Reynolds-averaged Navier-Stokes Equations Research Articles

Validation of the steady and unsteady simulation based on an axial-flow pump

Abstract An axial-flow pump offers high flow rates and efficiency with low power consumption, making it ideal for applications that require transferring the large volume of fluid. Applying the numerical simulation in predicting hydraulic performance, analyzing the phenomena, and optimizing the design of the axial flow pump is very cost-effective and flexible. This study is performed to clarify the difference between steady and unsteady simulations based on the axial flow pump. Numerical simulations are carried out using the steady and unsteady Reynolds-averaged Navier-Stokes (RANS and URANS) equations and a shear stress transport reattachment modification turbulence model with small y+ values at all wall surfaces. To show the accuracy, numerical simulations are analyzed and compared with testing results. The difference in steady and unsteady simulations is presented by a detailed analysis of the flow field under the deep stall condition. The result shows that the numerical and testing results are in good agreement with each other. However, the unsteady results are more accurate than the steady results, especially in the saddle zone. Under deep stall condition, it is difficult to accurately predict the hydraulic performance and fluid flow characteristics inside the axial flow pump through steady simulation because of the time-dependent flow.

Numerical study on the flow-induced vibration of a high-pressure-jet pump on a dredger and corresponding impeller optimization

Abstract Trailing suction hopper dredgers are usually equipped with high-pressure-jet pumps, which provide high pressure water to improve dredging efficiency. In a newly built trailing suction hopper dredger, the high-pressure-jet pump encountered serious vibration problem. In this study, unsteady Reynolds-averaged Navier-Stokes equations were solved with Shear Stress Transport k-ω turbulence model to carry out pump-pipeline matching analysis, and the causes of flow-induced vibration were discussed. The impeller was correspondingly optimized by increasing the blade number and moderately decreasing the blade inlet setting angle and wrap angle. The optimization results show that the high-pressure-jet pump works in the high-efficiency zone both for the high-speed dredging process and low-speed hopper discharging process, and the time-average value and amplitude of the hydraulic radial force drops by more than 30% under the required working condition, which effectively mitigates the flow-induced vibration.

Errors and uncertainties in CFD validation for non-equilibrium turbulent boundary layer flows at high Reynolds numbers

NATO AVT-RTG-349 was dedicated to the validation of computational fluid dynamics (CFD) methods based on the Reynolds-Averaged Navier-Stokes (RANS) equations and statistical turbulence models for non-equilibrium turbulent-boundary-layer flows at high Reynolds numbers. This paper describes and discusses the errors and uncertainties arising in the comparison of RANS simulation results with experimental data from wind-tunnel experiments. These errors and uncertainties are associated with the CFD grid and the discretization, the physical modelling, the measurement accuracy, and the differences in the flow conditions between the experimental facility and the computational set-up. The results show the need for a grid-convergence study using systematically-refined families of CFD grids. The two major sources of errors are the RANS turbulence model and the uncertainty originating from the differences between the computational set-up and the wind-tunnel. Then two possible paths for future research are described: future CFD mesh generation, and future validation experiments at high Reynolds numbers.

Performance improvement of a rotating gas separator for electrical submersible pump considering entropy generation method

