Turbulence Closure Research Articles

Formation and evolution of vortex breakdown consequent to post design flow increase in a Francis turbine

Draft tube flow instability encountered under off-design operating conditions in hydraulic turbines significantly limits their operational flexibility. The instability arises consequent to a higher than threshold swirl content in the runner outflow and leads to vortex breakdown phenomenon in the draft tube cone. At high load condition, the phenomenon presents as an enlarged vortex core counter-rotating with respect to the runner. The flow situation is known to compromise the turbine efficiency besides the generation of unwanted effects such as power swings and large-scale pressure fluctuations. The present paper is the first to encapsulate a thorough numerical investigation on the formation and evolution of the enlarged vortex core alongside the consequent effects. A transient operating sequence between best efficiency and high load operating points in a model Francis turbine is simulated. Turbulence closure has been attained using the shear stress transport-scale adaptive simulations turbulence model. Dynamic meshing based on a Laplacian smoothing scheme has been used to account for mesh deformation arising from guide vane motion during load change. The pressure and velocity fields have been determined and analyzed to elucidate the physics of vortex breakdown, the phenomenon underlying the formation of the enlarged vortex core. Furthermore, pressure fluctuations at salient points in the domain have been analyzed using Fourier and short-time Fourier transforms. Finally, the enlarged vortex core formed in the draft tube has been visualized through the λ2 criterion. The core takes the shape of a cork-screw like compactly wound spiral structure extending up to the draft tube elbow.

Dissipation closure of fluid turbulence from energy spectrum

Direct method of the turbulence closure consists of obtaining expression for small-scale velocity and inserting this expression in the Reynolds tensor and in the transport equations for turbulent energy, dissipation, eddy and so on, implementing some averaging. Previously such approaches were used for Burgers-Lundgren vortex. Here we used ‘naïve’ perturbation method for the transport equation for small-scale velocity incompressible fluid - the equation suggested by one of the authors earlier. It is assumed that the energy spectrum of turbulence is given.

Multi-objective optimization of a hypersonic airbreathing vehicle

Multi-objective optimization of a hypersonic airbreathing engine (scramjet technology) was carried out with the aim of maximizing thrust and minimizing drag while satisfying a series of design constraints, such as avoiding unstart (blockage of supersonic flow within the combustion chamber) by ensuring that the pressure ratio across the shock waves remains below the adverse pressure gradient given by the Korkegi limit, geometry correction to achieve shock on-lip condition, and temperature and pressure requirements at the inlet exit. Using the relations presented in the literature, pressure and viscous drag are estimated analytically. The analytical approach is verified against computational fluid dynamics data from Ansys Fluent to solve two-dimensional compressible Reynolds-averaged Navier–Stokes flow equations, with transition shear stress transport as the turbulence closure model. Comparing the total drag and the flow properties at the combustion chamber entrance shows the model's feasibility for the optimization approach. Three different approaches were conducted to formulate the multi-objective function to determine the one that can find the highest number of geometries satisfying the Korkegi limit with the highest net thrust. The best approach was the multi-objective function formulated with the uninstalled thrust, total pressure recovery, and pressure drag, concentrating the search in the region with greater uninstalled thrust and lower drag and nearly doubling the value of net thrust compared to the first formulation, which uses the uninstalled thrust, pressure drag, and viscous drag.

