Turbulence Model Research Articles

Numerical investigation of the response of the hybrid wave energy converter including oscillating water column and horizontal floating cylinder to irregular waves

The main goal of this research is to investigate the effect of some geometrical parameters on an onshore Hybrid Wave Energy Converter (HWEC) including an onshore Oscillating Water Column (OWC) and a Horizontal Floating Cylinder (HFC) under regular and irregular waves. The TMA spectrum is the basis of this study. The wave spectrum is used to generate irregular waves in a numerical wave tank using Ansys-fluent software based on URANS equations. Active wave absorption is used to avoid the effect of reflected waves. Also, the SST k−ω turbulence model and the VOF scheme are used for turbulence modeling and interface tracking, respectively. The results confirm that the efficiency of the HWEC is higher than the efficiency of an OWC and the efficiency of an HFC in both regular and irregular waves. Besides, the efficiency of the HWEC in irregular waves is lower than its efficiency in regular waves. A comparison of the TMA and JONSWAP spectrum on HWEC performance shows that HWEC performance is lower on the JOANSWAP spectrum. This study shows that the use of irregular waves is essential to obtain more realistic results from analyses of the onshore HWEC performance, despite their need for high computational cost.

A reduced-order model to estimate first wall particle and heat fluxes for systems codes

Current systems codes (SCs) do not assess the impact of plasma filament parameters and dynamics in the SOL when performing systems-level analyses. Simulation tools based on simplified turbulent transport models could address such need, such as the TOKES code, but these tend to run in timescales that are prohibitive for incorporation in SCs. This work presents a technique to build surrogate models for SCs, obtained with the modes of Reduced-Order Models (ROMs), and is exemplified with results from TOKES. These surrogates were developed with Principal Components Analysis (PCA), multivariate regression against TOKES inputs (filament temperatures, densities, and ejection speeds) and k-fold cross-validation, applied to the results after transformations based on rational powers of the inputs to optimize the prediction capabilities of the surrogates. Selection was performed with a modified Kullback-Leibler Divergence (KLD), and validation, with withheld cases. Main results include validation of the methodology due to the relatively low number of modes needed to represent more than 90% of the data variance, and the data transformation exponents that optimize the regression.

Study on heat transfer and pressure steady-state characteristics of a floating nozzle under a moving wall

This work considers the flow field as two-dimensional turbulent flow and studies the steady-state properties of heat transfer and the pressure of the suspension nozzle. An adiabatic wall parallel to the moving wall and two slit entrances at either end of the adiabatic wall make up the rectangular flow field. The SST k-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k - \\omega$$\\end{document} turbulence model is used in the turbulence computation. Both qualitative and quantitative analyses are conducted on the distribution of the flow field, temperature field, local Nusselt number, local pressure coefficient, average Nusselt number, and average pressure coefficient under various combination conditions. The findings indicate that when the suspension nozzle's flow field varies greatly, wall-jet velocity ratio is 0.1. A rise in Jet inclination angle is not helpful for the wall's suspension, and it has minimal effect on the flow field. The flow field is greatly influenced by separation space-slit width ratio. Larger separation space-slit width ratio values are advantageous for the wall's heat transmission but unfavorable for the wall's suspension. The flow field is most influenced by wall-jet velocity ratio. The wall's ability to convey heat is stronger the higher the wall-jet velocity ratio, but its ability to support weight falls.

Improved Prediction of the Flow in Cylindrical Critical Flow Venturi Nozzles Using a Transitional Model

AbstractCritical flow Venturi nozzles (CFVNs) are a state-of-the-art secondary standard widely used for gas flow measurements with high precision. The flow rate correlates with the type and thickness of the boundary layer (BL) inside the nozzle throat. In the cylindrical type—one of the two standard designs of CFVNs—the nozzle throat encompasses a defined axial length in which the BL develops. This numerical study is concerned with the BL effects in a cylindrical CFVN by means of two turbulence models. Compared to experimental data, the k-$$\omega$$ ω SST model predicts the discharge coefficient well for high and low Reynolds numbers, but not in the intermediate regime. The $$\gamma$$ γ -$$Re_{\theta }$$ R e θ model, on the contrary, agrees well with experimental data in the entire flow range. Relevant quantities and profiles of the BL are separately investigated in the laminar, turbulent, and transitional region. The calculated laminar and turbulent BL thicknesses correspond to predictions based on integral methods for solving the BL equations. Simple representations are proposed for the Zagarola-Smits scaled laminar and turbulent deficit BL profiles removing the effects of axial position, Reynolds number, and pressure gradient. Furthermore, the shape factor is investigated as a characteristic parameter for determining the transitional region.