The utilization of Electrical Submersible Pumps (ESPs) stands as one of the foremost methods in artificially extracting oil, primarily within the oil industry. Under typical conditions, the pump encounters a two-phase flow of oil and gas. Should the gas phase within this mixture surpass an acceptable threshold, it can lead to a significant decline in performance and inflict detrimental damage upon the pump. To address this issue, the incorporation of a gas separator unit, one of the pivotal components within ESPs, is imperative at the pump's inlet section. Enhancing the gas separator unit holds paramount importance for ensuring pump safety and optimizing performance, particularly in wells with elevated gas contents.The conventional approach to calculating hydraulic losses in turbomachinery, relying on pressure drop calculations, often falls short in pinpointing the precise locations of losses. This paper delves into enhancing gas separator performance by augmenting gas separation efficiency through the application of the entropy generation method and leveraging the second law of thermodynamics. To achieve this, pivotal entropy-generating geometrical parameters of the gas separator were identified as the design variables necessary for forming the Taguchi sample space. Numerical simulations were conducted utilizing steady three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations for incompressible fluid flow, coupled with a turbulence model. Results indicate that the gas separation efficiency (GSE) of the initial model surged from 45.6% to 88% in the improved sample, albeit with a concurrent rise in entropy generation rate (EGR) from 209 W/K to 243.1 W/K. To establish a more comprehensive criterion for analysis, the ratio of GSE to EGR was employed as an objective function. This ratio quantifies the efficiency of gas separation per unit of energy loss, and it escalated from 0.218 in the primary sample to 0.362 in the improved sample, representing a 66% increase. This signifies that despite simultaneous increases in EGR and GSE, the rate of energy loss per unit of gas separation has diminished. Furthermore, the heightened EGR in the improved sample can be attributed to an increase in total volume, leading to an expanded contact surface area and consequently an elevation in total entropy. This investigation underscores the advantages of the entropy generation method, particularly in delineating the precise location and magnitude of energy dissipation within the rotating gas separator.

Preliminary design and hydrodynamic study of power-driven float pole system in Pacific saury fishery

Pacific saury (Cololabis saira), an essential commercial fish species in the North Pacific Ocean, is captured primarily using the stick-held dip net (SHDN) method. During the netting process, the separation of the gear from the vessel is dependent on the wind and currents, which represents a passive operational approach. In this study, we designed a prototype power-driven device for SHDN gear. The device consists of two thrusters, a remote-control system, and an energy device. It was installed on a 1/10 length segment of a float pole, hereafter referred to as the power-driven float pole (PFP) prototype. Experiments were conducted on both the single-thruster and PFP prototype to investigate the relationship between their rotational speed and thrust. SolidWorks was used to model the single-thruster and PFP prototype, and Ansys Fluent was used to solve the Reynolds-averaged Navier–Stokes equations to obtain the hydrodynamic characteristics of both the thruster and PFP prototype. A comparative analysis of the experimental and simulated hydrodynamic results showed the following: (1) the flow velocity between the blade suction surface and pressure surface tended to decrease, and the pressure tended to increase; (2) the thrust of both the single-thruster and PFP prototype increased with the thruster rotational speed according to a quadratic polynomial relationship; (3) the thrust ratio between the PFP prototype and the combined thrust of the two thrusters under the no-load condition exhibited a logarithmic relationship with the increasing rotational speed; and (4) to meet the operational requirements of the PFP prototype with a working duration exceeding 350 min and a minimum thrust of 20 N, the recommended rotational speed range for the thrusters on the PFP prototype was 1569–1970 rpm. The results of this study provide a fundamental reference for the further optimization of the PFP configurations.

Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

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.

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

Physics-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 1×105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\ imes 10^{5}$$\\end{document}. 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∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}. 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.

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

Design and Analysis of a Base Bleed Unit for the Drag Reduction of a High-Power Rocket Operating at Transonic Speeds

In the present study, a passive flow device is considered for drag reduction purposes through implementation in a transonic high-power rocket. The high-power rocket serves as a reference platform that, apart from the operating conditions, enforces several constraints in terms of available volume and placement locations. A step-by-step methodology is suggested, where the unit is initially broken down into an inlet and an outlet component. The flow field is investigated by means of computational modeling (CFD), where the Reynolds-averaged Navier–Stokes equations are solved coupled with turbulence models that vary depending on the design phase and the individual component. In the first design phase, the best alternative configuration is selected for each component by comparing mass flow rates and discharge coefficients. In the second design phase, each component is analyzed in greater detail based on the first phase results. Indicatively, the protruding inlet diffuser-type channel is converted into a protruding inlet nozzle-type channel to avoid choked flow phenomena, and a nozzle geometry is selected as the outlet amongst the other considered scenarios. The two components are eventually integrated into a common base bleed unit and a final assessment is made. The computational results are used to predict the performance and trajectory of the rocket through a well-established trajectory software. The overall methodology is validated against full-scale test flight data. The results show that the base bleed unit developed in the framework of this study yields a drag reduction of approximately 15% at transonic speeds without impacting the rocket mass and stability.

