Multiple Reference Frame Approach Research Articles

Simulation Approaches for the Study of the Oil Flow Rate Distribution in Lubricating Systems with Rotating Shafts

This study addresses the issue of predicting the distribution of lubricant flow through the outlets of a rotating shaft used in vehicle power transmission. A typical geometry with closely spaced rows of holes, suitable for the lubrication of multi-disk clutches, was considered. Both lumped parameter and computational fluid dynamics approaches were applied and compared. The test rig for model validation was designed with a variable speed shaft featuring an axial oil inlet and three equally spaced pairs of radial outlet holes. The main characteristic of the experimental facility is the possibility to selectively measure the flow rates through each outlet. It was found that the three-dimensional model based on the multiple reference frame approach provides a reliable prediction of how the flow rate is distributed. Generally, the flow rate is lower through the outlet closest to the inlet and is maximum at the farthest exit. The flow distribution is minimally affected by the shaft speed. The influence of geometric parameters on making the flow distribution more uniform was studied. It was found that a better flow balance is obtained with a low ratio between the diameter of the radial holes and that of the axial channel. The results obtained offer best-practice guidelines for accurately simulating comparable systems, in order to optimize reliability of the mechanical transmission and energy efficiency of the flow generation unit.

Numerical Investigation of Oil–Air Flow Inside Tapered Roller Bearings with Oil Bath Lubrication

Oil–air flow within an oil bath lubrication tapered roller bearing is essential for the lubrication and cooling of the bearing. In this paper, we develop a simulation model to investigate the flow field of tapered roller bearings with oil bath lubrication. The multiple reference frame (MRF) approach is used to describe the physical motion of the bearing, and the volume of fluid (VOF) two–phase flow model is used to track the oil–air interface in the flow field. The effects of mesh scale, geometric gap, and oil reservoir size on calculation time and convergence accuracy are examined in detail, and the effects of inner ring rotational speed and lubricant viscosity on frictional torque are systematically studied. The results of the numerical simulation indicate that as the gap distance between the raceway and the rolling elements decreases, the frictional torque is mainly generated by churning losses at the inner raceway and the rolling elements. The frictional torque increases with increasing inner ring speed and lubricating oil viscosity, with the rolling element contributing the largest portion at approximately 50% of the total. We demonstrate the effectiveness of a method to reduce frictional torque by optimizing the internal structure of the bearing to control oil flow. By optimizing the cage structure and reducing the roller half-cone angle, frictional torque can be reduced by 29.1% and 26.2%, respectively.

Impact of lateral turbine spacing on the performance of a multi-rotor tidal energy device

In this work, the impact of local blockage on the power production of a tidal array due to multiple turbines positioned in close proximity is studied. A numerical model of the HydroWing tidal energy device, which features multiple turbines on a retrievable wing, is being developed using geometry-resolved computational fluid dynamics (CFD). For this paper, the influence of two turbines at several spacings is considered.
 The CFD model is used to perform quasi-static steady-state simulations of two turbines in a twin rotor configuration, where a multiple reference frame (MRF) approach is used to simulate rotor rotation. The lateral spacing between the rotors is varied and the resulting impact on the axial loads and power performance of the two turbines is studied, with the aim of identifying the optimal turbine spacing for the HydroWing device. The results will be used in future design optimisation work to minimize the levelized cost of energy of a large scale array using HydroWing technology at the proposed site for the Morlais tidal energy project.

