Reynolds Normal Stresses Research Articles

Application of a Distributed Element Roughness Model to Additively Manufactured Internal Cooling Channels

Abstract Design for cooling effectiveness in turbine blades relies on accurate models for dynamic losses and heat transfer of internal cooling passages. Metal additive manufacturing (AM) has expanded the design space for these configurations, but can give rise to large-scale roughness features. The range of roughness length scales in these systems makes morphology resolved computational fluid dynamics (CFD) impractical. However, volumetric roughness models can be leveraged, as they have computational costs orders of magnitude lower. In this work, a discrete element roughness model (DERM), based on the double-averaged Navier–Stokes equations, is presented and applied to additively manufactured rough channels, representative of gas turbine blade cooling passages. Unique to this formulation of DERM is a generalized sheltering-based treatment of drag, a two-layer model for spatially averaged Reynolds stresses, and explicit treatment of dispersion. Six different AM rough surface channel configurations are studied, with roughness trough to peak sizes ranging from 15% to 60% nominal channel passage half-width, and the roughness Reynolds number ranges from Rek = 60 to 300. DERM predictions for spatially and temporally averaged mean flow quantities are compared to previously reported direct numerical simulation results. Good agreement in the mean velocity profiles, stress balances, and drag partitions are observed. While DERM models are typically calibrated to specific deterministic roughness morphologies at comparatively small roughness Reynolds numbers, the present more generalized DERM formulation has wider applicability. Here, it is demonstrated that the model can accommodate random roughness of large scale, typical of AM.

Turbulent superstructure statistics in a turbulent boundary layer with pressure gradients

In turbulent boundary layers, streamwise elongated regions of high- and low-momentum in the log-law layer that can extent up to several boundary layer thicknesses are often referred to as turbulent superstructures. These structures contain a relatively large portion of the layer’s turbulent kinetic energy and have been shown to interact with the near-wall flow structures. In the last few decades extensive research on zero-pressure gradient (ZPG) turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent (APG) boundary layer flows are much less studied despite their strong significance aero-hydrodynamic vehicle design. Therefore, the three-dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow are investigated in the Atmospheric Wind Tunnel Munich (AWM) using a multi-camera 3D time-resolved Lagrangian particle tracking approach. In this study, Lagrangian and Eulerian statistics will be used to characterize the dynamics and interaction of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14 000 that then flows over a curved plate subjected to a favorable (FPG) and strong adverse (APG) pressure gradient, which eventually separates. An Eulerian analysis, using multi-point correlations of 3D velocity fields, found that the average superstructure topology is modulated by decelerating flow in the APG region when compared to the ZPG region, however the basic shape and spanwise pattern is preserved. Looking into the behavior of individual trajectories, it was found that the dispersion of single particles along trajectories in the log-law layer are capable of moving more than the average Eulerian superstructure spacing in the spanwise direction. Furthermore, the mean square of the single particle dispersion indicates that the maximum dispersion in the spanwise direction comes from particles released at the wall-normal location corresponding to the so-called “second-peak/plateau” region in the streamwise normal Reynolds stress.

Turbulence Kinetic Energy and High-Order Moments of Velocity Fluctuations of Flows in the Presence of Submerged Vegetation in Pools

The flow in arid and semi-arid regions changes significantly during seasons, letting many vegetation patches develop in different parts of rivers. In the presence of aquatic plants in streams, different flow structures have resulted. When the water level increases in these rivers, the presence of vegetation patches influences the turbulent flow structures, which may considerably change the estimation of key hydraulic parameters. The results of earlier investigations indicated that a wide range of submerged and non-submerged vegetation influences the hydrodynamic features of flows in rivers and streams. In the present investigation, two pools with various slopes of entry and exit sections were used to conduct eight independent experiment runs. In addition, a vegetation patch over the entire pool section has been set up to investigate the effects of the vegetation patch on flow structures in pools. The effect of two slopes of 5 and 10 degrees for both entrance and exit of the pools on flow structure has been investigated. Considering two aspect ratios of 2.0 and 2.7, the distributions of flow velocity, Reynolds normal and shear stresses, turbulence intensities, turbulent kinetic energy (TKE), quadrant analysis, and spectral analysis have been studied at the trailing edge of the vegetation patch along an artificial pool. Results show that, for large entrance and exit slopes (10 degrees), the TKE distribution profiles have no specific form. However, the TKE values have a convex-shaped distribution pattern with the maximum TKE value near the bed when the slopes of the entrance and exit sections of the pool are small (5 degrees). Results showed that both ejections and sweeps govern the turbulence structures and coherent motions at the trailing edge of the vegetation patch along the pool. The geometry, entrance, and exit slopes of the pool have no effect on the validation of power spectral function compared to the presence of a vegetation patch in a flatbed.

