Turbulent Flow Model Research Articles

Modeling of turbulent flows through annuli with smooth and rough walls; drag reduction and heat transfer

A model of a turbulent flow in an annular channel with rough walls is developed. An effect of roughness on hydraulic resistance of the channel is accounted for through the formal dimensionless negative velocity shift at the wall by using an empirical function linking this velocity shift to the dimensionless sandgrain wall roughness. The developed annular flow model is validated by experimental data found in literature for both smooth walls, both rough walls, smooth outer wall and rough inner wall as well as vice versa. The same flow model is applied also to a polymer solution turbulent flow in annular channel with hydraulically smooth walls. A turbulent drag reduction effect, observed in this case, is accounted for by a positive velocity shift at the wall determined for a certain drag reduction chemical from experiments in a round cross-section pipe. Also, an engineering approach for modeling heat transfer through either outer or inner wall of an annular channel with rough walls is suggested. This approach is based on the known analogy of heat transfer in a hydraulically smooth annular channel and a pipe. This analogy is extended to an annular channel with rough walls by using the developed flow model. The heat transfer model developed is validated, discussed and illustrated by calculation examples. Key attention is paid to analyzing an effect of the Reynolds number on both a Nusselt number increase and an efficiency change for different wall roughening cases.

Coupled CFD-DEM modeling of surface erosion in granular soils: Simulation of erosion function apparatus experiments

This study introduces a numerical modeling approach that couples the computational fluid dynamics (CFD) with the discrete element method (DEM) to simulate grain-scale soil erosion processes induced by water flows. In this modeling framework, CFD simulates fluid flows by solving the volume-averaged Navier-Stokes equations, and uses the k-ω turbulent model for turbulent flows. Simultaneously, DEM computes the displacement of solid particles by incorporating the fluid-particle interactions driven by fluid flows while adhering to Newton's laws of motion. These interactions encompass drag force, buoyancy force, pressure-gradient force, and viscous force exerted by fluid flows and acting on the particles. The coupled CFD-DEM modeling adeptly replicates soil erosion processes, demonstrating good alignment with results obtained from laboratory erosion function apparatus (EFA) tests. In particular, the DEM facilitates the estimation of shear stress acting on the soil surface based on fluid-particle interaction forces, which has been roughly approximated by empirical or semi-empirical models. This study underscores the capability of coupled CFD-DEM in providing valuable insights into the grain-scale behavior of soil particles subjected to fluid flows, with the potential for extension to address soil erosion and fines migration.

Study in Gas-Phase Agglomeration Characteristics of Spiral Flow Gas-Liquid Multiphase Pump

Abstract The spiral flow gas-liquid mixed transport pump experiences gas phase accumulation in the impeller flow passage, leading to blockage and a decrease in pumping performance. To understand the rules and mechanisms of gas phase aggregation in the spiral flow gas-liquid mixed transport pump, numerical calculations based on the Eulerian multiphase flow model and SST k – ω turbulent flow model were conducted. The effects of different gas volume fractions, speeds, and liquid phase viscosities on the pump were explored, and the external characteristics, flow characteristics, and gas phase aggregation processes in the impeller were analysed for these three variables. The results indicate that the head and efficiency of the pump gradually decrease with increasing gas volume fraction and liquid phase viscosity, while they increase with increasing speed. When the liquid phase viscosity changes from pure water to 50 times its viscosity, the gas phase aggregation at the impeller outlet decreases, resulting in reduced pressure and a smaller vortex region. The relative gas phase aggregation degree λ decreases from 0.5 to almost 0. When the gas volume fraction increases from 20% to 60%, the gas phase aggregation at the impeller outlet increases, the pressure difference between the impeller hub and the rim increases, and the vortex region expands, leading to an increase in λ by 8 times. When the speed increases from 3000 rpm to 5000 rpm, the gas phase aggregation at the impeller outlet increases, the pressure increases, and the vortex region expands, resulting in a 16-fold increase in λ.