Disaster evaluation of hydrogen explosion leakage from industrial-scale non-metallic pipeline

This work is aimed at evaluating the disaster consequence of leaked hydrogen explosion from the industrial-scale non-metallic pipeline. The flame evolution and explosion overpressure are experimentally obtained. A standard k-ε turbulence model and a beta flame model is established to analyze the explosion overpressure generation. The results indicated that whether there is an external ignition source or not, the hydrogen explosion still occurs when the high-pressure hydrogen leaks from non-metal pipelines. The formation of three overpressure peaks could be attributed to the non-metallic pipeline rupture, leaked hydrogen explosion and sand soil spread. The explosion overpressure peaks continue to decrease with increasing monitoring point distance. The moving speed of explosion overpressure is between 349.34 m/s and 436.21 m/s. The leaked hydrogen concentration outside non-metallic pipeline could reach up to about 10% and the explosion overpressure generation is dependent on the concentration distribution.

Numerical modeling of hydrodynamics of spouted bed in solid fuel boiler

The issues of numerical modeling of hydrodynamics of a spouted fuel bed in the furnace of a solid-fuel boiler are considered. At present, solid-fuel boilers are widely used in the power industry of the Russian Federation, with the share of coal-fired generation to remain significant in the projected terms. Therefore, the study of the efficiency of thermal and hydrodynamic processes that ensure the implementation of clean coal technologies is a relevant task both today and in the long term. The article presents the following main stages of numerical modelling of the hydrodynamics of the spouted bed: problem formulation with selection of boundary and initial conditions, methods of solving the Navier-Stokes and continuity equations for the air flow, Newton's equations and diffusion equations for particles. The k-omega turbulence model was used in the calculations that is described by means of two partial differential equations for the variables k (kinetic energy of turbulence) and omega (specific dissipation rate). A comparative analysis of environmental advantages and disadvantages of existing methods of combustion of low-grade coal in schemes with in-cycle gasification (ICG) is carried out. Advantages and difficulties of switching to structures with CFB in the spouted bed mode are shown. Numerical modeling of the cold spouted bed created by means of particle injection is performed, a set of initial settings and boundary conditions is presented, the adequacy of the obtained results is verified by hydrodynamic characteristics of the isothermal process. The obtained results allow us to proceed to the next stages with non-isothermal models, with heat exchange and combustion reactions in the spouted bed of coal taken into account. The following refinement of the physical model will allow to achieve more accurate and reliable results and to ensure their correct scaling.

Computational investigation of transportation and thermal characteristics in a bi-modal slurry flow through a horizontally placed pipe bend

In this study, we develop a three-dimensional computational model to explore the transportation and thermal characteristics of a bi-modal slurry flowing through a horizontally placed 90° pipe bend. The slurry comprises silica sand (SS) and fly ash (FA) granular, with varying combinations (65:35, 75:25, 85:15, 95:05, and 100:0). The computational investigation has been carried out for different carrier fluid's characteristics, including Prandtl number, and flow velocity (5 m/s), for efflux concentrations of Cw = 40–60% for each mixture. Validated with experimental data, the computational approach employs a two-phase Eulerian-Eulerian RNG k-ε turbulence model and the kinetic theory of granular flow. Results reveal that the 65:35 combination exhibits minimal pressure drop, and the 100:0 combination shows maximum heat transfer characteristics, particularly with low-viscosity fluid (Pr = 2.88) and high particle efflux concentration (Cw = 60%). The study also examines bend loss coefficients (Kt), concentration distribution, convective heat transfer coefficient (h), and Nusselt number (Nu) across different Prandtl fluids and efflux concentrations.

