Unsteady RANS Research Articles

Enhancing subsonic ejector performance by incorporating a fluidic oscillator as the primary nozzle: a numerical investigation

Primary flow structures affect ejector performance by impacting momentum transfer to the secondary flow and pressure reduction in the suction chamber. This study investigated the potential benefits of oscillating the primary flow in ejectors to enhance the shear-turbulence mixing and momentum exchange between the primary and secondary flows and improve the entrainment ratio. A vortex-based fluidic oscillator was scaled down and designed to serve as the primary nozzle in a two-dimensional subsonic ejector, embedded between the secondary channels. Prior to installation, optimal values for the nozzle exit position and mixing chamber height were obtained through a parametric study and used in the ejector with the oscillator. To evaluate the impact of the fluidic oscillator on the ejector entrainment ratio, unsteady Reynolds-averaged Navier–Stokes equations were solved using the k–ε standard and k–ω shear-stress transport turbulence models in the Fluent 2022 R2 software. The results indicated that a harmonically oscillating primary flow was generated, increasing the mixing entrainment and momentum transfer while reducing the pressure in the suction and mixing chambers. The oscillator improved the ejector's entrainment ratio by 38.3% compared to the baseline, and 11.6% compared to the parametrically optimized ejector. It also expanded the ejector's performance range.

Numerical Investigation of a Pulsed Jet Actuator Having Non-Negligible Switching Time

An internal unsteady compressible flowfield of a pulsed jet actuator (PJA) is simulated by unsteady Reynolds-averaged Navier–Stokes (URANS) and large-eddy simulation (LES) frameworks. The PJA’s feedback loops are short enough to have non-negligible jet switching time compared to the oscillation period. The results show that within a range of inlet pressure (which is the only control parameter) where the jet goes from subsonic to supersonic regime, the oscillation frequencies and the exit velocity waveform predicted by LES are in better agreement with the measured data than those predicted by URANS. Although URANS is able to capture the flowfield inside the feedback loops, it fails to predict the exit jet dynamics, unlike LES. This indicates the importance of a proper resolution of turbulence in the interaction region where jet switching occurs. Using LES data, it is found that the total jet switching time remains constant as the inlet pressure changes. It is also found that only the part of the jet switching period that ends at the first moment when the jet attaches to the opposite wall is involved in the oscillation period. Therefore, a new lumped model is proposed to estimate the oscillation frequency, which also explains the trend observed for the low inlet pressure values.

Hydrodynamic Forces on a Near-Bottom Pipeline Subject to Wave-Induced Boundary Layer

Abstract Hydrodynamic forces on small diameter subsea pipelines and cables placed near seabed are important for their on-bottom stability design. In offshore environments, these pipelines are usually subjected to extreme wave conditions. The present study investigates hydrodynamic forces acting on a pipeline near a flat seabed subjected to a wave-induced boundary layer flow. The Keulegan–Carpenter numbers of the wave-induced boundary layer flow are 20, 140, and 200, defined based on the pipeline diameter (D), the maximum velocity of the undisturbed near-bed orbital velocity (Uw), and the period of the incoming oscillatory flow (Tw). Reynolds number is 1 × 104 based on Uw and D. A seabed roughness ratio ks/D (ks is the Nikuradse equivalent sand roughness) of up to 0.1 and different gap ratios of G/D = 0.05–0.5 between the pipeline and the seabed are considered. Numerical simulations have been carried out based on two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes equations combined with the k–ω shear stress transport turbulence model. A preliminary one-dimensional (1D) simulation is carried out to obtain a fully developed wave-induced boundary layer velocity profile, which is used as inlet flow for the 2D simulations. The numerical model is validated against the experimental data reported by Sumer et al. [1991, “Effect of a Plane Boundary on Oscillatory Flow Around a Circular Cylinder,” J. Fluid Mech., 225, pp. 271–300] at KC = 10. Influences of KC, ks/D, and G/D on the hydrodynamic forces and the surrounding flows are discussed in detail.

Simulation of a confined and a free sweeping air jet impingement cooling from a fluidic oscillator

In this paper, the fluid flow behavior and cooling characteristics of a sweeping impingement jet were investigated. Also, the difference between free and confined impingement schemes was investigated. In addition, the conventional approach for the purpose of significantly reducing computational time by using a confined domain with a slip upper wall instead of an unconfined domain was evaluated. A 2D unsteady Reynolds averaged Navier-Stokes (URANS) simulation accompanied with the k-ω SST turbulence model is used in this study. The study has been conducted for a target wall with a constant heat flux of 3000 W/m2, jet-to-wall distance of 4, and a jet Reynolds number of 2500. The results show that the overall average cooling performance of the sweeping jet is better in the confined impingement scheme compared to that of the steady jet, while the steady jet is slightly better in the unconfined sweeping impingement scheme. Using a confined scheme with a slip upper wall does not reveal the complete thermal and flow behaviors, and the wall heat transfer distribution is very different from the unconfined domain.

