Turbulent Flow Model Research Articles

Toward the use of a reduced‐order and stochastic turbulence model for assessment of far‐field sound radiation: Low Mach number jet flows

AbstractThis work presents a novel framework for the evaluation of far‐field sound radiation, specializing to a low Mach number jet flow. The framework comprises an analytical and a numerical part. In the analytical part, a low Mach number asymptotic analysis is presented to obtain the spectral sources of sound radiation starting from a pressure wave equation that is directly obtained from the Navier–Stokes equations. The derivation procedure is based on the fundamental premise of Lighthill's acoustic analogy. In the numerical part, a reduced‐order model for turbulent flow, the one‐dimensional turbulence model, is used to simulate the velocity field of a low Mach number turbulent round jet, assumed fully developed and statistically steady, hence homogeneous in the azimuthal direction and for a cross‐sectional slab assumed locally homogeneous in axial direction, too. The generated velocity field is used for the calculation of the spectral pressure sources, and consequently, to estimate the far‐field sound pressure level (SPL) of the jet. The results of the analysis are compared against available experimental SPL measurements from a subsonic jet. A reasonable agreement is obtained for the SPL. Furthermore, the analysis sheds light into the different contributions of the subsonic flow to sound radiation. The framework is readily extendable for any kind of low Mach number flow, including variable density flows and jet flames.

Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts

Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts

Numerical modeling of turbulent puffs evolution

The results of numerical simulation of the formation and motion of turbulent puffs resulting from the blowing of pulsed jets with different initial velocities and durations are presented. A model of an axisymmetric turbulent flow described by non-stationary Reynolds equations is adopted. It is shown that, regardless of the initial conditions, after the same dimensionless time interval from the instant the jet outflow begins, a vortex cloud appears, which has a spherical shape of vortex. The vortex-induced flow in the rest of the space is close to potential. It has been established that the velocity profiles in vortices in the axial and transverse directions are close to self-similar and are similar for different conditions of the outflow of pulsed jets. Time dependences of the geometric and kinematic characteristics of puffs are presented and analyzed: the position of the cloud center (points with maximum velocity) and the radius of a sphere equivalent in volume to a puff, as well as maximum and average velocities. For the studied jet outflow conditions, the characteristics of puffs turn out to be similar.

A parameter-free LES model for anisotropic mesh adaptivity

Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method is tested using a flow past a sphere test case. The results are compared both qualitatively and quantitatively to results obtained with the standard Smagorinsky model, and demonstrate the better performance of our method with lower computational cost. This allows us to simulate large Reynolds number cases and compare our quantitative results to experimental results found in the literature, emphasising that our method produces good results at reasonable computational cost.

A theoretical study of the fractional-order p-Laplacian nonlinear Hadamard type turbulent flow models having the Ulam–Hyers stability

A theoretical study of the fractional-order p-Laplacian nonlinear Hadamard type turbulent flow models having the Ulam–Hyers stability

ANALYSIS OF THE INFLUENCE OF THE GEOMETRY OF THE BLADE MIXER ON THE TURBULENCE AND INTENSITY OF LIQUID MIXING

Turbulent fluid mixing is an important aspect of many industrial and technological processes where efficient mixing of various components is of paramount importance to achieve the desired results. Optimal mixing can improve product quality, ensure the unity of complex reactions, and reduce process lead times. In this regard, the study and understanding of the influence of the geometry of the mixer on the characteristics of the turbulent flow becomes an urgent task of scientific research. The relevance of the study is explained by the wide application of mixers in industrial and technological processes, where the efficiency of mixing is crucial for achieving optimal results. The work used methods of experimental and numerical modeling of turbulent flow in various geometric configurations of blade mixers. Indicators such as turbulence intensity, pressure gradient, and fluid mixing ratio were used to quantify the turbulent characteristics. The obtained results demonstrate that the geometric configuration of the blade mixer has a significant effect on the formation of the turbulent flow. Some geometric parameters of the mixer can contribute to increasing the intensity of liquid mixing, while others can reduce its efficiency. Scientific results can be useful for designing optimal paddle mixers for specific industrial tasks that require intensive liquid mixing. The use of optimized mixers can help increase process productivity, save energy resources, and improve product quality.