The role of annular 2-lobe nozzle in a strut injection system on the mechanism of fuel distribution at a scramjet engine

The strut injection system is a conventional technique for the injection of the fuel in combustor in hypersonic vehicles. The present article investigates the usage of the annular 2-lobe injector to improve the fuel jet behind the strut. Computational studies have been employed for the modeling of fuel jets released from 2-lobe injectors at the supersonic free stream of the combustion chamber. Simulation of the compressible flow is done by solving Reynolds-Averaged Navier-Stokes (RANS) equations with the turbulence model of SST. The roles of the proposed injection configuration on the flow and fuel jet penetration are disclosed in this work. The shape of fuel jet plume behind the injector is also investigated to explain the mechanism of fuel jet distribution in this technique. Presented data disclosed that the usage of the annular 2-lobe nozzle instead of a single circular jet improves fuel mixing by about 50 % behind the strut model.

Graph and convolutional neural network coupling with a high-performance large-eddy simulation solver

Computational Fluid Dynamics (CFD) traditionally relies on long-standing numerical simulation strategies for the Navier–Stokes equations. Recently, interest in data-driven hybrid CFD solvers has spiked, leveraging pre-computed datasets to enhance various weak links inside existing solvers, such as closure models, under-resolved physics, or even to guide numerical resolution strategies. Running these hybrid solvers, notably in High Performance Computing (HPC) environments, presents specific challenges. In particular, context-aware deep learning (e.g. Convolutional (CNN) and Graph (GNN) Neural Networks) is promising for this task, but requires passing data representations between the physics solver and the neural network. In relevant industrial configurations, CFD meshes can be Cartesian but highly irregular, or unstructured, both of which do not match the pixel/voxel structure needed to run CNNs. In addition, discrepancies in programming language and libraries are common between CFD and machine learning applications. This work explores the many challenges of running a parallel hybrid solver in an HPC context, through the coupling of the AVBP CFD solver with neural networks in turbulent combustion and wall friction modeling applications. The knowledge gained is showcased in this article, as well as assembled in an actionable open-source library.

Numerical simulation of flow over short crested weirs - case study: Quarter-circular crested weir

In this study, the flow characteristics over a quarter-circular crested spillway (QCCS) were investigated using computational fluid dynamics (CFD) simulations. The simulations included an in-depth analysis of parameters such as flow velocity, pressure distribution, and streamline patterns. The RNG turbulence model was used to simulate the flow field and hydraulic characteristics. In particular, the simulations were performed at the design discharge. The numerical results were carefully compared with laboratory observations, showing that there is good agreement between the simulated results and the observed data. The results of the numerical simulation showed that the streamlines are completely in line with the curvature of the crest and that there is no separation zone (separation of the streamlines from the surface of the crest). furthermore, there is no negative pressure zone along the crest, which means that the risk of cavitation is eliminated. The highest value of velocity and the lowest pressure of flow occur at the outlet end of the crest.

Analysis of the Flow Behavior and Pressure Fluctuation of a Pump Turbine with Splitter Blades in Part-Load Pump Mode

The internal flow of a pump turbine is unstable in part-load pump mode for small guide-vane openings, and the strong vibration caused by pressure pulsation is related to the safe and stable operation of the unit. A pump turbine with a six-splitter-blade runner was chosen for unsteady simulation analyses. A standard k-epsilon turbulence model was adopted to study the unsteady flow and pressure pulsation in part-load pump mode. The predicted results show that the flow in the draft tube and the runner with splitter blades was relatively stable and the flow of the blade-to-blade channel was symmetrical. When the inlet and outlet velocity distribution of the vanes was not uniform, a vortex began to form in the stay-vane domain. The reason for this vortex formation is explained, and it is pointed out that the existence of the vortex and backflow leads to uneven velocity distribution. The unsteady calculation results showed that the pressure-pulsation peak-to-peak amplitudes in the vaneless area and guide vanes were much higher than those of other monitor points because of rotor–stator interference between the rotating runner and the vanes. In addition, the pulsation characteristics of the monitor points at different circumferential positions in the vaneless region were quite different. In the vaneless area, the velocity gradient along the circumferential direction was very large, and there was a phenomenon of backflow. Also, the pressure pulsation was 0.2 times that of the runner rotational frequency, and the blade-passing frequency was a third-order frequency. At the outlet of the guide vane, the pressure pulsation was mainly of a low frequency with a complex vortex flow. Finally, the pressure pulsation began to decrease rapidly in the stay-vane region.

