Turbulence Closure Research Articles

Physics-informed machine learning based RANS turbulence modeling convection heat transfer of supercritical pressure fluid

Solving flow problems based on the Reynolds-averaged Navier-Stokes equations is a dominant method in terms of efficiency and accuracy for design and analysis of engineering applications, while the performance of RANS models in predicting the turbulent heat transfer of supercritical pressure fluid could be severely poor. To a great extent, the models are plagued by imperfect closures on higher order turbulence quantities with strongly varying thermal physical properties. This paper reports on an alternative approach to model the turbulent heat transfer at supercritical pressure, including the direct turbulent production models and the indirect transport closures using deep neural networks (DNN). This paper presents a method of modifying turbulence models of supercritical pressure fluid from high-fidelity simulation (DNS) data. An iterative DNS-DNN-RANS framework is proposed to establish explicit closures for turbulent momentum diffusion and turbulent thermal diffusion of turbulent heat transfer at supercritical pressure. Priori physics knowledge, feature engineering strategy and establish existing constitutive theory are involved to embed the special characteristics of supercritical pressure fluid into the turbulent closures to establish a proper regression system for machine learning (ML) algorithm. By embedding the explicit ML models, the low Reynolds number k-ε model was modified and was trained under a cross-case strategy with abundant DNS data. The modified model was successfully validated against DNS and experimental data for upward pipe flows, in which wall temperature were satisfactorily reproduced. The posterior simulations showed that the modified ML-KTVT model not only has a good performance in predicting the convection heat transfer of supercritical pressure fluid but also performs a favorable reproducibility of turbulence development in heat transfer deterioration cases.

Sensitivity analysis of a three-dimensional simulation of turbidity currents in a sloping flume

Sensitivity analysis is necessary in numerical models to establish the optimal model configuration and simulate turbidity currents accurately. The sensitivity of turbidity currents simulated by a three-dimensional numerical model named the semi-implicit cross-scale hydroscience integrated system model (SCHISM) was assessed using domain discretization, the turbulence closure model, and the transport scheme. The results show that a higher horizontal resolution with an appropriate aspect ratio, localized sigma coordinates with shaved cells (LSC2) grid with sufficient layers, a two-phase mixture turbulence closure model, and transport schemes with critical depth ratio lower than 1 could improve the model performance on the turbidity currents. The study can provide helpful guidance to establish accurate turbidity current simulations in complex water environments.

Investigations on offshore wind turbine inflow modelling using numerical weather prediction coupled with local-scale computational fluid dynamics

The computational power available nowadays to industry and research paves the way to increasingly more accurate systems for the wind resource prediction. A promising approach is to support the mesoscale numerical weather prediction (NWP) with high fidelity computational fluid dynamics (CFD). This approach aims at increasing the spatial resolution of the wind prediction by not only accounting for the complex and multiphysics aspects of the atmosphere over a large geographical region, but also including the effects of the fine scale turbulence and the interaction of the wind flow with the sea surface. In this work, we test a set of model setups for both the mesoscale (NWP) and local scale (CFD) simulations employed in a multi-scale modelling framework. The method comprises a one-way coupling interface to define boundary conditions for the local scale simulation (based on the Reynolds Averaged Navier–Stokes equations) using the mesoscale wind given by the NWP system. The wind prediction in an offshore site is compared with LiDAR measurements, testing a set of mesoscale planetary boundary layer schemes, and different model choices for the local scale simulation, which include steady and unsteady approaches for simulation and boundary conditions, different turbulence closure constants, and the effect of the wave motion of the sea surface. The resulting wind is then used for the simulation of a large wind turbine, showing how a realistic wind profile and an ideal exponential law profile lead to different predictions of wind turbine rotor performance and loads.

