full scale measurements, an advantage provided by wind tunnel experiments. The simulated boundary-layer wind-speed profile is the same in each case, its height slightly exceeding the blade-tip top height, and the velocity deficit at the turbine is also the same in each, implying a constant thrust coefficient. In the near wake the momentum deficit rises more rapidly in the stable cases, and stays higher further downstream where it is subsequently reduced by turbulent mixing. The wake grows less rapidly in the vertical direction in the stable cases, both above and below the hub height, the height above growing still less rapidly with an imposed inversion, while the height below is unaffected by the inversion. The wake width is largely unaffected by stability. Stability reduces the Reynolds stresses in the wake over and above the reduction in the undisturbed flow; there is not a simple superposition. In the lower part of the wake the stresses are not affected by the inversion, while they are in the upper part. Turbulent heat flux is increased in the bulk of the wake, more so with an inversion, but is reduced to the surface and unaffected by an inversion. [ABSTRACT FROM AUTHOR]

Quantitatively analyze the uncertainties in turbulence models is of great meaning for research and engineering. In this paper, we develop a Bayesian uncertainty analysis framework based on copulas. The proposed framework is applied to the parametric uncertainty quantification and calibration of the shear-stress transport turbulence model for the flow over a Gaussian bump. A copula function is used to establish the correlation between variables and construct the weight function, which enables greater consideration of Bayesian inference. Prior analysis is conducted based on Sobol indices with the nonintrusive polynomial chaos method, demonstrating the important effects of κ , a 1 , and β ∗ on the flow, both for the wall force coefficients and the Reynolds shear stress. Next, the wall force coefficients and Reynolds shear stress are used as training sets to verify the effectiveness of the method. The results show that modeling the relationship based on copulas is necessary and effective, and that the weight function adaptively balances the influence of physical quantities at different inference locations. The proposed method effectively corrects the computational deviations of the corresponding physical quantities. In addition, the confidence interval for the posterior sample is increased, enhancing the likelihood of obtaining results close to the actual values. • A copula-based Bayesian uncertainty quantification framework with adaptive weight function is proposed. • Gaussian bump is a recently proposed meaningful geometry shape, attracting wide concerns, but has not been studied enough by now. • Detailed and innovative prior and posterior analysis is conducted. • The physical mechanisms of the parameters for separated flow are analyzed. [ABSTRACT FROM AUTHOR]

This paper establishes a mean-field equation set and an energy theorem to provide a theoretical basis in view of the development of self-consistent, physics-based turbulent transport models for mean-field transport codes. A rigorous averaging procedure identifies the exact form of the perpendicular turbulent fluxes which are modelled by ad hoc diffusive terms in mean-field transport codes, next to other closure terms which are not commonly considered. Earlier work suggested that the turbulent $E\times B$ particle and heat fluxes, which are thus identified to be important closure terms, can be modelled to reasonable accuracy using the kinetic energy in the $E\times B$ velocity fluctuations ($k_{E}$). The related enstrophy led to further modelling improvements in an initial study, although further analysis is required. To support this modelling approach, transport equations are derived analytically for both quantities. In particular, an energy theorem is established in which the various source and sink terms of $k_{E}$ are shown to couple to mean-field and turbulent parallel kinetic energy, kinetic energy in the other perpendicular velocity components, the thermal energy and the magnetic energy. This provides expressions for the interchange, drift-wave and Reynolds stress terms amongst others. Note that most terms in these energy equations are in turn closure terms. It is suggested to evaluate these terms using reference data from detailed turbulence code simulations in future work. [ABSTRACT FROM AUTHOR]

With the recent development of Hydrogen Refueling Stations (HRS), the refueling of hydrogen composite tanks is an important issue for the safe handling of hydrogen. In particular, an appropriate protocol is needed to avoid tank overheating during refueling. To model the temperature distribution everywhere inside the tank during these processes, CFD (Computational Fluid Dynamics) simulations have been performed under cases where thermal stratification occurs. The performances of several CFD turbulence models are benchmarked through a comparison with experimental data. Two injector configurations are considered in this work: a straight one and another tilted upwards. The U-RANS (Unsteady-Reynolds Averaged Navier-Stokes) - Reynolds Stress Model (RSM) is found to be the most reliable turbulence model for both configurations. • The study focuses on the effect of turbulence model on the accuracy of the CFD simulation of H2 refueling tank. • Eddy viscosity, SAS and RSM turbulence models comparison. • Importance of accurately modeling thermal stratification in hydrogen tank. • Compare an validate the accuracy of CFD simulation with experimental data. • Define a unique methodology for accurately evaluating thermal evolution during H2 refueling tank for all configuration. [ABSTRACT FROM AUTHOR]