Turbulence Closure Research Articles

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields. The framework consists of a Reynolds-averaged Navier–Stokes (RANS) solver and a neural-network-represented turbulence model, each accompanied by its derivative computations. For computing the sensitivities of the indirect observations to the Reynolds stress field, we use the continuous adjoint equations for the RANS equations, while the gradient of the neural network is obtained via its built-in automatic differentiation capability. We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures. We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists. The trained deep-neural-network turbulence model showed predictive capability on similar flows.

A review on turbulent flow over rough surfaces: Fundamentals and theories

• Townsend hypothesis can explain large-scale motions near rough and smooth walls. • Is unable to describe all roughness regimes and does not scale d-type roughness. • Wall similarity hypothesis faces both supporting and conflicting evidence. • Roughness function can be scaled with height and effective slope of roughness. • Available models do not point to agreed conclusions or trends for all roughness types, Surface roughness can significantly influence the fluid dynamics and heat transfer in convective flows by inducing perturbations in the velocity profile which affect surface drag, turbulent mixing and heat transfer. While surface roughness can often negatively affect the performance of systems, it can also lead to performance improvements, such as in convective flows where roughness elements have been shown to enhance heat transfer. Turbulent flows over rough surfaces have been studied for about a century leading to significant developments in this field. Direct Numerical Simulation (DNS) has made significant contributions to the knowledge of turbulent flows over rough surfaces as well as evaluation of the developed theories. Moreover, the turbulent closures model has seen wide use for simulation of rough-wall turbulent flows in practical applications where DNS is hindered by its complexity and computational resources. Despite a significant number of experimental and CFD studies and the latest advances in this field, a recent review was not available. Therefore, this review surveys the past and recent experimental and numerical studies to address the fundamentals and theories related to the structure of turbulent flows over rough walls. This study chiefly investigates the structure of mean flow profile over rough surfaces, and its correlation with smooth wall mean flow profile. This review study can contribute to prospective experimental and CFD work, and for characterising rough-wall turbulent flows and heat transfer in different academic and engineering applications such as aerodynamics, hydraulics, meteorology, and manufacturing. The review concludes that despite significant progress, the structure of turbulent flow is still not fully understood. This is mainly due to a lack of systematic studies on the structure of turbulent flow and also due to the variety of roughness which influence the dynamics of the flow in the roughness sublayers. The current roughness scale (sand-grain roughness height) fails to completely characterise roughness in many cases. Therefore, there is a need for a universal roughness scale that can describe every type of roughness and be used in any rough-flow regimes, including fully rough and transitionally rough regimes.

A Reynolds shear stress model for constant-pressure boundary layers

Closure models for the Reynolds shear stress in wall-bounded flows are mostly based on various turbulence quantities like the turbulent kinetic energy (k), its dissipation rate (ϵ), the Reynolds stress (vr2) in the wall-normal direction, the mean flow velocity gradient (S), the normalized strain rate (Sk/ϵ), etc.; vr is the intensity of the fluctuating velocity component in the wall-normal direction (y). Close to the wall, (u′v′¯) is known to vary with y approximately as ∼y3. With an emphasis on this near-wall feature, a closure model is proposed here in terms of k, (vr/ur), and a weighted mean strain rate (Skvr+/ϵ); ur is the intensity of the fluctuating velocity component in the streamwise direction. The choice of ur in the present proposal is in view of the fact that, although the energy associated with ur2 in a simple flow, for example, is distributed to vr2 by fluctuating pressure, it has never been used in past closure models. In terms of the known approximate variations of k,vr,ur, etc., with y in the near-wall region, the present model suggests (u′v′¯)∼y3.25 and so nearly retains its known approximate variation ∼y3 (for small y). It is suggested here that vr+ in the weighted strain rate damps the strain rate (Sk/ϵ) significantly in the near-wall region and plays a similar role in Durbin's model [“Near-wall turbulence closure modeling without damping functions,” Theor. Comput. Fluid Dyn. 3, 1 (1991)]. It is also reported here that vr≈k1/2 and ur≈(ϵ/S)1/2 in the outer region, and these velocity scales are associated with (Sk/ϵ)∼ constant in this region; alternatively, in terms of these velocity scales, the normalized strain rate (Sk/ϵ) is the ratio of the Reynolds stresses (vr2/ur2) in the outer region.