Enhancing heat transfer with a hybrid vortex generator combining delta wing and winglet designs: A numerical study using the GEKO turbulence model

This paper presents a numerical study on the enhancement of heat transfer in a solar air heater (SAH) duct with Hybrid Vortex Generators (HVG) placed periodically along the flow direction on its heated wall (absorber plate) for fluid flow and convection heat transfer at Reynolds numbers between 4121 and 25,365. HVGs consist of a trapezoidal winglet (TWL) for HVG-winglet-base-angles θ = 45° and 30°, or a combination of a delta winglet (DWL) with a delta wing (DWG) for angles θ = 26°, 18° and 12°. The angle of attack for the winglet (TWL or DWL) in the HVG is set at 30°, while the merging angle with the DWG is 45°, and the relative height BR = e/H = 0.48 remains constant. Initially, the effects on heat transfer and friction factor of Trapezoidal Winglet Vortex Generator (TWVG) and HVG45 (θ = 45°) obtained by basic modification on TWVG are investigated under the same flow conditions for PR = 1.5 and Re = 11,205. Subsequently, parametric studies are performed for five different HVG-winglet-base-angles (θ = 45°, 30°, 26°, 18° and 12°) and three different longitudinal pitch ratios (PR = PL/H = 1.0, 1.5 and 2.0). The calculations are performed with ANSYS Fluent 2021R2 based on the finite volume method. In order to model turbulent flow, the GEKO (GEneralized K-Omega) turbulence model recently developed by ANSYS and based on the k-ω formulation is used. HVG45, obtained by basic modification on TWVG, produces slightly stronger and more effective longitudinal vortices compared to TWVG, showing a 3.87 % decrease in friction factor and a 4.11 % increase in Nusselt number and thus a 5.43 % increase in Thermal Enhancement Factor (TEF). Parametric investigations are conducted across a range of values for both θ and PR. The highest rise in friction factor is attained at the lowest Reynolds number, reaching a value of f/f0 = 54.52, while the most significant enhancement in heat transfer rate is noted at the highest Reynolds number, with Nu/Nu0 = 5.86 for θ = 45° and PR = 1.0. The TEF reaches 2.42 at the lowest Reynolds number for the HVG18 with a winglet-base-angle of 18° and a longitudinal pitch ratio of 1.5. The resulting findings not only offers a new approach to improve the thermal performance of solar air heaters but also hints at the potential success of the GEKO model in predicting turbulent flow and heat transfer analysis.

Characteristics of Deterministic and Stochastic Unsteadiness of Trailing Edge Cutback Film Cooling Flows

Abstract Trailing edge cutback film cooling flows are ubiquitous in small and medium gas turbines, but they are difficult to predict accurately due to the inherent deterministic and stochastic unsteadiness that controls the effectiveness of the cooling system. To help develop accurate closure models for such flows, the characteristics of both types of unsteadiness and their effects on the mean flows are analyzed in this research. Zonal detached eddy simulation (ZDES) is performed on a trailing edge cutback flow model, and the numerical results are validated against the measured data. Then, by using spectral proper orthogonal decomposition (SPOD) reconstruction, the original dataset is segregated into deterministic and stochastic unsteadiness. The characteristics of the stress tensor and the heat flux of each type of unsteadiness are analyzed in detail, and notable differences between the two unsteadiness are identified in terms of the stress tensor anisotropy and distribution of unsteady kinetic energy and heat flux. By propagating the unsteadiness through the Reynolds-averaged Navier–Stokes (RANS) equations, the effect of different unsteadiness on the mean flow prediction is quantified. An accurate prediction of the total stress tensor reduces the prediction error in the velocity field by 79% and cooling effectiveness by 55%. An accurate prediction of the total heat flux vector reduces the prediction error in cooling effectiveness further by 37%. These findings provide valuable knowledge for the physical understanding, turbulence modeling, and aerothermal design of cutback trailing edge flows.

Development and deployment of data-driven turbulence model for three-dimensional complex configurations

Abstract In recent years, the synergy between artificial intelligence and turbulence big data has given rise to a new data-driven paradigm in turbulence research. Data-driven turbulence modeling has emerged as one of the forefront directions in fluid mechanics. Most existing studies focus on feature construction, selection, and the development of modeling frameworks, often overlooking the practical deployment and application of trained models. This paper examines the entire process from model construction to real-world deployment, using data-driven turbulence modeling for high Reynolds number flows over complex three-dimensional configurations as a case study. Key stages include data generation, input-output feature construction, model training, model compilation and optimization, deployment, and validation. We successfully implemented the entire workflow in a heterogeneous supercomputing environment and, through mixed programming techniques, integrated the resulting turbulence model into the Platform for Hybrid Engineering Simulation of Flows (PHengLEI) open-source software framework. This allowed for mixed-precision simulations, with the main equations solved in double precision and the turbulence model in half precision. The new computational framework was validated through large-scale parallel numerical simulations on grids with tens of millions of elements for three-dimensional complex configurations. The results highlight the efficiency of our model deployment, with overall computational efficiency improving by 13.35% and the turbulence model’s solution speed increasing by approximately 3.9 times. The accuracy of the computations was also confirmed, with the average relative error in the lift and drag coefficients calculated by the data-driven turbulence model within 3%. Across various computing nodes, the relative error in the computed aerodynamic coefficients remained within 1%, demonstrating the framework’s scalability. Notably, our contributions have been incorporated as a case study in the latest PHengLEI open-source project5 5 https://forge.osredm.com/PHengLEI/PHengLEI-TestCases/tree/master/Y02_ThreeD_M6_Unstruct_Branch_Ascend. .