An Assessment of Second Moment Closure Modeling for Stratified Wakes Using Direct Numerical Simulations Ensembles

Abstract Buoyant wakes encountered in the ocean environment are characterized by high Reynolds (Re) and Froude (Fr) numbers, leading to significant space–time resolution requirements for turbulence resolving CFD models (i.e., direct numerical simulations (DNS), large eddy simulations (LES)). Therefore, Reynolds-averaged Navier–Stokes (RANS) based models are attractive for these configurations. The inherently complex dynamics of stratified systems render eddy-viscosity-based modeling inappropriate. RANS second-moment closure (SMC) based modeling is more suitable because it accounts for flow anisotropy by solving the transport equations of important second-moment terms. Accordingly, eleven transport equations are solved at the SMC level, and a range of submodels are implemented for diffusion, pressure strain and scrambling, and dissipation terms. This work studies nonstratified and stratified towed wakes using SMC and DNS. Submodels in the SMC are evaluated in terms of how well their exact Reynolds averaged form impacts the accuracy of the full RANS closure. An ensemble average of 40 and 80–100 DNS realizations are required and conducted for these temporally evolving nonstratified and stratified wakes, respectively, to obtain converged higher-order statistics. SMC over-predicts wake height by over a factor of 2, and under-predicts defect velocity, wake width, and turbulent kinetic and potential energies by factors ranging from 1.3 to 3.5. Also, SMC predicts a near isotropic decay of normal Reynolds stresses (a33→−0.25), in contrast to the anisotropic decay (a33→−0.64) returned by DNS. The DNS data also provide important insights related to the inaccuracy of the dissipation rate isotropy assumption and the non-negligible contribution of pressure diffusion terms. These results lead to several important recommendations for SMC modeling improvement.

Velocity spectra and scale decomposition of adverse pressure gradient turbulent boundary layers considering history effects

Experiments at relatively large Reynolds number were conducted to better understand the influence of an adverse pressure gradient on the turbulence in two-dimensional boundary layer flows. One focus is on documenting the scale contributions to the Reynolds normal and shear stress profiles under the influence of a positive streamwise pressure gradient. Toward these aims, velocity spectra at friction Reynolds numbers (7100≤Reτ≤8600) are presented, analyzed, and compared to a zero pressure gradient case from the same facility at nominally matching Reynolds number. Distance-from-the-wall scaling is central to numerous theoretical and modeling considerations of the canonical flat plate flow. Consistently, the present spectral measurements reveal clear evidence for its preservation on the inertial sublayer under modest adverse pressure gradients. Increases are seen in the viscous-scaled premultiplied spectra in the outer region as the pressure gradient increases — commensurate with the increases observed in the outer peaks of the streamwise and wall-normal velocity variances, as well as the Reynolds shear stress. Effects of varying Reτ on the streamwise and wall-normal velocity variances and the Reynolds shear stress are studied by comparing the present data at varying Clauser pressure gradient parameter, β, with previous experiments having similarly varying β at significantly lower Reτ (≈1900). This allows to study the effects of changing Reynolds number at matched β. Cases at similar β and Reynolds number, but with varying flow history are also examined, wherein the same β value is arrived either by starting from a smaller or larger initial β. The effects of β>0 on the large and small scale motions are investigated by segregating the signal contributions according to a cut-off wavelength established in previous zero pressure gradient flows. Under a normalization that uses a hybrid velocity scale this analysis reveals similarity between the outer regions of the spectrally-decomposed variances and Reynolds shear stress. These analyses also reveal a more dramatic reduction in the near-wall large scale contribution to the Reynolds shear stress gradient in the β>0 flow when compared to the β=0 flow.

