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The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. Most techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that is, they require access to all available samples of a time series at once. In addition to the impossibility of online monitoring of uncertainties during the course of simulations, such an offline approach can lead to input/output (I/O) deficiencies and large storage/memory requirements, which can be problematic for large-scale simulations of turbulent flows. Here, we designed, implemented and tested a framework for estimating time-averaging uncertainties in turbulence statistics in an in-situ (online/streaming/updating) manner. The proposed algorithm relies on a novel low-memory update formula for computing the sample-estimated autocorrelation functions (ACFs). Based on this, smooth modeled ACFs of turbulence quantities can be generated to accurately estimate the time-averaging uncertainties in the corresponding sample mean estimators. The resulting uncertainty estimates are highly robust, accurate, and quantitatively the same as those obtained by standard offline estimators. Moreover, the computational overhead added by the in-situ algorithm is found to be negligible allowing for online estimation of uncertainties for multiple points and quantities. The framework is general and can be used with any flow solver and also integrated into the simulations over conformal and complex meshes created by adopting adaptive mesh refinement techniques. The results of the study are encouraging for the further development of the in-situ framework for other uncertainty quantification and data-driven analyses relevant not only to large-scale turbulent flow simulations, but also to the simulation of other dynamical systems leading to time-varying quantities with autocorrelated samples. [ABSTRACT FROM AUTHOR]

We discuss wall-modeling of turbulent heat transfer of water channel flows with temperature-dependent viscosity via direct numerical simulations. We considered a top-cooled wall (293[K]) and a bottom-heated wall (353[K]) and varied the friction Reynolds numbers from 300 to 1000. The fluid viscosity varied depending on the local fluid temperature, whereas the other physical properties were assumed to be constant. The results show that semi-local scaling based on the local viscosity and wall friction velocity reasonably accounts for the effects of variable viscosity on turbulent flows, except in the vicinity of the wall, where wall cooling intensifies the turbulent vortical motion, leading to increased semi-locally scaled eddy diffusivities compared with those near the heated wall. In the vicinity of the cooled wall, turbulent transport is enhanced by increased viscous transport, which transfers more turbulent kinetic energy toward the cooled wall. The effectiveness of semi-local scaling for wall-modeling was validated by performing a wall-modeled large-eddy simulation at R e τ = 1000 , where we incorporated the semi-local viscous length scale into the classical mixing-length model. The modified mixing-length model reasonably reproduced the effects of variable viscosity on turbulent flows. • DNS of turbulent water channel flow with temperature-dependent viscosity is performed. • Effects of temperature-dependent viscosity on turbulence is studied. • Effectiveness of semi-local scaling based on local viscosity and friction velocity is investigated. • Wall-model for variable viscosity turbulent flows is proposed and assessed. [ABSTRACT FROM AUTHOR]

• Upstream turbulence can strongly affect a turbulent round jet. • Maximum values of turbulence may not be monotonic or well positioned. • Integral averages of turbulence can be both monotonic and well-defined. In many equilibrium-based models for droplet size prediction, the fundamental parameters of turbulence are removed in favour of bulk quantities like velocity, and diameter. In this work we show that the upstream conditions of the jet are of critical importance and cannot be neglected, as they influence the turbulence field in jets in ways that are not accounted for in models based entirely on bulk parameters. This work presents the results of a single-phase investigation into the effect of upstream disturbances on a turbulent free jet. Reynolds Averaged Navier-Stokes Simulations of turbulent free jets with disturbances (in the form of orifice plates with a β ratio of 0.5) located at varying locations upstream of the pipe exit have been undertaken. Validation against experimental data for an orifice plate in a pipe found the Standard k-ε model to be the most accurate of the RANS models tested for this geometry. The additional turbulence generated from the upstream disturbances was found to be advected downstream and did not dissipate prior to the jet exit. The increased turbulence levels and altered form of the turbulence profile at exit was found to affect the evolution and observed turbulence levels of the free jet. Two distinct 'modes' were observed for the influence of the disturbances on the free jet. When the orifice plate is near the exit the free jet is dominated by the behaviour of semi-confined jet forming from the blockage. For the deeper set disturbances, the predicted form of the free jet was similar to that of the free jet from a straight pipe, though the turbulence levels are still elevated at the exit, affecting spreading rates and turbulence levels in the jet. Measures based on averages of TKE and TDR over hemispheres of varying radii are proposed for the development of models that do take into account the turbulent state of the exiting jet. [ABSTRACT FROM AUTHOR]

In this paper, the original finite volume lattice Boltzmann method (FVLBM) on an unstructured grid (Part I of these twin papers) is extended to simulate turbulent flows. To model the turbulent effect, the k − ω SST turbulence model is incorporated into the present FVLBM framework and is also solved by the finite volume method. Based on the eddy viscosity hypothesis, the eddy viscosity is computed from the solution of the k − ω SST model, and the total viscosity is modified by adding this eddy viscosity to the laminar (kinematic) viscosity given in the Bhatnagar–Gross–Krook collision term. Because of solving for the collision term with the explicit method in the original FVLBM scheme, the computational efficiency is much lower for simulating high Reynolds number flow. This is due to the fact that the largest time step decided by the stability condition of the collision term, which is less than twice the relaxation time, is much smaller than that decided by the CFL condition. In order to enhance the computational efficiency, the three-stage second-order implicit–explicit (IMEX) Runge–Kutta method is used for temporal discretization, and the time step can be one or two orders of magnitude larger as compared with the explicit Euler forward scheme. Although the computational cost is increased, the final computational efficiency is enhanced by about one-order of magnitude and good results can also be obtained at a large time step through the test case of a lid-driven cavity flow. Two turbulent flow cases are carried out to validate the present method, including flow over a backward-facing step and flow around a NACA0012 airfoil. The numerical results are found to be in agreement with experimental data and numerical solutions, demonstrating the applicability of the present FVLBM coupled with the k − ω SST model to accurately predict the incompressible turbulent flows. [ABSTRACT FROM AUTHOR]