Square Cyclone Separator: Performance Analysis Optimization and Operating Condition Variations Using CFD-DPM and Taguchi Method

The square cyclone separator is an efficient separation device for high-temperature gas within Circulating Fluidized Bed (CFB) boilers. Additionally, other operating factors such as particle loading and gas velocity are frequently thought to have considerable influence on fluid flow in gas cyclones, making parameter optimization essential. Finding the most suitable operating configuration can be challenging because of a fundamental understanding of the operating principles, which has yet to be taken into consideration in the literature. The gas flow inside a square cyclone was analyzed using Computational Fluid Dynamics (CFD) for investigating parameters including particle mass flow rate, inlet velocity, inlet temperature, and turbulent intensity in this research. The Taguchi method was utilized as a Design of Experiment (DoE) methodology to maximize separation efficiency. The Analysis of Variance (ANOVA) was conducted to evaluate the relative contribution of each parameter to the performance of the gas cyclone, while the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations were solved using the Eulerian-Lagrangian approach to represent particle movement. Also, Discrete Random Walk (DRW) was incorporated to account for velocity fluctuation. According to a Taguchi analysis, particle mass flow rate is the parameter that has the least impact on cyclone performance, whereas inlet velocity has the most contribution. From the different range of factors examined here, it is proved that the optimal levels of factors for inlet velocity, inlet temperature, particle mass flow rate, and turbulent intensity are, respectively, 20 m/s, 300 K, 180 g/min, and 4%.

Experimental and numerical study on the effects of sweep angle on cavitation around a wedge-section hydrofoil

The influence of sweep angles on cavitation characteristics and mechanisms of a wedge-section hydrofoil is investigated experimentally and numerically. Four hydrofoils with sweep angles of 0° (straight), 30°, 45°, and 60° are considered across a range of cavitation numbers from 2.00 to 0.48 and angle of attack (AOA) of 0°, 5°, 10°, and 15°. Two high-speed cameras are used to visualize the cavitation flow in a high-speed cavitation tunnel. The numerical simulation is conducted using unsteady Reynolds-averaged Navier–Stokes equations through OpenFOAM. At an AOA of 0° and 5°, vortex cavitation first appears in the wake region of all models at a cavitation number of 0.98. However, at higher AOA values of 10° and 15°, tip-vortex cavitation (TVC) begins first for the straight foil, and this is followed by sheet and wake cavitation. In contrast, the swept foil does not succumb to TVC. Instead, as the sweep angle increases, sheet cavitation develops into root leading-edge vortex cavitation (LEVC). The inclination angle of the LEVC from the leading edge is observed to be between 6° and 15°, depending on the sweep angle, and it is independent of the cavitation number and AOA. The wake vortex changes from eddy vortex shedding at the wake region of the straight hydrofoil into two root trailing-edge vortices as the sweep angle increases. The swept hydrofoil reduces the average cavity volume by more than 45% compared with the straight foil. The lift coefficient of the straight hydrofoil increases as sheet cavitation is generated and reaches a maximum value of 0.6 when cavitation covers the suction side of the hydrofoil before dropping sharply when it extends to the wake region. However, there is only minor deterioration in the lift coefficient of the 60° swept-angle foil when the cavitation occurs. The drag coefficient reduces when cavitation forms for both foils. However, the drag coefficient of the swept hydrofoil is lower than that of the straight foil. These findings offer valuable insight into the design and optimization of foils for various applications where cavitation affects their performance and stability.

Structural optimisation of H-Rotor wind turbine blade based on one-way Fluid Structure Interaction approach

The paper aims to present structural topology optimisation of the structural topology of the H-Rotor wind turbine combined with the one-way Fluid Structure Interaction (FSI) approach. The developed methodology couples the set of Unsteady Reynolds Averaged Navier–Stokes Equations (URANS) with the steady state linear elasticity equations and density based topology optimisation method. This approach allowed us to reduce the mass of the blades with respect to the maximum stress and deformation limits. The results obtained provide detailed information on the unsteady flow fields around the operating wind turbine, as well as optimised topology of the blade interior without affecting the external aerodynamic profile. The load of pressure profile from the CFD simulation was implemented at the point of rotation at which the force values observed on the blade surface were the highest. The centrifugal force was considered in the structural model. Computations were carried out for wind speed equal to 30 m/s and rotational velocity equal to 90 rad/s. The turbine operating parameters were chosen to represent extreme operating conditions. The results obtained showed that the blade mass, made of the same material, can be easily reduced by around 60% with the reduction of the observed stress values and deformation.

