Turbulence Closure Research Articles

The Effect of Weber Number on Spray and Vaporization Characteristics of Liquid Jets Injected in Air Crossflow

AbstractThis paper details a numerical investigation conducted to systematically evaluate the effects of aerodynamic Weber number, in the range from 68 to 136, on spray characteristics and gaseous fluid dynamics when liquid jets are injected in high-temperature air crossflow. The momentum flux ratio and air temperature for all the cases studied in this research effort are 9 and 573 K, respectively. The computations are conducted using an Eulerian–Lagrangian framework, where the gas phase is modeled by the compressible form of the Navier–Stokes equations and the liquid phase is treated in the Lagrangian frame with appropriate models to account for jet injection and breakup phenomena. A modified version of two-way coupling, which takes into account the finite size of the dispersed phase, is used to account for the exchange of mass, momentum, energy and species between the two phases. Turbulence closure is achieved using the large eddy simulation technique. As a first step, the framework is validated against measurements for non-vaporizing and vaporizing conditions—our results agree well with experimental data. Next, three computations in the range of Weber numbers mentioned above are conducted—the effect of Weber number is quantified in terms of the spatiotemporal evolution of the mass fraction of the vaporized liquid, detailed distributions of droplet sizes, their velocities, and volumetric fluxes. It is found that with an increase in the Weber number, the droplet sizes and the penetration depth monotonically decreased. As a result, at higher Weber number conditions, the vaporized liquid in the domain increases due to the overall enhancement in the effective surface area of the liquid phase.

Machine-learning energy-preserving nonlocal closures for turbulent fluid flows and inertial tracers

Machine learning turbulence closures for non-homogeneous and non-isotropic flows is a challenging task. The novelty of the presented approach is the adoption of a universal constraint associated with the energy preservation of the nonlinear terms, which is valid for any turbulent system. This constraint is embedded in the training process, and in combination with nonlocal representations in space and time, results in significant improvement for the resulted coarse scale models.

Reynolds stress turbulence modelling of surf zone breaking waves

Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$turbulence closure model for this purpose, where$\omega$is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.

Comparison among the Turbulence Models to Simulate Flow Pattern over ogee Spillway Case Study (Mandali dam in Iraq)

The spillway is an important structure in the dams, used to pass the flood wave to the downstream safely. In the past decades, Computational fluid dynamics (CFD) has evolved. Research findings have shown the CFD models are a great alternative for laboratory models. According to it, the flow pattern over ogee spillways can be studied in a short time and without paying high expenses. Because the flow over the ogee spillway is turbulent and has a free surface, its properties are complex and often difficult to predict. Therefore, the present paper focuses on the study of turbulence closure models including the standard k-ε, RNG k–ε, k–ω, also, the large-eddy simulation (LES) models, to assess their performance to simulate flow over the spillway. The Flow-3d software with the volume-of-fluid (VOF) algorithm is applied to obtain the free surface for each turbulence model. The results of the analysis show that the LES model yielded better results when compared with laboratory results, while the turbulence closure models result of Reynold average Navier Stocks equations (RANS) was more stable, especially standard k-ɛ and RNG models.

A study of the heat transfer of an atomizer gas jet impinging perpendicular on a circular cylinder

This contribution presents the methodology and results from an experimental and numerical study of the heat transfer behavior of the gas-only jet flow from a close-coupled atomizer (CCA) configuration impinging on a heated cylindrical surface. A set of experiments are conducted under different operating conditions (gas pressures 0.6, 0.8 and 1.0 MPa) to measure the local heat transfer coefficient (HTC) on the surface of the cylinder by recording the cooling curve at specific locations along circumferential and axial directions. The numerical study of the heat transfer is executed by employing computational fluid dynamics (CFD) under the same conditions as in the experiments. The Transition SST model is selected for turbulence closure as it obtained results most close to the experimental ones. Predictions of HTC on the cylindrical surface are derived from this model with variable parameters, i.e., nozzle-to-substrate distance (110, 130 and 150 mm), diameter of the cylinder (80, 100, 120 mm) and the temperature difference between the cylinder and ambient temperature (20–730 K). In addition, the gas flows from a circular nozzle and the atomizer configuration with same exit area are compared by the CFD simulation, which shows that the gas jet flow becomes self-similar when the distance to the nozzle is > 80 mm. The experimental and numerical results both show that at each measured position the heat flux q˙ obtains a linear relationship with the temperature difference. The fitted line in the stagnation region has a small negative intercept while that at other positions is close to 0. The local HTC variation in the circumferential and axial directions on the cylinder surface and the parameters affecting the distribution of the HTC are outlined and discussed.