Reduced-order modeling of the two-dimensional Rayleigh–Bénard convection flow through a non-intrusive operator inference

Due to the increasing availability of large datasets provided by high-fidelity numerical simulations (HFNSs) of physical phenomena, data-driven reduced-order models (ROMs) have become a reliable alternative to those described by partial differential equations, especially when dealing with optimization problems that require multiple evaluations of parameter dependent solutions. These models may be built through different methodologies, among which are the physics-informed neural networks (PINNs) and operator learning frameworks (OLFs). While some recent studies suggest that PINNs have some difficulties in handling convective-dominant physical systems, others show OLFs struggle to accurately predict state variables of interest along the testing interval. In the present work, a ROM for the two-dimensional Rayleigh-Bénard convection flow was built through an incremental proper orthogonal decomposition (IPOD) of a high-fidelity dataset followed by a non-intrusive operator inference (OpInf) approach. Then, the predictive capabilities of the model were assessed for two test cases with different high Rayleigh numbers (Ra=109 and Ra=1011). Very good agreements were achieved between the OpInf-based ROMs and the HFNSs for temperature and velocity fields along training and testing intervals. For instance, time-averaged normalized ROM errors along the testing interval for all the flow variables were below 15% at a given probe location when Ra=109. For each case, while the computational fluid dynamics simulation took about 2 h, the reduced model required less than 3 s to predict the system’s states given its initial condition. This fact illustrates the substantial computational time reduction provided by the ROM. Regarding the case in which the Rayleigh number is higher, the ROM had more difficulties in approximating velocity fields due to the existence of more complex turbulence patterns. Finally, the quality of the data decomposition and of the selected regularization technique, often seen in artificial intelligence algorithms, was investigated. The results suggest the OpInf technique may be successfully applied on the surrogate modeling of turbulent buoyancy-driven flows.

Static Characteristics of High-Speed Water-Lubricated Journal Bearing Considering Turbulence and Cavitation Effects

Abstract The water-lubricated bearings tend to be turbulent and cavitating when running at a high speed. However, the modeling of the water-lubricated bearing considering the turbulence and cavitation effects has not been studied thoroughly. For high-speed water-lubricated journal bearings, a turbulent flow model considering cavitation effect was proposed on the basis of two-phase flow theory. The simulation was conducted to show the influence of turbulence and cavitation effects on the static characteristics of the water-lubricated journal bearing. The proposed model was validated with the test by using a self-developed experimental setup. The result shows that the turbulence effect has a great impact on static characteristics of bearing, and cavitation effect significantly affects the minimum film thickness and leakage flowrate, while the friction torque is hardly affected by the cavitation effect.

Explainability analysis of neural network-based turbulence modeling for transonic axial compressor rotor flows

Model–consistent training has become trending for data-driven turbulence modeling since it can improve model generalizability and reduce data requirements by involving the Reynolds–averaged Navier–Stokes (RANS) equation during model learning. Neural networks are often used for the Reynolds stress representation due to their great expressive power, while they lack interpretability for the causal relationship between model inputs and outputs. Some post–hoc methods have been used to explain the neural network by indicating input feature importance. However, for the model–consistent training, the model explainability involves the analysis of both the neural network inputs and outputs. That is, the effects of model output on the RANS predictions should also be explained in addition to the input feature analysis. In this work, we investigate the explainability of the model–consistent learned model for the internal flow prediction of NASA Rotor 37 at its peak efficiency operating condition. The neural–network–based corrections for the Spalart–Allmaras turbulence model are learned from various experimental data based on the ensemble Kalman method. The learned model can noticeably improve the velocity prediction near the shroud. The explainability of the trained neural network is analyzed in terms of the model correction and the input feature importance. Specifically, the learned model correction increases the local turbulence production in the vortex breakdown region due to non–equilibrium effects, which capture the blockage effects near the shroud. Besides, the ratio of production to destruction and the helicity are shown to have relatively high importance for accurately predicting the compressor rotor flows based on the Shapley additive explanations method.