High-performance ocean energy harvesting turbine design – A strategy of compound leaning

Blade leaning works well for steam, hydro and gas turbines, where the flow is unidirectional. In contrary, the turbine used in an oscillating water column wave energy device has a unique design which can work only in bidirectional flow and gives a unidirectional torque. In this article, a compound leaning concept is explored through numerical modelling. An impulse turbine with 0.3m diameter and two rows of guide vanes mirroring each other was considered as a case study. Reynolds-averaged Navier-Stokes equation with k-ε turbulence closure model was solved in ANSYS-CFX code. The present numerical result matches well with the existing experimental results. The modified rotor blade gave 8.8% higher efficiency as it reduced the intensity of trailing edge vortex shedding and the downstream recirculation region.

2-D simulation of atmospheric boundary layer in and around Delhi to determine air pollution scenarios during winter morning.

In this paper, a 2-D turbulent closure model, based on the pollutant mass conservation equation, is adopted to estimate the local and background pollutants in the predominant wind direction for the stable atmosphere during winter mornings. The background concentration of pollutants can severely affect the regional pollution level, and its monitoring is a challenging task. Here, the turbulent closure model is employed across three cities in India, viz., Patiala, Delhi, and Agra, to estimate SO2 and NOx concentration along the predominant wind direction to demonstrate the potential of numerical models. The direction of the prevailing wind in this area during January 2003 was NNW (330°). Patiala is followed by Delhi and then Agra in the predominant wind direction. The sensitivity analysis of surface temperature on pollutant concentration reveals that concentration would increase by its square as temperature dips. So, during low or no horizontal wind, pollution episodes will be inevitable. Thus, the pollution hotspots are also identified in these three cities. Delhi had a high pollution load. So, the impact of local pollution in Delhi, through dispersion, was found significant in Agra. NOx hot spots (exceed the 30 μg/m3 limit) are found all across Delhi, except IGI Airport and two other locations. However, no SO2 hotspot (exceed the 60 μg/m3 limit) is found in Delhi. The proposed model output is verified with the WRF-CFD model results. Compared to the WRF-CFD model, the proposed model has overestimated NOx and SO2 concentration maximum by 14.4% and 23.5%, respectively. The overestimation occurred primarily due to ignoring atmospheric chemical reactions (e.g., acid condensation, etc.) for which the atmospheric factors were not so conducive.

Modelling turbulent heat flux accounting for Turbulence-Radiation Interactions

The present work investigates the modeling of turbulent heat transfer in flows where radiative and convective heat transfer are coupled. In high temperature radiatively participating flows, radiation is the most relevant heat transfer mechanism and, due to its non-locality, it causes counter intuitive interactions with the turbulent temperature field. These so-called Turbulence-Radiation Interactions (TRI) largely affect the temperature field, modifying substantially the turbulent heat transfer. Therefore, in the context of modeling (RANS/LES), these interactions require a closure model. This work provides the inclusion of TRI in the modeling of the turbulent heat transfer by adopting a unique approach which consists in approximating the fluctuations of the radiative field with temperature fluctuations only. Based on this approximation, coefficients of proportionality are employed in order to close the unknown terms in the relevant model equations. A closed form of all radiation-temperature-velocity correlation is explicitly derived depending on the chosen turbulent heat transfer model. This model is applied to a standard two-equation turbulent heat transfer closure and used to reproduce results obtained with high-fidelity DNS simulations. While a standard approach (i.e., neglecting TRI) is not able to correctly predict the DNS data, the new model’s results shows exceptional agreement with the high-fidelity data. This clearly proves the validity (and the necessity) of the proposed model in non-reactive, radiative turbulent flows.

Efficient simulation of flame acceleration and deflagration-to-detonation transition in smooth pipes

Evaluation of accident scenarios including flame acceleration and deflagration-to-detonation transition (DDT) in chemical plant piping systems increases the need for an efficient numerical simulation tool capable of dealing with this phenomenon. In this work, a hybrid pressure-density-based solver including deflagrative flame propagation as well as detonation propagation is presented. The initial incompressible acceleration stage is covered by the pressure-based solver until the flame velocity reaches the fast flame regime and transition to the density-based solver is done. The deflagration source term is formulated in terms of a turbulent flame speed closure model incorporating various physical effects crucial for flame acceleration at low turbulence conditions (Katzy and Sattelmayer, 2018). Modelling of the detonation source term is based on a quadratic heat release function (Hasslberger, 2017). The presented numerical approach is validated in terms of DDT locations and pressure data from Schildberg (2015) as well as recently completed flame tip position measurements. For this purpose, H2/O2/N2 mixtures ranging from 25.6 vol-% H2 to 29.56 vol-% H2 in two different pipe geometries are considered. The focus of the current work is on predicting the DDT location correctly and good agreement is observed for the investigated cases.

