Strain Rate Tensor Research Articles

Direct calculation of the eddy viscosity operator in turbulent channel flow at Re τ = 180

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani & Park, Phys. Rev. Fluids, 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

Empirical evidence for multi-decadal transients affecting geodetic velocity fields and derived seismicity forecasts in Italy

This study critically examines the use of geodetic strain rates for forecasting long-term earthquake rates in a slow-deforming region such as Italy, challenging the prevailing assumption of their temporal stationarity in interseismic stages for seismic hazard analyses. Typically, earthquake-rate models derived from geodesy assume stationary interseismic loading rates, with stress rates in the upper crust proportional to geodetic strain rates, leading to earthquake rates directly proportional to these strain rate tensors. However, our analysis unveils a pronounced correlation between the epicenters of earthquakes that occurred in the past 60–120 years and areas forecasted for higher future earthquake rates based on geodetic strain rates. This correlation appears weak and scattered in analyses of even older earthquakes. To corroborate our findings, we select the 2009 L’Aquila earthquake (mw = 6.3) to prove that its apparently marginal viscoelastic relaxation significantly alters the time series of adjacent benchmarks for the following ~ 30–60 years, explaining the high correlation between recent earthquakes and strain rate peaks. Our findings require a methodological shift in interpreting geodetic data for earthquake forecasting, emphasizing the two-component (plate-tectonics-driven stationary long-term deformation, and decadal transient viscoelastic relaxation after an earthquake) nature of crustal stress accumulation recorded in geodetic data. We underscore the potential of geodesy-derived forecasts to provide deeper insights into seismic hazards, stressing the importance of acknowledging the long-term temporal variability inherent in geodetic measurements.

Numerical Study of Melt-Spinning Dynamic Parameters and Microstructure Development with Ongoing Crystallization.

In response to an investigation on the paths of changes in the crystallization and radial differences during the forming process of nascent fibers, in this study, we conducted numerical simulation and analyzed the changes in crystallization mechanical parameters and tensile properties through a fluid dynamics two-phase model. The model was based on the melt-spinning method focusing on melt spinning, the environment of POLYFLOW, and the method of joint simulation, coupled with Nakamura crystallization kinetics, including the development of process collaborative parameters, stretch-induced crystallization, viscoelasticity, filament cooling, gravity term, inertia, and air resistance. Finally, for nylon 6 BHS and CN9987 resin spinning, the model successfully predicted the distribution changes in temperature, velocity, strain rate tensor, birefringence, and stress tensor along the axial and radial fibers and obtained the variation pattern of fibers' crystallinity along the entire spinning process under different stretching rates. Furthermore, we also explored the effects of spinning conditions, including inlet flow rate, winding speeds, and the extrusion temperature, on the fibers' crystallization process and obtained the influence rules of different spinning conditions on fiber crystallization. Knowing the paths of changes in mechanical performance can provide important guidance and optimization strategies for the future industrial preparation of high-performance fibers.

Particle image velocimetry in the impeller of a centrifugal pump: Relationship between turbulent flow and energy loss