Novel adjustable backflow structure in electric coolant pump for balancing hydraulic performance and reducing temperature rise

An electric coolant pump serves as the source for coolant circulation in the thermal management of electric vehicles. To address the thermal issues for the printed circuit board integrated within the electric coolant pump, a novel backflow structure with an adjustable orifice diameter is designed from the impeller outlet to the printed circuit board to promote convective heat dissipation. Eventually, this flow returns to the impeller inlet, thereby altering the hydraulic performance of pump. The balance between hydraulic performance and temperature rise is achieved by adjusting the orifice diameter. Considering the variations in coolant properties with respect to temperature, numerical simulations of the electric coolant pump are performed using the unsteady compressible Reynolds-Averaged Navier-Stokes Equations. There is good agreement between experimental and numerical simulations results in both cases with and without an orifice. On an average, by increasing the orifice diameter by 1.5 mm which results in a 1.11 % decrease in efficiency, a 0.008 decrease in pressure coefficient, and a reduction of temperature by 2.98 K on printed circuit board. As the orifice diameter increases, leakage losses in the rear side chamber increases with the improvement of heat dissipation. The clash between the backflow jet and the inflow from the suction pipe results in significant entropy generation, forming jet vortices and increasing in pressure fluctuation. However, when the orifice diameter exceeds 3 mm, the cooling advantages no longer justify the trade-off in hydraulic performance. Thus, 3 mm orifice diameter is an optimal compromise between hydraulic performance and temperature control.

Broadband Noise Reduction of a Two-Stage Fan with Wavy Trailing-Edge Blades

In this paper, a numerical investigation is performed to study the broadband noise of a fan stage with wavy trailing-edge blades. A study of the wavelength and ratio of amplitude to wavelength (H/L) is conducted to better understand the noise reduction effect of wavy trailing-edge blades. A rotor–stator interaction broadband noise prediction method based on the result of a Reynolds-averaged Navier–Stokes equation is used. The results show that all wavy trailing-edge configurations reduce the sound power level of the fan stage. The noise reduction effect of H20L10 is the best among all the wavy trailing-edge configurations, and the sound power level is reduced by 2.4 dB at 1000 Hz. When the H/L remains unchanged, the noise reduction effect of the wavy trailing-edge configuration increases with the increase in wavelength. When the wavelength remains unchanged, the noise reduction effect of the wavy trailing-edge configuration with an H/L of 2 is the best. The use of wavy trailing-edge configurations reduces the turbulent kinetic energy and turbulent integral length scale upstream of the stator by changing the wake of the rotor, thereby reducing the rotor–stator interaction broadband noise of the fan stage.

Numerical Tools For Wave Overtopping At Rubble Mound Breakwaters With Submerged Berms

In the era of climate change, the adaptation of existing coastal structures as a response to potential increasing loads, has become a trending topic in coastal engineering. The combination of sea level rise, storm surge, tides and waves is going to dramatically increase the wave overtopping. In this context, this research is focused on the evaluation of wave overtopping for conventional rubble mound breakwaters, modified by the introduction of a submerged berm. Recent studies illustrated how the introduction of emerged berms on the seaward slope reduces the wave overtopping. The goal then becomes to turn the spotlight on the submerged berms, whose effectiveness has yet to be attested, although it has proven useful in reducing wave loads on the armour layer and seabed pressure under the structure. Therefore, the reliability of two different numerical models in detecting overtopping phenomenon have been assessed. IHFOAM and SWASH have been used (see Figure 1). The first one can solve both Reynolds Averaged Navier Stokes and the Volume Averaged Reynolds Averaged Navier–Stokes equations. The second one solves the non-linear shallow water equations with a non-hydrostatic pressure term, representing a simplified form of the Navier-Stokes equations, with associated limited computational cost. The numerical models have been validated based on experimental tests carried out in a wave flume at the University of L’Aquila.