Perspectives toward Stochastic and Learned-by-Data Turbulence in Numerical Weather Prediction

Abstract The increased social need for more precise and reliable weather forecasts, especially when focusing on extreme weather events, pushes forward research and development in meteorology toward novel numerical weather prediction (NWP) systems that can provide simulations that resolve atmospheric processes on hectometric scales on demand. Such high-resolution NWP systems require a more detailed representation of the nonresolved processes, i.e., usage of scale-aware schemes for convection and three-dimensional turbulence (and radiation), which would additionally increase the computation needs. Therefore, developing and applying comprehensive, reliable, and computationally acceptable parameterizations in NWP systems is of urgent importance. All operationally used NWP systems are based on averaged Navier–Stokes equations, and thus require an approximation for the small-scale turbulent fluxes of momentum, energy, and matter in the system. The availability of high-fidelity data from turbulence experiments and direct numerical simulations has helped scientists in the past to construct and calibrate a range of turbulence closure approximations (from the relatively simple to more complex), some of which have been adopted and are in use in the current operational NWP systems. The significant development of learned-by-data (LBD) algorithms over the past decade (e.g., artificial intelligence) motivates engineers and researchers in fluid dynamics to explore alternatives for modeling turbulence by directly using turbulence data to quantify and reduce model uncertainties systematically. This review elaborates on the LBD approaches and their use in NWP currently, and also searches for novel data-informed turbulence models that can potentially be used and applied in NWP. Based on this literature analysis, the challenges and perspectives to do so are discussed.

Rheology-based wall function approach for wall-bounded turbulent flows of Herschel–Bulkley fluids

Modeling fully developed turbulent flow for Herschel–Bulkley (HB) fluids in pipes is a long-standing challenge. Existing semi-empirical, theoretical, and numerical methods are either inconsistent with experimental data or are validated for low Reynolds numbers. This study focuses on validating a novel approach using rheology-based wall functions within Reynolds-averaged Navier–Stokes solvers. Simulations of wall shear stress and velocity profiles were conducted across a wide range of Reynolds numbers using a single-phase HB fluid, with measurements taken both upstream and downstream of a 90° pipe bend. Two turbulence closure models, the k–ε model and the Reynolds stress model, were employed with the wall function implemented as a specified shear boundary condition. Results demonstrate significant improvements over the Newtonian-based models, such as standard wall function by Launder–Spalding or with available semi-empirical models, achieving strong statistical correlations and minimal deviation (from the experimental findings) at high Reynolds numbers. The study also examines the utility of the wall viscosity Reynolds number and assesses the reliability of semi-empirical models for HB fluids. These findings offer valuable insights for enhancing modeling accuracy in complex fluid flow scenarios, with potential applications spanning industries like mining, chemical processing, petroleum transportation, and sanitation systems, providing practical alternatives to costly experimental procedures in pipe systems.

Numerical simulations of flow inside a stone protection layer with a modified k-ω turbulence model

A numerical model is developed to investigate the flow in porous media, for the purposes of simulating scour protection around coastal and offshore structures. In the present model, the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations are solved, coupled with the volume-averaged k-ω turbulence closure. The volume-averaged k-ω equations are derived by taking the spatial average of the standard k-ω equations. The unknown coefficients caused by the averaging procedure are determined by large eddy simulation (LES). The developed model is validated against existing experimental results of flow in stone covers under both oscillatory and steady current conditions. A gradual transition of porosity towards unity at the interface between the porous media and the free flow is assumed in the simulation to fit the irregular interface in practical engineering. In the presence of parabolic porosity variation at the interface, the calculated velocity profile, bed shear stress, and turbulent fluctuations inside the porous medium are compared to measurements. The numerical results match well against the experimental data. Comparison with the volume-averaged k-ε turbulence model shows that the volume-averaged k-ω turbulence model provides more accurate flow behavior within the porous media.

Improvements in the Prediction of Steady and Unsteady Transition and Mixing in Low-Pressure Turbines by Means of Machine-Learnt Closures