Numerical investigation of the interaction between the moving plate and sediment plume

A two-phase mixture model solver for simulating sediment plume and moving plate interaction is established based on the OpenFOAM. This solver treats the coupling of fluid and sediment as a mixture term according to each phase's volume fraction (or mass fraction) and incorporates with the RANS, LES, and Hybrid RANS/LES methods for turbulence closure. The arbitrary coupled mesh interface (ACMI) method is utilized to deal with the displacement of the plate over longer distances. The solver is validated against existing experiments (settling of particles cloud and sediment plume\\moving plate interaction) and corresponding Smooth Particle Hydrodynamics (SPH) simulation study. The results show a good agreement with others, and the influence of the mesh resolution and the comparison between CFD results and the SPH results are discussed. Furthermore, the sediment plume/moving plate study is extended to three-dimensional numerical simulations. The Ω method is used for vortex identification. The distribution of sediment concentration, the lift and drag on the moving plate, and the characteristics of vortex structure simulated by different turbulence models are compared and analyzed.

On the properties of energy flux in wave turbulence

We study the properties of energy flux in wave turbulence via the Majda–McLaughlin– Tabak (MMT) equation with a quadratic dispersion relation. One of our purposes is to resolve the inter-scale energy flux $P$ in the stationary state to elucidate its distribution and scaling with spectral level. More importantly, we perform a quartet-level decomposition of $P=\sum _\varOmega P_\varOmega$ , with each component $P_\varOmega$ representing the contribution from quartet interactions with frequency mismatch $\varOmega$ , in order to explain the properties of $P$ as well as to study the wave turbulence closure model. Our results show that the time series of $P$ closely follows a Gaussian distribution, with its standard deviation several times its mean value $\bar {P}$ . This large standard deviation is shown to result mainly from the fluctuation of the quasi-resonances, i.e. $P_{\varOmega \neq 0}$ . The scaling of spectral level with $\bar {P}$ exhibits $\bar {P}^{1/3}$ and $\bar {P}^{1/2}$ at high and low nonlinearity, consistent with the kinetic and dynamic scalings, respectively. The different scaling laws in the two regimes are explained through the dominance of quasi-resonances ( $P_{\varOmega \neq 0}$ ) and exact-resonances ( $P_{\varOmega =0}$ ) in the former and latter regimes. Finally, we investigate the wave turbulence closure model, which connects fourth-order correlators to products of pair correlators through a broadening function $f(\varOmega )$ . Our numerical data show that consistent behaviour of $f(\varOmega )$ can be observed only upon averaging over a large number of quartets, but with such $f(\varOmega )$ showing a somewhat different form from the theory.

Numerical Studies on Turbulent Flow Field in a 90 deg Pipe Bend

Abstract This paper deals with the modeling of turbulent flow through a 90 deg pipe bend using an unsteady Reynolds-averaged Navier–Stokes (U-RANS) approach where k–ε model is used for turbulence closure. While limitations in solving complex flows of the k–ε model have been reported in the literature, this study demonstrates that for pipe flows with curvature, the k–ε model performs reasonably well. Investigations have been carried out to find out the influence of Reynolds number (Re) and bend curvature ratio (Rc/D) on turbulent flow parameters, namely, instantaneous axial velocity, turbulent kinetic energy, turbulent intensity, and wall shear stress. Bend curvature is found to strongly influence the turbulent flow characteristics, while no such high Reynolds number dependency is observed in this study range. In general, this paper presents a computationally cost-effective numerical study on the time averaged turbulent flow field in a 90 deg pipe bend, which may be used for the design and development of 90 deg pipe bends at a high Reynolds number regime.