Physics-informed Machine Learning for Modeling Turbulence in Supernovae

Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSNe), but current simulations must rely on subgrid models, since direct numerical simulation is too expensive. Unfortunately, existing subgrid models are not sufficiently accurate. Recently, machine learning (ML) has shown an impressive predictive capability for calculating turbulence closure. We have developed a physics-informed convolutional neural network to preserve the realizability condition of the Reynolds stress that is necessary for accurate turbulent pressure prediction. The applicability of the ML subgrid model is tested here for magnetohydrodynamic turbulence in both the stationary and dynamic regimes. Our future goal is to utilize this ML methodology (available on GitHub) in the CCSN framework to investigate the effects of accurately modeled turbulence on the explosion of these stars.

Robust data-driven turbulence closures for improved heat transfer prediction in complex geometries

Data-driven turbulence closures have been used to successfully improve the prediction of first order effects in flows where the test case is similar to the training conditions. In this work, we examine the ability of such closures to improve second order effects, such as heat transfer for complex geometries. First, an upper bound for the available performance of the data-driven model is shown by inserting the Reynolds stresses from the high fidelity training data in a stable manner to a modified Reynolds-Averaged Navier–Stokes (RANS) model. Data-driven closures are then developed from this data set with a focus on robustness and the improvement in the heat transfer effects analysed. The geometries considered are four topology optimised square ducts. Each duct is optimised with varying weights of a multi-objective function to maximise heat transfer and minimise pressure losses. One duct is used in training and the remaining three are set aside for testing the developed closure. For the training case, it is found that simple data-driven closures for the Reynolds stresses alone, are capable of improving prediction of the velocity and temperature fields by 38.2% and 34.8% respectively even in complex geometries. These improvements are largely retained in the testing cases demonstrating the robust generalisation of the developed model for this class of flow.

A generalized partially stirred reactor model for turbulent closure

A generalized Partially-Stirred Reactor (PaSR) model is presented in this work based on the inclusion of multiple chemical times. The PaSR model has shown promising results at modelling turbulence-chemistry interaction in Large-Eddy Simulations (LES) and Reynolds-Averaged Navier-Stokes (RANS), providing an extension of the well-known Eddy Dissipation Concept (EDC). PaSR model divides the computational domain into reactive and non-reactive parts. The factor defining this partition is expressed as a function of the system characteristic chemical and mixing times. However, the estimation of these factors, particularly the chemical one, is often oversimplified. The approach proposed in this study seeks to include in the PaSR model the whole set of chemical times involved in the reactive system. Besides, the concept of fine structures, first introduced in the EDC and often adopted also in the PaSR model to characterize the evolution of chemistry in the reactive part of the fluid, is here abandoned in favour of direct manipulation of species production rates. The mean source term is formulated according to the new generalized model through a modal decomposition of the Jacobian matrix. The method is validated a priori with DNS data of a syngas non-premixed jet flame, whose filtered data represent the validation benchmark. A good agreement is found between the new PaSR model and the filtered data for all species at different filter widths. Comparison with the single time scale based model clearly shows the limitations of the old standard approach and the necessity of including the whole spectrum of chemical times for a more comprehensive description of turbulence-chemistry interaction. A thorough analysis with the time scale participation index reveals the complexity of reaction rates contributions to the development of a specific time scale, underlying the importance of developing a model able to inherit all kinetic pathways in the turbulent closure.

Geometrical investigation of cooling channels with two alternated isothermal blocks under forced convective turbulent flow

The present work performs a numerical analysis of the geometrical investigation of a two-dimensional channel with two alternated isothermal rectangular blocks subjected to turbulent forced convective flows. Constructal Design associated with Exhaustive Search is used to investigate the influence of the geometry of the isothermal blocks over the performance of the cooling convective flows in a multi-objective viewpoint, i.e., considering the pressure drop and heat transfer rate. The time-averaged equations of continuity, momentum, and energy conservation are solved with the finite volume method. The k–omega shear stress transport model is used for the closure of turbulence. The effect of the two proposed degrees of freedom, the height/length ratio of the two blocks (H_{1}/L_{1} and H_{2}/L_{2}), is analyzed in relation to the proposed objectives. Regarding the thermal purpose, the geometry with the highest insertion into the channel led to the best performance, while the opposite configuration led to the best fluid dynamic performance. This behavior was similar to that previously found in the literature for forced convective laminar flows. For a multi-objective perspective, the use of technique for order preference by similarity to ideal solution indicated that asymmetric blocks led to the best multi-objective performance when both performance indicators had the same weight.