Turbulent flows play a dominant role in the operation of centrifugal pumps, which find widespread use in industrial settings and various aspects of human life. The dissipation rate of turbulent kinetic energy emerges as a key parameter within these devices, with its local values exerting a significant influence on centrifugal pump performance. Recent advances in particle image velocimetry (PIV) techniques have expanded the ability to analyze complex turbulent flows across a broad spectrum of scales. In this context, this paper aims to deepen our understanding of the turbulent flow field and its correlation with energy loss in centrifugal pump impellers. To achieve this, experiments were conducted using PIV on a transparent pump operating under different conditions. Statistics of the turbulent flow were then obtained from phase-ensemble averages of velocities, vorticity, turbulence production, and local dissipation of turbulent kinetic energy. To overcome the limited spatial resolution constraint of PIV, the large-eddy PIV (LES-PIV) method was employed to estimate the local dissipation rate. In this method, it is assumed that the motion of larger scales is measured by the PIV technique, while the smaller scales (unresolved scales) are modeled by a sub-grid scale model, calculated from the strain rate tensors obtained from the measured fields. Energy losses in the impeller were studied using two methodologies: (i) a conventional method based on power measurements, and (ii) an alternative approach based on the budget of turbulent kinetic energy. Our results reveal that turbulent loss caused by turbulence production is the main source of energy loss in the pump impeller, and it is particularly pronounced in low-flow operating conditions characterized by large-scale structures. On the other hand, in situations where flow rates exceed the best efficiency point (BEP) condition, the predominant flow structures are marked by small-scale features, mainly attributed to local dissipation of turbulence. Our findings clarify the characteristics of energy losses in centrifugal pump impellers and their relationship with the turbulent flow field, and, in addition, providing a methodology for calculating the local turbulent dissipation rate and its limitations when derived from PIV measurements.

Continuum Model of Peridynamics for Brittle Fracture Problems

The article investigates the nonlocal method of peridynamics, which makes it possible to simulate the brittle fracture of a solid body without using spatial derivatives. The basic motion equation of a particle with a given volume is written in integral form. A model combining the key features of continuum mechanics and of the nonlocal method is considered. To determine the forces of pair interaction, the dependence of the Cauchy stress tensor on the rate-of strain tensor was used. This formulation correctly describes the behavior of the material during damage and allows to get rid of the limitations inherent to simple bond-based model and ordinary state-based model. The maximum value of the tensile stress is used as a criterion of fracture, which describes the process of nucleation and evolution of damage. To test the implemented model, tasks in a two-dimensional formulation were used. Using the example of the elastic problem about uniaxial tension of a thin rod, the convergence of the numerical solution is shown with a decrease of interaction horizon and an increase of particles number. The second task demonstrates the capabilities of the implemented model to describe the nucleation and evolution of a crack under uniaxial load on a plate with an initial horizontal defect.

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials

AbstractA novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

Assessment of RANS-based turbulence models for isothermal confined swirling flow in a realistic can-type gas turbine combustor application

The present study assesses RANS-based turbulence models to simulate the isothermal confined swirling flow in a combustor representing a constituent can combustor of the can-annular configuration used in jet engines. The two-equation models (standard k−ϵ, realizable k−ϵ, standard k−ω, SST k−ω), and seven-equation model (linear pressure strain-Reynolds stress model, LPS-RSM), are assessed by comparing their predictions of mean axial velocity, mean transverse velocity, turbulent kinetic energy, and shear stress with the experimental data at two different positions (i.e., the primary and dilution hole planes) in the combustor. While the two-equation models generally have failed to predict the confined swirling flow at both positions accurately, the SST k−ω model yielded the most accurate, followed by standard k−ω and realizable k−ϵ models. The discrepancies between the computational and experimental results could be attributed to the isotropic turbulence assumptions, which, however, are invalid for confined swirling flows. Further, the two-equation model formulations cannot capture the intricacies of vortex flow and its interaction with the surroundings in confined swirling flows. The LPS-RSM, which considers turbulence anisotropy, showed some promise, although overpredicted results follow the trend with experimental values at the primary holes plane. However, at the dilution holes plane, the model overpredicted the velocity field, and underestimated the turbulence field, including turbulent kinetic energy and shear stress. These observed discrepancies can be ascribed to the pressure-strain correlation in the LPS-RSM, which assumes the pressure is a linear function of the strain-rate tensor. However, this linear assumption is quite simplistic for complex flows. Further, the influence of discretization (SOU and third-order MUSCL) schemes of convective terms is also assessed, and the differences in predictions resulted from MUSCL scheme having lower diffusion and superior ability to capture sharper gradients, however, did not translate into improving the solution accuracy. Hence, this study suggests that more advanced high-fidelity turbulence models (e.g., hybrid RANS-LES, LES, DNS) are needed to accurately predict the confined swirling flow in combustors.