Two-fluid simulations of an aerated lab-scale bioreactor

We report the findings of a detailed assessment of various options for computational two-fluid RANS simulations of an aerated agitated 2-L bioreactor equipped with a single baffle and several dip tubes. The simulations were carried out by using the commercial flow solver ANSYS/Fluent. Our focus was on (1) the outlet condition at the liquid’s surface (i.e., including an air head space in the simulation yes or no); (2) the choice between the steady-state Multiple Reference Frames (MRF) approach for modelling the impeller rotation and the dynamic Sliding Mesh (SM) option; (3) the choice between two computational meshes (mosaic or polyhedral); and (4) the effect of using either the realizable k-ε model or the SST k-ω model for dealing with the turbulence in combination with different values for the fixed bubble size (either 1.8 or 2.8 mm). The final conclusion is that the SM impeller model in combination with a polyhedral computational mesh and the SST k-ω turbulence model is to be preferred. All simulations suffer from the occurrence of spurious velocities larger than the impeller tip velocity.

Topology optimization for fluid flow devices modeled through the Multiple Reference Frame approach

Fluid flow devices have been algorithmically designed through optimization methods, and this task is relatively complex for flow machines. Particularly, one recent development is the use of the topology optimization method for this task, which is capable of achieving possibly non-intuitive geometries and even auxiliary structures, such as splitter blades without ever imposing them as a condition for the design. The design of the rotating part of the rotor has already been previously considered. However, in the presence of stationary parts surrounding the rotor, such as diffuser blades, the fluid flow behavior may change, meaning that it may be interesting to consider this different dynamic in the design. One possible approach for this is the Multiple Reference Frame approach, which considers the fluid flow dynamics inside the rotor being computed in the rotating reference frame, whilst the fluid flow dynamics outside the rotor is being computed in the stationary reference frame. In particular, this implies the need for some changes in the topology optimization formulation, also impacting the choice of objective functions. Therefore, here the topology optimization method is formulated for the Multiple Reference Frame approach, and a new combination for the multi-objective function is proposed. The discrete design variable configuration from the Topology Optimization of Binary Structures approach is adopted with some adjustments to account for the Multiple Reference Frame approach. The fluid flow is chosen to be laminar or turbulent. Numerical examples are presented in 2D for the rotor-diffuser in order to consider some aspects that affect the overall topology optimization design.

Numerical Investigations on the Fluid Behavior in the Near Wake of an Experimental Wind Turbine Model in the Presence of the Nacelle

Accurate predictions of the near wake of horizontal-axis wind turbines are critical in estimating and optimizing the energy production of wind farms. Consequently, accurate aerodynamic models of an isolated wind turbine are required. In this paper, the steady-state flow around an experimental horizontal-axis wind turbine (known as the MEXICO model) is investigated using full-geometry computational fluid dynamics (CFD) simulations. The simulations are performed using Reynolds-Averaged Navier-Stokes (RANS) equations in combination with the transitional k-kl-w turbulence model. The multiple reference frame (MRF) approach is used to allow the rotation of the blades. The impacts of the nacelle and blade rotation on the induction region and near wake are highlighted. Simulation cases under attached and detached flow conditions with and without the nacelle were compared to the detailed particle image velocimetry (PIV) measurements. The axial and radial flow behaviors at the induction region have been analyzed in detail. This study attempts to highlight the nacelle effects on the near wake flow and on numerical prediction accuracy under various conditions, as well as the possible reasons for these effects. According to simulation results, the rotation of blades dominates the near wake region, and including the nacelle geometry can improve both axial and radial flow prediction accuracy by up to 15% at high wind speeds. At low wind speeds, the nacelle effects can be ignored. The presence of the nacelle has also been shown to increase flow separation at the trailing edges of the blade airfoils, increasing both root and tip vorticities. Finally, small nacelle diameters are recommended to reduce flow separation on the blades and increase the average velocity downstream of the rotor, thereby optimizing wind farm output power.