Abstract In this article, novel machine-learnt transition and turbulence models are applied to the prediction of boundary-layer transition and wake mixing in a low-pressure turbine (LPT) cascade, including unsteady inflow cases with incoming wakes. A laminar kinetic energy (LKE) transport approach is employed as baseline transition framework. The application of the machine-learnt explicit algebraic Reynolds stress models (EARSMs) takes advantage of a zonal strategy based on a newly developed sensing function that allows automated wake demarcation. This work compares the performance of several approaches that are based on the application of improved transition models without machine learnt EARSMs, baseline transition model with EARSMs trained for improved wake mixing, and new transition and turbulence closures that are simultaneously developed in a fully coupled way and aimed at improving both transition and wake mixing predictions in LPTs. The investigation is carried out on a cascade of industrial footprint, representative of modern LPT bladings. First, the various modeling frameworks are evaluated, without bar wakes (steady conditions), over a wide range of Reynolds number values. Unsteady Reynolds-averaged Navier–Stokes (URANS) analyses have also been carried out to investigate the predictive capabilities of machine-learnt closures in the presence of incoming bar wakes. Reynolds-averaged Navier–Stokes (RANS)/URANS results are scrutinized against large eddy simulation (LES) calculations and experimental data. It will be demonstrated that machine-learnt EARSMs are capable of producing realistic wake mixing when simply applied on top of the baseline transition models. However, the most accurate predictions will be shown to be provided by fully integrated machine-learnt transition/turbulence closures.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics.

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

Large-eddy-model closure and simulation of turbulent flux patterns over oasis surface

Abstract. Large-eddy simulations (LESs) have been increasingly used for studying atmosphere and land surface interactions over heterogeneous areas. However, parameterizations based on Monin–Obukhov Similarity Theory (MOST) often violate the basic assumptions of the very theory, generate inconsistencies with the LES turbulence closures, and produce surface flux estimates depending on LES model resolutions. Here, we propose a novel scheme for turbulent flux estimates in LES models. It computes the fluxes locally using the LES subgrid closure, which is then constrained on the macroscopic scale using MOST. Compared with several other schemes, the new scheme performs better for the various types of land surfaces tested. We validate our scheme by comparing surface flux estimates with field measurements obtained over an oasis surface at various height levels. Additionally, we scrutinize other quantities related to the surface energy balance, including net radiation, ground heat flux, and surface skin temperature, all of which align well with observational data. Our sensitivity experiments, focusing on model horizontal resolution, underscore the robustness of our scheme, as it maintains its corrective efficacy despite changes in horizontal grid spacing. We find that the macroscopic constraint imposed by MOST on LES-estimated fluxes strengthens as the horizontal grid spacing decreases, with a more pronounced influence on sensible than latent heat fluxes. These findings collectively highlight the promise and adaptability of our scheme for improved surface flux estimates in LES models.

Optimization-Inspired Pin-Fin Array for Supercritical Carbon Dioxide Recuperator

Additively manufactured heat exchangers are one possible route to cost-effective sCO2 power cycles. In this paper, experimental results are obtained for two helical pin fin tubes that were designed following parametric optimization of the fin array. Neither the numerical optimization nor the experimental testing have been previously reported in the literature. The two tube designs were, (1) the optimization inspired design, and (2) the optimization-inspired design with a fin diameter increased by a factor of 2. To characterize the print, the designs were scanned using X-ray computed tomography to measure feature sizes and heat transfer area. The optimization was conducted in a commercial, computational fluid dynamics code. The code solved the Reynolds Averaged Navier-Stokes (RANS) and energy equations with turbulence closure provided by the shear stress transport (SST) k-ω model. In the experiments, the Nusselt number augmentation was measured using the Wilson plot technique and the friction factor was determined with mass flow and pressure drop measurements. The experimental testing indicated that the optimization-inspired design had a friction factor that was four times less than the baseline tube design at equal Nusselt number. Additionally, the optimization-inspired design had a 14% improvement in Nusselt number, at equal friction factor, relative to the best performing computational fluid dynamics (CFD) trial points. Tube design (2), with the larger diameter pin fins, had similar performance, within experimental error, as the tube with the smaller diameter pin fins (1). Both tubes achieved overall fin array efficiencies near 1. A performance factor, V/V0, equal to the volume of the enhanced heat exchanger divided by the volume of the baseline (no-fins) heat exchanger, is recommended to quantify internal cooling performance. The experimental shell and tube heat exchanger, using the additively manufactured tube, is competitive with printed circuit heat exchangers in its pressure drop class and could be further improved by optimizing a shell-and-tube heat exchanger utilizing this heat transfer enhancement feature.