Mechanisms of propeller jet-induced migration, release, and distribution of perfluoroalkyl acids in sediment–water systems

Perfluoroalkyl acids (PFAAs) are continuously accumulated in surface sediments due to extensive and long-term application. However, the mechanisms through which disturbances induced by ship propeller jets at the riverbed cause secondary release of PFAAs from sediments remain unclear. In this study, the effects of different propeller rotational speeds on PFAA migration, release, and distribution in multiphase media were investigated by performing indoor flume experiments combined with particle tracking velocimetry. Moreover, key factors influencing PFAA migration and distribution were identified, and partial least squares regression (PLS) method was applied to develop quantitative prediction models of relationships among hydrodynamics, physicochemical parameters, and PFAA distribution coefficients. The total PFAA concentrations (ΣPFAAs) in overlying water under propeller jet action exhibited transient characteristics and hysteresis with time after the disturbance. In contrast, the ΣPFAAs in suspended particulate matter (SPM) exhibited an upward trend throughout the process with consistent characteristics. The spatial distribution trends of PFAAs in overlying water and SPM at different propeller rotational speeds featured vertical variability and axial consistency. Furthermore, PFAA release from sediments was driven by axial flow velocity (Vx) and Reynolds normal stress Ryy, while PFAA release from porewater was inextricably linked to Reynolds stresses Rxx, Rxy, and Rzz (p < 0.05). PLS regression models showed that variations in Vorticity, dissolved organic carbon, and pH influenced the decreases in PFAA distribution coefficients between SPM and overlying water (KD-SW) as propeller rotational speed increased, except for very long-chain PFAAs (C > 10). The increases in PFAA distribution coefficients between sediment and porewater (KD-SP) were mainly determined by physicochemical parameters of sediments, and the direct effect of hydrodynamics was relatively weak. Our study provides valuable information regarding the migration and distribution of PFAAs in multiphase media under propeller jet disturbance (both during and after disturbance).

The effects of a spur dike location in a 90° sharp channel bend on flow field: Focus on anisotropy degree and anisotropy nature

In this research, the flow features around a spur dike located in a 90˚ sharp channel bend have been studied experimentally in detail. Results showed that the effects of the spur dike on upstream sections increased by increasing α (spur dike location from the beginning of the bend). In addition, by increasing α, the horseshoe vortex (C3) and secondary flow in the channel bend (C1) strengthened. The energy and the Reynolds shear stress in the C3 region decreased by increasing α. It is recommended to use a Barycenteric Map (BM) instead of the normal Reynolds stresses to find the anisotropy nature accurately. A strong anisotropic condition was detected at the border of the recirculation flow region and the main flow. However, in the C3 and the interaction regions, the isotropy condition improved. In the main flow region, by increasing α, the isotropy degree improved. However, by increasing α, an increase in the development of the region with a high anisotropy degree towards the recirculation region was observed. The anisotropy degree in the near-bed layer region and the shear layer region is comparable. However, the anisotropy nature is different. The maximum error of the numerical simulation based on isotropic turbulence occurred at the shear layer region where the severe cigar-shaped turbulence occurred.

Numerical investigation of subcritical and supercritical carbon dioxide fluidized beds using two fluid model and discrete element method

Fluidization state of ambient, subcritical and supercritical carbon dioxide (CO2) fluid fluidized beds are simulated using Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) and Two-Fluid Model (TFM) combined with Low Density Ratio-Kinetic Theory of Granular Flow (LDR-KTGF). Quantitative and qualitative analysis were executed between TFM and CFD-DEM simulation results. Fluidization process using two methods coincides with predictions of stability function and different criteria for distinguishing from particulate and aggregative fluidizations. A transitional fluidization with the wave-like and chunk-like flows occurs in subcritical CO2 fluid fluidized bed, and the bubble-like and particle aggregative-like flows are observed in ambient and supercritical states, respectively. The discrepancies in volume fractions and velocities obtained using TFM and CFD-DEM approaches were small, while the predicted turbulent kinetic parameters and bubble-like kinetic energy show sensitivity to the turbulence model. Statistical analysis of the turbulent normal Reynolds stresses indicated an anisotropic flow of particles.