Variational autoencoders (VAEs) have shown promising potential as artificial neural networks (NN) for developing reduced-order models (ROMs) in the context of turbulent flows. In this study, we propose a method that combines β -VAEs for modal decomposition and transformer neural networks for temporal-dynamics prediction in the latent space to develop ROMs. We apply our method to an existing database of a turbulent flow around a wall-mounted square cylinder obtained by direct numerical simulation (DNS). A parametric study is performed to investigate the effects of the hyperparameters of the proposed β -VAEs and determine the optimal values. For the first time, we incorporate the consideration of the complexity of architecture into our studies, providing new insights into hyperparameter selection for β -VAEs, which remains a challenging problem for optimising model performance. Results regarding the influence of the different hyperparameters and guidelines to design these architectures are reported. Our optimal model achieves a reconstruction accuracy of 97.18% of the entire dataset using only ten modes. Subsequently, we employ the transformer models to identify latent-space temporal dynamics learned by the optimal β -VAE model and build ROMs to predict instantaneous fields. The resulting model achieves promising accuracy in temporal-dynamics predictions and yields energy reconstruction levels of 96.5% and 83% for a field 25 and 50 steps into the future, respectively, showcasing the potential of the transformer in predicting the temporal dynamics. Overall, the proposed method has potential applications in advanced flow control and fundamental studies of complex turbulent flows. • β -VAEs and transformer neural networks are combined to create ROMs of turbulent flows. • Parametric studies of β -VAEs, considering architecture complexity and providing guidelines. • The most energetic β -VAE modes represent dynamics associated with the first POD modes. • Transformer models outperform LSTM models in temporal-dynamics prediction. [ABSTRACT FROM AUTHOR]

The present study compares the Lagrangian and Eulerian approaches under the same operating conditions with an emphasis on their performance in predicting particle deposition in turbulent flows. In the study, for small particles (d p < 5 μm), the results of the two approaches were not in satisfactory accordance with each other, and the results obtained using the Eulerian approach look more reasonable than those obtained using the Lagrangian approach. For large particles (d p > 9 μm), the results obtained using the two approaches gradually converge and agree well with the experimental results at 16 μm. For the same investigation, the Eulerian approach requires less computational time than the Lagrangian approach, that is, the Eulerian approach has less computational cost. Furthermore, the total fouling mass calculated using both approaches exhibits asymptotic properties, and can predict the total fouling mass. However, the total fouling mass calculated using the Eulerian approach is closer to the experimental curve. Image 1 • This study compares the results of two approaches of Lagrangian and Eulerian. • The simulated results obtained with the two approaches were compared with the published experimental data. • The Eulerian approach requires less computational time than the Lagrangian approach. • The total fouling mass calculated using the Eulerian approach is closer to the experimental curve. [ABSTRACT FROM AUTHOR]

This paper presents new measurements of species concentrations, temperature and mixture fraction in selected regions of a turbulent ethanol spray flame. The line-Raman–LIF–CO OH setup developed at the Sandia's Combustion Research Facility is utilised to probe regions of a spray flame where laser breakdown of liquid droplets is avoided and the remaining interferences can be corrected. The spray flame is stabilised on the piloted Sydney needle spray burner, where axial translation of the liquid injecting needle in the air-blast stream can transition the spray from dilute to dense. The solution to obtaining successful measurements is found to be multifaceted and includes: the appropriate selection of flame conditions; high sensitivity of the Raman detection system permitting reduced laser energies; development of a pre-processing algorithm to reject strong droplet interferences; and application of the hybrid matrix inversion method combined with wavelet denoising to account for interference corrections and noise at the very low signal levels obtained. Unique and necessary for the successful measurements reported in this paper, a pre-processing algorithm is outlined that removes data points corrupted with strong interferences from droplets. These interferences arise from a range of sources, but the most intense are due to the laser interaction with surrounding mist or liquid fragments, such that measurements near the jet centreline are corrupted and hence discarded. Reliable measurements of mixture fraction, temperature obtained from the sum of the species number densities, and species mole fractions are reported for regions in the flames sufficiently far from the centreline. The paper demonstrates the feasibility of the judicious use of Raman scattering in turbulent spray flames, the results of which will be extremely useful for validating numerical simulations. [ABSTRACT FROM AUTHOR]

• A new friction factor-heat transfer analogy is derived for supercritical fluids. • The new analogy is much more accurate than the Chilton-Colburn analogy. • The new analogy performs well for He, H 2 O, CO 2 , R134a and R22. A new friction-heat transfer analogy for the prediction of heat transfer to turbulent fluids at supercritical pressure is presented. This analogy is based on the observation that the predominent events that determine the turbulent heat flux known as hot ejections and cold sweeps have different thermophysical properties. This observation is used to derive a new friction-heat transfer analogy, which we call the ejection-sweep analogy. It is shown that the ejection-sweep analogy yields very good results with respect to predicting heat transfer coefficients for different fluids (water, CO 2 , Helium, R22 and R134a) that are heated at supercritical pressure at low heat flux to mass flux ratios. Furthermore, the new analogy performs much better than the Chilton-Colburn analogy. The new analogy was also compared with two well-known relations from literature. It was found that the ejection-sweep analogy predictions are more consistent with respect to the investigated fluids than the relations from literature and that the analogy can be applied to at least all fluids studied in this work. The ejection-sweep analogy can be used in the development of more advanced heat transfer models that include buoyancy and acceleration effects. [ABSTRACT FROM AUTHOR]

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation (Dns). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number R e τ ranging from 125 to 730 where R e τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration. [ABSTRACT FROM AUTHOR]