Effects of porous structures on point source dispersion across the sediment–water interface

Abstract Understanding the transport of point source solutes across the sediment–water interface (SWI) is important for the protection of river environments. Conventional coupled models assume the porous media layer as Darcy's laminar flow and therefore cannot accurately capture the transport processes within the porous media. Furthermore, the effect of the porous structure of the riverbed on the transport process is largely unknown. In this study, we performed pore-scale numerical simulations of point source solutes transport across the SWI to investigate the effects of different porous structures in the riverbed on flow and point source dispersion. By solving the Reynolds-averaged Navier–Stokes equations with the k–ω shear stress transport turbulence closure model, we determine the complex flow field information and the spatial distribution of point source solutes for the coupled model. The results indicate that the presence of porous structures creates recirculation zones in the coupled model, which prevents turbulent structures reaching deeper layers. Random porous structures induce more preferential flow, inhibit the formation of recirculation zones, and exhibit higher solute dispersion, which is directly related to turbulent solute fluxes. Furthermore, our study reveals that the release position of point sources significantly influences the distribution of solute concentrations within the porous bed.

A comparative study of internal heat transfer enhancement of impingement/effusion cooling roughened by solid rib and slit rib

In the present study, we conducted a conjugate heat transfer (CHT) analysis for double-wall cooling with impingement and effusion, incorporating various types of ribs, using the Reynolds-averaged Navier–Stokes (RANS) method and the modified shear stress transport (SST) turbulence closure model (SST-KIC), accounting for the Kato-Launder modification (K), intermittency (I), and crossflow (C) transition effects. We comprehensively discussed the impact of slit type (parallel, inclined, convergent, and divergent), open-area ratio (β = 5%, 20%, and 40%), and jet Reynolds number on the turbulent flow and heat transfer in a double-wall cooling with slit ribs. Our findings indicated that the introduction of slit ribs significantly improved heat transfer and its uniformity on the target wall, albeit with a slight increase in pressure loss. The overall Nusselt number and thermal-hydraulic performance (THP) in cases with slit ribs gradually decreased with β, yet remained up to 17% and 13% higher than those observed on a smooth target wall. Notably, the open-area ratio of the slit rib exhibited a more pronounced effect on heat transfer over the target plate. For the divergent slit rib within the Reynolds number range of 4000–16 000, the heat transfer enhancement ratio reached the highest value at β of 0.05. In addition, we computed the entropy production caused by fluid friction and heat transfer, as well as the overall entropy production in double-wall cooling at different β and Re. The analysis revealed that the slit rib target plate performed better than the solid rib target plate, showing a distinct advantage in terms of total entropy production.

Active Air Injection Control to Enhance Performance of Hollow-bladed Axial Fan: A Numerical Study

Nowadays, axial fans participate in the most important areas of industry and research, including aviation, navy, wind tunnels, cooling towers, and even automobiles. Thus, more emphasis has been placed on improving their aerodynamic performances. It is important to notice that the parameters involved in designing a fan are mainly concerned with aeraulic power, torque and efficiency. This study investigates the utilization of flow control techniques to improve performances of an axial fan equipped with hollow blades, shroud, and hub. These features grant the fan crucial characteristics, namely, its lightweight and facilitate the blowing action by taking advantage on its hollow parts. The fan's performance is evaluated using a steady RANS numerical model with a k-ω SST turbulence closure, which was validated with experimental data. An active control air blowing through a slot was introduced with various positions and dimensions. The results demonstrate a significant improvement in the fan's performance, with an up to 56% increase in aeraulic power gain, accompanied by changes in the overall flow topology, noticed by closely analyzing the flow structure near the tip clearance.