CFD simulations of the refueling of long horizontal H2 tanks with tilted injector

With the recent development of Hydrogen Refueling Stations (HRS), the refueling of hydrogen composite tanks is an important issue for the safe handling of hydrogen. In particular, an appropriate protocol is needed to avoid tank overheating during refueling. To model the temperature distribution everywhere inside the tank during these processes, CFD (Computational Fluid Dynamics) simulations have been performed under cases where thermal stratification occurs. The performances of several CFD turbulence models are benchmarked through a comparison with experimental data. Two injector configurations are considered in this work: a straight one and another tilted upwards. The U-RANS (Unsteady-Reynolds Averaged Navier-Stokes) - Reynolds Stress Model (RSM) is found to be the most reliable turbulence model for both configurations.

Numerical improvement to Glauert correction for the flow around a wind turbine

AbstractAccurate and reliable computation of the aerodynamic characteristics of wind turbines is very important for the development of new efficient designs. The flow around a wind turbine is modeled by a permeable disc (PD), solved through the Unsteady Reynolds-Averaged Navier–Stokes equations (URANS), here named PD/URANS method. The finite volume method and a total variation diminishing (TVD) scheme solve numerically the flow governing equations. The turbulent flow in the wake of the wind turbine is simulated utilising a one-equation turbulence model. The Glauert correction calculation considers a uniform normal force distribution (CT) on the virtual permeable disc applied to the flow, while the axial induction factor is obtained directly from the numerical solution of the URANS equations. The numerical axial induction factor obtained agrees fairly well with Glauert correction, except if the flow behind the turbine is highly unsteady and Reynolds number dependent.

Parameter Analysis of Active Flap Control for Rotor Aerodynamic Control and Design

Active rotor control of helicopters is the future development direction, and active flap control (AFC) is one of the most promising technologies. However, the numerical simulation of an AFC rotor is challenging. It is necessary to consider the fidelity of the local flow details while dealing with complex shapes and motions. Therefore, few simulations of the flow field and analyses of the influencing parameters have been conducted. In particular, there is a lack of aerodynamic design criteria and recommendations for the AFC rotor. Thus, a new overset assembly algorithm, an arbitrary multilevel moving grid transformation algorithm, and a solver for the unsteady Reynolds-averaged Navier-Stokes equations (URANS) are proposed to establish a suitable numerical method for AFC rotor simulation. The aerodynamic characteristics of the rotor and key influencing factors are systematically analyzed under different flow conditions and design and control parameters, and suggestions for the design of the AFC rotor are provided. The results show that the AFC significantly changes the load distribution of the rotor. The thrust loss of the rotor is approximately 1%, but the offset angle compensates for the loss. The control parameters show relatively consistent trends under different working conditions. The phase is the key control parameter, and the effect on the load is more pronounced when the control frequency is an integral multiple of the rotor’s natural load frequency. Increasing the chord length, span length, and deflection amplitude can also enhance the active control performance.

Assessment of RANS Turbulence Models in Prediction of the Hydrothermal Plume in the Longqi Hydrothermal Field

In this paper, the numerical models are selected to simulate the hydrothermal plume based on the water temperature observation data of the Longqi hydrothermal field in the Southwest Indian Ridge (SWIR). Then, the unsteady Reynolds-averaged Navier–Stokes equations are solved to evaluate the performance of the Realizable k-ε (rke) model and the SST k-ω (sst) model in hydrothermal plume simulation. By comparing the calculated results with the Conductivity Temperature Depth (CTD) observation data and the literature results, the difference in prediction performance between the two models is evaluated. Before the numerical simulation, the optimal mesh parameters are determined by considering the grid independence test. The results show that the relative difference of the maximum plume height calculated by the two models is within 5%. Compared with the CTD 05-2, the rke model calculates the root mean square error of the velocity is 0.5081, which is smaller than that of the sst model. In terms of turbulent viscosity, the rke model is in good agreement with reference value in predicting turbulent viscosity. Therefore, the turbulent viscosity distribution calculated by the rke model is more consistent with the plume development process than that calculated by the sst model. In addition, the two models have the same effect on the prediction of turbulent kinetic energy and plume temperature.

