Turbulent Flow Model Research Articles

Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas — subsurface transport, turbulence, and anomalous materials — in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

Validation of URANS and STRUCT-ε turbulence models for stratified sodium flow

Simulations of a transient stratified sodium experiment are carried out using a classic unsteady RANS model and the second-generation URANS model, STRUCT-ε. Turbulence modeling challenges and their implications to stratified flow prediction are discussed in the context of other sources of error. Input errors are discussed and addressed; discretization error is calculated to be less than 5% of the inlet velocity, for 80% of the domain; and remaining errors in temperature distributions are attributed to the turbulence model. Qualitative flow features from the simulations are presented and discussed. Compared to the experiment, the STRUCT-ε turbulence model provides a more physically accurate prediction of temperature and momentum mixing in key regions of the domain. Quantitative measures such as the L2 norm of the temperature discrepancy demonstrate the improved performance of the STRUCT-ε approach. The magnitude of the temperature fluctuations is very well-predicted by the STRUCT-ε, while URANS overpredicts them by approximately 50%.

Application of Prandtl, von Kármán, and lattice Boltzmann methods to investigations of turbulent slip incompressible flow in a flat channel

The paper focuses on the modeling of turbulent slip incompressible flow in a flat channel. Slippage on the channel wall can be caused by two reasons. The first reason is microchannels when the mean free path of molecules exceeds a certain value, which is characterized by the Knudsen number. The second reason is hydrophobic surfaces, which are used to reduce hydraulic resistance. Two models of turbulence were used to derive analytical solutions of fully developed flow. The first model is the Prandtl model (model of mixing length). The second model is the von Kármán model (model of similarity of pulsation velocities). Analytical models were built in a two-layer approximation: a laminar sublayer and a turbulent core. Both models showed a good agreement with the lattice Boltzmann method. An increase in the Knudsen number leads to an increase in the flow rate and a decrease in shear stress on the walls, which reduces the friction factor. This is due to the weakening of the interaction between the flow and the wall, which also leads to a decrease in the shear stress on the walls. As the Reynolds number increases, this effect becomes more noticeable.

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L2-, H1- and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

Numerical Simulation on Temperature and Moisture Fields Around Cooling Towers Used in Mine Ventilation System

For heat rejection, small air-cooling towers are widely used in mine ventilation systems. However, the thermal efficiency of the cooling towers can be significantly affected by their geometrical arrangement and crosswind conditions. In certain ambient conditions, heated air coming from an exit of one tower can flow to intakes of other towers, which leads to a reduction in the thermal efficiency of the entire ventilation system. The aim of this study was to investigate the influence of crosswind speed and tower spacing on the temperature and moisture content of intakes of cooling towers. For this purpose, a three-dimensional CFD model of the non-isothermal turbulent flow of moist air around cooling towers is proposed. The model is based on the Reynolds-averaged Navier–Stokes equations with a standard turbulence model which are supplemented by heat transfer and moisture transport equations. The investigation of the effects of the crosswind speed and the tower spacing was carried out for two cooling towers by multiparametric numerical simulation using the CFD model. It was shown that the upstream tower protects the downstream one from the effect of the crosswind. The increase in the crosswind speed causes a rise in temperature and moisture content at the intakes of the downstream tower. The increase in the tower spacing, in general, contributes to a decrease in air temperature at the intakes of the downstream tower. However, at low crosswind speed, the heat transfer at the intakes can rise with the tower spacing due to a reduction in the protection possibilities of the upstream tower. Results of the numerical simulation of airflow around three cooling towers indicated that the increase in the number of cooling towers contributes to a rise in temperature and moisture content at the intakes.

Hybrid turbulence models for flows around a stationary smooth circular cylinder

The aim of this paper is to evaluate the accuracy, stability and efficiency of the different hybrid turbulence models via the benchmark computations of flows around a stationary smooth circular cylinder. The hybrid turbulence models have been validated and applied a lot in turbine flow, combustion, aerodynamic and aeroacoustic problems, while not much in hydrodynamic problems. In order to verify the simulation performance of the newly proposed hybrid strategies, this paper uses the SST-PANS, SST-SAS and SST-IDDES to compare the numerical simulation of the large separation flow problem. The model performance is assessed by a detailed comparison of predictions regarding the turbulence characteristics, the hydrodynamic characteristics, and the distribution of eddy-viscosity. The self-developed CFD solver, vim-FOAM-SJTU, is used in the present simulations. From the assessment, it is confirmed that the hybrid models have the abilities to calculate the small-scale motions, and all models can be employed to predict the unsteady characteristics of wake vortices advantageously. Both the SST-PANS and SST-IDDES models can capture complex flow structures and physics mechanism. The SAS model using the Lvk scale with features of local-adaptive and grid-independent can predict the eddy-viscosity reasonable. When the constant Cs = 0.11 contained in the Lvk limiter is modified to be Cs = 0.08, SST-SAS is also able to achieve better performance in the same mesh. The hybrid model can calculate and simulate the 3D vortex structure well, which is closer to the real physical phenomenon. And SST-IDDES has the best simulation results. The numerical results from SST-IDDES show its comparable capabilities for simulation of massively separated hydrodynamic flows and its potential application in the prediction of industrial turbulent flows for vortex-induced motions (VIM).

Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model’s input parameters. We develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model’s response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow.

Experimental validation of a computational fluid dynamics model using micro-particle image velocimetry of the irrigation flow in confluent canals.

This study aimed to experimentally validate a computational fluid dynamics (CFD) model, using micro-particle image velocimetry (micro-PIV) measurements of the irrigation flow velocity field developed in confluent canals during irrigation with a side-vented needle. A microchip with confluent canals, manufactured in polydimethylsiloxane was used in a micro-PIV analysis of the irrigation flow using a side-vented needle placed 3 mm from the end of the confluence of the canals. Velocity fields and profiles were recorded for flow rates of 0.017 and 0.1ml/s and compared with those predicted in CFD numerical simulations (using a finite volume commercial code - FLUENT) for both laminar and turbulent regimes. The overall flow pattern, isovelocity and vector maps as well as velocity profiles showed a close agreement between the micro-PIV experimental and CFD predicted data. No relevant differences were observed between the results obtained with the laminar and turbulent flow models used. Results showed that the laminar CFD modelling is reliable to predict the flow in similar domains.

Investigation of the influence of turbulence to tribological performance on smooth and multistep journal bearing with hydrodynamics simulation

A bearing is an element that maintains the relative motion between two components in industrial machines, while a journal bearing is often used to maintain the shaft constantly rotating on its axis. Generally, an increase in journal bearings’ performance is essential for industrial development. An increase in engine speed affects the distribution of pressure, temperature, and acoustics. Scientists have proposed various methods to analyze pressure distribution, load-bearing capacity, acoustic power, friction force, cavitation, and elastic phenomena to improve journal bearings’ tribological performance. Therefore, this study aimed to discuss the differences in the flow type modeling between smooth and multistep journal bearings. The results indicated that tribological performance increased significantly in turbulent flow in smooth and multistep journal bearings. The simulation results showed a difference between k-epsilon turbulent flow modeling and k-omega flow modeling.

Verification of the analytical design model of a subcritical air ejector and assessment of the behavior of the manufactured machine under different operating conditions

ABSTRACT Ejectors are dynamic energy machines that can be designed using analytical methodologies that have been in use for decades. These calculation methods consist of coefficients and equations, which are now untraceable and have not been updated since they were first proposed. Modern literature is devoid of ejector design; therefore, to conduct research on ejectors, it is first necessary to verify the validity of existing computational methods. In this study, we conducted computational fluid dynamics (CFD)-assisted experiments to simulate a subcritical air-to-air ejector with the possibility of controlling the distance of the nozzle mouth from the mixing chamber inlet. It was found that the optimum distance of the nozzle mouth from the mixing chamber inlet (i.e. 7.9 mm) corresponds to the design condition when the ejection coefficient is 1.673 and the secondary medium quantities reach the maximum value of 31.19 kg/h. A change in the position of the nozzle outside the optimum point leads to a deviation in the ejection coefficient and flow rate. The experimental results were compared with those from CFD analysis and the deviation between them did not exceed 2%. Two turbulent flow models, namely k–Ω BSL and k–ε standard, were used for the comparison.

Application of immersed boundary based turbulence wall modeling to the Ahmed body aerodynamics

This paper applies a recently developed immersed boundary-turbulence wall modeling approach to turbulent flows over a generic car geometry, known as the Ahmed body, under massive flow separation within a lattice Boltzmann solver. Although the immersed boundary method combined with hierarchical Cartesian grid offers high flexibility in automatic grid generation around complex geometries, the near-wall solution is significantly deteriorated compared to the body-fitted simulation, especially when coupled to wall models for turbulent flows at high Reynolds number. Enhanced wall treatments have been proposed in the literature and validated for attached flow configurations. In this work, the Ahmed body with a slant surface of angle 35° is considered where the flow separates massively over the slant surface and the vertical base. The large eddy simulation is performed with a Reynolds stress constraint near-wall. The eddy viscosity is computed dynamically by taking into account the actually resolved Reynolds stresses. It approaches the mixing length eddy viscosity in attached boundary layers and returns to the subgrid eddy viscosity in detached boundary layers. An explicit equilibrium wall model has also been proposed to accelerate the calculation. Comparison with the no-slip boundary condition on the separated surfaces shows that the near-wall treatments with the equilibrium wall model operate reasonably well on both attached and detached boundary layers.