Особенности численного моделирования работы воздушно-тепловой завесы в OpenFOAM

The issues of mathematical modeling of turbulent heat-conductive flow of compressible viscous medium in the internal volume of the body of an air-thermal curtain equipped with a tangential fan are considered. The solution of the problem is constructed on the basis of averaged Reynolds (Favre) Navier-Stokes equations. The solution of the problem is obtained using the MRF (Multiple Reference Frame) approach, which uses a rotating reference frame, and using a transformation of the basic Navier-Stokes equations in the rotation zone. In order to correctly describe the working processes occurring in the internal volume of the air-thermal curtain and in the environment, modular multiblock meshes are applied in the work, including those allowing to separate rotating and stationary areas. The solution of the set tasks is constructed using the tools of the OpenFOAM package. As a result of the work, the peculiarities of the flow structure in the flowing part of the air-heat curtain are described in detail, and the gas velocities achieved at different fan speeds are estimated. The self-similarity of velocity profiles at the air curtain nozzle outlet is shown.

Constraint Handling and Flow Control in Stirred Tank Bioreactors with Magnetically Coupled Impellers

In this study, Computational Fluid Dynamics (CFD), applied to a non-Newtonian fluid, was developed to characterize gas-liquid interaction and mixing process in a 15 m3 (working volume) bioreactor. The bioreactor was equipped with four arrangements of standard Rushton, Pitch-blade and Scaba® impellers. Gas-liquid hydrodynamics was estimated based on CFD results. The chosen operating conditions were defined by the settings used for production of xanthan gum via fermentation route by Xanthomonas campestris. The mixing process was simulated by using the k-epsilon turbulence model, Multiple Reference Frame and Population Balance Model approaches. The simulation results have been compared and analyzed by isosurfaces, volume fractions, velocity graphs, torques and flow analysis calculations. Obtained results revealed that for the Pitched-Pitched-Pitched arrangement to avoid the constraint-imposed overload torque limitations impeller diameter size should be reduced by 10%. The use of Rushton-Rushton-Rushton impeller arrangement was discouraged for non-Newtonian pseudoplastic fluid mixing, whereas Pitched-Rushton-Scaba and Scaba-Rushton-Pitched impeller arrangements were both acceptable.

Aerodynamic Characteristics of a Ducted Fan Hovering and Transition in Ground Effect

Ducted fans installed on vertical takeoff and landing vehicles experience significant ground effect during takeoff and landing. The aerodynamic characteristics of a ducted fan hovering and transitioning in the ground effect are studied using numerical simulations in this paper. The flowfields are obtained by solving Reynolds Averaged Navier–Stokes equations with the Multiple Reference Frame approach. When a ducted fan hovers in the ground effect, the blade thrust increases due to the combined effect of the increase in the effective angle of attack of the blade and the increase in ambient pressure; the duct thrust decreases due to the combined effect of the decrease in the effective angle of attack of the duct and the increase in ambient pressure. Stall occurs at a certain advance ratio and angle of attack when transitioning in the ground effect. The ground effect delays the occurrence of stall at some advance ratios. The ground effect is hardly detectable at angles of attack less than 30° even if the height drops to 0.5 times the duct exit diameter. At this height and high angles of attack, the different positions and influence regions of the ground vortex at different advance ratios contribute to the different variation trends in the ducted fan performance.

Physical Reasoning of Double- to Single-Loop Transition in Industrial Reactors using Computational Fluid Dynamics

Double- to single-loop pattern transition and a significant reduction in the power number with a decrease in the clearance of the Rushton turbine impeller in a baffled reactor was elucidated in earlier research works. The present work investigates the physical reasons behind these phenomena using the computational fluid dynamics approach. The Reynolds Averaged Navier–Stokes equations with standard turbulence model closure were used to model the turbulent flow conditions in the reactor vessels. The Multiple Reference Frame (MRF) approach was adopted to model the impeller baffle interactions in the reactor vessels. The implicit Volume of Fluid (VOF) method was employed to simulate the aeration process in the reactor configurations considered. The development of a low pressure region below the impeller of a low clearance vessel deflects the discharge streams downward, leading to the formation of a single-loop pattern. The downward movement of the discharge streams reduces the vortex activity behind the impeller blades, leading to weaker form drag and a decrease in the power number of the impeller. Similarly, a high clearance vessel provides a low pressure region above the impeller which deflects the discharge streams above the impeller, resulting in a single-loop pattern and a considerable increase in the air entrainment due to superior vortex and turbulence activity present near the free liquid surface. The standard reactor vessel was found to provide superior bulk mixing of fluid as the overall turbulent dissipation rate is 35% more than that associated with low and high clearance vessels.