An open-source anisotropic k−ε−v2−f model for turbulent viscoelastic duct flows

A novel open-source anisotropic k−ε−v2−f model is presented for turbulent viscoelastic duct flow with dilute polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin constitutive model. The turbulence model for channel and square duct flow of Newtonian fluids is adapted to incorporate the polymeric terms within the governing equations. All the required non-linear terms are validated with simple closure models and are assessed a priori against independent direct numerical simulation data in fully developed channel flow. The NLTij term, which accounts for the interaction between fluctuating components of the conformation tensor and the velocity gradient tensor, is modeled with the mean flow direction, ti, and wall-normal, ni, present in the Newtonian model, based on the streamwise alignment of mean polymer stretch. The implicit polymer effects on pressure–strain are assessed with a simple ad hoc closure accounting for the reduced near-wall production of turbulent kinetic energy. The same closure is also adapted for the spanwise Reynolds stress predictions of polymer-enhanced secondary flow. The model performs well in channel flow and captures low, intermediate, and high drag reduction features for a wide range of rheological parameters. The capabilities are extended for square ducts (or any regular polygon) due to the symmetric modeling of the closure models, which can predict the mean streamwise and secondary flow features associated with second normal Reynolds stress differences. Accessible codes and models are crucial for the advancement and improvement of turbulent viscoelastic models, and an OpenFOAM C++ code package is developed and freely available on GitHub (https://github.com/MikeMcDermott-Code/v2f).

NUMERICAL SIMULATION OF THE FLOW AROUND AN AIRFOIL TYPE TRANSPORT VEHICLE NEAR THE GROUND

The problem of modeling the flow around an airfoil type transport vehicle near the ground is considered. The flow around the vehicle is turbulent. Nowadays, the most advanced mathematical models of aerodynamics are based on the physical properties of a viscous compressible gas and are based on the Reynolds-averaged Navier – Stokes equations. Mathematical modeling of turbulent flows remains one of the most challenging problems. Reliable prediction of the characteristics of turbulent flows is an extremely important scientific problem. This is due to the complexity and insufficient study of turbulence as a physical phenomenon. The aim of this work is to build a mathematical model, a numerical method, an algorithm for solving the problem, and to develop software for studying the aerodynamic characteristics of a vehicle of the airfoil type. To close the Reynolds-averaged Navier –Stokes equations, the one-parameter Spalart – Allmaras turbulence model was used. The initial system of differential equations is written in a curved coordinate system. The initial and boundary conditions for the flow parameters are formulated. The methodology, algorithm for solving the problem, and software are developed. The finite-volume method was used for numerical integration of the system of differential equations. The problem was solved in a multi-block formulation. The developed methodology of algorithms and a set of programs were tested on standard aerodynamic problems: the flow around a transversely placed circular cylinder and a ball. Numerical modeling of the flow of compressed gas around a vehicle moving near the ground was performed. All calculations were carried out for the Reynolds number Re=1,0*10^6 and the Mach number M=0,4. Numerical simulations were performed on a curved multi-block grid. The influence of the ground on the characteristics of the flow around the vehicle was investigated. The studies have shown that the presence of a nearby ground has a significant impact on the flow characteristics around the vehicle. Thus, in order to ensure the required parameters of vehicle dynamics near the ground, it is necessary to take into account the influence of the ground on its aerodynamic characteristics.

Muzzle flow field characteristics of underwater sealed launch system under different projectile shapes

The underwater sealed launch is one of effective launch technologies for enhancing the velocity of underwater vehicle and also for achieving better interior ballistic performance. However, the underwater muzzle flow field based on this sealed technology is a major consideration as it decides initial kinetic stability and subsequent shooting accuracy. Hence, this study establishes a comprehensive model involving in a modified sealed interior ballistic model, muzzle multiphase turbulent flow model and supercavitation model due to high-velocity moving vehicle, and mainly investigates the effect of the vehicle shapes on the underwater sealed muzzle field. An experiment for the muzzle field of underwater sealed launch is also carried out using a 12.7 mm-caliber launch device and water tank. Comparisons on flow patterns of muzzle field and expansion displacements of Taylor cavity on computational results are done with experimental studies, and a reasonable match has been obtained in these comparisons. The results show that the gas sealed in the launch barrel firstly injects into the water forming an initial Taylor cavity once the sealed device is broken. Then, the propellant combustion-gas just with high pressure and high temperature injects into the water with the moving vehicle. Consequently, a complicated interaction effect between these two types of gases and high-density water takes place, generating complicated shock wave phenomena in the muzzle field. Different vehicle shapes can affect the formation of the shock waves and expansion characteristics of Taylor cavity in the water. Eventually, the diameter of the Mach disk is always the largest for the cylindrical underwater vehicle and the axial pressure fluctuation for the vehicle with a cavitator are most significant with a lowest temperature field due to strong gas-liquid interaction.