Highlights • A new approach is proposed to simulate TIV using URANS models. • This approach is capable of simulating TIV without requiring an external perturbation. • The obtained results have shown a good agreement with the DNS. Abstract Nuclear reactor designs such as PWR and BWR are susceptible to vibrations induced on the nuclear fuel rods due to fast flowing coolants around the rods. The non-linear behaviour of flexible components have always been a challenge to compute especially when dealing with strongly coupled fluid–structure interaction cases as found in the reactors. Simulating such a behaviour involves a two-way coupling of a well resolved turbulent flow Computational Fluid Dynamics (CFD) solver to a Computational Solid Mechanics (CSM) solver. The use of a high fidelity CFD solver to resolve turbulent flows in an FSI (Fluid-Structure Interaction) simulation is computationally expensive ergo is not practical in for industrial purposes. To address this issue, a different approach is discussed in this article to simulate turbulence induced vibrations through the use of U-RANS models. The method is based on computing the modeled turbulent pressure and velocity fluctuations from values obtained by solving U-RANS (Unsteady-Reynolds Averaged Navier Stokes) equations. The calculated turbulent fluctuating field is combined with mean values to compute an instantaneous turbulent pressure field to apply an external pressure and shear force on the structure and vice-verse until convergence is achieved. This method can be used to accurately estimate the behaviour of a flexible structure in a turbulent flow. The article provides a detailed explanation of the model followed by validation with three numerical test cases. The first case involves a CFD simulation where results from the pressure fluctuation model (PFM) is compared to a benchmark DNS (Direct Numerical Simulation) of a turbulent channel flow with friction Reynolds number, Re τ = 640. Later the PFM is applied to a 2-dimensional strongly-coupled FSI simulation with a flexible steel flap in turbulent water flow to study the feasibility and stability of PFM applied to an FSI problem. Finally, the PFM is used to simulate an experimental case of a brass rod excited by turbulent water performed by Chen and Wambsganns (1972). The results show that the PFM is capable of simulating turbulence induced vibration (TIV) with low-fidelity U-RANS models. [ABSTRACT FROM AUTHOR]

This work explores the feasibility of real-time large-eddy simulations of flow over urban canopies at the neighborhood scale. The cumulant lattice Boltzmann method is employed using a single General Purpose Graphic Processing Unit (GPGPU). In order to demonstrate the validity and efficiency of this approach we simulate wind flow in a neighborhood of Basel. Simulation results are validated against measurements from the Basel Urban Boundary Layer Experiment (BUBBLE) and are compared to previous CFD simulations. Turbulence statistics are found to be in agreement with corresponding tower measurements according to several validation metrics. While quantitative comparisons are limited to the six measurement locations of the field measurements, the available data supports the conjecture that real-time simulation of urban air flow is feasible at the neighborhood scale with the proposed numerical technique. • LES of urban air flow of a neighborhood of Basel, Switzerland. • Simulation results are validated against tower measurements. • First application of cumulant LBM with quartic parametrization to real world problem. • It is shown, that LBM on GPGPUs can offer real-time simulations for urban air flows. [ABSTRACT FROM AUTHOR]

Abstract Numerical investigation of mixing is performed at Mach 2.0 model Scramjet combustor employing parallel strut injection schemes for fuel. In the present investigation, basic strut injector is modified in such a way to produce additional vortices in streamwise direction and improve fuel-air mixing. Air is injected at Mach 2.0 at the combustor inlet and fuel is injected at sonic speed from the blunt end of the strut. The flow field involving high-speed turbulent mixing and heat addition was modeled by three-dimensional Reynolds averaged Navier-Stokes equations. A realizable k-ε model was chosen to close the turbulence problem with the default model constants. Non-premixed combustion of hydrogen and air is modeled using the mixture fraction β-pdf framework. Turbulence-chemistry interactions are handled by a strained flamelet model. Comparisons of numerical results with experimental results have demonstrated the accuracy and applicability of computational grid and a numerical scheme for hot and cold flow solutions. The shock-shear layer interaction present within the combustor increases the local turbulent intensity and has a positive effect on mixing. The mixing efficiency obtained with improved strut injector is compared with the basic strut. Improved strut injection scheme showed a mixing efficiency of >95% with a 45% reduction in length. Further combustion efficiency is calculated in the streamwise direction and plot follows the similar trend as the mixing efficiency. The proposed modification of strut geometry showed improved mixing and combustion performance. Highlights • Turbulence chemistry modeled by flamelet accurately predicts reaction features. • Mixing of air and fuel is strongly influenced by vortices and turbulence. • Total pressure loss within the supersonic combustor is due to shocks and vortices. • Shock increases mixing locally by increasing the turbulent kinetic energy. • Length of mixing efficiency >95% is reduced by 15 mm by modified strut injector. [ABSTRACT FROM AUTHOR]

Highlights • We analise the role played by the aging of aloe vera on its drag reduction property. • We use 1H NMR to indicate the compositions of our different kinds of leaves. • We use two kinds of apparatus to take into account the DR ability of aloe vera. • Samples richer in complex polysaccharides are more efficient. Abstract Polymeric drag reducers have been developed over many years due to the great number of practical applications. In all of them, the molecular stability is an essential requirement. Usually, polymers break down under turbulent flows, which causes a decrease in their efficiency as drag reducers. Besides that, some specific applications, in agro and biomedical fields, impose a specific requirement that must be fulfilled, which is the use of non-toxic materials. A suitable stable material that is elected to accomplish this necessity is the mucilage of aloe vera, which is a bio-polymer that can be used as an alternative to the synthetic ones. Here, we investigate the role played by the aging of aloe vera on its capacity to reduce drag. The results obtained by 1H nuclear magnetic resonance indicate that the compositions of young and mature leaves of aloe vera are different and such a difference plays an important role on their efficiency as drag reducers. Tests were performed to analyse the drag reduction in a rotating apparatus and in a pipeline system and the efficiencies of leaves of different ages were compared to their composition. The main conclusion of these experiments is that the young mucilage samples, which are richer in complex polysaccharides and exhibit lower acid contents, are more efficient drag reducers. [ABSTRACT FROM AUTHOR]

