Three-dimensional Navier-Stokes Solver Research Articles

Simulation and Validation of Fluid Inertia Effects in External Gear Machines Using Lumped Parameter Modeling

Abstract Lumped parameter modeling is a consolidated technique for analyzing the fluid dynamic behavior of positive displacement machines, owing to their computational swiftness and the ease of integrating other physical domains affecting the operation of the machine. With some very limited exceptions, this modeling technique typically neglects fluid inertia and momentum effects. This paper proposes an approach to study the effects of fluid inertia affecting the pressurization and depressurization of the tooth space volumes of an external gear pump. The approach is based on considering the fluid inertia in the pressurization grooves and inside the control volumes with a peculiar subdivision. Further, frequency-dependent friction is also modeled to provide realistic damping of the fluid inside these channels. Validation of the model has been performed by comparing the lumped parameter model with a full three-dimensional Navier–Stokes solver. The quantities compared, such as tooth space volume pressures and outlet volumetric flow rate, show a good match between the two approaches for varying operating speeds. A comparison with the experiments supports the modeling approach as well. The paper finally, also discusses which operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place.

물리 기반 자유후류 모델링을 통한 소형 무인기용 동축 로터 블레이드의 최적 설계

Coaxial rotors can generate high thrust with a small aircraft volume, which makes them an attractive configuration for small unmanned aerial vehicles (UAV), particularly for hovering and low-speed flights. However, the aerodynamic interference between the upper and lower rotors makes it more challenging to predict design trends for aerodynamic performance. Three-dimensional compressible unsteady Reynolds-averaged Navier-Stokes (3D URANS) solver can be a suitable choice, however, it requires burdensome computational cost for design optimization. One alternative that can alleviate the computational burden of design optimization with little loss of accuracy is lifting-line theory coupled with a free-wake method. Although the free-wake method provides a high degree of freedom in modeling the wake effects, a well-adjusted wake model can provide an accurate prediction of aerodynamic performance and design trends. In this study, the free-wake model has been adjusted to correlate the aerodynamic environment, such as sectional thrust, induced velocity, the effective angle of attack, and wake geometry, predicted by the 3D URANS simulation for the baseline coaxial rotor. By adjusting the physical model parameters of free-wake, such as core type, growth rate, and its initial strength, the free-wake model is adjusted based on the physical relationship, not the simple linear scaling factor generally used to inflow factor. The optimal coaxial rotor was derived based on the performance prediction of the adjusted free-wake model. The 3D URANS simulation was also conducted for the optimal coaxial rotor and compared the aerodynamic environments predicted by the adjusted freewake model. The performance index and aerodynamic environments predicted by both solvers also showed similar results for the optimal coaxial rotor. The present physics-based freewake adjustment can be an efficient design approach with consideration of the complex aerodynamic phenomena of a coaxial rotor system.

Unsteady Aerodynamic Response of a Flat Plate Encountering Large-Amplitude Sharp-Edged Gust

This study presents numerical findings of the response of a flat plate to transverse, sharp-edged gusts at a low Reynolds number (). A split velocity method was implemented in a three-dimensional Navier–Stokes solver to simulate a rigid flat plate wing at steady velocity and 0° angle of incidence encountering a sudden sharp-edged gust. The gust perturbations in the flow domain were prescribed to the grid points, and source terms were added to the governing equations to account for the full interaction between the wing and the gust. Two sharp-edged gust profiles are considered: 1) a top-hat profile gust of finite width and 2) a step profile gust of infinite width. The gust amplitude varies from 4 to 120% of the freestream velocity (). The split velocity method was found to be capable of capturing the physical phenomenon of flat plate undergoing sharp-edged gust, and the predicted lift coefficient is found to be in good agreement with that of experiments. The duration and magnitude of the wing–gust interaction were both found to affect the airfoil response. In the step gust encounter, the lift behaves similarly to that predicted by the Küssner’s model for small-amplitude gusts where . The lift buildup is nonlinear for larger gust amplitudes where . Convolution with the computed step gust response shows good agreement with the simulated response during long and large gust encounters. However, both computational fluid dynamics and Küssner-convolution-based methods fail to predict the exit phase from gust and the recovery to a steady-state value.