A New Hybrid Mass‐Flux/High‐Order Turbulence Closure for Ocean Vertical Mixing

AbstractWhile various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first‐order closure schemes such as the K‐Profile Parameterization (KPP) lack energetic constraints; two‐equation models like directly solve an equation for the turbulent kinetic energy but do not account for non‐diffusive fluxes, and high‐order closures that include the high‐order transport terms are computationally expensive. To address these, we extend the Assumed‐Distribution Higher‐Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second‐order and higher‐order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non‐diffusive fluxes without the computational cost of a full higher‐order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and for surface buoyancy‐driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results.

Fast macroscopic forcing method

The macroscopic forcing method (MFM) of Mani and Park [1] and similar methods for obtaining turbulence closure operators, such as the Green's function-based approach of Hamba [2], recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has already been used to successfully quantify Reynolds-averaged Navier–Stokes (RANS)-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Schäfer and Owhadi [3] to recover elliptic integral operators from a polylogarithmic number of matrix–vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix–vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first “peels” long-range effects with dense matrix–vector products to expose a more local operator. We demonstrate the algorithm's performance for the eddy diffusivity and eddy viscosity operators, which correspond to the unclosed parts of the ensemble-averaged transport equations, excluding the analytically known, closed parts of such equations. However, the algorithm can also be applied to the full operators. We focus on scalar transport in a laminar channel flow and momentum transport in a turbulent channel flow. For these problems, we recover eddy diffusivity- and eddy viscosity-like operators, respectively, at 1% of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13% for the turbulent one. Applying these operators to compute the averaged fields of interest has visually indistinguishable behavior from the exact solution. Our results show that a similar number of simulations are required to reconstruct the operators to the same accuracy under grid refinement. Thus, the accuracy corresponds to the physics of the problem, not the numerics, so long as the grid is sufficiently refined. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity, and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

The impact of lake shape and size on lake breezes and air-lake exchanges on Titan

Titan, the largest moon of Saturn, has many lakes on its surface, formed mainly of liquid methane. Like water lakes on Earth, these methane lakes on Titan likely profoundly affect the local climate. Previous studies (Rafkin and Soto, 2020; Chatain et al., 2022) showed that Titan's lakes create lake breeze circulations with characteristic dimensions similar to the ones observed on Earth. However, such studies used a model in two dimensions; this work investigates the consequences of the addition of a third dimension to the model. Our results show that 2D simulations tend to overestimate the extension of the lake breeze over the land, and underestimate the strength of the subsidence over the lake, due to divergence/convergence geometrical effects in the mass conservation equations. In addition, 3D simulations including a large scale background wind show the formation of a pocket of accelerated wind behind the lake, which did not form in 2D simulations. An investigation of the effect of shoreline concavity on the resulting air circulation shows the formation of wind currents over peninsulas. Simulations with several lakes can either result in the formation of several individual lake breeze cells (during the day), or the emergence of a large merged cell with internal wind currents between lakes (during the night). Simulations of several real-shaped lakes located at a latitude of 74°N on Titan at the autumn equinox show that larger lakes trigger stronger winds, and that some sections of lakes might accumulate enough methane vapor to form a thin fog. Additionally, we adapted the Turbulent Kinetic Energy closure scheme of the model to better represent the extremely low turbulence at the surface of Titan, of 2 10−4 m2.s−2 above the land, and inferior to 3 10−5 m2.s−2 above the lake. The addition of a third dimension, along with adjustments in the parametrizations of turbulence and subsurface land temperature, results in a reduction in the magnitude of the average lake evaporate rate, namely to ∼6 cm/Earth year.