Numerical study of shock wave boundary layer interaction flows using a novel turbulence model

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows.

A spectral collocation scheme for the two dimensional flow of a regularized viscoplastic fluid: Numerical results and comparison with analytical solution

In this paper we present a numerical scheme based on spectral collocation method (SCM) for the two dimensional incompressible creeping flow of a non-Newtonian fluid in a symmetric channel of variable width. Afters a suitable scaling of the governing equations and of the boundary conditions, we discretize the problem getting a nonlinear system that is solved via Newton–Raphson method. We focus on two regularized viscoplastic fluids (Bingham, Casson), but the method can be applied to any fluid in which the apparent viscosity depends on the modulus of the strain rate tensor. In the case of small aspect ratio of the channel we explicitly determine the lubrication solution at the leading order and we prove some symmetry properties. We validate the numerical scheme through a comparison with the analytical solution, showing an excellent agreement between the latter and the numerical solution. We consider three types of wall functions (convergent, divergent and non-monotone) and we perform numerical simulations for channels with general aspect ratio. We observe that the symmetries of the lubrication solution are maintained also when the characteristic length and width of the channel are of the same order. We have proved that the monotonicity of the yield surface follows the one of the channel profile when the aspect ratio of the channel is “sufficiently small”. This is no longer true when the latter hypothesis is removed.

Analysis and Modeling of Turbulence Anisotropy of a Swirled Hot Streak Flow

Abstract This study is carried out in the context of hot streak flows in high-pressure turbines, for which a correct prediction of the temperature evolution is required. The present work particularly focuses on the turbulence anisotropy analysis of a swirled hot streak flow in a bent channel representative of a nozzle guide vane (NGV) passage of a high-pressure turbine. Large-eddy simulations are conducted with the in-house solver IC3 in order to measure and characterize the anisotropy of turbulence. Moreover, to evaluate turbulence modeling, steady simulations of the bent channel are performed with the elsA software, which solves the Reynolds-averaged Navier–Stokes (RANS) equations. LES is first used to complete a turbulent kinetic energy (TKE) budget that enables to understand the energetic transfers associated with turbulence. This budget reveals two distinct zones where turbulence activity is impacted when the curvature is reached. The analysis of the anisotropy of turbulence based on two metrics highlights a misalignment of the Reynolds stress tensor and the mean strain-rate tensor (Schmitt's criterion), and a strong anisotropy developing inside the bent duct (Lumley's analysis) that may cause the failure of the classical RANS turbulence models based on Boussinesq's hypothesis. To check this hypothesis, RANS is positioned against LES with different turbulence models that accounts or not for the anisotropy of turbulence. Both turbulence activity (TKE budgets, Lumley's analysis) and aerothermal fields (radial distributions) are compared. Results show that Explicit Algebraic Reynolds Turbulence Models (EARSM) enable to better account for the anisotropy of turbulence, which in turn promote a better prediction of temperature, both in terms of intensity and trajectory.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.

Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method.

In this paper, we develop a macroscopic finite-difference scheme from the mesoscopic regularized lattice Boltzmann (RLB) method to solve the Navier-Stokes equations(NSEs) and convection-diffusion equation(CDE). Unlike the commonly used RLB method based on the evolution of a set of distribution functions, this macroscopic finite-difference scheme is constructed based on the hydrodynamic variables of NSEs (density, momentum, and strain rate tensor) or macroscopic variables of CDE (concentration and flux), and thus shares low memory requirement and high computational efficiency. Based on an accuracy analysis, it is shown that, the same as the mesoscopic RLB method, the macroscopic finite-difference scheme also has a second-order accuracy in space. In addition, we would like to point out that compared with the RLB method and its equivalent macroscopic numerical scheme, the present macroscopic finite-difference scheme is much simpler and more efficient since it is only a two-level system with macroscopic variables. Finally, we perform some simulations of several benchmark problems, and find that the numerical results are not only in agreement with analytical solutions, but also consistent with the theoretical analysis.