Effects of the simplification in the geometry of a cyclone test facility on the swirling flow: a CFD study

A study about the influence of geometry simplification on the swirling flow of a cyclone was performed by comparing CFD results with experimental data. The numerical results were obtained by solving the mass and momentum equations with the Reynolds Stress Model (RSM) for the turbulence closure. On other hand, the experimental data were obtained in the literature, the authors used the Particle Image Velocimetry (PIV) technique to measure the velocity fields and a differential manometer to measure the pressure drop. In this work, different test facility geometries configurations were simulated: the complete test facility; and others with some simplifications downstream and upstream of the cyclone. The boundary condition for both numerical and experimental analysis was performed with inlet velocity in 10.5 and 12.25 m/s. Results showed a decrease in the gas vortex velocity in the cyclone center when simplifications in the test facility geometry are made. These bring significant consequences in the performance parameters, like almost 20% in the pressure drop values.

Effects of the Simplification in the Geometry of a Cyclone Test Facility on the Swirling Flow: a CFD Study

A study about the influence of geometry simplification on the swirling flow of a cyclone was performed by comparing CFD results with experimental data. The numerical results were obtained by solving the mass and momentum equations with the Reynolds Stress Model (RSM) for the turbulence closure. On other hand, the experimental data were obtained in the literature, the authors used the Particle Image Velocimetry (PIV) technique to measure the velocity fields and a differential manometer to measure the pressure drop. In this work, different test facility geometries configurations were simulated: the complete test facility; and others with some simplifications downstream and upstream of the cyclone. The boundary condition for both numerical and experimental analysis was performed with inlet velocity in 10.5 and 12.25 m/s. Results showed a decrease in the gas vortex velocity in the cyclone center when simplifications in the test facility geometry are made. These bring significant consequences in the performance parameters, like almost 20% in the pressure drop values.

Investigation of Swirl Stabilized CH4 Air Flame with Varied Hydrogen Content by using Computational Fluid Dynamics (CFD) to Study the Temperature Field and Flame Shape

In the current paper, numerical simulations of the combustion of turbulent CH4-H2 are presented employing the standard k-epsilon and the RNG k-epsilon for turbulence closure. The Fr-ED concept is carried out to account for chemistry/ turbulence interaction. The hydrogen content is varied in the fuel stream from 0% to 100%. The numerical solutions are validated by comparison with corresponding experimental data from the Combustion Laboratory of the University of Milan. The flow is directed radially outward. This method of fuel injection has been already been explored experimentally. The results show that the structure of the flame is described reasonably and both standard k-ɛ and RNG k- ɛ models can predict the flame shape. The general aspect of the temperature profiles is well predicted. The temperature profiles are indicating a different trend between CH4 and CH4/H2 fuel mixtures.

Effect of building cross-section shape on air pollutant dispersion around buildings

This research investigates the effect of building cross-section shape on the air pollutant dispersion around an isolated building. A Computational Fluid Dynamic (CFD) model was developed and validated based on detailed wind tunnel experimental data. Both Large Eddy Simulation (LES) and Realizable k-ε models were used for turbulence closure and LES was found to provide a better agreement with experimental results than the RANS model, particularly in replicating pollutant dispersion characteristics associated with wind-structure interaction. The LES model was then utilized to study the effect of building cross-section shape. Four building cross-section shapes, square, chamfered, curved and circular, along with different air pollutant emission locations were studied. It has been found that the area around an isolated building can be categorized into three emission regions, namely the windward critical emission region, the leeward critical emission region and the side non-critical emission region. The air pollutant emissions from the leeward critical emission region affect the building the most. Furthermore, the size of this region depends on the building cross-section shape, with the circular and curved buildings having a smaller leeward critical emission region than those for the chamfered and square buildings. Evidently, air pollutant dispersion around a building is dominated by wind-structure interaction which in turn is dependent on the building cross-sectional shape. These characteristics can be utilized to mitigate air pollutant dispersion in urban environments in conjunction with careful consideration of the air pollutant emission location relative to a building.