Simulations of the Rotor-Stator-Cavity Flow in Liquid-Floating Rotor Micro Gyroscope

When rotating at a high speed in a microscale flow field in confined spaces, rotors are subject to a complex flow due to the joint effect of the centrifugal force, hindering of the stationary cavity and the scale effect. In this paper, a rotor-stator-cavity (RSC) microscale flow field simulation model of liquid-floating rotor micro gyroscopes is built, which can be used to study the flow characteristics of fluids in confined spaces with different Reynolds numbers (Re) and gap-to-diameter ratios. The Reynolds stress model (RSM) is applied to solve the Reynolds averaged Navier–Stokes equation for the distribution laws of the mean flow, turbulence statistics and frictional resistance under different working conditions. The results show that as the Re increases, the rotational boundary layer gradually separates from the stationary boundary layer, and the local Re mainly affects the distribution of velocity at the stationary boundary, while the gap-to-diameter ratio mainly affects the distribution of velocity at the rotational boundary. The Reynolds stress is mainly distributed in boundary layers, and the Reynolds normal stress is slightly greater than the Reynolds shear stress. The turbulence is in the state of plane-strain limit. As the Re increases, the frictional resistance coefficient increases. When Re is within 104, the frictional resistance coefficient increases as the gap-to-diameter ratio decreases, while the frictional resistance coefficient drops to the minimum when the Re exceeds 105 and the gap-to-diameter ratio is 0.027. This study can enable a better understanding of the flow characteristics of microscale RSCs under different working conditions.

Turbulence in waked wind turbine wakes: Similarity and empirical formulae

Turbulence of wind turbine wakes increases the power fluctuations and dynamic loads of downwind turbines. In this work, we analyze the large-eddy simulation (LES) data of the Horns Rev wind farm, and find that the streamwise variations of the Reynolds normal stresses in the wakes of the waked wind turbines located in different rows collapse well with each other for both rise and decay portions when they are normalized using the maxima. Empirical formulae in the form of a power function are then proposed to describe the streamwise variations of the Reynolds normal stresses for different blade spanwise positions. Notably, linear relations are observed between the exponent and the coefficient. The LES data of the two tandem wind turbine cases with different inflows and turbine spacings are then employed to test the proposed empirical formulae. The tests show that the empirical formulae can capture the downstream variations of the Reynolds normal stresses especially for the streamwise component.

Numerical simulation of the fluid flow and heat transfer of the supercritical water in the 64-element Canadian SCWR fuel bundle

ABSTRACT Canada has participated in the Generation IV nuclear energy systems focusing on the Supercritical Water-cooled Reactor (SCWR) system. The 64-element fuel rods channel is used in the Canadian SCWR. There are few publicly available experimental studies for the flow in the fuel channels with multiple fuel rods. To date, the CFD simulation reported in open literature for rod bundle flow in the 64-element SCWR is relatively scarce. The cladding surface temperature is of key importance in assessing the safety of the reactor. Since the inhomogeneities in the bundle cross-section can present complex flow phenomena, a CFD study can provide substantial insight into the flow physics. In this work, the full-scale CFD simulation of the supercritical water flow in the 64-element rod bundle was performed. The results suggest the possibility of the presence of gap vortices in the flow subchannels. Higher streamwise velocities and normal Reynolds stresses always exist at the center subchannel regions. The circumferential cladding surface temperature distribution is extremely non-uniform and there is a large difference between the maximum cladding surface temperatures for different fuel rods.