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

AbstractFlow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Wind Tunnel Investigation and Numerical Analysis of Fume Behavior in the Vicinity of Rectangular Building Under Moderate Velocity Wind

Abstract A research was conducted to examine the dispersion of pollutants ejected from a chimney around three-dimensional rectangular building. Regarding the experimental study, the wind tunnel experiment comprises data acquired through the dispersion of continuous source tracer discharges from a punctual source situated in a regular network of building-like obstacle, and these data include measurements of mean velocity and turbulence parameters. The relevant data are followed using Particle Image Velocimetry to track various instantaneous and mean dynamic characteristics. Concerning the numerical study, the suggested model simulates both the dynamics and the heat transfer flow field using the overall mean three-dimensional Navier-Stokes equations with an RSM turbulence closure model. The findings of a deep comparison of turbulent flow and dispersion between a full wind tunnel experiment and the model predictions are reported. A high degree of concordance was obtained with the experimental flow and numerical simulation data. The detailed investigation, in which numerical and wind tunnel studies, was performed to evaluate the impact of wind velocity on the pollutant dispersion issued from a chimney around the building in their vicinity. the results clearly showed how wind velocity influenced the environmental air flows and pollutant dispersal pathways. The results of this study show that the shape of the building and the resulting interaction between the wind structure play a determining factor in the distribution of pollutants around a building, thereby affecting the air quality in the various parts of the building.

Modelling of waves and wave-induced currents in the vicinity of submerged structures under regular waves using nonlinear wave-current models

The evolution of waves and wave-induced currents around submerged structures under regular waves is simulated using two nonlinear wave-current models (Boussinesq-type); coupled with a one equation turbulence closure model to simulate the energy dissipation due to wave breaking. The first model is utilized to simulate the evolution of waves and wave-induced currents around porous structures, while the second model is used to simulate those around impermeable structures. The equation of motion for the porous medium in the first model incorporates an empirical Forchheimer-type term for laminar and turbulent frictional losses and inertial term to account for acceleration effects. In both models, an artificial energy dissipation term is introduced to overcome unrealistic flow patterns and surface water fluctuations, which lead to numerical instabilities near steep faces of submerged structures. In the present study, an improved wave breaking sub-model is introduced in 2DH, and the predictive skills of two improved models are investigated with a published and a new set of experimental data. The comparison between simulations and laboratory data show promising results for the wave height, mean-water level and current distribution around submerged structures for 2DH wave propagation.

Large Flow Separations around a Generic Submarine in Static Drift Motion Resolved by Various Turbulence Closure Models

A thorough numerical introspection for assessing the particular issues of large flow separations around a submersible hull by using various turbulence models is described. The generic Defense Advanced Research Projects Agency (DARPA hereafter) Suboff hull is considered in the present study. Detailed descriptions of the mathematics behind the hybrid Shear Stress Transport (SST), Detached Eddy Simulation (DES) and the Improved Delayed Detached Eddy Simulation (IDDES) are given. The ISIS solver of the FineTM/Marine package is used to solve the flow problems. An adaptive mesh refinement is employed for resolving the flow inside the areas hosting significant flow gradients. Two sets of computations are analyzed: one refers to the straight-ahead course, whereas the other is focused on the static drift motions. Four angles of incident flow and three different incoming flow velocities are proposed for clarifying the details of the flow separation. Extensive grid convergence tests are performed for both working regimes and for all the meshes used in the present investigation. Extended verification and validation (V&V hereafter) of the numerical approach is performed through extensive comparisons with the experimental data. Global hydrodynamic performance of the hull as well as the local flow features are discussed in detail. The study is concluded by a series of final remarks aimed at providing useful information for further similar investigations.