Wake and Performance Predictions of Two- and Three-Bladed Wind Turbines Based on the Actuator Line Model1

Abstract This paper challenges the standard wind turbine design numerically assessing the wake and aerodynamic performance of two- and three-bladed wind turbine models implementing downwind and upwind rotor configurations, respectively. The simulations are conducted using the actuator line model (ALM) coupled with a three-dimensional Navier Stokes solver implementing the k−ω shear stress transport turbulence model. The sensitivity of the ALM to multiple simulation parameters is analyzed in detail and numerical results are compared against experimental data. These analyses highlight the most suitable Gaussian radius at the rotor to be equal to twice the chord length at 95% of the blade for a tip-speed ratio (TSR) of ten, while the Gaussian radius at the tower and the number of actuator points have a low incidence on the flow field computations overall. The numerical axial velocity profiles show better agreement upstream than downstream the rotor, while the discrepancies are not consistent through all the assessed operating conditions, thus highlighting that the ALM parameters are also dependent on the wind turbine's operating conditions rather than being merely geometric parameters. Particularly, for the upwind three-bladed wind turbine model, the accuracy of the total thrust computations improves as the TSR increases, while the least accurate wake predictions are found for its design TSR. Finally, when comparing both turbine models, an accurate representation of the downwind configuration is observed as well as realistic power extraction estimates. Indeed, the results confirm that rotors with fewer blades are more suitable to operate at high TSRs.

Flow morphology in bottom-propagating gravity currents over immersed obstacles

The interaction of bottom-propagating gravity currents with immersed obstacles in the path of the lock-exchange configuration was numerically investigated based on large eddy simulations. The three-dimensional Navier–Stokes solver was quantitatively employed to resolve the flow structure of gravity currents and their dynamics during impact. The integral measure of analysis comprises the front condition, the energy budget, the turbulent mixing, and the force response. Some flow parameters involved in momentum and energy fluctuations are the fractional depth of volume release, relative density difference, and obstacle dimensions. A particular focus in this study was on the scale effect of obstacles (W/D, the aspect ratio of a cross-sectional obstacle with side length W to height D) that affect the propagation of gravity currents. Depending on integral measures of the simulation, the flow morphology could be demarcated for the condition W/D = 2 with different flow regimes in accordance with the reattachment of the current as the plunged front overflows and separates from the obstacle. For W/D > 2, as the current impinges on the obstacle, the plunged current front overtops and travels on the obstacle surface and consequently causes the entrainment without intense mixing to form a circulation zone at the downstream of the obstacle. Accordingly, the predicted drag forces acting on the downstream surface are reduced by ∼25% for W/D ≥ 4 comparing to the case of W/D = 0.5, which is beneficial to the structural stability of the barrier in practical aspect. Notably, the integrated analysis of gravity currents provides insights into physical mechanisms by identifying distinct propagation stages during transitions, including the impact stage, transient stage, and quasi-steady stage.

Experimental investigation of the tip leakage flow in a low-speed multistage axial compressor.