An improved EMMS model for turbulent flow in pipe and its solution

Based on the existing energy-minimization multi-scale (EMMS) model for turbulent flow in pipe, an improved version is proposed, in which not only a new radial velocity distribution is introduced but also the quantification of total dissipation over the cross-section of pipe is improved for the dominant mechanism of fully turbulent flow in pipe. Then four dynamic equality constraints and some other constraints are constructed but there are five parameters involved, leading to one free variable left. Through the compromise in competition between dominant mechanisms for laminar and fully turbulent flow in pipe respectively, the above four constructed dynamic equality constraints can be closed. Finally, the cases for turbulent flow in pipe with low, moderate and high Reynolds number are simulated by the improved EMMS model. The numerical results show that the model can obtain reasonable results which agree well with the data computed by the direct numerical simulation and those obtained by experiment. This illustrates that the improved EMMS model for turbulent flow in pipe is reasonable and the compromise in competition between dominant mechanisms is indeed a universal governing principle hidden in complex systems. Especially, one more EMMS model for a complex system is offered, promoting the further development of mesoscience.

A computational slip boundary condition for near-wall turbulence modeling

Near-wall turbulence modeling represents one of challengers in the computational fluid dynamics. To tackle this problem, the near-wall non-overlapping domain decomposition (NDD) method proved to be very efficient. It has been successfully used with different Reynolds-averaged Navier–Stokes models. In NDD the computational domain is split into two non-overlapping sub-domains: an inner region near the wall, which is characterized by high gradients, and the outer region. To simplify the solution, in the inner region the thin-layer model can be used. In this case, NDD represents a trade-off between the accuracy and computational time. It has been demonstrated on numerous test cases that NDD is able to save up to one order of computational time while retaining practically high accuracy. A practical drawback of the algorithm is a need to split the computational domain into two regions. In the present paper, for the first time the NDD is realized implicitly. For this purpose, specific boundary conditions of Robin type are derived at the wall. Such boundary conditions reduce the gradients of the solution near the wall. The key property is that the solution can be obtained on a relatively coarse grid and then be recalculated in the inner region. In the approach it is guaranteed that the original outer and updated inner solutions are linked smoothly. The algorithm with the new boundary conditions can be easily implemented in standard codes. This is demonstrated with the code OpenFOAM. In addition, in the paper a more accurate approach to obtain the solution in the inner region is realized. The efficiency of the entire technique is demonstrated on test cases with modeling turbulent flows in a channel and asymmetric diffuser.

On the explainability of machine-learning-assisted turbulence modeling for transonic flows

Machine learning (ML) is a rising and promising tool for Reynolds-Averaged Navier–Stokes (RANS) turbulence model developments, but its application to industrial flows is hindered by the lack of explainability of the ML model. In this paper, two types of methods to improve the explainability are presented, namely the intrinsic methods that reduce the model complexity and the post-hoc methods that explain the correlation between the model inputs and outputs. The investigated ML-assisted turbulence model framework aims to improve the prediction accuracy of the Spalart–Allmaras (SA) turbulence model in transonic bump flows. A random forest model is trained to construct a mapping between the input flow features and the output eddy viscosity difference. Results show that the intrinsic methods, including the hyperparameter study and the input feature selection, can reduce the model complexity at a limited cost of accuracy. The post-hoc Shapley additive explanations (SHAP) method not only provides a ranked list of input flow features based on their global significance, but also unveils the local causal link between the input flow features and the output eddy viscosity difference. Based on the SHAP analysis, the ML model is found to discover: (1) the well-known scaling between eddy viscosity and its source term, which was originally found from dimensional analysis; (2) the well-known rotation and shear effects on the eddy viscosity source term, which was explicitly written in the Reynolds stress transport equations; and (3) the pressure normal stress and normal shear stress effect on the eddy viscosity source term, which has not attracted much attention in previous research. The methods and the knowledge obtained from this work provide useful guidance for data-driven turbulence model developers, and they are transferable to future ML turbulence model developments.

Variational Multiscale immersed boundary method for incompressible turbulent flows

This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on surfaces that are immersed in the stationary background discretizations. An interface stabilized form is developed by applying the Variational Multiscale Discontinuous Galerkin (VMDG) method at the immersed boundaries. The formulation is augmented with a variationally derived ghost-penalty type term. The weak form of the momentum balance equations is embedded with a residual-based turbulence model for incompressible turbulent flows. A significant contribution in this work is the variationally derived analytical expression for the Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions at the immersed boundary. In addition, the analytical expression for the interfacial stabilization tensor emerges which accounts for the geometric aspects of the cut elements that are produced when the immersed surface geometry traverses the underlying mesh. A unique attribute of the fine-scale variational equation is that it also yields a posteriori error estimator that can evaluate the local error in weak enforcement of the essential boundary conditions at the embedded boundaries. The method is shown to work with meshes comprised of hexahedral and tetrahedral elements. Numerical experiments show that the norm of the stabilization tensor varies spatially and temporally as a function of the flow physics at the embedded boundary. Test cases with increasing levels of complexity are presented to validate the method on benchmark problems of flows around cylindrical and spherical geometric shapes, and turbulent features of the flows are analyzed.