Wall Modeling of Turbulent Flows with Varying Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states, including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity and, consequently, the wall-shear stress. The model training is in situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows them to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flows over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.

An accurate and robust method for intensification of wastewater sludge pipe flow

Globally, environmental impacts and population growth are driving the process intensification of wastewater treatment plants (WWTPs) via transition from conventional (2–3 wt% solids) to highly concentrated (4–6 wt% solids) wastewater sludges (HCWS). This presents an industrial challenge as HCWS are complex, non-Newtonian materials whose viscosity increases nonlinearly with solids concentration. This viscosity increase is particularly relevant for sludge pipe flow as it leads to considerable pumping pressure that ultimately limits the feasibility of pipe flow transportation. Hence, process intensification demands accurate prediction of HCWS turbulent pipe flow to design and optimise pumping infrastructure and piping systems. Such prediction requires accurate rheological characterisation of HCWS and numerical prediction of HCWS turbulent pipe flow, neither of which has been achieved to date due to respective limitations associated with benchtop rheometry and numerical turbulence models. We address these challenges by first developing accurate methods for rheological characterisation of HCWS via laminar flow of digested sludge at various solids concentrations (2–5 %) in a fully instrumented pipe loop facility at a large-scale WWTP. These rheological parameters are used in direct numerical simulation (DNS) computations (that avoid turbulence models) of turbulent pipe flow of HCWS. These predictions are then validated against turbulent flow pipe loop data. This method yields accurate (2–15 % error) predictions of HCWS turbulent pipe flow, compared with up to ∼75 % error for conventional pipe flow correlations. This validation highlights the need for accurate rheological characterisation and numerical simulation to predict HCWS pipe flow and provides a sound basis for the intensification and optimisation of WWTP pipeline systems.

Effect of Wear on Symmetric Hole-Entry Hybrid Journal Bearing Compensated by Orifice Restrictor Under Turbulent Regime

This study examines the impact of wear and turbulent flow on symmetric hole-entry hybrid journal bearings with orifice restrictors. Dufranes’s abrasive model for wear effect and Constantinescu’s lubrication model for turbulent flow have been used. A modification has been made to the Reynolds equationand utilized the finite element method to solvealong withflow equation of an orifice restrictor. For selected wear depth parameter values and Reynolds numbers,computed results have been acquired. The minimum fluid film thickness increases for worn bearings when operating under a turbulent regime rather than a laminar regime. Further, the stiffness coefficient decreases for constant external load when worn/unworn bearings function in a turbulent regime.

Investigating the effect of using aluminum oxide nanofluid and twisted tapes with different twisted pitches on the heat transfer efficiency and using perceptron artificial neural networks in data prediction

This study investigates the effect of aluminum oxide nanofluid with 1% and 2% volume fractions (VFs) in four different tubes with identical bending and the uniform, low-high-low, low-high, and high-low-high longitudinal states with twist ratios of 0, 2 and 4. These tubes are affected by a constant thermal flux of 10000 W/m2 and Reynolds numbers of 2000-10000. For the numerical solution of these equations, the finite difference method on the basis of the control volume and the SIMPLEC algorithm and the K-ε-RNG method were applied for the turbulent flow modeling. The determined Nusselt number from the numerical methods were evaluated applying the perceptron neural network. The most optimal increase in the Nusselt number was in the twisted tube with twist ratio of 4 in the Reynolds number of 10,000 and VF of 1% and 2% nanofluid with increasing trend of length from low to high. The most optimal increase in Nusselt number compared to base fluid was about 25%. The sum of squared error and the relative error data obtained from the hyperbolic tangent function for the training and test data were 0.080-1.331 and 0.113-0.675, and from the sigmoid function for the training and test data were 0.093-0.392 and 0.097-0.147.