Casing pressure measurements and Stereoscopic Particle-Image Velocimetry (SPIV) measurements are used together to characterize the behavior of the rotor tip leakage flow at both the design and near-stall conditions in a low-speed multistage axial compressor. A three-dimensional Navier-Stokes solver is also performed for the multistage compressor and the prediction of tip leakage flow is compared with SPIV data and casing dynamic static pressure data. During the experiment 10 high-frequency Kulite transducers are mounted in the outer casing of the rotor 3 to investigate the complex flow near the compressor casing and Fourier analyses of the dynamic static pressure on the casing of the rotor 3 are carried out to investigate the tip leakage flow characteristics. At the same time, the two CCD cameras are arranged at the same side of the laser light sheet, which is suitable for investigating unsteady tip leakage flow in the multistage axial compressor. The SPIV measurements identify that the tip leakage flow exists in the rotor passage. The influence of tip leakage flow leads to the existence of low axial velocity region in the rotor passage and the alternating regions of positive and negative radial velocity indicates the emergence of tip leakage vortex (TLV). The trajectory of the tip leakage vortex moves from the suction surface toward the pressure surface of adjacent blade, which is aligned close to the rotor at the design point (DP). However, the tip leakage vortex becomes unstable and breaks down at the near-stall point (NS), making the vortex trajectory move upstream in the rotor passage and causing a large blockage in the middle of the passage.

Effects of Blade Fillet Structures on Flow Field and Surface Heat Transfer in a Large Meridional Expansion Turbine

This paper is a continuation of the previous work, aiming to explore the influence of fillet configurations on flow and heat transfer in a large meridional expansion turbine. The endwall of large meridional expansion turbine stator has a large expansion angle, which leads to early separation of the endwall boundary layer, resulting in excessive aerodynamic loss and local thermal load. In order to improve the flow state and reduce the local high thermal load, five typical fillet distribution rules are designed. The three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solver for viscous turbulent flows was used to investigate the different fillet configurations of the second stage stator blades of a 1.5-stage turbine, and which fillet distribution is suitable for large meridional expansion turbines. The influence of fillet structures on the vortex system and loss characteristics was analyzed, and its impact on wall thermal load was studied in detail. The fillet structure mainly affects the formation of horseshoe vortexes at the leading edge of the blade so as to reduce the loss caused by horseshoe vortexes and passage vortexes. The fillet structure suitable for the large meridional expansion turbine was obtained through the research. Reasonable fillet structure distribution can not only improve the flow state but also reduce the high thermal load on the wall surface of the meridional expansion turbine. It has a positive engineering guiding value.

Experimental and Computational Investigation of Transverse Gust Encounters

The flow over a flat-plate wing passing through a transverse gust was investigated using both experimental and computational methods. The gust created physically in a water-filled towing tank was found to have a sine-squared velocity profile and was modeled as such in the computations. The physical gust system was designed so that the gust velocity could be varied, thereby allowing for independent variation of the Reynolds number and gust ratio. Dynamically scaled numerical simulations of the physical flow were performed using a three-dimensional Navier–Stokes solver, where the field velocity method with the source term was implemented to simulate the gust. Küssner’s function was also used with Duhamel superposition to find the analytical lift response of a flat plate for the aforementioned transverse velocity profile for comparison with experimental and numerical results. During the gust encounter, forces were found to increase significantly relative to the steady values but fully recovered after the wing exited the gust. The measured forces on the wing were found to scale with the exposed projected area of the wing. Computational forces broadly agreed with experimental and analytical data, and it was shown that the proposed numerical method captures the force trends observed in this transient flow.

Modeling of Ice Accretion over Aircraft Wings Using a Compressible OpenFOAM Solver

A method to simulate ice accretion on an aircraft wing using a three-dimensional compressible Navier-Stokes solver, a Eulerian droplet flow field model, a mesh morphing model, and a thermodynamic model, is presented in this paper. The above models are combined together into one solver and implemented in OpenFOAM. Two-way coupling is achieved between airflow field calculation and ice simulation. The density-based solver rhoEnergyFoam is used to calculate the airflow field. The roughness wall function is proposed to simulate the roughness effect caused by ice accretion. For droplet flow field calculation, the Eulerian model is applied and the permeable wall boundary condition is used on the wing to simulate the droplet impingement. The icing thermodynamic model is built based on the Messinger model. The mesh morphing model adjusts the wing’s shape every time step based on the amount of accreted ice so that the airflow field is updated during the simulation. The effect of the ice accretion on the airflow is studied by comparing the aerodynamic performance—with and without ice. The ice accretion on the ONERA M6 wing model under a specific condition has been simulated to validate the solver’s performance and investigate the effect of the accreted ice on the aerodynamic performance.