Characterization and evolution of local streamline geometry in an incompressible turbulent channel flow

We investigated the statistical characterization and time evolution of local streamline geometry in typical regions of an incompressible turbulent channel flow at the friction Reynolds number Reτ∼1000. Local streamline structure is completely and uniquely determined by one magnitude factor—the magnitude of velocity gradient tensor (VGT) A—and four shape parameters—the second and third invariants of normalized VGT q and r, the intermediate eigenvalue of normalized strain-rate tensor a2, and the cosine of the angle between vorticity and the intermediate eigendirection of normalized strain-rate tensor | cos β|. As the distance to the wall decreases, the joint probability distribution function of q and r becomes more symmetrical and concentrated, while outside the viscous sublayer, the distribution of A in q–r plane gets dispersed. Interestingly, the inertial conditional mean trajectories (CMTs) exhibit a symmetrical picture only in the buffer layer, and outside the viscous sublayer, the pressure CMTs contributing to slow evolution from unstable focus compression geometry to stable focus stretching geometry tend to dominate the q–r plane as getting closer to the wall. Due to combined effects of inertia and pressure, the origin of the q–r plane (pure-shear geometry) acts as an attractor in the central region, the logarithmic region, and the upper part of the buffer layer while acts as a repeller in the lower part of the buffer layer and the viscous sublayer.

Kinematics of the Kahramanmaraş triple junction and of Cyprus: evidence of shear partitioning

Triple junctions involving convergent plate boundaries extend beyond local implications, which is crucial for studying the geology of convergent plate boundary zones. However, kinematic models overlook Cyprus-Anatolia motion due to limited geodetic constraints. Our study area comprises Cyprus, southern Turkey, and the Levant coast, focusing on the Kahramanmaraş triple junction, where a destructive earthquake sequence occurred on February 6, 2023. We present precise positioning data merged with published velocities, constructing an up-to-date velocity field for the interseismic period. Employing two kinematic approaches, we analyze its tectonic implications. In Cyprus, we find the relative motion of Africa (Sinai Plate) and Anatolia is partitioned between convergence in the Cyprus subduction, with a rate of 3.5–6.2 mm/yr, progressively decreasing from west to east and left-lateral transpressive Kyrenia fault, situated along the northern coast of Cyprus, with rate 3.3–4.2 mm/yr. The relative strike-slip motion between Arabia and Anatolia is partitioned between the East Anatolian Fault (slip rates 5.2–6.2 mm/yr) and some secondary faults such as Çardak and Malatya faults (slip rates 2.0–1.7 mm/yr respectively) and causes distributed deformation for a 50–60 km wide region. The largest second invariant strain rate tensors from the continuum kinematic model also coincide with the same region, the East Anatolian shear zone. A shear partitioning system exists around the Kahramanmaraş triple junction, from Cyprus to southeast Turkey. The Levant Fault has a 3.5–4.7 mm/yr left-lateral slip rate, decreasing northward as part of it is transferred to offshore faults. Strain rates appear relatively small in the Taurus range and Adana/Cilicia basin, transitioning from extensional/transtensional to compressional from east to west.

New non-augmented mixed finite element methods for the Navier–Stokes–Brinkman equations using Banach spaces