Influence Evaluation of Open Propellers with Boss Cap Fins: Case Studies on Types B4-70 and Ka4-70

Numerical analysis of fins effect on propeller performance was conducted, specifically using the B4-70 and Ka4-70 propellers. The study investigated different types of fins, including bare fins and PBCF (Propeller Boss Cap Fins) using computational fluid dynamics (CFD) simulations. The explicit algebraic stress model (EASM) based on Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence modeling was employed to determine the optimal results. The main objective of this research was to enhance energy efficiency in ships by examining various open propeller configurations. The CFD simulation results for open propellers B4-70 and Ka4-70, with the addition of boss cap fins, revealed interesting phenomena. When the open propellers B4-70 and Ka4-70 were equipped with PBCF, they would experience an increase in efficiency (η0). This was because the performance of the fins functioned optimally when the advance ratio (J) is high, as evident from the high velocity values. Thus, with higher velocity and lower pressure in the boss cap region at high J values, there was an elevation in thrust force due to the reduction of hub vortex. In the case of open propeller B4-70 with added PBCF, there was an increase in the efficiency value (η0) ranging from 3% to 5% when J varied from 0 to 0.7. Similarly, for propeller Ka4-70 with the addition of PBCF, there was an increase in the efficiency value (η0) ranging from 1% to 3% when J varied from 0 to 0.7. Notably, the use of an Energy-Saving Device (ESD) in the form of PBCF can increase the efficiency of ship propeller, as reported in this paper. Consequently, these findings affirmed the reliability of the overall calculations using the CFD approach.

Development of a high-order solver for large eddy simulation of turbulent heat transfer at supercritical pressure based on Nek5000

Turbulent heat transfer at supercritical pressure is a complex flow phenomenon due to drastic variations in fluid properties near the pseudocritical point. Numerical simulation is an important method to reveal the underlying physics. Currently, low-order numerical methods together with Reynolds-averaged Navier–Stokes equations are the mainstream in which empirical parameters are required, preventing high-fidelity simulations. Through inventing iterative properties updating and density-weighted explicit filtering, this work develops a high-order spectral element solver based on the open-source code Nek5000. By simulating a classical problem of supercritical CO2 flowing in a heated pipe and comparing it with benchmark data, the capability of the solver in direct numerical simulation is validated. Further results suggest lowering the mesh resolution leads to inaccurate predictions of bulk parameters and turbulent statistics. Therefore, filtering-based large eddy simulation (LES) is explored with different filter weights under a coarse mesh. Results show such a method can significantly improve most of the bulk parameters, including the bulk Nusselt number. The optimal filter weight can be determined from a simple optimization problem minimizing the deviation of overall energy conservation. Being high-order and capable of LES without empirical parameter, the current solver is a powerful tool for high-fidelity simulation of turbulent heat transfer at supercritical pressure.

Numerical simulation of local scour around an inclined monopile in steady current

Local scour around the underwater supports of constructions would reduce the embedment depth and bearing capacity of support structures, seriously threatening the safety of the structures. Most existing investigations focused on the local scour of a vertical pile. However, in practical engineering, inclined piles are widely applied in underwater foundation structures to withstand lateral loads. The pile inclination can result in flow field alteration around the pile, thereby affecting the development of local scour. Consequently, a threedimensional numerical model of local scour around an inclined pile under steady current is established using the open-source CFD package OpenFOAM, in which the hydrodynamics are solved based on the Reynolds-averaged Navier-Stokes (RANS) equations together with k – ω SST turbulence closure in this model. It is then coupled with both bed load and suspended load transport descriptions, which drive the resultant morphology of the bed. The numerical model is verified by comparing it with the existing laboratory experiment. Discussions are carried out on the effects of inclination angles on the flow field alteration and the local scour depth variation.