Improvement of corner separation prediction using an explicit non-linear RANS closure

In this paper, an investigation into the effect of explicit non-linear turbulence modelling on anisotropic turbulence flows is presented. Such anisotropic turbulence flows are typified in the corner separations in turbomachinery. The commonly used Reynolds-Averaged Navier-Stokes (RANS) turbulence closures, in which the Reynolds stress tensor is modelled by the Boussinesq (linear) constitutive relation with the mean strain-rate tensor, often struggle to predict corner separation with reasonable accuracy. The physical reason for this modelling deficiency is partially attributable to the Boussinesq hypothesis which does not count for the turbulence anisotropy, whilst in a corner separation, the flow is subject to three-dimensional (3D) shear and the effects due to turbulence anisotropy may not be ignored. In light of this, an explicit non-linear Reynolds stress-strain constitutive relation developed by Menter et al. is adopted as a modification of the Reynolds-stress anisotropy. Coupled with the Menter’s hybrid "k-ω" ⁄"k-ε" turbulence model, this non-linear constitutive relation gives significantly improved predictions for the corner separation flows within a compressor cascade, at both the design and off-design flow conditions. The mean vorticity field are studied to further investigate the physical reasons for these improvements, highlighting its potential for the widespread applications in the corner separation prediction.

Analysis and Interpretation of Data-Driven Closure Models for Large Eddy Simulation of Internal Combustion Engine

<div class="section abstract"><div class="htmlview paragraph">We present an automatic data-driven machine learning (ML) approach for the development, evaluation and interpretation of deep neural networks (DNNs) for turbulence closures and demonstrate their usage in the context of cold-flow large-eddy simulation (LES) of the four-stroke Darmstadt engine using an open-source compressible multi-dimensional CFD solver OFICE, in a hybrid PDE-ML framework. Rather than explicitly using canonical formulations of closure terms, these DNNs robustly discover the functional relationships between the large-scale features of the resolved flow (cell Re, strain and rotation rate tensors etc.) obtained by solving the Navier Stokes to the small-scale unresolved terms. Experimentally validated high-fidelity LES solutions of the engine at different crank angles are utilized as the ground truth to train the DNN based closure models. Since optimizing these DNNs can be a laborious process for scientific datasets, and often require specialized expertise, we propose a Bayesian optimization framework that automatically determines the best set of network parameters, including the architecture and training hyperparameters - batch size, regularization etc. for optimum performance. We compare and contrast various networks for their effectiveness in an <i>a-priori</i> testing setting. Finally, the best ‘learnt’ network is integrated with the open-source CFD solver (OFICE), and solutions are obtained over several injection cycles. These experiments reveal that the DNN models temporally track resolved scalar variance with a good accuracy. Additionally, we interpret the artificial neural networks with sensitivity analysis to determine the relevant large-scale features for the learning process.</div></div>

A Parameterization of Turbulent Dissipation and Pressure Damping Time Scales in Stably Stratified Inversions, and its Effects on Low Clouds in Global Simulations

AbstractIt is difficult for coarse‐resolution global models of the atmosphere to accurately simulate the observed distribution of low clouds. In particular, it is difficult for moist turbulence closure models to simulate sufficiently bright near‐coastal stratocumulus (Sc) without simulating overly bright marine shallow cumuli (Cu). To parameterize bright Sc, a turbulence parameterization must damp the turbulent fluxes of heat and moisture above cloud top in order to prevent excessive entrainment of dry air into cloud top. To parameterize dim shallow Cu, the subgrid variances of temperature and moisture must remain large, in order to permit partial cloudiness. However, damping the fluxes but not the variances just above cloud top is difficult if a parameterization uses a single “master” time scale to damp both. In nature, the above‐cloud fluxes are damped by pressure fluctuations, whereas scalar variances are damped by a different process, namely, turbulent dissipation. In a stably stratified inversion above cloud, pressure damping is large but turbulent dissipation is small. To avoid this problem, a multitime scale parameterization for damping has been developed. The damping parameterization has been implemented in a global model and evaluated. The parameterization is capable of dimming shallow Cu while producing adequately bright Sc.

Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures

Abstract

Progresses and challenges of high-order-moment turbulence closure

High-order-moment model is one of the focuses and frontier topics in the research of turbulence closure theory. Since Mr. Chou first established the Reynolds-stress transport equation in general turbulence, scholars have never stopped to study the high-order-moment model in order to predict the complex flow more accurately. Especially in the new century, thanks to the rapid development of computer hardware and the breakthrough of high-order numerical methods, turbulence simulation is in the course of turning from RANS into LES. In either RANS framework, LES framework, or the hybrid one, high-order-moment models are representative of advanced closure models. According to this, the paper gives a general review of the high-order-moment models. The focus includes the modeling approach of each source item, the evolution process of scale providing equations, and the research demand of numerical solution technology. Through several typical turbulence problems, their advantages over the traditional eddy-viscosity models are shown. Moreover, the integration of high-order-moment models in some CFD software is given. Finally, the future challenges and development direction of the high-order-moment turbulence model are prospected.