Highlights • Low- (LDR) and high-extent drag reduction (HDR) are qualitatively different stages. • Sharp changes in flow statistics are established between LDR and HDR. • Drag-reducing polymers affect different wall regions between LDR and HDR. • Turbulent structures become clustered and localized during the LDR–HDR transition. • A mechanism is proposed based on the changing vortex re-generation dynamics. Abstract Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of drag reduction (DR) and the eventual convergence to the maximum drag reduction (MDR) asymptote. Between the onset and MDR, recent experimental and numerical observations prompted the need to further distinguish the low- and high-extent drag reduction (LDR and HDR). Fundamental knowledge of this transition will be important for understanding turbulent dynamics in the presence of polymers, as well as for inspiring new flow control strategies for efficient friction reduction. We use direct numerical simulation (DNS) to explore all these transitions in the parameter space and, in particular, demonstrate that the LDR–HDR transition is not merely a quantitative effect of the level of drag reduction, but a qualitative transition into a different stage of turbulence. A number of sharp changes in flow statistics are found to accompany the transition and at HDR, turbulence becomes localized with vortices forming clusters. These observations suggest that polymer-induced drag reduction follows two distinct stages. The first starts at the onset of drag reduction, where the coil-stretch transition of polymers causes an overall suppression of turbulent fluctuations. The second starts at the LDR–HDR transition, where flow statistics become fundamentally changed in the log-law layer and turbulence localization is observed. A mechanism is then proposed for the latter based on the changing vortex regeneration dynamics between LDR and HDR. [ABSTRACT FROM AUTHOR]

Highlights • Develops a new Second Moment Closure turbulence model for stably stratified, wall-bounded flows. • Introduces an additional length scale due to buoyancy in the elliptic relaxation equation. • Formulates a coupled set of Helmholtz equations for elliptic relaxation. • Derives the boundary conditions from an analysis of the budget of near-wall terms in the transport equations. • Results of the new model show significant improvement compared to the standard model. Abstract The article presents a new elliptic relaxation procedure for Second Moment Closure (SMC) turbulence modeling of wall-bounded, stably stratified flows. Specifically, it directly introduces buoyancy effects in the elliptic relaxation equation. The new formulation results in an additional length scale that produces a coupled set of Helmholtz equations. The study then extends the new technique to Reynolds scalar fluxes. Furthermore, it examines the budgets of the different terms of their transport equations near the wall and systematically derives the relevant boundary conditions. Comparison of model predictions with Direct Numerical Simulation (DNS) data for stably stratified plane channel flows available in the literature rounds off this paper. [ABSTRACT FROM AUTHOR]

This paper presents a robust, efficient, and strongly scalable solution methodology for simulation of complex turbulent flows on unstructured grids. The compressible Reynolds averaged Navier–Stokes (RANS) equations and the negative Spalart–Allmaras (SA) turbulence model are discretized, in coupled form, using a Streamline Upwind Petrov–Galerkin (SUPG) scheme. The time integration is fully implicit, and the discretized equations are advanced towards a steady-state solution using a pseudo-transient continuation (PTC). For solution of the linearized systems, a preconditioned Krylov solver is used. Seeking robustness, Krylov solvers are commonly preconditioned using incomplete factorization methods such as ILU(k). However, these methods are neither memory efficient, nor strongly scalable. To provide a better alternative, the implicit line solution method, which has been traditionally used in finite-volume methods, is revised and enhanced to solve stiffer linear systems. In the developed method, the lines are generated using a matrix-based approach, which connects the strongly-coupled unknowns. In addition, to improve the robustness of the line solver for high-CFL systems, a dual-CFL strategy, with a lower CFL number in the preconditioner matrix, is developed. Also, it is shown that for high-order continuous finite-element discretizations, the interconnections of the degrees of freedom on a line form a banded matrix which is wider than tridiagonal, but still can be factorized completely without generating any fill-ins. The developed line preconditioner is strongly scalable and, in contrast to the ILU factorization, its convergence behavior does not depend on the number of partitions. Two three-dimensional numerical examples are presented in which the performance of the line preconditioner is compared with that of the ILU(k) preconditioner. This comparison shows that, in addition to robustness improvements, the line preconditioner offers significant benefits in terms of memory efficiency. [ABSTRACT FROM AUTHOR]

Abstract We present an efficient solver for massively-parallel direct numerical simulations of incompressible turbulent flows. The method uses a second-order, finite-volume pressure-correction scheme, where the pressure Poisson equation is solved with the method of eigenfunction expansions. This approach allows for very efficient FFT-based solvers in problems with different combinations of homogeneous pressure boundary conditions. Our algorithm explores all combinations of pressure boundary conditions valid for such a solver, in a single, general framework. The method is implemented in a 2D pencil -like domain decomposition, which enables efficient massively-parallel simulations. The implementation was validated against different canonical flows, and its computational performance was examined. Excellent strong scaling performance up to 1 0 4 cores is demonstrated for a domain with 1 0 9 spatial degrees of freedom, corresponding to a very small wall-clock time/time step. The resulting tool, CaNS , has been made freely available and open-source. [ABSTRACT FROM AUTHOR]

Turbulent flow around bluff bodies generates pressure fluctuations which propagate as acoustic waves. Differences in the shape of a body can affect frequencies and amplitudes of the propagating pressure signals. In the present work three elementary geometries (sphere, cube and prolate spheroid), immersed in a uniform water flow, are examined in order to analyze the differences of the resulting hydroacoustic fields. The turbulent flow at R e A = 4430 (based on the cross-sectional area of the bodies) is reproduced through wall-resolving Large-Eddy Simulation and the hydroacoustic far-field is analyzed by adopting the Ffowcs Williams and Hawkings analogy. The quadrupole term of the acoustic equation is first reformulated in the convective form and then solved through direct computation of the volume integrals. This procedure is found possible in hydrodynamics where the speed of sound is very large and the flow velocities are small. In spite of the fact that the frontal section of the bodies has the same area, the analysis shows that a streamlined body is able to produce a pressure signal one order of magnitude lower than that generated by a bluff geometry. The separate analysis of the loading noise and of the quadrupole one has shown that the former is larger than the latter in case of 3D-shaped bluff body (sphere and cube), whereas the opposite is true in case of a streamlined body. A preliminary analysis between the case of an elongated square cylinder and a cube, shows that the persistence of a two-dimensionally shaped wake when compared to a three-dimensional one contributes to increase the quadrupole part of the radiated noise. [ABSTRACT FROM AUTHOR]