Numerical study of aerodynamics drag and flow characteristics of the high-speed train head design

A native design of the Indonesian high-speed train has been developed as an improvement of the previous medium-speed train model. As the design speed is proposed to be increased from 160 km/h to 250 km/h, the nose shape and nose length of the train head were modified into a sharper and longer nose. In this study, numerical simulation of computational fluid dynamics was used to investigate the aerodynamic phenomena and flow behavior around the modified train head and carbodies. The CFD simulation was used as the verification of the shape design and a tool for rapid design changes and optimization. The model configuration is three cars on a real scale by ignoring other parts like the train window and door, pantograph, and train connecting. A k-ε turbulence model was used in the simulation. From this investigation, it is found that the coefficient of drag on the model is calculated to be 0.34. Meanwhile, an experimental wind tunnel test validates the result with a coefficient drag is 0.38 or 10% divergence from the numerical method.

Data-assisted training of a physics-informed neural network to predict the separated Reynolds-averaged turbulent flow field around an airfoil under variable angles of attack

AbstractPhysics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of $$1\times 10^{5}$$ 1 × 10 5 . Using our technique, the angle of attack was introduced as an additional input parameter of the network and the model was trained to predict the Reynolds-averaged velocity and pressure fields around the airfoil for arbitrary angles of attack between 10.0 and 17.5$$^{\circ }$$ ∘ . Furthermore, we present an effective method to generate the training points for the parameterized geometry. The model was trained with data from simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier–Stokes equations was attained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand for labeled training data in the domain. The trained network was capable of predicting the flow separation progressing with angle of attack on the suction surface and exhibited excellent agreement with numerically simulated results, even in the proximity of the wall for interpolations as well as extrapolations from the labeled data set. Our study demonstrates that physics-informed neural networks can be used to obtain accurate flow field surrogate models of variable geometries.

Numerical simulation of jet boiling characteristics of high-pressure water injected into high-temperature liquid lead–bismuth in a confined space

The steam generator heat transfer tube rupture (SGTR) accident is potentially devastating and is one of the most serious design basis accidents for lead–bismuth cooled fast reactor (LFR). It is important to study the mechanism of water jet injecting into liquid lead–bismuth eutectic (LBE) for the safety analysis of SGTR accidents. In this paper, based on the volume of fluid (VOF) model, the large eddy simulation (LES) turbulence model and the Lee phase transition model, a three-dimensional numerical model is developed to investigate the typical characteristics of a high-pressure sub-cooled water jet injecting into high-temperature LBE in a confined space. The study focuses on examining the impact of water temperature, inlet pressure, and nozzle diameter on jet development and its surroundings, including the cover gas layer and LBE phase. The results indicate that the central region of the jet is primarily subject to flash boiling, particularly at the nozzle position, whereas the jet interface undergoes heat-transfer boiling. The residual liquid phase migrates upward along the interface and gradually boils. Based on the phase distribution characteristics, a typical jet can be categorized into four zones: the water-steam transition zone, the multiphase flow zone, the end water phase zone, and the steam block zone. Under the conditions analyzed in this paper (water temperature 140–260 °C, injection pressure 2–10 MPa, nozzle diameter 2–10 mm, LBE temperature 400 °C), the jet volume expands approximately exponentially, correlating positively with the three factors studied. It is also found that at high injection pressures and large nozzle diameters, the steam at the top of the jet is prone to destabilization and fragmentation, with steam volume and pressure oscillations being the dominant factors. Steam migration triggers pressure oscillations in the LBE region, and the intensity of these oscillations is closely linked to the migration rate. Under the conditions studied, the maximum pressure oscillation reached 5.5 times the initial pressure. The expansion of the jet steam drives the pressurization of the cover gas layer, which correlates positively with all three factors studied. The nozzle diameter has the greatest effect, increasing the maximum pressure by 168 % from the initial pressure.