Criteria to switch from tabulation to neural networks in computational combustion

Motivated by the need to reduce computational costs, look-up tables are widely used in numerical simulations of laminar and turbulent flames, for the thermodynamics of the mixture, for detailed chemistry, and for turbulent combustion closures. At the same time, there have been many studies where artificial neural networks have been trained to replace the classic tabulation approach, and their performance against tabulation typically evaluated a posteriori. In the majority of applications the focus is on accuracy, and the objective is to obtain the best network structure which minimises the inference error during training. Computational efficiency however is also important, and criteria are needed to decide whether or not it is worthwhile in the first place to employ neural networks at all, and if so what the potential bounds on the computational time and memory gains (if any) over tabulation are. This is examined analytically in this work by developing scaling laws for the computational cost of tabulation and of neural networks including the effect of network structure. The scaling laws are validated using both model test-data but also data based on a canonical problem which involves inferring laminar flame speeds of methane/hydrogen mixtures at off-training conditions. The proposed scaling laws lead naturally to a framework for effective decision-making between adopting look-up tables or neural networks.

Computational Fluid Dynamics Modeling of Argon–Steel (–Slag) Multiphase Flow in an Ruhrstahl–Heraeus Degasser: A Review of Past Numerical Studies

Many metallurgical functions such as dehydrogenation, decarburization, and inclusion removal are achieved during Ruhrstahl–Heraeus (RH) treatment. The realization of these functions is closely related to argon–steel–slag flow in an RH degasser. Recently, computational fluid dynamics (CFD) methods have been widely adopted to understand such multiphase flow. This review summarizes and analyzes CFD modeling of argon–steel (–slag) flow from the aspect of fundamentals of the numerical approach, focusing on CFD models and validation (homogeneous fluid model, volume of fluid–discrete phase model, and Eulerian model), bubble behaviors (deformation, expansion, coalescence, and breakup), interfacial closure laws (drag, turbulent dispersion, lift, virtual mass, and wall lubrication forces), and turbulence closures (Reynolds‐averaged approach with standard, renormalization group, and realizable k–ε models, and large eddy simulation with Smagorinsky–Lilly model). This review also suggests that future challenge is to further develop a model for coupling the dispersed interface with a wide bubble size distribution and the sharp interface with a large interfacial scale, accompanied by appropriate bubble behaviors and general closure laws of interfacial forces. As a precondition for the development of CFD models, more experiments are required to fully understand the multiphase flow in a real RH degasser.

Numerical Simulation of Scalar Mixing and Transport through a Fishing Net Panel

With the rapid development of commercial aquaculture in recent decades, large numbers of submerged cages or pens are clustered in fish farms that are commonly located within inland lakes, reservoirs, and coastal embayments around the world. The submerged structures have significant influence on both the flow fields and mass transport processes in surrounding water bodies. While existing studies have concentrated mainly on the flow blockage effects produced by fish cages, the associated effect on near-field mass transport processes, important for pollution transport and dispersal, remains largely unclear. To address this knowledge gap, a CFD (computational fluid dynamics) model was established using OpenFOAM to investigate the wake characteristics and scalar transport processes through a fishing net panel, as representative of a key component of the fish cage or pen. In this model, the net panel was represented as porous media, and the finite volume method was applied to solve the governing flow equations with the standard k-ε model used for turbulence closure. Experimental data from previous studies were used to calibrate and validate the numerical model, which was applied to different scenarios over a range of net solidities and incoming flow velocities. Overall, the numerical model results demonstrated that porous media schematization could adequately reproduce the blocking effect from the net panel on the mean flow field, as well as the induced changes to scalar transport, with satisfactory accuracy. The flow velocity reduction across the net panel was found to strengthen with increasing net solidity and decreasing incoming velocity, while the scalar concentration decay tended to become enhanced when the incoming velocity was decreased. The lateral profile of the scalar concentration exhibited a self-similar Gaussian distribution with the spreading width of the plume reduced by increasing the incoming velocity. This lateral concentration distribution was minimally affected by the upstream scalar source location relative to the net panel, when adopting the current RANS and porous media modelling approach. The model results provide useful references for the assessment of the environmental impacts and carrying capacity of cage-based fish farming.