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes' solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and "canonical" distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing. • Direct numerical simulations of oscillatory flow over a bed of spherical particles. • Reduced phase delay in turbulent flow compared to the laminar case. • Turbulence is observed during deceleration with "canonical" statistics. • Anisotropy maps show similar distributions to unidirectional flows. [ABSTRACT FROM AUTHOR]

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of R e τ ≈ 1000. Turbulent flow over two groups of rough walls – a homogeneous random arrangement and a clustered arrangement – is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements. [Display omitted] • Turbulent flow over a random rough surface is simulated by LESs. • The effects of the differently arranged rough walls on turbulent flow are examined. • Large-scale SMs lead to failure of outer-layer similarity for clustered rough wall. • The self-similar structures satisfying the attached-eddy hypothesis still exist. [ABSTRACT FROM AUTHOR]

An efficient Navier–Stokes solver for the infinite-swept wing problem is presented. The new flow solution, that reproduces correctly the physics responsible for cross-flow effects, is obtained around a two-dimensional stencil. On the contrary, existing state-of-the-art methods rely on a three-dimensional stencil. Numerical details are followed by an extensive validation campaign, including steady and unsteady compressible flows. The test cases are for single and multi-element aerofoils in both laminar and turbulent regimes. Under identical conditions (numerical settings, grids, etc.), the computational cost of the proposed solver was reduced by at least 75% compared to that of existing state-of-the-art methods. This was also confirmed employing various turbulence models. With a limited effort required to enhance an existing computational fluid dynamics solver (either two or three-dimensional), the infinite-swept wing method was implemented in an industrial-grade package used across Europe for rapid engineering analysis. [ABSTRACT FROM AUTHOR]

Optical diagnostics for fluid temperature measurements continue to further our understanding of flows involving heat transfer and/or chemical reactions, which are intrinsic to key areas including energy production, the process industries, transportation, heating/cooling systems and naturally-occurring thermal convection. Besides temperature, all flows must also be described by their velocity. As these flows are often turbulent, an important capability is to measure both velocity and temperature at the same time to capture, for example, the turbulent heat flux term appearing in the energy conservation equation. This paper reviews temperature measurement techniques for fluid flows that are based on thermographic phosphors, which are materials that possess temperature-dependent luminescence properties. Phosphor particles are seeded into the fluid flow of interest. Following laser excitation, the luminescence of the particles is detected, and the temperature measurement is derived using either the spectral intensity ratio or the lifetime. The same particles can also be used for velocity measurements using well-established particle-based approaches, such as laser Doppler velocimetry (LDV) or particle image velocimetry (PIV), producing instantaneously correlated vector-scalar data. First introduced over a decade ago, this concept has since evolved and is currently capable of two-dimensional measurements in the temperature range 200–900 K. At lower temperatures a single-shot spatial precision better than 4 K is possible, as is imaging at sampling rates in the multi-kHz range. The approach is flexible, allowing, for example, techniques which probe single particles for point measurements with a 200 µm spatial resolution. Besides many validation experiments, the method has been applied in internal combustion engines, a falling film absorber, a high-pressure reaction vessel and in enclosed wind tunnels to study various turbulent heat transfer and reactive flow phenomena. The objective of this article is to provide the first review of this emerging field. The focus is on 1) the method: how has the principle of phosphor thermometry been used for flow measurements, and what instrumentation and processing steps were implemented; 2) how phosphor particles were characterised, and which phosphors are best-suited to temperature measurements in flows; and 3) the applications of the technique. Throughout, and with a detailed analysis of various sources of error, the review endeavours to compare the work and identify common aspects, advantages and limitations of the studies that led to successful flow measurements, and therefore should serve as a guide for researchers using the method. The article also briefly summarises the various challenges which the authors consider are key to the future development of these diagnostics. [ABSTRACT FROM AUTHOR]

This study presents an innovative wind tunnel approach to evaluate the efficiency of Vertical-Axis Wind Turbines (VAWT) in turbulent flows, to study their integration in urban environments. The first part of the research is devoted to obtaining highly-turbulent wind profiles in the wind tunnel, with the use of different configurations of square grids. A careful study and validation of this technique is done, in order to obtain uniform wind conditions with the adequate values of turbulence intensity and length scales to model the urban flows. The set-up is used to test a H-Darrieus VAWT under values of turbulence over 5%, in comparison with the operation of the turbine under free stream. The preliminary results show that high levels of turbulence do have a significant effect in turbine performance, causing a drop of power for high rotational speeds, increased vibrations in the structure and more difficult control of the rotor. More tests are advised to validate these observations, as well as to expand the study over higher values of turbulence intensity, in order to present a more detailed study with empirical conclusions. [ABSTRACT FROM AUTHOR]

The efficient mixing of fluids is key in many applications, such as chemical reactions and nanoparticle precipitation. Detailed experimental measurements of the mixing dynamics are however difficult to obtain, and so predictive numerical tools are helpful in designing and optimizing many processes. If two different fluids are considered, the viscosity and density of the mixture depend often nonlinearly on the composition, which makes the modeling of the mixing process particularly challenging. Hence water-water mixtures in simple geometries such as T-mixers have been intensively investigated, but little is known about the dynamics of more complex mixtures, especially in the turbulent regime. We here present a numerical method allowing the accurate simulation of two-fluid mixtures. Using a high-performance implementation of this method we perform direct numerical simulations resolving the spatial and temporal dynamics of water–ethanol flows for Reynolds numbers from 100 to 2000. The flows states encountered during turbulence transition and their mixing properties are discussed in detail and compared to water-water mixtures. [ABSTRACT FROM AUTHOR]