Numerical investigations of vortex dynamics and loss generation in the corner separation region of a high subsonic compressor blade

Three-dimensional corner separation seriously deteriorates the aerodynamic performance of a compressor blade. In this study, the complicated vortex dynamics and loss mechanism in the corner region of a high subsonic compressor blade (the inlet Mach number is 0.67) are investigated using large eddy simulations (LESs) at a Reynolds number (Re) of 5.6 × 105. The results show that the predicted total pressure loss and outlet flow angle match well with the experimental data, indicating that the LES method can accurately predict the size and strength of corner separation in the compressor blade. With the passage vortex rolling up and further interacting with the low-momentum fluids originating from the end wall boundary layers and the local blade boundary layers, strong shear strain induces a large-scale concentrated shedding vortex (CSV) near the spanwise location of x/H = 0.3. The formation and rolling-up of the CSV not only cause the strongest flow blockage but also strengthen the turbulence anisotropy. As the CSV moves toward the trailing edge, the strong interaction with a pair of counter-rotating vortices shed in the wake region (wake shedding vortex) further accelerates the local generation of turbulent kinetic energy (TKE). Detailed TKE budget analysis shows that the streamwise Reynolds normal stress (w′w′¯) plays the most decisive role in the TKE production term. Furthermore, we demonstrate that the strength of turbulence anisotropy is positively correlated with the TKE budget. Therefore, turbulence anisotropy should be considered carefully in predicting the loss level in the corner region of a compressor blade.

Wake flow field of a wall-mounted pipe with spoiler on a rough channel bed

This research work focuses on the wake flow region of a cylinder with a spoiler on a rough bed under steady flow conditions. The acoustic Doppler velocimetry was used for the measurement of three-dimensional velocity data for two Reynolds numbers in a fully developed turbulent flow around the cylinder with a spoiler. The mean flow velocities, second-order turbulence structures, and conditional statistics were investigated in the wake region of the spoilered cylinder. The flow was separated from the spoiler with the formation of two shear layers between free surface flow and recirculating flow. It is observed that the flow is reattaching to the bed at 11D irrespective of the Reynolds number. Downstream of the cylinder, the mean velocity distributions are asymmetric due to the wall–wake effect, and the point of inflection is observed for each velocity profile at z = 0.40ẟ. The turbulence intensities, Reynolds stresses, and TKE are highly enhanced in the wake region of the cylinder as compared to their respective upstream values for both runs. The turbulence intensities, Reynolds normal stresses, Reynolds shear stresses, and turbulent kinetic energy are attaining peaks at z = 0.4 ẟ for all the streamwise locations, and the peaks are found to be highest at x = 10D. The quadrant analysis results indicate that the sweeps are dominating bursting events in the inner and intermediate layers, while ejections are dominating in the outer layer of the wake region. As the hole size, H increases ejections stress fraction rises as compared to that of the sweeps in the wake region for z = 0.2–0.7 h.

Investigation on Circular Array of Turbulent Impinging Round Jets at Confined Case: A CFD Study

Jet impingement has immense applications in industrial cooling, such as glass tempering, turbine blades, electrical equipment, etc. The interplay in-between several jet arrangements and the effect of swirl intensity require enormous study to achieve steady heat transfer. This paper numerically investigates an inline array of 25 circular confined swirling air jets impinging vertically on a flat surface. In this regard, three-dimensional simulations are executed using the finite volume method for a number of control parameters, such as Reynolds number (Re = 11600, 24600, and 35000), impinging distance (H/D = 0.25, 0.5, 1), swirl number (S = 0.3 and 0.75) and jet-to-jet separation distance (Z/D = 2.5), where, D is the nozzle diameter. Impinging pressure distribution, flow velocity, surface Nusselt number, and Reynolds stresses are investigated for different operating conditions. The results reveal that both the wall pressure and surface Nusselt number are comparatively uniform in the case of high swirl flow. Moreover, distinct heat transfer behavior is observed from the unconfined condition for high swirl flow in which the heat transfer is constant after a certain radial distance. The Reynolds normal stress adjacent to the nozzle exit is more rigorous than the downstream regions while Reynolds shear stress varies unpredictably along the radial direction. In addition, an estimated 102 % enhancement in average Nusselt number is observed for high swirl flow, at a Reynolds number increment from 11600 to 35000. This enhancement is evident by 23 % in terms of thermal performance factor. Besides, the average Nusselt number and thermal performance factor augmented by 19 % and 8 %, respectively, for an increased swirl intensity at low a Reynolds number (Re =11600).