Bayesian interface technique-based inverse estimation of closure coefficients of standard k−ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier–Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k−ϵ RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k−ϵ turbulence model are calibrated among the five coefficients ( Cμ,Cϵ1,Cϵ2,σϵ and σ k ). The Bayesian inference technique using the Metropolis–Hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x/h=2 and x/h=4 , along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k−ϵ turbulence model (baseline). The deviation of calibrated C µ is almost 50%–60% from baseline and for Cϵ1 and Cϵ2 it is 3%–12% and 6%–9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.

Anisotropic turbulence modeling for natural channel flow: A numerical approach with finite element method

In this study, we propose a numerical model aimed at improving the understanding and prediction of flow velocities in natural channels. This model specifically focuses on the challenges presented by anisotropic turbulence and bottom roughness. By incorporating the mixing length concept into an algebraic turbulence model and employing the finite element method with Streamline-Upwind/Petrov–Galerkin (SUPG) stabilization, our model seeks to refine the simulation of axial velocity distribution and secondary motions. Validation was achieved through Acoustic Doppler Current Profiler (ADCP) measurements in three sections of the Canal do Rodeador, showing our model’s predictions of discharge and average velocity to have a deviation of approximately 9.34% from experimental data. The results underline the significance of secondary currents and turbulence anisotropy in shaping channel flow behaviors, offering new insights into the interactions between flow characteristics and channel bed features. This model stands out as a robust tool for hydraulic structure design and hydrokinetic potential evaluation, providing a non-intrusive, cost-effective alternative to traditional methods.

Turbulent Channel Flow Simulation Using LES Dynamic Model

Turbulent flow modelling has increasingly becomeone of the main scientific research occupations, seeking todevelop a universal modelling approach that can describeaccurately the dynamics of all turbulent flow scales. Modernattempts try to bring together two main objectives; theapplicability of the turbulent flow models to complex flowconfigurations of industrial interest as well as reducing thecomputational costs needed for their resolution. Large EddySimulation (LES) modelling approach has many promisingfeatures among all other turbulent flow modellingapproaches such as RANS or DNS. In this study, LESmodelling approach has been demonstrated and applied toturbulent channel flow at moderate Reynolds number using Fluent solver. The obtained turbulent flowstatistics were compared to their corresponding values of a detailed, well resolved DNS simulation. The obtained LESturbulent flow statistics have an acceptable trend to those ofthe reference DNS results, which reflects the validity of theLES approach to model turbulent flows accurately andencourages its use in predicting turbulent motion forindustrial and engineering applications.

Numerical and experimental approach for dust dispersion and deposition behavior for safe decommissioning activities

ABSTRACT The use of high-fidelity modeling is a promising technique for studying the mechanisms of dust dispersion and deposition in safe decommissioning operations. Detailed multiphysics models for poly-dispersed turbulent flow, particle-laden flow, and particle surface interaction were coupled with a Reynolds Averaged Navier Stokes method for numerical simulation of dust dispersion and deposition. A model that considered the critical viscosity was utilized to estimate the interaction between particles and substrate. The deposition behavior of particles was a result of the competition between adhesion and rebound probabilities during the impact process, and only when the critical viscosity exceeded that of the impacting particles could they attach to the surfaces. To validate the accuracy of the simulation results, deposition experiments using zirconia particles were conducted. The experimental setup included a 3.2 m polycarbonate pipe, a fan regulated by an inverter to control the flow, an ultra-low penetration air filter capable of capturing particles with a minimum diameter of 120 nanometers. An air pump connected to a particle tank and a mixing tank was used for homogenizing the injection of particles. Particle concentration was measured during the experiments using a light scattering spectrometer system, WELASⓇ 2000, from the manufacturer PalasⓇ. This optical measurement technique functioned with a white light source and scattered light detection. The scattered light was collected via optical fibers, which led to the control and evaluation point, and results were displayed through special software. The numerical simulation results were compared with the experimental data and used to validate the numerical approach for flow with zirconia particles deposited on various material surfaces, including iron, titanium, stainless steel 304, and stainless steel 316, for airflow rates ranging from 54 L/min to 124 L/min.

Numerical simulation of aluminum-steel clad strip production using horizontal single belt casting process

A 3-D steady-state turbulent flow and solidification model was developed to simulate melt flow in a Horizontal Single Belt Caster for the production of an Al-Steel composite strip. The steel substrate is attached to the moving belt and moves at the same speed as the belt while the aluminum melt is introduced onto the substrate via an extended nozzle melt delivery system. A finite volume method was used to numerically solve the governing equations. In order to model the turbulent flow, a low Reynolds k − ε turbulent model was adopted. The developed numerical model was further employed to investigate the effect of such parameters as clad thickness, casting speed, molten aluminum superheat, and heat extraction rate from the belt surface on fluid flow and temperature fields in the system. It was found that for a certain clad thickness, casting speed and cooling rate should be adjusted properly and outlet strip temperature is independent of Inlet melt superheat.