The influence of the radiative heat transfer and the effects of air variable properties on the natural convection flows established in square cavities with thermal passive device geometry are numerically investigated. Two-dimensional, laminar, transitional and turbulent simulations are obtained, considering both uniform heat flux and uniform wall temperature heating conditions. The average Nusselt number and the dimensionless mass-flow rate have been obtained for a wide range of the Rayleigh number varying from 10 3 to 10 16 . The results obtained for different heating intensities are analyzed and compared. In addition, the influence of considering surface radiative effects on the differences reached for the Nusselt number and the mass flow rate obtained with several heating intensities is studied. The obtained results show that the effects of thermal radiation on the appearance of the burnout phenomenon are particularly relevant under given circumstances. The influence of the wall-to-wall spacing of the vertical channel inside the cavity is also analyzed. The changes produced in the flow patterns into the cavity when the radiative heat transfer and the effects of variation of properties are relevant, are also shown. [ABSTRACT FROM AUTHOR]

A new residual-based variational multiscale (RBVMS) formulation for incompressible turbulent flows is proposed that is suitable for discretization using divergence-conforming B-splines. The proposed methodology results in a pointwise satisfaction of the zero-divergence constraint on the discrete velocity field. The velocity fine scales are residual-driven and constructed in a manner that is consistent with the divergence-free constraint on the discrete velocity solution. The resulting formulation is tested on laminar- and turbulent-flow benchmark problems showing excellent stability and accuracy characteristics in both regimes. [ABSTRACT FROM AUTHOR]

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall ( u τ,S ) and half the channel height ( h ) is Re τ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Re τ ,S . The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated. [ABSTRACT FROM AUTHOR]

This work details the assessment of the performance of the drag-porosity model implemented in ARPS (Advanced Regional Prediction System) atmospheric Large-Eddy Simulation (LES) solver for simulating the atmospheric boundary layer developing over the urban canopy with comparison with literature. The flow within and above an idealized urban canopy consisting of a staggered array of cubes with various packing densities modeled with the drag-porosity approach immersed into a neutral, Coriolis-free atmospheric boundary layer at high Reynolds is investigated. Besides one-points statistics, particular interest was given to the ability of the model to reproduce the turbulent coherent structures and their characteristic scales. A detailed analysis of one-point statistics, one- and two-dimensional spectra and two-point correlation functions revealed the presence of typical structures and features found in wall-bounded turbulent flows (two-scale behavior in the roughness sublayer, ejections, sweeps, self-similar wall-attached large scale streaky motions, canopy-independent very large scale motions). Further investigation to identify the interaction mechanisms between large and small scales based on spectral filtering highlighted an interaction mechanism that resembles an amplitude modulation process, as observed in literature on wall-bounded flows. These findings therefore show that the proposed approach is able to reproduce all the key features of the flow developing over urban terrain. • Evaluation of a drag-porosity model for LES of flows over urban canopies. • Drag alone drives turbulent boundary layer processes at high Re above canopy-top. • Canopy density influence on the scale content in and above the roughness sublayer. [ABSTRACT FROM AUTHOR]

To clarify the effects of surface topology on the scaling of roughness effects, we conduct experiments on turbulent rough-walled channel flows from transitionally to fully rough regimes. We considered three-dimensional irregular rough surfaces with different effective slope E S , skewness factor S k , and fixed roughness height scales. The E S values are varied from 0.09 to 0.72 for positively and negatively skewed surfaces with S k = ± 0. 4. It is revealed that the transitional behavior to the fully rough regime is not influenced by S k , but rather by E S. The transition to the fully rough regime for surfaces with E S ≥ 0. 18 is insensitive to the E S values, whereas wavy surfaces with E S = 0. 09 lead to a moderate transition. The equivalent sand-grain roughness k s steeply increases with increasing E S values from 0.09 to 0.36, whereas a further increase in the E S value does not significantly influence k s. It is also found that positively skewed surfaces with S k = + 0. 4 yield larger k s values compared to surfaces with S k = − 0. 4 ; this S k effect is more pronounced for wavy surfaces with small E S values. • Turbulent flows over three-dimensional irregular rough surfaces are studied. • Particle image velocimetry and pressure measurements are performed. • Effects of the skewness and effective slope of rough surfaces on hydrodynamics are discussed. • Scaling of the roughness function and equivalent sand-grain roughness is explored. [ABSTRACT FROM AUTHOR]

A numerical investigation is carried out to examine the effect of a new baffle design in a membrane tube on the hydrodynamics and filtration efficiency. Two different orientations of hemispherical baffles named as RO baffle for the Right Orientation and LO baffle for the Left Orientation, respectively, are explored. Two values of the carbonate calcium suspensions are used: 5 and 10 g/L. The axial velocity, stream function, static pressure, wall shear stresses and turbulent characteristics are the physical parameters utilized to evaluate the filtration performance. The obtained results showed that the presence of an array of hemispherical baffles can develop the local shear stresses on the membrane surface and create the fluid eddy movement which enhances considerably the filtration performance. When the feed concentration is 5 g/L and in a comparison with the unbaffled tubes, the RO and LO cases achieved an increase in the filtration flux rate by 57% and 64%, respectively. For the second feed concentration (10 g/L), the enhancements are 85% and 96% for the RO and LO cases, respectively. In a comparison between the LO and RO cases, the LO baffle gives the best performance. Our results were compared with experimental data and a satisfactory agreement has been found. [ABSTRACT FROM AUTHOR]

Scalar dissipation rate (SDR) is a key quantity in turbulent flow modeling since it measures the scalar mixing intensity. It is well known that turbulence-scalar interaction (TSI) processes play an essential role in turbulent scalar mixing and drive to a large extent the SDR evolution. These processes are characterized by the tensor inner product between the scalar gradient vector and the strain-rate tensor. Direct numerical simulations are conducted to analyze the physics of this interaction in vaporizing turbulent two-phase flows. The well known alignment of the scalar gradient with the most compressive principal direction of the strain-rate tensor – resulting in production of the scalar gradient by turbulence – is recovered in statistics collected sufficiently far from the liquid–gas interface. By contrast, the action of the turbulence-scalar interaction is progressively attenuated as we approach this interface, where the scalar gradient tends to have a direction intermediate between the extensive and the compressive directions. This result questions the validity of passive-scalar turbulence concepts and closures that are commonly used for to tackle the modeling of scalar behavior in vaporizing two-phase flows featuring (or not) subsequent chemical reactions. [ABSTRACT FROM AUTHOR]