Experimental and numerical investigation of three-dimensional open channel with simulated partial ice-covers

This paper presents both experimental measurements and three-dimensional (3D) numerical simulations of turbulent flow in open channels with simulated partial ice-covers. The experiments were conducted with a particle image velocimetry system while the simulations were performed with five eddy-viscosity and second-moment closure turbulence models. Four coverage ratios based on the channel width were examined in each case: a reference fully open channel and 25%, 50% and 75% partially covered channels. The results showed that the influence of the partial ice-covers and secondary currents near the sidewall dramatically altered the distributions of the mean velocity, Reynolds stresses and turbulence production across the channel. Based on the 3D simulations, it was shown that the modifications to the turbulence quantities were largely influenced by strong counter-rotating secondary circulations in the core of the partially covered channels and eight smaller secondary cells at the corners. The core secondary circulations interact with adjacent corner cells to form a dynamic link between the open water and ice-covered sections of the channel.

Effects of the Advance Ratio on the Evolution of Propeller Wake

This study numerically carried out the propeller open water test (POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the Κ-ω SST model. Numerical simulations were performed at wide range of advance ratios. A great difference of velocity magnitude between the inner region and the outer region of the slipstream tube forms the thick and large velocity gradient which originates from the propeller tip and develops along the downstream. Eventually, the strong shear layer appears and plays the role of the slipstream boundary. As the advance ratio increases, the vortical structures originated from the propeller tips quickly decay. The contraction of the vortices trace is considerable with decreasing the advance ratio.

Two‐sided turbulent surface‐layer parameterizations for computing air–sea fluxes

AbstractStandard methods for determining air–sea fluxes typically rely on bulk algorithms set in the frame of Monin–Obukhov similarity theory (MOST), using ocean surface fields and atmosphere near‐surface fields. In the context of coupled ocean–atmosphere simulations, the shallowest ocean vertical level is usually used as bulk input and, by default, the turbulent closure is one‐sided: it extrapolates atmosphere near‐surface solution profiles (for wind speed, temperature, and humidity) to the prescribed ocean surface values. Using near‐surface ocean fields as surface ones is equivalent to considering that, in the ocean surface layer, solution profiles are constant instead of also being determined by turbulent closure. Here we introduce a method for extending existing turbulent parameterizations to a two‐sided framework by explicitly including the ocean surface layer within the aforementioned parameterizations. The formalism we use for this method is derived from that of classical turbulent closures, so that our novelties can easily be implemented within existing formulations. Special care is taken to ensure the smoothness of the resulting solution profiles. Other physical phenomena, such as the penetration of radiative fluxes in the ocean and the formation of waves, are then included within our formalism, and their effects are assessed. We also investigate the impact of such two‐sided bulk formulations on air–sea fluxes evaluated from a setting similar to those of coupled ocean–atmosphere simulations.

Numerical Investigation of Turbulent Offset Jet Flow Over a Moving Flat Plate Using Low-Reynolds Number Turbulence Model

Abstract The present study reports the numerical simulation of turbulent plane offset jet flow over a moving plate. The effect of plate velocity on various flow characteristics is discussed in detail including the special case of a stationary plate. For turbulence closure, the low-Reynolds number (LRN) turbulence model proposed by Yang and Shih (YS) is applied because it is computationally robust and reported to work quite effectively in several complex flow situations. The computations have been carried out with a Reynolds number of 15,000 for various offset ratios (OR = 3, 7, and 11) and different velocity ratios (Uplate) of the plate in the range 0–2. The finite volume method (FVM) with a staggered grid arrangement has been used to solve the transport equations. The application of the LRN model along with the integration to wall (ITW) approach enables us to capture one closed loop of the Moffatt vortex near the left corner of the wall for the stationary plate case. The spreading of the jet has been found to reduce by increasing the velocity of the plate. The jet half-width lies very close to the wall for the plate to jet velocity 1.5 and 2. For two extreme limits of plate velocity, i.e., Uplate = 0 and 2, the nearly self-similar profiles are observed at different axial locations in the wall jet region. Also, the flow is observed to exhibit nearly self-similar behavior when velocity profiles are plotted for various offset ratios at a given axial location in the wall jet region for Uplate = 0 and 2. It has been found that the flow characteristics are significantly influenced by the plate velocity.