Numerical investigation of flow control in low-pressure turbine cascade using Gurney Flaps

Abstract This paper reports the numerical investigations to analyze the effect of the application of Gurney Flaps on various configurations in a Low-Pressure Turbine (LPT) cascade in mitigating the laminar flow separation during low Reynolds number operations. T106 LPT blade of chord 60 mm has been selected for the present study. Gurney Flaps of flat type and quarter round type of a particular height of the chord length are selected. Flaps are provided near the blades’ trailing edges for numerical analysis. The numerical computations are performed using STARCCM+ software, and the K-ω SST turbulence Model is used for turbulence closure. The studies are performed at various Reynolds numbers ranging from 37,500 to 138,750 to understand the application of various configurations of Gurney Flap vis a vis turbine blade without Gurney Flap. Performance parameters such as lift coefficient, drag coefficient, aerodynamic efficiency, and static pressure distributions over the blade surface are used to analyse the alterations in the performance of aerodynamic characteristics of the LPT Blade. All the Gurney Flap configurations improved the overall blade aerodynamics. Among these configurations, the flat Gurney Flap configuration is found to be superior as it improves the aerodynamic efficiency of the blade.

A numerical wave tank with large eddy simulation for wave breaking

A three-dimensional (3D) numerical wave tank (NWT) is developed based on OpenFOAM. The propagation and breaking of waves with a moderate wavelength that could be generated in the laboratory are studied. The wave periods range from 0.5 to 1.79 s and wave steepness goes up to 0.05. The volume of fluid method (VOF) is employed for interface capturing. The relaxation zone method is implemented for wave generation and absorption at the boundaries. Computationally significant factors like grid size, relaxation weight and time step are investigated to find the optimal parameters of the numerical models for various wave regimes. A relationship between grid size and time step, similar to the wave dispersion relation, is found. The accuracy and performance of the NWT are assessed through the reflecting coefficient, wave damping and phase distortion rates. Simulation conditions are monitored to achieve an error rate of less than 3%. To mitigate the effects of numerical errors on the calculation of the reflection coefficient, a modified version of Goda's approach is proposed. The coefficient of wave reflection at the outlet boundary calculated by the conventional Goda's method is as high as 4.3%. This value can be modified to be less than 2% after utilizing the revised Goda's method. Turbulent flows, especially for the breaking wave regime, are investigated by large eddy simulation. A one-equation sub-grid eddy viscosity model, with coefficients being derived from local flow properties, is employed for turbulence closure. A case study of wave breaking on a fixed bar is simulated. The validation of this NWT model is confirmed by comparing the numerical results with experimental data.

Scouring mechanism of suspended and partially-buried pipelines under steady flow

Offshore pipelines are often suspended or partially-buried during operating process. Understanding the scouring mechanism of the suspended and partially-buried pipelines is important for protecting the pipelines. The numerical models of pipelines under steady flow are established, in which Reynolds Averaged Navier-Stocks equation (RANS) with the k-ω turbulence closure, as well as the sediment transport equation, are solved with the finite volume method. After experimental verification, the models are applied to a series of parametric analysis for the suspended and partially-buried pipelines under steady flow. The effect of different variables such as the pipe diameter D , the suspension height e , the pipe shape, the embedment depth, on the scour process of the pipelines are investigated in detail based on more than 150 simulation results. For the suspended pipelines, the gap-to-diameter ratio e / D is the key parameter to predict scour depth. The pipe shape has an influence on the scour depth and the position of the scour hole. A formula to predict scour depth in terms of e/D and the relation between gap velocity and scour depth is obtained. For the partially-buried pipelines, the block height and the curvature of the pipeline is proposed as the key parameters to analyze the flow field around the pipeline. • The numerical model of pipelines under steady flow are established and verified. • Effect of different parameters on scour process of offshore pipelines are studied. • Formula to predict scour depth in terms of e / D is proposed for suspended pipelines. • Block height and curvature are key data to analyze flow of partially-buried pipelines.