Abstract In this paper we consider the Navier–Stokes–Brinkman equations, which constitute one of the most common nonlinear models utilized to simulate viscous fluids through porous media, and propose and analyze a Banach spaces-based approach yielding new mixed finite element methods for its numerical solution. In addition to the velocity and pressure, the strain rate tensor, the vorticity, and the stress tensor are introduced as auxiliary unknowns, and then the incompressibility condition is used to eliminate the pressure, which is computed afterwards by a postprocessing formula depending on the stress and the velocity. The resulting continuous formulation becomes a nonlinear perturbation of, in turn, a perturbed saddle point linear system, which is then rewritten as an equivalent fixed-point equation whose operator involved maps the velocity space into itself. The well-posedness of it is then analyzed by applying the classical Banach fixed point theorem, along with a smallness assumption on the data, the Babuška–Brezzi theory in Banach spaces, and a slight variant of a recently obtained solvability result for perturbed saddle point formulations in Banach spaces as well. The resulting Galerkin scheme is momentum-conservative. Its unique solvability is analyzed, under suitable hypotheses on the finite element subspaces, using a similar fixed-point strategy as in the continuous problem. A priori error estimates are rigorously derived, including also that for the pressure. We show that PEERS and AFW elements for the stress, the velocity, and the rotation, together with piecewise polynomials of a proper degree for the strain rate tensor, yield stable discrete schemes. Then, the approximation properties of these subspaces and the Céa estimate imply the respective rates of convergence. Finally, we include two and three dimensional numerical experiments that serve to corroborate the theoretical findings, and these tests illustrate the performance of the proposed mixed finite element methods.

A constitutive relation generalizing the Navier–Stokes theory to high-rate regimes

We propose a constitutive equation for flows of gases in high-rate regimes where the Navier–Stokes theory breaks down. The model generalizes the Navier–Stokes relation and agrees well with that model in all lower rate flows examined. Our proposed constitutive relation is calibrated with the method of objective molecular dynamics (OMD) using families of compressible and incompressible flows of Lennard-Jones argon. The constitutive relation makes use of the higher-order objective strain rates due to Rivlin and Ericksen (J. Rat. Mech. Anal., vol. 4, 1955, pp. 323–425). The constitutive relation is fully frame-indifferent, and the macroscopic flows corresponding to the OMD simulations are exact solutions for the proposed model. The model is shown to agree with atomistic results much better than the Navier–Stokes equations in the transition regime. The success of our model indicates that it is not higher gradients that become important in the high-rate regime, but rather higher rates of change of the strain rate tensor. While somewhat more complicated to implement than the Navier–Stokes relation, the proposed model is expected to be compatible with existing methods of computational fluid dynamics and may extend those methods to higher rate regimes, while preserving their ability to handle large spatial scales.

Multiscale dynamics in streamwise-rotating channel turbulence

In this paper the multiscale dynamics of streamwise-rotating channel turbulence is studied through direct numerical simulations. Using the generalized Kolmogorov equation, we find that as rotation becomes stronger, the turbulence in the buffer layer is obviously reduced by the intense spatial turbulent convection. On the contrary, in other layers, the turbulence is strengthened mainly by the modified production peak, the intense spatial turbulent convection and the suppressed forward energy cascades. It is also discovered that under a system rotation, small- and large-scale inclined structures have different angles with the streamwise direction, and the difference is strengthened with increasing rotation rates. The multiscale inclined structures are further confirmed quantitatively through a newly defined angle based on the velocity vector. Through the budget balance of Reynolds stresses and the hairpin vortex model, it is discovered that the Coriolis force and the pressure–velocity correlation are responsible for sustaining the inclined structures. The Coriolis force directly decreases the inclination angles but indirectly induces inclined structures in a more predominant way. The pressure–velocity correlation term is related to the strain rate tensor. Finally, the anisotropic generalized Kolmogorov equation is used to validate the above findings and reveals that the multiscale behaviours of the inclined structures are mainly induced by the mean spanwise velocity gradients.