Wind Profile in the Wave Boundary Layer and Its Application in a Coupled Atmosphere‐Wave Model

AbstractCurrent models cannot capture well the impacts of wind waves on the atmospheric boundary layer. Here, we proposed a new turbulence closure model to estimate the wind stress in the wave boundary layer from viscous stress, shear‐induced turbulent stress, wind‐sea induced stress, and swell‐induced upward stress separately. The misalignment between the wind stress and wind is also considered in the model. Single‐column simulations indicate that (a) the swell‐induced upward momentum flux increases the surface wind and changes the wind direction, (b) the misalignment between the upward momentum flux and wind has a more significant impact on the wind profile than that from the downward momentum flux, and (c) the impact of swell‐induced upward momentum flux decreases with atmospheric convection. The proposed closure scheme was implemented into an atmosphere‐wave coupled model. A month‐long simulation over the ocean off California shows that the surface wind can be altered up to 5% by ocean surface gravity waves.

Dynamic tensorial eddy viscosity model: Effects of compressibility and of complex geometry

A previous paper by Cimarelli et al. [“General formalism for a reduced description and modelling of momentum and energy transfer in turbulence,” J. Fluid Mech. 866, 865–896 (2019)] has shown that every decomposition of turbulent stresses is naturally approximated by a general form of tensorial eddy viscosity based on velocity increments. The generality of the formalism is such that it can also be used to give a reduced description of subgrid scalar fluxes. In the same work, this peculiar property of turbulent stresses and fluxes has been dynamically exploited to produce tensorial eddy viscosity models based on the second-order inertial properties of the grid element. The basic idea is that the anisotropic structure of the computational element directly impacts, although implicitly, the large resolved and small unresolved scale decomposition. In the present work, this new class of turbulence models is extended to compressible turbulence. A posteriori analysis of flow solutions in a compressible turbulent channel shows very promising results. The quality of the modeling approach is further assessed by addressing complex flow geometries, where the use of unstructured grids is demanded as in real world problems. Also in this case, a posteriori analysis of flow solutions in a periodic hill turbulent flow shows very good behavior. Overall, the generality of the formalism is found to allow for an accurate description of subgrid quantities in compressible conditions and in complex flows, independent of the discretization technique. Hence, we believe that the present class of turbulence closures is very promising for the applications typical of industry and geophysics.

Assessment of Finite-Rate Chemistry Effects in a Turbulent Dilute Ethanol Spray Flame

Simulations of a benchmark ethanol dilute spray flame are performed with four combustion models at different levels of closure for turbulence–chemistry interaction (TCI) to provide a head-to-head comparative analysis on the closure effects of TCI. The evaluation is performed in the context of Reynolds-averaged Navier–Stokes simulations taking advantage of the simple jet configuration, together with a Lagrangian discrete phase model for tracking the spray droplets. Two well-validated ethanol mechanisms consisting of 40 and 50 species, respectively, are employed to describe the chemical kinetics and reveal the impact of chemistry. Results are compared against measurement, including gas-phase velocity, temperature, and droplet velocity, demonstrating the improvement with the increasing accuracy in TCI modeling from characteristic time scale model, laminar finite rate model, eddy dissipation concept model, and transported probability density function (PDF) model. Effects of micromixing in PDF simulation are further investigated considering different model formulations and mechanical-to-scalar timescale ratios (). The Euclidean minimum spanning tree model with yields the best prediction of the mean temperature. The analysis on flame structure suggests that the flame exhibits a mixed mode of combustion, i.e., a stratified premixed flame in the upstream and a typical non-premixed flame in the downstream.

Conceptual model to quantify uncertainty in steady-RANS dissipation closure for turbulence behind bluff bodies

In turbulent bluff body flows, the presence of vortex shedding, a form of coherent structures, introduces a new characteristic scale that is distinct from the scale of background stochastic turbulence. This double-scale picture essentially invalidates the conventional single-scale modeling for the turbulence energy dissipation in steady-RANS simulations. This paper presents a conceptual model to quantify the uncertainty in the steady-RANS dissipation closure for flows past bluff bodies with vortex shedding.