A two‐fluid single‐column model of turbulent shallow convection. Part 1: Turbulence equations in the multifluid framework

AbstractThe multifluid equations are derived from the compressible Euler equations (or any of the usual approximate equation sets used in meteorology) by conditional filtering. They have the potential to provide the basis for an improved representation of cumulus convection and its coupling to the boundary layer and larger scale flow in numerical models. The present article derives the prognostic equations for subfilter‐scale turbulent second moments in the multifluid framework, along with certain systematic simplifications of them, thus providing a multifluid analogue of the well‐known Mellor and Yamada hierarchy of turbulence closures. As well as enabling a more accurate calculation of subfilter‐scale fluxes and the effects of subfilter‐scale variability on cloud fraction, liquid water, and buoyancy, the second moment information can be used to obtain a more accurate parameterization of entrainment and detrainment. A subset of the turbulence equations derived here is employed in the two‐fluid single‐column model described in Part 2 and applied to the simulation of shallow cumulus cases in Part 3.

Dependence of submesoscale simulation on turbulence closure schemes in the Regional Ocean Modeling System (ROMS)

Submesoscale processes with spatiotemporal scales of 0.1∼10 km and hours to 1 day play an important role in the ocean energy cascade and material transport. Up to now, most studies focusing on submesoscales are based on high-resolution numerical simulations, since observations are scarce due to a limitation of their small scales. However, numerical studies on submesoscales deeply depend on the choice of sub-grid turbulence closures that are of significance in determining the simulation performance. Here, submesoscale processes generated at an idealized mesoscale eddy are investigated based on a 1-km resolution Regional Ocean Modeling System (ROMS) model, and the model performance in terms of submesoscales is analyzed and emphasized with three popular turbulence closure schemes, K-Profile Parameterization (KPP), Mellor–Yamada​ (MY) and General length-scale closure schemes (GLS). The analysis shows that the magnitude of the submesoscale kinetic and potential energy follows: GLS>MY>KPP, despite a general consistent variation by the three closures. To figure out the dominant factors controlling the submesoscale energy budget, three terms including the baroclinic term (BC), the barotropic term (BT), and the background to submesoscale potential energy conversion term (BSP) are analyzed. The results show that the BC is the source of submesoscale kinetic energy, while the BT tends to transfer submesoscale kinetic energy to mesoscales inversely, and the BSP is the submesoscale potential energy source. In comparison, the GLS simulates the largest BC, BT, and BSP. Overall, the order of the BC and BSP is: GLS>KPP>MY, and the order of the BT is: GLS>MY>KPP.

Study of radiative heat transfer and flow physics from medium-scale methanol pool fire simulations

A medium-scale (30 cm diameter) methanol pool fire was simulated using Sandia National Laboratories’ Sierra/Fuego low-Mach number multi-physics turbulent reacting flow code. Large Eddy Simulation (LES) with subgrid turbulent kinetic energy closure was used as the turbulence model. Combustion was modeled using a strained laminar flamelet library approach. Radiative heat transfer was modeled using the gray-gas approximation. This paper details analysis done to support a validation study for the fire model. In this analysis, integral quantities were primarily examined. The radiant fraction was computed and used as a model calibration parameter. Integrated buoyancy flux was calculated and compared to an engineering correlation. Entrainment rate was computed with and without a mixture fraction threshold filter and compared to engineering correlations. Turbulent kinetic energy was computed and the effect of mesh size on the subgrid and total turbulent kinetic energy was examined. Flame height was calculated using an intermittency definition with two input parameters. A sensitivity study was then conducted to determine the sensitivity of the estimated flame height to the input parameters. This analysis aided in achieving the primary validation study objectives by providing model calibration and expanding the scope of the validation effort. In addition, the range of physics examined was increased, enhancing the understanding of the model's overall performance and of the relationship between phenomena.