Computational and Experimental Investigation of a Flapping-Wing Micro Air Vehicle in Hover

Experimental and computational study of flapping-wing insect at low Reynolds number is conducted in this work. The paper is broadly divided into two sections: experiments and computational fluid dynamics–based numerical analysis. A dynamically scaled wing is simulated using Overset Transonic Rotor Unsteady Navier–Stokes (OVERTURNS) computational platform, a three-dimensional Navier–Stokes solver. The computational results are compared with experimental results of an isolated flapping wing performed in an oil tank. Good agreement was observed between the experiments and numerical simulations in terms of magnitude and trend of the unsteady instantaneous lift and drag forces over the flapping cycle. A parametric study was performed to observe the influence of the kinematic, flapping frequency and pitch angle, on the force production and power requirements. As a consequence of the study, lift-to-power ratio versus average lift was identified as a principal efficiency metric to assess the performance of flapping-wing vehicles for given geometry and kinematic parameters. A clear advantage for a wing pitch angle of 40° was observed compared with that of 30° or 60°.

Numerical investigation of the effect of airfoil thickness on onset of dynamic stall

Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack ($=4^{\circ }$). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness.

Optimisation and analysis of efficiency for contra-rotating propellers for high-altitude airships

ABSTRACTAn improved variational optimization approach is established to optimize and analyse the propulsion efficiency of the high-altitude contra-rotating propellers for high-altitude airships based on the Vortex Lattice Lifting Line Method. The optimum radial circulation distribution, chord and pitch distribution are optimized under the maximum lift-to-drag ratio of aerofoils. To consider the effects of the actual Reynolds number and the Mach number of each aerofoil section, aerodynamics such as lift coefficient, drag coefficient and lift-to-ratio are obtained by interpolating a CFD database, which is established by numerical simulations under different Reynolds number, Mach number and angles-of-attack. The improved method is verified by validation cases on a high-altitude CRP using the three-dimensional steady Reynolds-averaged Navier-Stokes solver and moving reference frames technique. The optimization results of thrust, torque and efficiency for both the individual front/rear propeller and CRP are shown to agree reasonably well with the CFD results. Using the improved approach, the influence of blade numbers, diameter, rotation speeds, axial distance and torque ratio on the optimum efficiency of CRPs is illustrated in detail by conducting parametric studies.

Effect of Tip Clearance on Flow Field and Heat Transfer Characteristics in a Large Meridional Expansion Turbine

The large meridional expansion turbine stator leads to complex secondary flows and heat transfer characteristics in the blade endwall region, while the upstream tip clearance leakage flow of the rotor makes it more complex in flow and heat transfer. The influence of the upstream rotor tip clearance on the large meridian expansion stator is worth studying. The flow and heat transfer characteristics of the downstream large meridional expansion turbine stator were studied by comparing the tip leakage flow of 1.5-stage shrouded and unshrouded turbines using a three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solver for viscous turbulent flows. Validation studies were performed to investigate the aerodynamics and heat transfer prediction ability of the shear stress transport (SST) turbulence model. The influence of different tip clearances of the rotor including unshrouded blade heights of 0%, 1% and 5% and a 1% shrouded blade height were investigated through numerical simulation. The results showed that the upper passage vortex separation was more serious and the separation, and attachment point of horseshoe vortex in the pressure side were significantly more advanced than that of non-expansion turbines. The tip leakage vortex obviously increased the negative incidence angle at the downstream inlet. Furthermore, the strength of the high heat transfer zone on the suction surface of the downstream stator was significantly increased, while that of the shrouded rotor decreased.