Numerical Investigation of Hydrodynamic in a Full-Scale Surface Aeration Tank

This study presents a computational fluid dynamics (CFD) model of a full-scale surface aeration tank (SAT) equipped with a low speed surface aerator, model Landy-7. The multiple reference frames (MRF) approach coupled with the volume of fluid (VOF) model and k-ε turbulence model is applied to predict the turbulent flow induced by the surface aerator and the free surface motion. Simulations are performed for different rotational speeds and the predicted results in terms of steady-state power consumption are compared with literature data. After validation, the CFD model is used to study in detail the flow behavior in the SAT and then to optimize the submergence depth ratio of the surface aerator. Two different flow cases are observed depending on the aerator rotation speed. For low rotational speeds, the Landy-7 aerator acts as a surface aerator affecting mainly the water near the surface and has little effect on the shallow layers and the air-water interface is identified as the optimal position for the surface aerator. For aerator rotation speeds above 24 rpm, this effect persists longer in the SAT, even for large submersion depth ratios, which means that the Landy-7 aerator acts as an agitator as well as a surface aerator.

Gas–liquid mixing in the stirred tank equipped with semi-circular tube baffles

Abstract Despite extensive contributions have been made over the past several decades, there are still ongoing challenges in improving gas dispersion performance in stirred tanks. To that end, a stirred tank equipped with four semi-circular (SC) tube baffles was designed. Hydrodynamics in the stirred tank before and after aeration were studied. The turbulent fluid flow was simulated using the standard k-ε turbulence model. The gas–liquid two-phase flow was simulated by the Eulerian–Eulerian multiphase model and the k-ε dispersed turbulence model. The impeller rotation was modeled with the multiple reference frame (MRF) approach. Firstly, the grid independence test was made. By comparing the distributions of gas holdup in the flat-plate (FP) baffled stirred tank with literature results, the reliability of the numerical model and simulation method was verified. Subsequently, the flow field, gas holdup and power consumption of the SC and FP configurations were studied, respectively. Results show that the former can increase the fluid velocities and promote the gas holdup dispersion. Besides, it is energy-saving and has a higher relative power demand (RPD). The findings obtained here lay a preliminary foundation for the potential application of the SC configuration in the process industry.

Experimental and numerical study of novel Coanda-based unmanned aerial vehicle

Conventional Coanda-based unmanned aerial vehicles (UAV) experience thrust losses in the radial direction. To address these losses, a rectangular, linear arrangement of the Coanda surface was adopted in the proposed novel design. This arrangement minimizes the area change in the radial direction to recover such thrust losses. A prototype of the proposed UAV structure was 3D printed and assembled with a single 9-inch propeller. Performance characteristics of the UAV were evaluated through static testing on a dynamometer under different loading conditions. Experimental results were validated through computational fluid dynamics (CFD) simulations, using the k-ε realizable turbulence model, while the multiple reference frame (MRF) approach was applied in steady state. CFD simulations provided good overall agreement with experimental results having errors less than 8%. Numerical comparison between the novel Coanda design and a conventional Coanda design, having similar radial dimensions, showed that the novel design offered an overall 17% improvement in thrust per the side surface area, thus demonstrating an effective reduction of thrust losses in the radial direction.