Numerical studies on wake and turbulence characteristics of aquaculture nets

This paper aims to understand the drag coefficient discrepancy between the equivalent-twine and twisted-twine nets based on their wake and turbulence characteristics. To that end, we conduct unsteady Reynolds-averaged Navier-Stokes (URANS) and the second-moment (Reynolds stress, RSM) simulations at a Reynolds number,Re=4.5×103, based on the effective diameter of the net twine, which corresponds to the subcritical flow regime. Then, the vortex structures and the turbulence statistics are assessed at AOA=90°. The results highlight that the wake interactions for the twisted-twine net are relatively strong compared to the equivalent-twine net, due to the disturbance of the helixes on the twisted twines. In comparison to the classical Karman vortex, the overall vortex shedding of these two nets is well organized. Symmetric vortices form behind the equivalent-twine net, while single vortices form behind the twisted-twine net. Moreover, the Reynolds normal and shear stresses show symmetric and anti-symmetric profiles. The addition of helixes to smooth circular cylinders changes the flow development, leading to a decrease of turbulence kinetic energy. With this understanding, engineers need to be carefully select the net type for preliminary design of marine aquaculture cages to avoid over- or underestimation of the drag forces.

Effects of Wall Topology on Statistics of Cube-Roughened Wall Turbulence

In this work, we carried out roughness-resolved direct numerical simulations of cube-roughened turbulent channel flows to investigate the effects of aligned and staggered arrangements, element spacings, and element orientations on the statistics of rough-wall turbulence. The results show that the equivalent sandgrain roughness, Reynolds stresses and dispersive stresses are affected by element spacings and arrangements in different ways depending on the cube orientations. Placing the roughness elements in a staggered way in general increases the equivalent sandgrain roughness, unless when the element–element interaction is insignificant for the cube orientation with wakes of short length. As for the Reynolds normal stresses and the streamwise component of the dispersive stresses (both are normalized by the total friction velocity), placing the cube elements in a staggered way decreases their maximal values when compared with the aligned arrangements. As for the effects of element spacing on the equivalent sandgrain roughness and the maximums of the Reynolds normal stresses, similar trends are observed for different element orientations and arrangements when increasing the element spacing l/r (where r is the cube height) from 2.0 to 2.8. When further increasing the element spacing l/r from 2.8 to 3.5, however, different trends are observed for different element orientations. As for the dispersive stresses, greater maximal values of their streamwise components are observed for larger element spacing for all the considered cube-roughened surfaces. For the turbulence statistics in the wake of the cube element, certain similarities are observed for different element spacings.

Evolution of Turbulence and Its Modification by Axial Casing Grooves in a Multi-Stage Axial Compressor

Abstract This experimental study examines the evolution of turbulence across an axial compressor and its modification by semicircular axial casing grooves (ACGs) at the pre-stall and near the best efficiency (BEP) flowrates. The turbulence is highly anisotropic and spatially inhomogeneous, with each normal Reynolds stress component evolving differently. Most of the observed trends can be explained by examining the dominant production rate terms. At the pre-stall flowrate, the turbulence increases significantly upon entering the rotor with peak RMS values of axial velocity fluctuations reaching as high as 71% of the mean axial velocity. The region with elevated turbulent kinetic energy (TKE) covers 30% of the outer span near the rotor leading edge, expanding to 50% near the trailing edge. While the TKE in the outer span decays rapidly in the stator, the local turbulence production persists in the stator blade boundary layer. By stabilizing and homogenizing the flow, the ACGs reduce the turbulence production, hence the TKE, in the rotor and the stator. The only exception is an increase in turbulence in the region dominated by groove–passage flow interactions. Near BEP, the TKE is much lower everywhere, except for the region influenced by the outflow from grooves. Downstream of the rotor and the stator, the turbulence level with or without ACGs are similar. The large variations in the magnitude and even the sign of the measured eddy viscosity highlight the extreme non-equilibrium conditions over the entire machine, questioning the fundamental assumptions of local equilibrium in eddy viscosity-based Reynolds stress models.