EBFOG: Deposition, Erosion, and Detachment on High-Pressure Turbine Vanes

Fouling and erosion are two pressing problems that severely affect gas turbine performance and life. When aircraft fly through a volcanic ash cloud, the two phenomena occur simultaneously in the cold as well as in the hot section of the engine. In the high-pressure turbine (HPT), in particular, particles soften or melt due to the high gas temperatures and stick to the wet surfaces. The throat area, and hence the capacity, of the HPT is modified by these phenomena, affecting the engine stability and possibly forcing engine shutdown. This work presents a model for deposition and erosion in gas turbines and its implementation in a three-dimensional Navier–Stokes solver. Both deposition and erosion are taken into account, together with deposit detachment due to changed flow conditions. The model is based on a statistical description of the behavior of softened particles. The particles can stick to the surface or can bounce away, eroding the material. The sticking prediction relies on the authors' Energy Based FOulinG (EBFOG) model. The impinging particles which do not stick to the surface are responsible for the removal of material. The model is demonstrated on a HPT vane. The airfoil shape evolution over the exposure time as a consequence of the impinging particles has been carefully monitored. The variation of the flow field as a consequence of the geometrical changes is reported as an important piece of on-board information for the flight crew.

Surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow

This paper deals with the surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow. An interface condition with finite-rate thermochemistry was established to balance the three-dimensional Navier-Stokes solver and TPS thermal response solver, and a series of coupled simulations of chemical non-equilibrium aerothermodynamics and structure heat transfer with various surface catalycities were performed for hypersonic Mars entries. The analysis of surface thermochemistry reveals that the surface chemical reactions have great contribution to aerodynamic heating, and the temperature-dependence of finite-rate catalysis highly influences the evolution of the coupling aerodynamic heating in the coupling process. For fixed free stream parameters with proper catalytic excitation energy, a “leap” phenomenon of the TPS-coupled heat flux with the coupling time appears in the initial stage of the coupling process, due to the strong thermochemical effects on the TPS surface.

Numerical Model Study on the Wave and Current Control by Coastal Vegetation

ABSTRACT Lee, W.D.; Cox, D.T., and Hur, D.S., 2017. Numerical model study on the wave and current control by coastal vegetation. In: Lee, J.L.; Griffiths, T.; Lotan, A.; Suh, K.-S., and Lee, J. (eds.), The 2nd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 79, pp. 219–223. Coconut Creek (Florida), ISSN 0749-0208. In this study, three-dimensional numerical simulations were conducted to investigate the effect of the coastal vegetation on the wave and current controls. The model was modified to apply three-dimensional Navier-Stokes solver based on porous body model for the direct simulation of the wave energy dissipation through the vegetation. The new formula of a vegetation drag coefficient based on the wave-vegetation interaction was proposed through the hydraulic model tests and the formula was implemented to the model. The modified numerical model was tested and the results were compared with the experimental results to verify the numerical model capability. The mod...

Enhancement of heat and mass transfer performance on humidification tower using injection of different carrier gases into water bed

The present study is presented an approach attempting for enhancement of heat and mass transfer between a continuous gas phase and liquid phase in a non-packed humidification towers by injection of different carrier gases such as air, carbon dioxide and helium through water bed. The computational technique utilized was a three-dimensional Navier-Stokes solver in the laminar flow regime with free-surface simulation in Piecewise Linear Interface Construction method to compute density variation on the two-dimensional two-phase flow field and pressure on a water bed. This work studied the influence of the operating conditions such as the water bed temperature and carrier gas type on the overall gas phase heat and mass transfer coefficient. The present study included also determining the overall pressure drop of the carrier gases through water bed, consumed power and humidification efficiency. It has been found that the mass transfer coefficient increases with increasing carrier gas molecular weight. The heat transfer coefficients are more than 5 times for carbon dioxide than air flow and less for helium than air, about 50% flow at water bed temperature 353K. The mass transfer coefficients are more than 2.5 times for helium than air and less for carbon dioxide than air, about 50% at water bed temperature 353K. The obtained maximum humidification efficiency of the helium was about 87%. The pressure drop was about 51.4kPa for helium and 47.2kPa for carbon dioxide at a water bed temperature 353K. The consumed power was about for helium about 45.45W and for carbon dioxide was 41.25W at a water bed temperature 353K. The comparison between the numerical and other experimental results shows a good matching of outlet humidity ratios for air as a carrier gas except that the numerical values were slightly smaller than experimental ones. This may be attributed to the laminar flow computation without including turbulence effects and the two-dimension computational model consideration.