Quasi-random frequency sampling for optical turbulence simulations

Optical turbulence modeling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of spectrum-based optical turbulence Monte-Carlo simulations, we present an alternative approach to the methods based on the fast Fourier transform (FFT) using a quasi-random frequency sampling heuristic. This approach provides complete control over the spectral information expressed in the simulated measurable without the drawbacks encountered with FFT-based methods such as high-frequency aliasing, low-frequency under-sampling, and static sampling statistics. The method’s heuristics, implementation, and an application example from the study of differential piston fluctuations are discussed.

Investigation of two phase liquid jet ejector with simultaneous air and water suction in fresh water distillation system

Liquid jet ejectors can be utilized to generate vacuum in thermal desalinations, power plant applications and chemical industries. Liquid jet ejectors have no moving parts and have the advantage of reliability and low maintenance cost and also entrainment of non-condensable gas and brine simultaneously relative to pumps. The aim of this work is to model a liquid jet ejector with mixed air and water suction, applicable in fresh water distillers. The design is numerically simulated by two-phase Eulerian model and Realizable k-ε turbulence model. The results of the numerical model of liquid jet-air ejector are compared with experimental data and good agreement is achieved with deviation of about 7.4 % and 11.2 % for flow ratio and maximum discharge pressure respectively. In order to study robustness of the design, the value of suction entrainment and motive load of ejector is studied for different values of brine and suction pressure (8–12.5 kPa) of a 12 m3/day fresh water distiller. The results show constant air entrainment in off-design condition. In addition, mixing behavior and hydrodynamics of the flow in such ejector is studied by the parameters of pressure, velocity, flow and turbulent intensity distribution and compared with the ejector with air-only suction.

The influence of roll angles on unsteady aerodynamics in a canard‐configured missile

AbstractDuring the initial stage of vertical launch, a missile may exhibit an uncertain roll angle (φ) and a high angle of attack (α). This study focuses on examining the impact of roll angle variations on the flow field and the unsteady aerodynamics of a canard‐configured missile at α = 75°. Simulations were performed using the validated k‐ω SST turbulence model. The analysis encompasses the temporal development of vortices, the oscillatory characteristics of the lateral force, and the fluctuation of kinetic energy distribution within the framework of proper orthogonal decomposition (POD). The results indicate that the flow field surrounding the canard‐configured missile is characterized by inconsistent shedding cycles of Kármán‐like and canard‐separated vortices. A distinct transition zone is identified between these vortices, where vortex tearing and reconnection phenomena occur. With increasing roll angles from 0° to 45°, there is an observed shift in the dominant frequency of the lateral force from the higher frequency associated with Kármán‐like vortex shedding to the lower frequency of canard vortex shedding. The shedding frequency of Kármán‐like vortices corresponds to the harmonics of the canard vortex shedding frequency, indicative of a higher‐order harmonic resonance. The frequency of the lateral force is observed to decrease with an increase in roll angle, except in configurations lacking distinct canard‐separated vortices, which are characterized by a “+” shape. The POD analysis reveals that the majority of the fluctuation energy is concentrated in the oscillations and shedding of the canard‐separated vortices, leading to pressure fluctuations that are primarily observed on the canard and the downstream region of the canard.

Numerical Simulation of the Plant Shelterbelt Configuration Based on Porous Media Model