The myth of URANS

ABSTRACT Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a theoretical justification for this unsteady RANS (URANS) approach. Here, we extend the dynamical system fixed point analysis to create a theoretical model for URANS dynamics. The results are compared to URANS simulations for homogeneous isotropic decaying turbulence. The model shows that URANS can predict incorrect decay rates and that the solution tends towards steady RANS over time. Similar analysis for forced turbulence shows a fixed modelled energy of about 30% of total energy, regardless of the model parameters. The same analysis can be used to show how hybrid type models can begin to address these issues.

Aerodynamic Simulation and Optimization of Micro Aerial Vehicle Rotor Airfoil at Low Reynolds Number

This paper describes the aerodynamic simulation and optimization of NACA 0012 airfoil at a low Reynolds number using unsteady Reynolds-averaged Navier-Stokes (URANS) and Spalart–Allmaras turbulence model in Ansys Fluent. The purpose of this paper is to simulate and optimize the airfoil to get better aerodynamic performances at low Reynolds numbers. The Parsec method was selected for the optimization of the NACA 0012 airfoil. Both of these airfoils are simulated using CFD Fluent between 0 to 13-degree angle of attack at a low Reynolds number of 200000. To simulate the airfoil, mesh generation is crucial so an O-grid structured mesh is created. After the simulation, several aerodynamic performances are compared between the airfoils, such as lift coefficient, drag coefficient, pressure coefficient, and lift-to-drag ratio. And the calculated results from Xfoil are taken as references. Between NACA 0012 and optimized NACA 0012, the optimized airfoil showed better aerodynamic performances than the normal one, which was the goal of this paper. Later on, the different flow field variables, such as density, temperature, pressure, and vorticity magnitude were analyzed and compared. Both the airfoils at a different angle of attack were analyzed for these functions, like 7°, 11°, and 20° AOA. During the analytical process, Q-criterion appears to be a very important method of vortex identification in the flow field. With this analysis, we came to know, that as the angle of attack increases the adverse pressure gradient also increases, which creates a big reverse flow.

Large-Amplitude Gusts on the NASA Common Research Model

To date, there is limited knowledge on the topic of unsteady nonlinear transonic flow caused by large-amplitude excitations. The Certification Specifications for Large Aeroplanes, however, demand loads computations for large-amplitude excitations, e.g., for gust encounters of an aircraft. In this paper, numerical solutions to the unsteady Reynolds-averaged Navier–Stokes equations will be used to analyze gust responses of a transport aircraft configuration for a variety of sinusoidal gusts with different lengths and amplitudes at different Mach numbers. On the one hand, it is shown that unsteady nonlinear responses can lead to lower maximum lift values compared to their time-linearized reference due to unsteady shock-induced flow separation. This nonlinear effect dominates for large gust lengths and higher Mach numbers. On the other hand, for the lowest Mach number considered, the coalescence of a double shock at medium gust lengths introduces nonlinear effects leading to an overprediction of the time-linearized maximum lift by the nonlinear computations. Though the turbulence model of Spalart and Allmaras shows completely different separation patterns than a differential Reynolds stress model, the variation of the turbulence model does not alter the overall qualitative findings, but has an effect on the quantitative values.

Numerical investigation of the effect of dielectric barrier discharge plasma actuator-induced momentum jet parameters on flow control of an oscillating wind turbine airfoil

Wind turbine blades that undergo pitch-oscillating motion exhibit dynamic stall behavior, deteriorating their aerodynamic performance. In this regard, dielectric barrier discharge (DBD) plasma actuators are promising tools for controlling flow by inducing momentum jet flow. Four key parameters typically determine the momentum jet: length, power, angle, and injection location. This paper presents a numerical study that investigates the effect of these parameters on flow control around an SG6042 wind turbine airfoil at a Reynolds number of Rec=1.35×105. For this sake, the study considers various numbers of actuators, force directions, and installation locations. This study utilizes two-dimensional, unsteady Reynolds-averaged Navier–Stokes equations with the γ–Reθ transition model. The results demonstrate the significant effects of momentum jet parameters on flow control. As the location of single-DBD moves closer to the leading edge, its effectiveness on the low-pressure vortex growth increases, resulting in a smaller vortex and a lower drag coefficient. Furthermore, an increase in the power and length of the jet leads to effective flow control. Vortices on the airfoil's suction surface are recognized as influential factors in the aerodynamic performance. As a result, the co-flow actuator significantly improves the performance of the airfoil by inducing the momentum jet in this region. Flow control is augmented when the actuator is installed at a location with a near-surface jet angle. The leading edge case with a co-flow single-DBD achieves the best control performance. In this instance, the dynamic stall occurs approximately 5% later than in the case of the clean configuration.