Fluid flows in chemical engineering are mainly characterized by the coexistence of turbulent and non-turbulent fluids. Nonetheless, in traditional turbulence models, the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids. We perceived this situation is a source of inaccuracies in modeling practical engineering flows. In this work, a stability criterion for turbulent flows, originating from the principle of compromise-in-competition between viscosity and inertia, is used to obtain closure in the turbulence model, which defines the energy-minimization multi-scale (EMMS)-based turbulence model. Analogous to two-phase flow, the model regards single-phase complex flows as a mixture of turbulent and non-turbulent fluids, and the effect of meso-scale eddy structure on the effective coefficient of viscosity is also considered. The EMMS-based turbulence model is tested against three benchmark problems, namely, the lid-driven cavity problem, flow through a conical diffuser, and flow over an airfoil using experimental and direct numerical simulation (DNS) data. Numerical results show that the EMMS-based turbulence model improves the accuracy of turbulence modeling, demonstrating its feasibility and practicality for accurate simulations of engineering complex flows. [ABSTRACT FROM AUTHOR]

The effects of the radiative effects and the air variable properties (density, viscosity and thermal conductivity) on the buoyancy-driven flows established in open square cavities are investigated. Two-dimensional, laminar, transitional and turbulent simulations are obtained, considering both uniform wall temperature and uniform heat flux heating conditions. In transitional and turbulent cases, the low-Reynolds k − ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate have been obtained for a wide range of the Rayleigh number varying from 10 3 to 10 16 . The results obtained taking into account the variable thermophysical properties of air are compared to those calculated assuming constant properties and the Boussinesq approximation. In addition, the influence of considering surface radiative effects on the differences reached for the Nusselt number and the mass flow rate obtained with several intensities of heating is studied; specifically, the effects of thermal radiation on the appearance of the burnout phenomenon is analyzed. The changes produced in the flow patterns into the cavity when the radiative heat transfer and the effects of variation of properties are relevant, are also shown. [ABSTRACT FROM AUTHOR]

• Different NIROMs are used for turbulent airflow prediction. • Model verification is performed using validated high-fidelity CFD data. • SA-CAE can capture long-range dependence among data. • SA-CAE is the most promising model, followed by CAE and MS-CAE. Computational fluid dynamics (CFD) has been considered as a promising numerical approach in fluid dynamics problems, such as urban airflow prediction. However, airflow field prediction using CFD models is time-consuming. Thus, they cannot be used for (near) real-time and long-term simulations. Reduced-order models (ROMs) are emerged to obviate this limitation. Deep learning (DL) algorithms have been used for developing non-intrusive ROMs (NIROMs) in fluid dynamics applications. In the present study, three different approaches, namely, convolutional autoencoder (CAE), multi-scale CAE (MS-CAE), and self-attention CAE (SA-CAE), are developed for dimensionality reduction, which is considered the first step of the development of a NIROM. The developed models are then used to find a low-dimensional representation of the original data. Afterward, a parallel long short-term memory (LSTM) network is employed for computing the temporal dynamics of the obtained low-dimensional space. The models are trained to reconstruct a turbulent airflow field in the wake region of an isolated high-rise building, located in an unstable thermal stratification condition, using validated CFD data. The models show promising performance in reconstructing the airflow field. However, discrepancies can be observed in the regions with intense gradients. Also, power spectral density functions (PSD) obtained from the reconstructed data are in good agreement with those obtained from the CFD results. On the whole, SA-CAE performs better in reconstructing the airflow field than the other models, followed by MS-CAE and CAE. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional numerical model is developed, in which an Euler implicit method for the temporal discretization and the Finite Volume Method for the spatial discretization are applied to solve the Reynolds-averaged Navier–Stokes (RANS) equations for free surface flows over hydraulic structures in natural channels and rivers. At the free surface two different methods, the front-tracking and the front-capturing, are applied to calculate free surface profiles. The model has been validated against typical benchmarking experiments, and applied to a number of practical applications for natural rivers in Germany. Due to the limitation of the observation data in some application cases, in order to verify our numerical model, we besides have modified and applied the well-known open source CFD toolbox OpenFOAM to the same applications, then compared the results obtained from the OpenFOAM with our model results. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to provide a comprehensive account of Lagrangian stochastic methods for polydisperse two-phase reactive flows. In this work, the emphasis is put on the description of the dispersed phase and on one-particle probabilistic approaches to general non-homogeneous flows. This is a domain where significant progress has been achieved in the last decade and reporting on these advances brings out the current status of Lagrangian stochastic methods. A first objective of this paper is to recall the main aspects of the existing theoretical framework where developments are shown to be set in. A second objective is to clarify the physics contained in present stochastic models. To that effect, the presentation of the main aspects of the reference Langevin model as well as the detailed analysis of several applications covering a range of practical concerns reveal the actual possibilities of these modeling approaches. A third objective is to report on recent developments that open possibilities for Lagrangian stochastic methods, including for example first steps toward structure-based models, hybrid numerical formulations as well as new accounts of particle–particle interactions. Building on these results, a formalism is introduced in the last section for the extension of Lagrangian stochastic methods to particle-laden turbulent flows where the fluid flow is calculated with a Large Eddy Simulation. Finally, the research areas where work is still needed are outlined. [ABSTRACT FROM AUTHOR]