General Relativistic Implicit Monte Carlo Radiation-hydrodynamics

We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++: an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of the radiation-hydrodynamics equations, but generalized for both Newtonian and relativistic regimes. A multiple reference frame approach is used to geodesically transport photon packets (and solve the hydrodynamics equations) in the coordinate frame, while radiation–matter interactions are handled either in the fluid or electron frames then communicated via Lorentz boosts and orthonormal tetrad bases attached to the fluid. We describe a method for constructing estimators of radiation moments using path-weighting that generalizes to arbitrary coordinate systems in flat or curved spacetime. Absorption, emission, scattering, and relativistic Comptonization are among the matter interactions considered in this report. We discuss our formulations and numerical methods, and validate our models against a suite of radiation and coupled radiation-hydrodynamics test problems in both flat and curved spacetimes.

Probabilistic CFD analysis on the flow field and performance of the FDA centrifugal blood pump

The present study is set out to systematically investigate the combined impact of operational, geometrical, and model uncertainties on the hemodynamics and performance characteristics in the U.S. Food and Drug Administration (FDA) benchmark centrifugal blood pump. Non-intrusive Polynomial Chaos Expansion (NIPCE) has been utilized to propagate the uncertainty of 12 random input variables in the flow field and the performance characteristics of the blood pump at three working conditions. The global sensitivity of the Quantities of Interest (QoI) to the uncertain input parameters was measured through the Sobol’ indices. The Multiple Reference Frames (MRF) approach and the SST k−ω turbulence model were employed to conduct the 3D CFD computations of the pump. In addition, we quantified the device-related hemolysis using the semi-empirical power-law model. The stochastic CFD results of the pump velocity field and hydraulic performance parameters showed a satisfactory agreement with measurements. Statistical analysis indicated that the effect of operational and geometrical uncertainties on the velocity field of the blood pump chiefly emerges at the outlet diffuser region, more specifically along the center-line of the fluid jet formed inside the diffuser. This study has also clarified that the uncertainties in the flow field and the hydraulic performance of the blood pump are mainly due to the variations of impeller diameter, rotational speed, radial clearance, and flow rate. By contrast, the hemolysis index is profoundly affected by the model parameters. Additionally, higher robustness against uncertainties was observed for hydraulic efficiency compared to the pump head. Eventually, it was shown that the maximum value of the distribution function of the relative hemolysis index lies within the bounds of the measurements.

Numerical Investigation of The Effect of Impeller Blade Angle for Stirred Tank

In this study, the most widely used Rushton turbine in the industry was discussed, and the effect of different blade angles on the mixture was investigated numerically. As a standard model, 6 bladed propellers were used and 4 baffles were placed in the stirred tank. The selected tank model is in the form of a flat bottom cylindrical container. Flow characteristics were obtained by giving angles (10°, 20°, 30°, 40°, 50°, 60°) to the propeller blades used in the straight model. The obtained results were compared with each other. In addition, analyzes were repeated at different rotation speeds (600 rpm, 750 rpm, 1000 rpm) for each model at each angle. ANSYS Fluent 18 commercial software, which is the most preferred CFD program in the literature, was used for this numerical study. The analyzes were provided in the standard k-epsilon (ε) turbulence model. The Multiple Reference Frame (MRF) approach was used to simulate impeller rotation. The velocity profiles obtained from the simulations have been shown to be in consistent with the experimental estimates and the results of previous studies. As a result, it has been revealed that the best mixing balance is provided by the impeller blade at 40 and 50 degrees.

Impact of impeller modelling approaches on SBES simulations of flow and residence time in a draft tube reactor

Predictions for flow and residence time in a draft tube reactor were investigated using momentum source, Multiple Reference Frame (MRF) and sliding mesh approaches together with the Stress Blended Eddy Simulation (SBES) turbulence model. Predictions of mean and fluctuating velocities in the annulus, and the exit residence time distribution, are found to be similar and in close agreement with experimental data with all impeller modelling approaches, confirming that the flow in the bulk of the vessel is dominated by the turbulence generated at the draft tube exit and is relatively insensitive to the small-scale turbulence generated by the impeller. On consideration of both accuracy and computational cost, momentum source and MRF approaches offer significant advantages for industrial simulation in this geometry. The SBES model is found to work well in a complex internal flow geometry with an impeller, negating the need for simplifications like zonal LES approaches.