Flow and thermal fields modeling in jet impingement configurations using a Reynolds stress turbulence closure within the RANS and Sensitized-RANS framework

The flow and thermal field characteristics underlying turbulent convective heat transfer in two reference configurations, representing a jet exiting a planar slot and a circular tube and impinging on a heated wall, are studied computationally. The performance of a conventional Reynolds Stress Model (RSM) and its scale-resolving variant, employed in the context of a time-accurate Reynolds-Averaged Navier–Stokes (RANS) simulation, is investigated in conjunction with different modeling approaches for the turbulent heat flux uj′θ′¯, whose gradient represents the turbulence-induced heat source in the temperature transport equation. In this so-called Sensitized-RANS modeling strategy, employing an improved eddy-resolving instability-sensitive Reynolds Stress Model (IISRSM, Jakirlić and Maduta (2015)), the unresolved ‘sub-scale’ turbulent correlations represent the solutions of a set of corresponding transport equations for the entire stress tensor ui′uj′¯. The turbulent scalar-flux models follow from the classical gradient-diffusion approach with the diffusion-like coefficients formulated as a function of both the scalar eddy-viscosity and the anisotropic Reynolds stress tensor. The latter model expressions also take into account various non-linear relationships in terms of turbulent stress components. The computational results of the fully-developed channel flow, featured only by the mean shear and constant wall heat flux, representing a preliminary investigated flow configuration, agree very well with the corresponding DNS (Direct Numerical Simulation) database for both RSM versions in conjunction with all the turbulent heat flux models adopted. However, the study of the two flow impingement cases with the different structure of the impinging jet and nozzle-to-wall distance variations, characterized by a much more complex flow straining, using the considered conventional Reynolds stress model shows significantly different results for the Reynolds stress and thermal fields compared to the available DNS data, especially in the immediate impact region manifested by a significant overprediction of the turbulence intensity. In contrast, the IISRSM-relevant results for the mean flow and temperature fields, the associated integral characteristics, and the corresponding turbulence quantities are in very good agreement with the reference DNS data, due to the much higher predictive capabilities of this eddy-resolving turbulence model compared to its baseline counterpart.

Interrelationships of entropy production and turbulence kinetic energy associated with simple angle and compound angle full coverage film cooling

The present paper compares experimentally-measured distributions of entropy generation with numerically-predicted distributions of streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy. These comparisons are provided for two full-coverage film cooling environments which are designed to model the thermal management arrangements employed for combustor liners within gas turbine engines. One of these arrangements includes alternating compound angle values of +30° in one row of holes, followed by −30° in the next row of holes. The other arrangement includes simple angle holes with a zero degree compound angle value. The associated full-coverage film cooled boundary layers are investigated within a double-wall cooling test facility wherein the air for each full-coverage film cooling arrangement is provided by an impingement jet array. Experimentally-measured entropy generation values are obtained from film cooled boundary layer measurements of local total pressure variations, obtained in isothermal flow, relative to the freestream values outside of the boundary layer. The resulting entropy generation values quantify second law losses, which are associated with aerodynamic gains. To obtain the associated numerical-prediction results for a steady-state, three-dimensional flow field, employed is the ANSYS FLUENT Version 2022 R2 computational code with a SST k–ω turbulence closure model. The resulting comparisons of entropy generation, streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy are provided for a blowing ratio BR of 2.9 for simple angle film cooling with a main flow Reynolds number Rems of 138,000, and for compound angle film cooling with a main flow Reynolds number Rems of 142,000. Overall, evidence is provided of strong relationships between local turbulence kinetic energy and local entropy production since the two quantities are highly correlated with each other over s substantial range of experimental conditions and configurations. For example, ratio of turbulence kinetic energy to entropy generation data collapse for Z/de values from 0 to 3.5 for Y/de = 0.5, Y/de = 1.5, and both film cooling arrangements. Here, the value of the TKE/Sgen ratio is approximately constant for these conditions, which evidences direct and simple dependences of local turbulence kinetic energy upon local entropy generation, even for lower magnitudes of Z/de. The direct and simple dependences of local turbulence kinetic energy upon local entropy generation are further illustrated by the simplicity of linear correlation equations, which represent physical behavior for different conditions and configurations. These correlation equations are developed for three arrangements, which are associated with X/de = 54.54.