Flow induced by propellers of waterborne vessels can cause sediment resuspension in estuaries, bays and harbors, where sediments are usually contaminated. Bottom shear stress due to propeller wash is the key parameter that determines the initiation of sediment resuspension and the subsequent erosion. A novel self-contained underwater miniature particle image velocimetry (UWMPIV) system has been developed and deployed to study sediment resuspension under propeller wash in a US Navy harbor in San Diego, CA. Near bed profiles of mean velocity and Reynolds stresses were measured to evaluate the bottom shear stress, and to validate the shear stress measured with an acoustic Doppler velocimeter (ADV) that is simultaneously deployed with the PIV system. The critical shear stress was estimated by directly observing PIV images and identifying the moment when sediment resuspension started. PIV measurement became unfeasible as the propeller speed increased and the optical access was blocked by high level of suspended solids. However, the development of the bed erosion was able to be recorded in PIV images at several intervals when sediment concentration was relatively low and the sediment bed was visible. The observed time series of cumulative erosion depth agreed well with an erosion rate model that depends linearly on the bottom shear stress excess. [ABSTRACT FROM AUTHOR]

The movement of suspended sediments in a turbulent boundary layer over a flat bed was numerically studied. Large Eddy Simulation was used to generate the velocity field, and the motion of individual particles was calculated using a modified version of the Maxey and Riley equation (1992). Three types of flows were considered: steady unidirectional, oscillating, and pulsating, with particle sizes ranging from silt to fine sand. In each experiment, 4096 particles were released at the upper edge of the viscous sublayer. The suspension rate, defined as the percentage of particles still afloat after the initial shakedown, depended strongly on the ratio of vertical root-mean-square (rms) velocity fluctuation to settling velocity in all types of flows. This is because the individual motion of sediment particles was strongly influenced by fluctuating flow structures even in the steady unidirectional flows, although the fluctuating small eddies did not last long. In the unsteady cases, a nontrivial relationship was also found with the phase of the flow as the survival rate of sediments was strongly correlated with the time of their initial releases. The survival rate significantly reduced with height in the oscillating flow compared with the pulsating flow because the turbulent fluctuations were confined within the thin boundary layer and did not extend to higher elevations in the oscillating flow. [ABSTRACT FROM AUTHOR]

Modal-decomposition techniques are computational frameworks based on data aimed at identifying a low-dimensional space for capturing dominant flow features: the so-called modes. We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow data useful for flow analysis, reduced-order modeling and flow control. Our approach is based on β -variational autoencoders (β -VAEs) and convolutional neural networks (CNNs), which enable extracting non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions, where the energy percentage captured by the proposed method from five modes is equal to 87.36% against 32.41% of the POD. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes with the determinant of the correlation matrix equal to 0.99, which may lead to interpretability. • Learning a minimal and near-orthogonal set of non-linear modes from turbulent flows. • Based on variational autoencoders (VAEs) and convolutional neural networks (CNNs). • Ranking VAE-based modes with respect to their contribution to the reconstruction. • Leading to the extraction of interpretable non-linear modes. [ABSTRACT FROM AUTHOR]

This paper presents a method for estimating output errors and adapting computational meshes in simulations of unsteady turbulent flows. The chaotic nature of such problems prevents a stable unsteady adjoint solution, and existing regularization techniques are costly for large simulations. The method presented foregoes the unsteady adjoint and instead relies on a field-inversion machine-learning (FIML) framework, which only requires unsteady primal solutions without full-state storage or checkpointing. The FIML model yields an adjoint for the averaged solution, which is combined with an averaged unsteady residual to obtain an output error estimate and adaptive indicator. This error estimate is shown to be accurate when the FIML model augments the original unsteady equations with corrections that are not excessively large. The unsteady residual comes from sampling fine-space residual evaluations during the unsteady simulation. A novel objective function based on an adjoint-weighted residual is presented for the field inversion to improve the ability of the FIML model to predict output errors and the domain-interior state. The localized output error drives adaptation of the mesh size and approximation order. Results for three aerodynamic problems ranging in Reynolds number demonstrate accuracy of the error estimates and efficiency of the computational meshes when compared to other adaptive strategies, including uniform and residual-based refinement. • Dynamically corrected turbulence models well-approximate unsteady turbulence. • FIML adjoint-weighted residual estimates output error in unsteady turbulent flows. • Localized error estimates drive order and mesh adaptation for static meshes. • Output-adapted meshes save degrees of freedom over heuristic adaptative approaches. [ABSTRACT FROM AUTHOR]

• Implemented five simultaneously independent proportional integral derivative controllers to maintain thermal stability in CFD using a similar methodology as employed in the plant. • Developed a comprehensive model of an industrial scale LDPE autoclave reactor consisting of rotating mesh elements, reaction kinetics, and complex geometry. • Validated numerical methods of time step size, grid resolution, and turbulence model sensitivity. • Replicated proposed mixing patterns in CFD. CFD was employed to develop a rigorous model of an LDPE autoclave reactor. Different numerical settings within the solver are evaluated to eliminate false diffusion and to reflect the sensitive heat generation taking place during free radical polymerization. An accurate model can allow geometry and process adaptations to be evaluated for much lower costs than physical experiments. Improving the reactor design allows for longer run times and a higher degree of catalyst conversion. The rigorous CFD model employed reaction kinetics, PID-automated thermal management, and a rotating stirrer shaft. Validation was carried out to determine the sensitivity to time-step size, turbulence model, and grid resolution. Data were compared to an industrial scale plant autoclave to guide the development of CFD. In a comparison of turbulence models, the shear stress transport (SST) model was found to predict higher concentrations of turbulent kinetic energy (TKE) resulting in a lower temperature distribution throughout the reactor than the differential Reynolds stress model (DRSM). The less diffusive DRSM was recommended for future studies. A mesh refinement study revealed slight variation in the results between the base mesh of 6 million computational elements and the refined mesh consisting of 40 million. Ultimately, the variation between different grid resolutions was not significant enough to justify slowing down the solver speed by 14X by using the refined mesh. Increased rigor improved the model's ability to match plant data, and CFD thermocouples were within 2.5% of temperatures from plant data. [ABSTRACT FROM AUTHOR]