Film Cooling Performance Prediction for Air and Supercritical CO2

Abstract The current study explores the possibility of cooling the vanes and blades of a direct-fired sCO2 turbine using film cooling. The operating conditions of a direct-fired sCO2 cycle and thermophysical properties of the fluid at those conditions can alter the flow field characteristics of the coolant jet and its mixing with the mainstream. Very little information is present in the literature regarding the performance of film cooling geometries employing supercritical CO2. The objective of this study is to estimate the resulting film cooling effectiveness while also capturing the effects of the crossflow-to-mainstream velocity ratio on the coolant jet. A computational fluid dynamic model is used to study the coolant jet exiting a cylindrical hole located on a flat plate, with the coolant fed by an internal channel. Steady-state Reynolds-averaged Navier–Stokes equations were solved along with the (shear-stress transport) SST k–ω model to provide the turbulence closure. The operating conditions for the direct-fired sCO2 turbine are obtained using an in-house Cooled Turbine Model. Numerical predictions revealed that the crossflow effects and jet lift-off were more pronounced in the case of sCO2 when compared to air. Spatial distribution of flow field and cooling effectiveness are presented at different operating conditions.

Characterizing the Impacts of Turbulence Closures on Real Hurricane Forecasts: A Comprehensive Joint Assessment of Grid Resolution, Horizontal Turbulence Models, and Horizontal Mixing Length

AbstractHurricanes are highly complex geophysical flows that have caused billions of dollars in damage in recent years. Despite the significance of these extreme weather events, the turbulence mechanisms that derive the dynamics of hurricane flow systems are poorly understood and ineffectively parameterized in numerical weather prediction (NWP) models. The objective of this study is to bridge these knowledge gaps by assessing the accuracy and deficiencies of existing horizontal turbulence models in NWPs for hurricane forecasts. In particular, the Weather and Research Forecasting (WRF) Model is employed to conduct 135 simulations of five real hurricanes by varying the grid resolution, turbulence models, and horizontal mixing length values. Decreasing the default horizontal mixing length values both in low and high resolution WRF simulations significantly improves the wind intensity forecasts. This result indicates that the existing horizontal diffusion parameterizations are overly dissipative for hurricane flows, and thus, generate a weaker vortex compared to observations. These deficiencies are shown to stem from the horizontal mixing‐length parameterization in WRF that is prescribed as a function of grid size without considering the physics of the flows (e.g., rotation). The paper provides notable insights into the role of turbulent fluxes in simulated hurricane evolutions that can be useful to advance the turbulence parameterizations of NWP models for hurricane forecasts.

Sensitivity Analysis of Wind and Turbulence Predictions With Mesoscale‐Coupled Large Eddy Simulations Using Ensemble Machine Learning

AbstractCoupling between mesoscale models and large‐eddy simulation (LES) models is increasingly used to more realistically represent the wide range of scales of atmospheric motions affecting boundary layer winds and turbulence that need to be simulated accurately for applications such as wind energy. However, such mesoscale‐to‐microscale coupled modeling frameworks are potentially affected by a large number of uncertain closure parameters. Here, we investigate the sensitivity associated with six closure parameters related to a 1.5‐order subgrid‐scale turbulence closure for an ensemble of mesoscale‐coupled LES. The simulations are performed using the Weather Research and Forecasting model nested from horizontal resolutions of greater than a kilometer down to tens of meters. Closure parameters are varied to generate perturbed parameter ensembles for two case studies of highly sheared, convective boundary layers observed in the Columbia Basin of Oregon and Washington during the Second Wind Forecast Improvement Project. Machine learning algorithms are used to explore the sensitivity of LES predictions, considering the effects of the perturbed physical parameters alongside categorical factors such as the case study identity, measurement location, and LES resolution. For the conditions we examine, a single parameter, the eddy viscosity coefficient, is the dominant source of parametric sensitivity and its importance is comparable to the categorical factors for several of the simulation response variables we examine.

Numerical proof of shell model turbulence closure

The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure, based on deep recurrent neural networks, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, we employ shell models of turbulence. Our results encourage the development of similar approaches for 3D Navier-Stokes turbulence.