Development of a Fluid-Structure Model for Gas-Lubricated Bump-Type Foil Thrust Bearings

In the present study, a computational model for the coupled fluid-structure simulation of bump-type foil thrust bearings is developed. A three-dimensional compressible Navier-Stokes solver is extended to model the fluid flow within the thin gap. In addition, a new solver is developed to model the bump and top foils within the foil thrust bearings. These two solvers are linked with a coupling algorithm that maps pressure and deflection at the fluid-structure interface. The theory and verification of this coupling algorithm are detailed as the focus of this paper. Finally, this coupled fluid-structure simulation for the foil thrust bearings is validated with experiment results from the literature. The resulting fluid-structure model can be used to assist the design of bump-type foil thrust bearings for various applications.

Optimization of lift force for a bio-inspired flapping wing model in hovering flight

The lift force is an important component that affects the aerodynamic performance of bio-inspired flapping-wing micro aerial vehicles. However, there is a lack of endeavors in the optimization of the flapping wing parameters that affect the lift force of micro aerial vehicles. This research is therefore to establish a methodology that combines computational fluid dynamic simulation for the evaluation of the lift generation and wing parameters. The Taguchi’s framework for design of experiments, combined with the computational fluid dynamics simulations, is performed on a simplified robotic fly wing model used in the experiment found in Dickinson et al. (1999), under the hovering flight mode, to identify the most influential parameters on the lift generation of micro aerial vehicles. A commercial computational fluid dynamics code, ANSYS/FLUENT, along with a three-dimensional Navier–Stokes solver is used to simulate the unsteady flow field. With the optimization of the time-averaged lift force as the optimization objective, five typical parameters (flapping frequency, maximum angle of attacks during the upstroke and downstroke motions, stroke amplitude, and rotation type) in the flapping trajectory equation are selected as the input factors with each having four levels. Specific computational fluid dynamics cases are simulated in accordance with the chosen orthogonal arrays. By conducting statistical analyses with analyses of means and variance, the flapping frequency and the stroke amplitude are determined to be the two most influential parameters. The response surface of the time-averaged lift force and the power consumption contour are constructed with respect to these two parameters to determine the optimal combination for the generation of lift forces under a specific power constrain and provide a guideline for bio-inspired micro aerial vehicle designs.

Double bubbles sans toil and trouble

Simulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional many-phase Navier-Stokes solver, even though their visual appearance is completely dominated by the thin liquid surface. We depart from earlier work on soap bubbles and foams by noting that their dynamics are naturally described by a Lagrangian vortex sheet model in whichcirculationis the primary variable. This leads us to derive a novel circulation-preserving surface-only discretization of foam dynamics driven by surface tension on a non-manifold triangle mesh. We represent the surface using a mesh-based multimaterial surface tracker which supports complex bubble topology changes, and evolve the surface according to the ambient air flow induced by a scalar circulation field stored on the mesh. Surface tension forces give rise to a simple update rule for circulation, even at non-manifold Plateau borders, based on a discrete measure of signed scalar mean curvature. We further incorporate vertex constraints to enable the interaction of soap films with wires. The result is a method that is at once simple, robust, and efficient, yet able to capture an array of soap films behaviors including foam rearrangement, catenoid collapse, blowing bubbles, and double bubbles being pulled apart.