Improved prediction of turbomachinery flows using Reynolds stress model with [formula omitted] transition model

Transition is a prominent flow phenomenon in turbomachinery, especially at low and moderate Reynolds numbers. The turbomachinery internal flow often encounters complex vortex structures, typically accompanied by strong turbulence anisotropy and non–equilibrium. Conventional Reynolds–averaged Navier–Stokes (RANS) modeling with linear eddy–viscosity models (LEVMs) may fail short in capturing certain complex flow features. The Reynolds stress model (RSM) based on a higher turbulence closure level has more potential to reasonably consider turbulence anisotropy and non–equilibrium for such complex flows within turbomachinery than the LEVMs. However, the current RSM lacks an effective representation of transition phenomena. This paper presents an improved prediction of turbomachinery flows using RSM with transition modeling. The transition effects are incorporated into the RSM (SSG/LRR–ω model) via Menter's γ transport equation. The blending of the SSG/LRR–ω model with the γ transition model (SSG/LRR–ω–γ model) is firstly validated based on the T3 series flat plate cases with zero pressure gradient (T3A, T3B, T3A–) and variable pressure gradients (T3C1–C5). Comparisons with experiments show that the SSG/LRR–ω–γ model predicts corner separation flows with transition more accurately, although there is still room for further improvement. Then, the performance of the SSG/LRR–ω–γ model is assessed in a linear highly loaded prescribed velocity distribution (PVD) cascade and a NACA65 K48 compressor cascade. Comparisons with experiments indicate that, in both compressor cascades, the SSG/LRR–ω–γ model can predict more accurately corner flows with boundary layer transition on suction surfaces than the SSG/LRR–ω and SST model. Nevertheless, it still exhibits a tendency to overestimate the size of corner separation, especially in cases characterized by strong adverse pressure gradients. Comparisons of skin friction and velocity profiles predicted by the SSG/LRR–ω model with and without transition modeling illustrate the rationale behind the improved prediction. Further improvement of the SSG/LRR–ω–γ model for predicting turbomachinery corner flows should be conducted in future.

Impact of PBL schemes on multiscale WRF modeling over complex terrain, Part I: Mesoscale simulations

This study investigates the performance of two commonly used planetary boundary layer (PBL) schemes, the local turbulence closure (Mellor-Yamada-Janjić: MYJ) and the nonlocal turbulence closure (Yonsei University: YSU), over the tropical coastal region of Shenzhen, China, using the Weather Research and Forecasting (WRF) model. The simulation results are evaluated by comparing them to various measurements. Additionally, we also investigate the performance of the PBL schemes over different land cover types and their ability to reproduce the physical relationships between several pairs of interrelated near-surface atmospheric parameters. The results show that both PBL schemes underestimate temperature and PBL height and overestimate wind speed and turbulent fluxes throughout the whole day, but this can be improved by increasing horizontal resolution. We find that the overestimation of wind speed and turbulent heat fluxes is mainly caused by the strong mechanical mixing in the model. Some improvements are required such as more accurate surface morphology parameters and momentum transport coefficients. Overall, the YSU scheme outperforms the MYJ scheme at all horizontal resolutions over complex terrain in terms of near-surface variables, PBL vertical structures, and the internal relations between turbulent heat fluxes and atmospheric instability. However, the difference between the two PBL schemes, varying over different land covers and with time periods and altitudes within the PBL, is generally greater over the land than over the sea for thermal-related variables (especially during daytime), while for variables associated with water vapor is the opposite. This highlights the importance of the underlying surface for the performance of PBL schemes and the need to select appropriate PBL schemes for simulating the evolution of PBL processes over different land covers.