Numerical Simulation of Transonic Compressors with Different Turbulence Models

One of the most commonly used techniques in aerospace engineering is the RANS (Reynolds average Navier–Stokes) approach for calculating the transonic compressor flow field, where the accuracy of the computation is significantly affected by the turbulence model used. In this work, we use SA, SST, k-ɛ, and the PAFV turbulence model developed based on the side-biased mean fluctuations velocity and the mean strain rate tensor to numerically simulate the transonic compressor NASA Rotor 67 to evaluate the accuracy of turbulence modeling in numerical calculations of transonic compressors. The simulation results demonstrate that the four turbulence models are generally superior in the numerical computation of NASA Rotor 67, which essentially satisfies the requirements of the accuracy of engineering calculations; by comparing and analyzing the ability of the four turbulence models to predict the aerodynamic performance of transonic compressors and to capture the details of the flow inside the rotor. The errors of the Rotor 67 clogging flow rate calculated by the SA, SST, k-ɛ, and PAFV turbulence models with the experimental data are 0.9%, 0.8%, 0.7%, and 0.6%, respectively. The errors of the calculated peak efficiencies are 2.2%, 1.6%, 0.9%, and 4.9%. The SA and SST turbulence models were developed for the computational characteristics of the aerospace industry. Their computational stability is better and their outputs for Rotor 67 are comparable. The k-ɛ turbulence model calculates the pressure ratio and efficiency that are closest to the experimental data, but the computation of its details of the flow field near the wall surface is not ideal because the k-ɛ turbulence model cannot accurately capture the flow characteristics of the region of high shear stresses. The PAFV turbulence model has a better prediction of complex phenomena such as rotor internal shock wave location, shock–boundary layer interaction, etc., due to the use of a turbulent velocity scale in vector form, but the calculated rotor efficiency is small.

Entropy: An Inspiring Tool for Characterizing Turbulence-Combustion Interaction in Swirling Flames via Direct Numerical Simulations of Non-Premixed and Premixed Flames.

This article focuses on entropy generation in the combustion field, which serves as a useful indicator to quantify the interaction between turbulence and combustion. The study is performed on the direct numerical simulations (DNS) of high pressure non-premixed and premixed swirling flames. By analyzing the entropy generation in thermal transport, mass transport, and chemical reactions, it is found that the thermal transport, driven by the temperature gradient, plays a dominant role. The enstrophy transport analysis reveals that the responses of individual terms to combustion can be measured by the entropy: the vortex stretching and the dissipation terms increase monotonically with the increasing entropy. In high entropy regions, the turbulence behaves as the "cigar shaped" state in the non-premixed flame, while as the axisymmetric state in the premixed flame. A substantial increase in the normal Reynolds stress with the entropy is observed. This is due to the competition between two terms promoted by the entropy, i.e., the velocity-pressure gradient correlation term and the shear production term. As a result, the velocity-pressure gradient correlation tends to isotropize turbulence by transferring energy increasingly from the largest streamwise component to the other smaller normal components of Reynolds stress and is dominated by the fluctuating pressure gradient that increases along the entropy. The shear production term increases with the entropy due to the upgrading alignment of the eigenvectors of strain rate and Reynolds stress tensors.

Development of a new dynamic smagorinsky model by an artificial neural network for prediction of outdoor airflow and pollutant dispersion

Fast fluid dynamics (FFD) with the dynamic Smagorinsky model can provide accurate predictions of outdoor airflow and pollutant dispersion. However, it is a time-consuming process because the model coefficient is calculated through a formula consisting of subgrid stress difference Lij and strain rate tensor difference Nij, which are obtained by filtering the flow field twice. To reduce the computing time, this investigation proposed a new dynamic Smagorinsky model which calculated Lij and Nij by means of an artificial neural network (ANN). The method was implemented in an open-source program, OpenFOAM. A single-building case was selected as the training set for the ANN. Other cases of varying complexity were used as testing sets to verify the model's generalizability. The dynamic model coefficient has the same distribution characteristics and similar values in different outdoor cases. The ANN model can capture those distribution characteristics and predict the dynamic model coefficient accurately. This study compared the accuracy and computing efficiency of FFD with the new dynamic Smagorinsky model, the standard Smagorinsky model, and the original dynamic Smagorinsky model. Compared with the original dynamic Smagorinsky model, the new dynamic Smagorinsky model saved the computing time by more than 60% when calculating turbulent viscosity, thus reducing the overall computing time by more than 20%, while maintaining similar accuracy. The use of FFD with the new dynamic Smagorinsky model is recommended for outdoor airflow and pollutant dispersion studies.