Low-coverage line-belt-pattern protective forests offer significant advantages in terms of wind and sand control measures. It is important to study the windbreak effectiveness of sand-fixing forests with different spacing for the construction and optimization of plant shelterbelt configurations. The effect of plant spacing on the flow field around a row of trees was investigated using the k-ε turbulence model coupled with the porous media model. In order to accurately simplify the complex and stochastic plant constitutive features, we simplify the plant canopy to a circular platform geometry, which introduces a porous media model, and the plant trunk is simulated as a solid cylinder. The simulation results show that windbreaks only affect wind profiles up to 1.25-times the height of the tree; on the leeward side of the canopy, large-spaced shelterbelts provide greater protection in the near-wake zone, while small-spaced shelterbelts are more effective at reducing velocity in the re-equilibration zone. The flow field recovery properties of the trunk and canopy indicate that the canopy wake zone is longer. In this study, we also quantitatively analyze the relationship between average wind protection effectiveness as a function of plant spacing and streamwise distance from the leeward side of the canopy, and the given parameterized scheme shows a power exponential relationship between wind protection effectiveness and plant spacing and a logarithmic relationship with streamwise distance. This scheme can provide a predictive assessment of the effects during the implementation of the plant shelterbelt.

Sweeping jet impingement heat transfer on concave surface: Influence of trapped vortex ring revealed by generalized k-ω (GEKO) model

Jet impingement-based heat transfer enhancement is widely employed due to the significant mass, momentum, and energy it accompanied. While the steady jet with high energy flux is commonly favored, it still exhibit few defects, including heat transfer deterioration away from the stagnation point and mutual flow interference in the jet arrays, which are particularly critical in demanding applications. Recently, the sweeping jet has been proposed to resolve the above challenges owing to its self-excited and self-sustaining unsteady oscillation. However, current research predominately focuses on impinging on the flat surface, neglecting impinging on the concave surface, such as internal cooling at the gas turbine blade leading-edge as well as the hot gas de-icing at the aircraft wing leading-edge. Understanding the heat transfer characteristics in these scenarios is crucial as they notably differ from those on flat surfaces. Therefore, this paper investigates the heat transfer characteristics and the related essential flow dynamics of a sweeping jet with a Reynolds number of 2577 impinging on a concave surface, and those of a steady jet under the same conditions are compared. The jet-to-wall distance and the curvature of the impingement surface are 4 and 10 times the jet's hydraulic diameter, respectively. To correctly capture the three-dimensional characteristics of the sweeping jet, this research employs the Reynolds stress model for turbulence modeling and the Generalized k-ω (GEKO) model for better calibration of the jet's spreading and dissipation rates, as well as the characteristics of trapped vortex generated due to the confined concave flow channel. The study initially focuses on the average Nusselt number on the impingement surface, revealing a 15.2% increase in heat transfer intensity of the sweeping jet compared to the steady jet, and the sweeping jet covers a larger area with enhanced uniformity. Subsequent analysis on streamlines in two perpendicular planes and Q criterion iso-surfaces in the spatial domain shows the formation of a trapped vortex ring with a constant location around the jet, restricting the effective cooling range to its inner side and thus resulting in a steep temperature rise on the two lateral sides of the vortex ring. The stability of the trapped vortex is enhanced by the curved impingement wall in the oscillation plane, which on the one hand forces the high-temperature fluid that has exchanged heat with the wall to repeatedly wash the same location, and on the other hand significantly reduces the jet oscillation angle compared to a free sweeping jet. Consequently, the heat transfer intensity of the sweeping jet is lower in the main oscillation plane than in the non-oscillation plane. Analysis of the near-wall flow parameters indicates that the sweeping jet generates higher velocity and turbulence kinetic energy in the wall jet zone far away from the stagnation point compared to the steady jet, which results in a higher local heat transfer intensity. The unsteady transverse oscillation of the sweeping jet disturbs the wall jet zone and disrupts the formation of the wall boundary layer, causing a higher velocity gradient at the wall and hence the lower thicknesses of the velocity boundary layer and the thermal boundary layer than those of the steady jet. In conclusion, this study reveals the flow and heat transfer features of the sweeping jet impingement on confined concave surface, with the influence of the trapped vortex ring mattering significantly. The findings provide a reference for designing a more effective jet arrangement. Future work will focus on investigating the effects of jet Reynolds number and impingement distance variations on the trapped vortex ring, and how to mitigate the adverse effects of the trapped vortex ring on impingement heat transfer.

Improvement of Aerodynamic Performance of NACA 2412 Airfoil using Active and Passive Control Techniques

Improvement of Aerodynamic Performance of NACA 2412 Airfoil using Active and Passive Control Techniques