High-Fidelity Velocity and Concentration Measurements of Turbulent Buoyant Jets

Accurate models of turbulent buoyant flows are essential for the design of the cooling circuit of nuclear reactors and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous particle image velocimetry and laser-induced fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The refractive index matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy-driven flows (e.g. natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in a uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as a basis for the development of a new model that captures turbulent mixing.

Design and Evaluation of Face Mask Filtration: Mechanisms, Formulas, and Fluid Dynamics Simulations

The global adoption of face masks as a preventive measure against the spread of the SARS-CoV-2 virus (COVID-19) has spurred extensive research into their filtration efficacy. This study begins by elucidating various mechanisms of particle penetration and comparing filtration efficiency formulas with experimental data from prior studies. This is compared to the filtration efficiency experimental measurement developed in our previous study. Moreover, it delves into fluid dynamics simulations to examine different turbulent airflow models. Specifically, it contrasts the airflow velocity distribution of the k-ω and k-ε turbulent flow models with that of a quadrant-based average velocity model developed within this research. Furthermore, the study conducts fluid dynamic simulations to assess airflow profiles for six distinct medical and non-medical face masks. The results underscore substantial disparities among the simulations, emphasising the criticality of employing accurate fluid dynamics models for evaluating airflow patterns during diverse respiratory activities such as breathing, coughing, or sneezing, thereby enhancing environmental health in the realm of infectious disease prevention.

The system of the vortex-like structures: The viewpoint on a turbulence modeling

In this study we suggest new approach to turbulence modeling. To develop this approach, we construct the set of the vortex-like dynamical systems evolving in the space E3. These systems are constructed using the AKNS hierarchy so that they generalize thin closed vortex filament described in the local induction approximation. We construct and investigate the Hamiltonian dynamics of these systems in terms of the non-standard variables. We formulate the principles of quantization these systems focusing on the quantum description of the filaments with linearized dynamics. To describe the energy of vortex-like structures, we apply a new method based on the use of the central extended Galilei group. In a special case, we calculate the energy levels of a system of quantized vortices. The proposed approach makes it possible to describe both the interaction of such vortex-like filaments and the processes of their creation and annihilation in a natural way. As a result, we have constructed a quantum turbulent flow model that demonstrates the relationship between stochastic and integrable dynamics.

Numerical and Analytical Estimation of the Wind Speed Causing Overturning of the Fast-Erecting Crane—Part II

The currently presented work is a continuation of the previous one, where the estimation of the forces induced by the wind flow acting on the fast-erecting crane. In that work, the values of the aerodynamic forces were determined experimentally and numerically for the sectional models of the tower and jib. Next, the obtained results were compared with the appropriate standards. Now, the main aim is to determine the critical wind speed causing the overturning of the whole structure. At the very beginning, the numerical analysis of the simplified model of the crane on the real scale is studied. The computations are performed with the use of the ANSYS FLUENT R22. The simulations are performed for three different wind profiles, namely: urban terrain, village terrain, and open terrain. Moreover, the various geometric configurations of the crane in the wind direction are studied. The k-ε model of turbulent flow is exploited. The obtained critical values of the wind speed are confronted with those that are obtained from standards and estimations based on the results obtained from previous investigations performed for sectional models. The influence of the load carried by the crane is also taken into consideration in the overturning of the structure.

Comparing Turbulence Models for CFD Simulation of UAV Flight in a Wind Tunnel Experiments

Wind tunnel tests are costly and time-consuming, and the accuracy of the tests is limited by the size of the tunnel, to solve this problem, researchers use computational fluid dynamics (CFD) to conduct wind tunnel experiments using a computer because it is less timely and less costly. Computerized testing of drone's models using wind tunnel experiment simulation in computational fluid dynamic (CFD) software requires knowledge of the most suitable turbulence model for this drone. In this paper ANSYS fluent program has been used to test four most common turbulence models for use (Spalart-Allmaras, K-Epsilon, K-Omega and Reynolds stress) and laminar flow on the ScanEagle drone model (an aerial reconnaissance drone used in military and intelligence operations) and calculated their effect on aerodynamic parameters In terms of accuracy and time to solution, concluded that the best turbulence model in terms of balancing accuracy and the time taken for the calculation is K-Omega model.