Dynamic calibration of differential equations using machine learning, with application to turbulence models

We present a methodology for calibration of parametric ordinary and partial differential equation models, using off-the-shelf software for back-propagation in Neural Networks (NN). As a prototypical example, we consider calibration of a Reynolds-averaged Navier-Stokes (RANS) turbulence closure model, against ground truth data from direct numerical simulations (DNS) of two different turbulent flows. Numerical time integration is represented as a custom NN, where only the RANS model parameters are trainable. A loss function is defined to quantify the mismatch between the NN prediction and the ground truth over a predefined, finite time integration window. This loss function is then minimized using a gradient descent method utilizing the back-propagation algorithm. This dynamic approach to training is to be contrasted with a static approach, wherein a least square regression estimate for parameters is obtained in the limit of an infinitesimal time integration window. In a first test of static and dynamic approaches against ground truth data generated by the model, the former proves to be significantly faster and more accurate than the latter at recovering the parameters. When both calibration approaches are tested against DNS data, for which it is known that the model cannot achieve a perfect fit, the static approach yields a good prediction only for short times, while the dynamic approach results in physical and stable predictions over the entire integration window. After optimization of the dynamic approach for time step, spatial resolution, stability, and physics-based constraints, we obtain a 50% improvement of outcomes over those obtained from the existing, manually calibrated set of parameters, demonstrating the merits of this systematic and automated procedure.

Decreasing Wintertime Mixed‐Layer Depth in the Northwestern North Pacific Subtropical Gyre

AbstractThe deep winter mixed layer (ML), ∼240 m, in the northwestern North Pacific subtropical gyre exchanges heat and absorbs carbon dioxide from the atmosphere, and receives nutrients through the Kuroshio. The ML water spreads broadly in the subsurface ocean over the subtropical gyre. Compiling historical temperature measurements, we show that the winter ML depth (MLD) has decreased by ∼6% over the last six decades. Observations, atmospheric reanalyzes, simulation outputs from a one‐dimensional turbulent closure model, and climate projections reveal that the strengthening of the upper‐ocean stratification due to surface warming under global warming is responsible for the MLD decrease. Climate models project further decrease of winter MLD attributable to the marked strengthening of ocean stratification with climate warming, of up to 27%–40% by 2100 under the highest emission scenario. A monitoring system for winter ML should be established so that important changes for marine ecosystems can be foreseen.

Generalization enhancement of artificial neural network for turbulence closure by feature selection

Feature selection targets for selecting relevant and useful features, and is a vital challenge in turbulence modeling by machine learning methods. In this paper, a new posterior feature selection method based on validation dataset is proposed, which is an efficient and universal method for complex systems including turbulence. Different from the priori feature importance ranking of the filter method and the exhaustive search for feature subset of the wrapper method, the proposed method ranks the features according to the model performance on the validation dataset, and generates the feature subsets in the order of feature importance. Using the features from the proposed method, a black-box model is built by artificial neural network (ANN) to reproduce the behavior of Spalart-Allmaras (S-A) turbulence model for high Reynolds number (Re) airfoil flows in aeronautical engineering. The results show that compared with the model without feature selection, the generalization ability of the model after feature selection is significantly improved. To some extent, it is also demonstrated that although the feature importance can be reflected by the model parameters during the training process, artificial feature selection is still very necessary.

Development of a Computational Model for Investigation of and Oscillating Water Column Device with a Savonius Turbine

The present work aims to develop a computational model investigating turbulent flows in a problem that simulates an oscillating water column device (OWC) considering a Savonius turbine in the air duct region. Incompressible, two-dimensional, unsteady, and turbulent flows were considered for three different configurations: (1) free turbine inserted in a long and large channel for verification/validation of the model, (2) an enclosure domain that mimics an OWC device with a constant velocity at its inlet, and (3) the same domain as that in Case 2 with sinusoidal velocity imposed at the inlet. A dynamic rotational mesh in the turbine region was imposed. Time-averaged equations of the conservation of mass and balance of momentum with the k–ω Shear Stress Transport (SST) model for turbulence closure were solved with the finite volume method. The developed model led to promising results, predicting similar time–spatial-averaged power coefficients (CP¯) as those obtained in the literature for different magnitudes of the tip speed ratio (0.75 ≤ λ ≤ 2.00). The simulation of the enclosure domain increased CP¯ for all studied values of λ in comparison with a free turbine (Case 1). The imposition of sinusoidal velocity (Case 3) led to a similar performance as that obtained for constant velocity (Case 2).