Experimental and numerical characterization of the airflow in the wake of a heavy truck

The wake flow of a heavy truck model is investigated at Re=8.5×104 using particle image velocimetry measurements combined with computational fluids dynamics-simulations. Experimental measurements are carried out on a 1:28-scale model, focusing exclusively on the central longitudinal plane, in the rear of the truck model. Numerical simulations are performed based on the URANS (unsteady Reynolds averaged Navier–Stokes) approach using two statistical turbulence models, i.e., the shear stress transport k–ω and the baseline Reynolds stress (BSL-RSM) models. A comparison between the numerical and experimental results of the mean velocity profiles in the wake of the heavy truck is found to be relatively consistent. The BSL-RSM model, however, gives a better prediction of experiments, with a deviation of 6% in the near wake, against 13% for the SST k–ω. Both URANS models undervalue the streamwise and spanwise turbulence intensity components with a deviation around 24%, compared with the experimental results. The characteristic feature of the wake flow topology is the formation of a recirculation bubble resulting from the shear layers separated from the truck surfaces. Different identification methods, including visualization of closed streamlines, vorticity magnitude, and the Q-invariant criterion, are considered and highlight the existence of two particular vortex regions in the mean flow: a vortex-shedding area in the upper recirculation region and a back-truck attached vortical structure. It is found that the Q criterion-based technique is a relevant indicator of the vortex cores regions.

A data-driven reduced-order model based on long short-term memory neural network for vortex-induced vibrations of a circular cylinder

A data-driven reduced-order model (ROM) based on long short-term memory neural network (LSTM-NN) for the prediction of the flow past a circular cylinder undergoing two-degree-of-freedom vortex-induced vibration in the upper transition Reynolds number regime with different reduced velocities is developed. The proper orthogonal decomposition (POD) technique is utilized to project the high-dimensional spatiotemporal flow data generated by solving the two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) equations to a low-dimensional subspace. The LSTM-NN is applied to predict the evolution of the POD temporal coefficients and streamwise and cross-flow velocities and displacements of the cylinder based on the low-dimensional representation of the flow data. This model is referred to as POD-LSTM-NN. In addition, the force partitioning method (FPM) is implemented to capture the hydrodynamic forces acting on the cylinder using the surrounding flow field predicted by the POD-LSTM-NN ROM and the predicted time histories of the lift and drag forces are compared with the numerical simulations.

Numerical treatments for large eddy simulations of liquid–liquid dispersions via population balance equation

In this work, we employ the two-fluid model under the large eddy simulations (LES) framework to investigate liquid–liquid dispersions in stirred tanks. The population balance equation was solved by the one primary and one secondary particle method, which was proven as identical as one-node quadrature method of moments. First, Aiyer's break-age kernel was investigated for its capability in the context of chemical stirred tank applications [Aiyer et al., “A population balance model for large eddy simulation of polydisperse droplet evolution,” J. Fluid Mech. 878, 700–739 (2019)]. Second, two new methods were proposed to handle the consistency problem and boundedness problem. These numerical problems were shown in our previous studies but had never been discussed in detail. Three test cases were launched, and results showed that our implementation ensures the moments' boundedness. The inconsistency problem was also treated properly. The predicted diameter also agrees well with experiments. Meanwhile, the phase segregation problem as observed in the unsteady Reynolds-Averaged Navier–Stokes simulations disappeared when a LES turbulence model was employed.

Numerical analysis of the performance of a three-bladed vertical-axis turbine with active pitch control using a coupled unsteady Reynolds-averaged Navier-Stokes and actuator line model

Numerical analysis of the performance of a three-bladed vertical-axis turbine with active pitch control using a coupled unsteady Reynolds-averaged Navier-Stokes and actuator line model

Oscillatory flow around a vertical circular cylinder placed in an open channel: coherent structures, sediment entrainment potential and drag forces

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumeret al.(J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake forKC = 1.5. By contrast, forKC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle asKCis increased to 30.8. For an intermediate range ofKCnumbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with differentKCnumbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For allKCnumbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. ForKC = 1.5, the in-line force is only due to inertia effects. ForKC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. ForKC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases withKC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed aroundKC = 8. ForKC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. AsKCis increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.