Evaluating wave force and interface fluid velocity distribution at the vicinity of a breakwater by considering consolidation of porous media

Previous studies have successfully simulated the interaction between wave and porous media using volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations. However, the consolidation of porous media subject to wave loading affects the progressing wave, which is crucial to computation of wave force and wave-porous media interface fluid velocity. Research on this aspect is scarce. This study adopted the u -p approximation for Biot dynamic consolidation theory to quantify the consolidation of porous media. The continuity condition on the interfaces between the wave and porous seabed was considered to achieve their interaction. Coupling algorithms of wave and porous seabed were validated against experimental measurements in the literature. An engineering case of wave traveling over a breakwater was examined, and computation results of wave pressures and interface fluid velocities at the vicinity of a breakwater by VARANS equations and wave-porous seabed coupling algorithm of this study were compared to explore the influence of the consolidation effect on the progressing wave.

Numerical study of wave run-up on sea dikes with vegetated foreshores

Integrating coastal vegetation into sea dikes is a nature-based approach aimed at combining disaster prevention with ecological sustainability in coastal areas. This study investigates the impact of vegetation on the wave run-up on dikes through numerical analysis. The numerical model used in the study solves the Reynolds-averaged Navier–Stokes equations by adding a vegetation resistance force to account for momentum loss. A stabilized k–ω shear stress transport model considering the vegetation effect was adopted for turbulence closure. A series of numerical simulations was carried out on the wave run-up (Ru) on dikes, focusing on the effects of different vegetation heights, densities, zone lengths, and dike slopes under various wave conditions. The results indicate that vegetation can significantly decrease Ru and may cause the wave to change from breaking to nonbreaking on dikes. The Ru behaviors depend on whether waves break and can be well characterized by the Iribarren number and dimensionless wave momentum flux parameter under breaking and nonbreaking conditions, respectively. Finally, the multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to explore a prediction model for evaluating Ru. Comparisons showed that the prediction performance of the ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining wave run-up on dikes with vegetated foreshores under breaking and nonbreaking conditions.

Suppression of the vortex-induced vibration of the cylinder by the baffle plates at different submerged depths

In this paper, the suppression effect of baffle on VIV of cylinder at different depths is studied. According to two-dimensional transient model and RANS equation, VIV responses of a cylinder with two baffle plates at a fixed distance and a fixed Angle at different depths are numerically simulated. The submersion depth radio h* is mainly 1.2, 1.5, 2.5 and 5. The experimental data and predicting results are compared to display the accuracy of numerical method. When h* is 2.5, the baffle plates have the best suppression effect on VIV. Compared to the bare cylinder, the amplitude is decreased by 69%. Meanwhile, the vibration of the cylinder at different depths shows instability, and the motion response has great jitter. The lower baffle plate is subject to a unidirectional force when h* = 1.5 and 1.2.

Integrating Computational Fluid Dynamics for Maneuverability Prediction in Dual Full Rotary Propulsion Ships: A 4-DOF Mathematical Model Approach

To predict the maneuverability of a dual full rotary propulsion ship quickly and accurately, the integrated computational fluid dynamics (CFD) and mathematical model approach is performed to simulate the ship turning and zigzag tests, which are then compared and validated against a full-scale trial carried out under actual sea conditions. Initially, the RANS equations are solved, employing the Volume of Fluid (VOF) method to capture the free water surface, while a numerical simulation of the captive model test is conducted using the rigid body motion module. Secondly, hydrodynamic derivatives for the MMG model are obtained from the CFD simulations and empirical formula. Lastly, a four-degree-of-freedom mathematical model group (MMG) maneuvering model is proposed for the dual full rotary propulsion ship, incorporating full-scale simulations of turning and zigzag tests followed by a full-scale trial for comparative validation. The results indicate that the proposed method has a high accuracy in predicting the maneuverability of dual full-rotary propulsion ships, with an average error of less than 10% from the full-scale trial data (and within 5% for the tactical diameters in particular) in spite of the influence of environmental factors such as wind and waves. It provides experience in predicting the maneuverability of a full-scale ship during the ship design stage.