Turbulence Modeling via Data Assimilation and Machine Learning for Separated Flows over Airfoils

Reynolds-averaged Navier–Stokes (RANS) models, which are known for their efficiency and robustness, are widely used in engineering applications. However, RANS models do not provide satisfactory predictive accuracy in many engineering-relevant flows with separation. Aiming at the difficulties of turbulence modeling for separated flows at high Reynolds number, this paper constructs turbulence models using data assimilation technique and deep neural network (DNN). Due to the uncertainty of traditional turbulence models, the parameters of Spalart–Allmaras (SA) turbulence model are optimized with experimental data to provide high-fidelity flowfields. Then DNN model maps the mean flow variables to eddy viscosity and replaces the SA model to be embedded within a RANS solver by iterative mode. Different from many existing studies, this DNN model does not depend on traditional turbulence models during the simulation process. This approach is applied to turbulent attached and separated flows and can significantly improve the accuracy for new flow conditions and airfoil shapes. Results show that the mean relative error of lift coefficient above the stall decreases by over 57% for all the airfoils.

Numerical Modeling of Turbulent Biogas Combustion

The primary purpose of this research is to investigate the combustion properties of three different types of biogas using a 300 KW BERL combustor. Biogas is a renewable type of this fossil fuel; it is an intelligent fuel that offers an incredibly environmentally beneficial alternative to existing fuels.In order to study the impact of the biogas compositions on the flow field prediction, we perform the calculation using the FLUENT code, which has been used to present the numerical modeling of turbulent diffusion flames by using the realizable k-–ε model of turbulent flow interacting with a two-dimensional PDF combustion scheme. Some comparisons of biogas performance in turbulent diffusion flame mode and methane performance in conventional mode are shown, in addition to the 9-steps, GRI 2.11 mechanisms and experiment data are used to validate the case investigated.

The SquAd derivation: A Square Additive approach to the turbulent Prandtl number

Liquid metals have been chosen as primary coolant of innovative nuclear systems under current development. They present a very high thermal conductivity and hence a very low molecular Prandtl number. This feature challenges the modeling of turbulent thermal flows applying the Reynolds analogy. This paper addresses this challenge. A new formula for the turbulent Prandtl number is derived in terms of local variables available from two-equations turbulence models. The derivation is a direct consequence of the expected square additivity of the molecular and flow parameters defining the effective viscosity and the effective conductivity. The formula does not degenerate and leads to a Kays like formulation if approximated. While constrained by the quality of the turbulent viscosity modeling, it has the potential to improve the numerical simulation of turbulent thermal flows.

An energy-based lengthscale for reduced order models of turbulent flows

In this paper, we propose a novel reduced order model (ROM) lengthscale that is constructed by using energy distribution arguments. The new energy-based ROM lengthscale is fundamentally different from the current ROM lengthscales, which are built by using dimensional arguments. To assess the novel, energy-based ROM lengthscale, we compare it with a standard, dimensionality-based ROM lengthscale in two fundamentally different types of models: (i) the mixing-length ROM (ML-ROM), which is a ROM closure model; and (ii) the evolve-filter-relax ROM (EFR-ROM), which is a regularized ROM. We test the four combinations (i.e., ML-ROM and EFR-ROM equipped with the energy-based and dimensionality-based lengthscales) in the numerical simulation of the turbulent channel flow at Reτ=395. The numerical investigation yields the following conclusions: (i) The new energy-based ROM lengthscale is significantly (almost two orders of magnitude) larger than the standard dimensionality-based ROM lengthscale. As a result, the energy-based lengthscale yields more stable ML-ROMs and EFR-ROMs than the dimensionality-based lengthscale. (ii) The energy-based lengthscale displays the correct asymptotic behavior with respect to the ROM dimension, whereas the dimensionality-based lengthscale does not. The energy-based lengthscale is intrinsically adaptive with respect to the ROM dimension, which is important in realistic settings where using the full order model data to determine an optimal ROM lengthscale may not be possible. (iii) The energy-based lengthscale yields ML-ROMs and (when significant filtering is effected) EFR-ROMs whose parameters are less sensitive (i.e., more robust) than the parameters of the ML-ROMs and EFR-ROMs based on the dimensionality-based lengthscale. The novel energy-based lengthscale could enable the development of better scale-aware ROM strategies for flow-specific applications and is expected to have long term applications in nuclear reactor thermal-hydraulics.