Analytical and Computational Fluid Dynamics Models of Wells Turbines for Oscillating Water Column Systems

AbstractThe sea is an important renewable energy resource for its extension and the power conveyed by waves, currents, tides, and thermal gradients. Amongst these physical phenomena, sea waves are the source with the highest energy density and may contribute to fulfilling the global increase of power demand. Despite the potential of sea waves, their harnessing is still a technological challenge. Oscillating water column systems operating with Wells turbines represent one of the most straightforward and reliable solutions for the optimal exploitation of this resource. An analytical model and computational fluid dynamics models were developed to evaluate the functioning of monoplane isolated Wells turbines. For the former modeling typology, a blade element momentum code relying on the actuator disk theory was applied, considering the rotor as a set of airfoils. For the latter modeling typology, a three-dimensional multi-block technique was implemented to create the computational domain with a fully mapped mesh composed of hexahedral elements. The employment of circumferential periodic boundary conditions allowed for the reduction of computational power and time. The models use Reynolds-averaged Navier-Stokes (RANS) or u-RANS schemes with a multiple reference frame approach or the u-RANS formulation with a sliding mesh approach. The achieved results were compared with analytical and experimental literature data for validation. All the developed models showed good agreement. The analytical model is suitable for a fast prediction of the turbine operation on a wide set of configurations during the first design stages, while the computational fluid dynamics (CFD) models are indicated for the further investigation of the selected configurations.

Effect of stator geometries on flow fields and mixing performance for viscous fluids

High shear mixers (HSMs) find wide applications in industrial processes where intense mixing and dispersion of fluids play a vital role. In this work, the flow fields and mixing performance is analyzed in different batch HSMs with varying stator heads, such as disintegrated, slotted, and mesh. Further, the effect of viscosity, flow behavior and rotor speed on hydrodynamics and mixing performance is assessed through numerical investigations. The turbulent flow fields and mixing enhancement are characterized using standard k-ɛ turbulence model with multiple reference frames approach for various HSMs. The turbulent statistics like turbulent kinetic energy are found to be maximum in the stator hole region and varied with flow behavior. The energy dissipation within the rotor vicinity is found higher for mesh head geometry followed by disintegrated and slotted heads. The effect of tracer injection locations is evaluated to gain comprehensive information on the mixing performance inside the mixing tank. Mixing time (t95) was evaluated and correlated with the existing results. For viscous fluids, complete mixing is hard to achieve due to the presence of cavern effect in smaller stator holes HSM. Moreover, the results provided guidance for further selection, design and development of HSMs for process industries.

CFD modeling and optimization by metamodels of a squirrel cage fan using OpenFoam and Dakota: Ventilation applications

The constraints related to air quality are progressively increasing making the optimization of the air system crucial. Multiple fan configurations are currently used in vacuum systems, the most widely employed one being the squirrel cage fan (SCF), also known as forward-curved multi-blade centrifugal fan. Most of researches so far used commercial software to optimize the SCF focusing mostly on the impeller region. In the present work, a complete automatic optimization process loop is developed based only on open source libraries: Dakota to manage all the processes, Salome to generate the geometry and the mesh grid and OpenFoam for the numerical calculations. Up to seven design parameters are selected for the impeller, blades, and volute. The Latin Hypercube Sampling (LHS) method is preferred to determine the design points and then different metamodels are built. A 3D incompressible simpleFoam solver is coupled to the Multiple reference frame (MRF) approach to model the flow in the SCF. The total efficiency is improved by 8.46% by changing the hub shape and by adding further design parameters. A strong interaction is observed between the cut-off vortex and flow separation on the blade upper side. The optimal design is finally validated against the produced prototype, with an error of 3.4% on the pressure gradient at the design point.