Effect of upstream deflector utilization on H-Darrieus wind turbine performance: An optimization study

This paper aims to enhance the performance of H-Darrieus Vertical Axis Wind Turbine (VAWT) via introducing upstream deflectors. The impact of this addition has been investigated and discussed through different deflector configurations. The turbine performance before and after adding different wind rotor barriers was compared. A two dimensional, incompressible, transient, and turbulent flow model was built up in order to simulate the air flow around the turbine blades. Model verification and validation were performed through comparing the model solutions using different mesh sizes, time steps, turbulent models, and discretization schemes. Computational Fluid Dynamics (CFD) models were validated to provide novel insights on the effect of the deflectors on the aerodynamic characteristics of a VAWT blades. Results showed that the presence of a single deflector increases the highest value of the moment coefficient of the bare configuration by 24%, either increases the negative torque values, while two defectors increase the maximum value by 22% and the overall average value of the moment coefficient over the optimal range for the tip speed ratio.

Depth- averaged large eddy simulation of shallow turbulent mixing layer

This paper presents the DA-LES large-scale simulation model of turbulent shallow flows, which is based on dual filtering, the first filter removes vertical scales and the second filtering, as a filter spatial, removes all scales from the movement of sizes smaller than the mesh size. To validate this model, we consider the mixing layer problem in a shallow flow of two different velocities imposed on the input Uijttewaal, Booij,Van Prooijen and Uijttewaal [1,2]. In this work, we consider the finite volume method based on an unstructured mesh for turbulent equations, the numerical results are presented and compared to experimental data.

Gassing During Tapping of Silicon

During tapping of metal from silicon furnaces, a significant amount of gas is often released through the tap-hole. The gas is combustible, and a flame jet is created which poses a safety threat to operators. Due to the high temperatures involved, thermal NOx is also produced. This is a threat to the environment and the health of the operators. These phenomena, known as gassing, have been studied here by a mathematical model for reactive turbulent flows. The results show that the flame jet can extend several meters out from the tap-hole, and that the strength of the flame jet increases with the amount of gassing. The simulations also show that the NOx production increases with the amount of gas exiting the tap-hole, and that the thermal NOx formation does not substantially impact the length of the gas jet.

Artificial neural network modeling to examine spring turbulators influence on parabolic solar collector effectiveness with hybrid nanofluids

Numerical simulation and artificial neural network modeling of turbulent flow inside a pipe equipped with two spring turbulator samples with two different scales and a segmental cross-section have been investigated. Increased heat transfer rate (HTR) due to the use of a spring turbulator is predicted for the TiO2Cu-Water hybrid nanofluid based on the single-phase model, feed-forward artificial neural network (ANN) and fitting method. The role of Reynolds number (Re), scale and volume fraction (ϕ) on Nusselt number (Nu), pressure drop (ΔP), performance evaluation coefficient (PEC), solar collector efficiency (η), and the field synergy principle (FSP), compared to simple pipe, is considered using the finite volume method. The results show that increasing the spring turbulator scale increased the contact surface of the working fluid and the spring turbulator. As a result, the flow turbulence is increased, which leads to better mixing of the nanofluid as the operating fluid of the solar collector absorber pipe. Finally, ANN outputs and fitting results are compared, and it has been observed that the obtained ANN could predict the targets accurately.

Eulerian-Lagrangian Modelling of Turbulent Two-Phase Particle-Liquid Flow in a Stirred Vessel: CFD and Experiments Compared

A 3D Eulerian-Lagrangian CFD model is set up to simulate the turbulent flow and mixing of coarse dense particles in a standard batch vessel, mechanically agitated by a down-pumping pitched-blade turbine. Flow is investigated in the just-suspended regime and regimes much above. All simulations are fully and successfully validated by experimental Lagrangian measurements provided by positron emission particle tracking. Predicted distributions of the local 3D phase-velocity components, local particle slip velocities and local particle concentration show very good agreement with experiment. Lagrangian particle trajectories are exploited to infer detailed accurate information on particle circulation time and local residence time. The predicted two-phase flow number is in excellent agreement with experimental values under all flow regimes. Being accurate and robust, the numerical model can be extended to study even more complex particle-liquid suspensions of industrial relevance, and to provide much needed Lagrangian data to other data-driven modelling techniques.