A review on rheological models and mathematical problem formulations for blood flows

A review on constitutive equations proposed for mathematical modeling of laminar and turbulent flows of blood as a concentrated suspension of soft particles is given. The rheological models of blood as a uniform Newtonian fluid, non-Newtonian shear-thinning, viscoplastic, viscoelastic, tixotropic and micromorphic fluids are discussed. According to the experimental data presented, the adequate rheological model must describe shear-thinning tixotropic behavior with concentration-dependent viscoelastic properties which are proper to healthy human blood. Those properties can be studied on the corresponding mathematical problem formulations for the blood flows through the tudes or ducts. The corresponding systems of equations and boundary conditions for each of the proposed rheological models are discussed. Exact solutions for steady laminar flows between the parallel plates and through the circular tubes have been obtained and analyzed for the Ostwald, Hershel-Bulkley, and Bingham shear-thinning fluids. The influence of the model parameters on the velocity profiles has been studied for each model. It is shown, certain sets of fluid parameters lead to flattening of the velocity profile while others produce its sharpening around the axis of the channel. It is shown, the second-order terms in the viscoelastic models give the partial derivative differential equations with high orders in time and mixed space-time derivatives. The corresponding problem formulations for the generalized rhelogical laws are derived. Their analytical solutions in the form of a normal mode are obtained. It is shown, the dispersion equations produce an additional set for the speed of sound (so called second sound) in the fluid. It is concluded, the most general rheological model must include shear-thinning, concentration and second sound phenomena

NumericalStudy of Turbulent Flows over a NACA 0012 Airfoil: Insights into Its Performance and the Addition of a Slotted Flap

This work provides a comprehensive overview of various aspects of airfoil CFD simulations. The airflow around a 2D NACA 0012 airfoil at various angles of attack is simulated using the RANS SST turbulent flow model and compared to experimental data. The airfoil is then modified with a slotted flap and additionally the angle of the flap is altered. The flow model is subsequently coupled to a heat transfer model to compare the isothermal versus non-isothermal performance. The airfoil with the slotted flap shows increased CL and CD values compared to the standard NACA 0012. Larger flap angles further increase the CL and CD. The lift and drag coefficients show no difference in the non-isothermal model compared to the isothermal model, indicating the isothermal model is sufficient for this system. The 3D model without wingtips shows a similar CL to the 2D model as it effectively has an infinite span. Adding a wingtip reduces the lift coefficient, as the air can flow around the wingtip, increasing the pressure on top of the wing. Overall, these results match the behavior expected from wing theory well, showing how CFD can be effectively applied in the development and optimization of wings, flaps, and wingtips.

Statistical laws of a one-dimensional model of turbulent flows subject to an external random force

This paper provides mathematical and numerical analysis of a one-dimensional model of turbulent flow generating the anomalous cascade of the inviscid conserved quantity. The model is based on the generalized Constantin–Lax–Majda–DeGregorio (gCLMG) equation with viscous dissipation under a large-scale forcing. Suppose that the forcing function and the initial data are random variables defined on a certain probability space. Then, the equation is regarded as a random partial differential equation. We prove the global existence of a unique solution to the gCLMG equation, from which a stochastic process is defined. In addition, by approximating the solutions numerically by Galerkin approximation of random variables with generalized polynomial chaos, we confirm the existence of a steady distribution. We find that the steady distribution reproduces qualitatively the same cascades of the energy and the enstrophy spectra as those of a turbulent flow generated by randomly moving pulse (Matsumoto and Sakajo 2016 Phys. Rev. E 93 053101). We also investigate the structure functions, showing intermittency.

Numerical modeling of two‐phase flows in the presence of dynamic and thermal interactions

AbstractThe study of turbulent flow in mixtures consisting of gas and particulate matter is a current area of research among modern scientists. The main objective of this area is to prevent the reduction of burnout in flow‐through systems. Therefore, the purpose of this research is to develop a mathematical model of turbulent gas flow with solids to explore the structure of the combustion region in a channel with a partially open boundary to determine the interfacial interaction of the injection of a flat heterogeneous flow in a confined area and the influence of regime parameters on the ignition process. For this purpose, a modeling method was used, which involved using the fundamental laws of continuity of flow, conservation of energy, and the quantity of motion and matter, and an experiment was conducted to reconcile the proposed model with theoretical data. As a result of this work, a model based on the averaged Reynolds Navier–Stokes equations and an algorithm for solving a turbulent subsonic two‐dimensional flow in a heterogeneous medium based on an Euler–Lagrange representation have been developed. Thus, the effects of the parameters of entrainment, temperature, and component concentration on the combustion range and mixing intensity were determined. The proposed methodology can be applied to solve application problems of various kinds, for example, in the design of thermal power plants. The scope of the mathematical and numerical models developed is sufficiently broad that they are universal.