Higher-order aerodynamic numerical simulations in compressible RANS framework with inverse-ω scale variable

The use of higher-order methods to robustly compute turbulent flows governed by the multi-equation turbulence model in Reynolds-averaged Navier-Stokes (RANS) framework is a challenging topic in the computational fluid dynamics (CFD) community. In this paper, we propose two aspects of measures involving the physical model and the numerical scheme. Firstly, a λ-scale (=1/ωn) is derived instead of the well-known ω in SSG/LRR Reynolds-stress model (RSM) and SST eddy viscosity model (EVM) due to its natural boundary conditions for viscous walls and help to the positivity preservation of dissipation rate ε in turbulence equations when n=1/(2m),m=1,2,3.... Secondly, a geometric-conservation-preservation negativity-correction (GCPNC) method is proposed on the implicit time integration procedure with right-hand-side (RHS) term discretized by high-order weighted compact nonlinear schemes (WCNSs). It can guarantee the positivity of normal Reynolds stresses or turbulent kinetic energy. Numerical tests with real-life compressible flows are reported to demonstrate the robustness and accuracy of the present methods. Relevant cases include the supersonic square duct flow, the flows over delta wing, wing-body configuration and high-lift configuration.

Shear-layer dynamics at the interface of parallel Couette flows

This article aims to make a detailed analysis of co-flowing plane Couette flows. Particularly, the variation of flow quantities from the turbulent to non-turbulent region is studied. While the enstrophy exhibits a sharp jump, the other quantities (e.g., mean velocity, Reynolds normal stress, and kinetic energy) show a continuous variation across the interface. The budget analysis of Reynolds normal stresses reveals that the terms playing a key role in turbulence transportation vary depending on the Reynolds normal stress under study. The terms production, diffusion, and redistribution play an important role in streamwise Reynolds stress (u′u′¯). In the spanwise Reynolds stress (v′v′¯), the diffusion terms play a significant role. In the wall-normal Reynolds stress (w′w′¯), only the redistribution term is significant. The influence of one flow over another in the co-flow state was observed through the additional mean velocity and Reynolds normal stress found in the system compared to a standard plane Couette flow (pCf). Comparing the co-flow system with a conventional pCf system, the former exhibits greater vorticity, vortex stretching, and kinetic energy. A detailed analysis on the geometry and topology of flow structures was studied using flow invariants.

Effects of free-stream turbulence on the near wake flow and aerodynamic forces of a square cylinder

Despite a large volume of preceding studies on the effects of free-stream turbulence (FST) on the aerodynamic forces of a square cylinder, limited knowledge is available regarding the evolutionary characteristics of flow with the change of turbulence integral length scale and turbulence intensity. This paper presents a systematic experimental study of the near wake flow and aerodynamic forces of a two-dimensional (2D) square cylinder in grid-generated turbulent flows and smooth flow. Particular attention is devoted to exploring the respective influences of turbulence integral length scale and turbulence intensity. The effect of FST with a higher-level turbulence intensity than previous investigations is also investigated. The near wake flow and aerodynamic forces are studied by particle image velocimetry (PIV) and synchronous pressure measurements. The proper orthogonal decomposition (POD) analysis is also performed to further understand the effects of FST on the coherent structures of fluctuating pressures around the square cylinder. The results show that the FST with a larger turbulence integral length scale and higher turbulence intensity can cause an increase in the vortex formation length, weaker vortex shedding process and interactions between the oppositely signed vortex rows. These changes lead to significant reductions in Reynolds normal and shear stresses, turbulence kinetic energy and fluctuating lift forces. A completely different flow pattern featured with flow reattachment and reseparation is interestingly captured on the square cylinder in a highly turbulent flow with a turbulence intensity of 20%. This flow pattern results in an obvious mean pressure recovery on the side surfaces and much larger pressure fluctuations near the leading edges and fluctuating torsional moments compared to those in smooth flow and turbulent flows with lower turbulence intensities.