Vorticity Transport Model Research Articles

High-resolution simulation for rotorcraft aerodynamics in hovering and vertical descending flight using a hybrid method

A high-resolution simulation tool for rotorcraft aerodynamics is developed by coupling CFD with a Vorticity Transport Model (VTM). An Eulerian-based CFD module is used to model the blade near body flowfield, and a Lagrangian-based VTM module is employed for vortex tracking in the far wake. The coupling procedure is implemented by transmitting vortex sources to the VTM module and feeding boundary conditions back to the CFD module. The presented CFD/VTM hybrid solver is firstly validated by hover cases of three different rotor configurations. Simulation results, including the blade surface pressure distribution, rotor downwash, and hover figure of merit, exhibit favorable correlations with available experimental data. Then, a rotor operated in vertical descending flight with a fixed collective pitch is investigated. It is shown that the CFD/VTM coupling method is suitable for rotor wake simulation. Wake instabilities (far wake breakdown in hover and toroidal wake pattern in the vortex ring state) are successfully demonstrated with a moderate computational cost.

Development and validation of a hybrid method for predicting helicopter rotor impulsive noise

Prediction of helicopter rotor impulsive noise is practically a very challenging task. This paper describes a hybrid method to predict rotor impulsive noise for both high-speed impulsive noise and blade–vortex interaction noise. The hybrid solver has been developed by combining the advantages of three different methods: (1) a computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations to account for the viscous and compressible effects near the blade; (2) a vorticity transport model to predict rotor wake system without artificial dissipation; and (3) an acoustic calculation method, based on Ffowcs-Williams Hawkings equation implemented to a permeable data surface. The developed hybrid solver is validated through available test data, for the cases of UH-1H model rotor, AH-1 Operational Loads Survey rotor, and Helishape 7A rotor. Peak sound pressure level of high-speed impulsive noise is accurately predicted with relative errors less than 7%. Additionally, acoustic waveform of blade–vortex interaction noise is well captured though it is sensitive to small changes in aerodynamic load. It is suggested that present hybrid method is versatile for the prediction of rotor impulsive noise with moderate computational cost.

Simulating the Wake Downstream of a Horizontal Axis Tidal Turbine Using a Modified Vorticity Transport Model

To decrease the need for fossil fuels, the alternative energy resources must be not only economically viable but also sustainable in the long term. One of the most promising alternatives is the marine renewable energy resource. The relatively young marine energy industry is presented with two challenges: first, to deliver a continuous reliable power supply, and second, to minimize potentially harmful effects of the power extraction on the marine environment. The requirement to understand the interactions between a tidal turbine and the surrounding flow environment motivated this work. A tidal turbine mounted on the seabed induces a wake that extends far downstream of the device. As the direction of tidal flow changes, so does the position of the wake with respect to the device. The detailed study of the turbine wake has been conducted by means of computer simulations. An existing finite-volume computer model called the vorticity transport model has been modified to suit the purpose of simulating the wake of a horizontal axis tidal turbine subjected to a nonuniform flow typical of that close to the seabed. High-resolution computer simulations suggest that a progressive fragmentation of the vortical structure occurs during the development of the wake of a tidal turbine. The predicted fragmentation generates small-scale unsteady flow phenomena beyond five rotor diameters downstream of the device in the area previously thought unaffected by the presence of a tidal turbine. The effects of nonuniform flow on the vorticity structure downstream of a tidal turbine and the fragmentation process are analyzed in this work.

Modelling the aerodynamics of vertical‐axis wind turbines in unsteady wind conditions

ABSTRACTMost numerical and experimental studies of the performance of vertical‐axis wind turbines have been conducted with the rotors in steady, and thus somewhat artificial, wind conditions—with the result that turbine aerodynamics, under varying wind conditions, are still poorly understood. The vorticity transport model has been used to investigate the aerodynamic performance and wake dynamics, both in steady and unsteady wind conditions, of three different vertical‐axis wind turbines: one with a straight‐bladed configuration, another with a curved‐bladed configuration and another with a helically twisted configuration. The turbines with non‐twisted blades are shown to be somewhat less efficient than the turbine with helically twisted blades when the rotors are operated at constant rotational speed in unsteady wind conditions. In steady wind conditions, the power coefficients that are produced by both the straight‐bladed and curved‐bladed turbines vary considerably within one rotor revolution because of the continuously varying angle of attack on the blades and, thus, the inherent unsteadiness in the blade aerodynamic loading. These variations are much larger, and thus far more significant, than those that are induced by the unsteadiness in the wind conditions. Copyright © 2012 John Wiley & Sons, Ltd.

Influence of Blade Aerodynamic Model on Prediction of Helicopter Rotor Aeroacoustic Signatures

Brown’s vorticity transport model has been used to investigate how the local blade aerodynamic model influences the quality of the prediction of the high-frequency airloads associated with blade–vortex interactions, and thus the accuracy with which the acoustic signature of a helicopter rotor can be predicted. The vorticity transport model can accurately resolve the structure of the wake of the rotor and allows significant flexibility in the way that the blade loading can be represented. The Second Higher-Harmonic Control Aeroacoustics Rotor Test was initiated to provide experimental insight into the acoustic signature of a rotor in cases of strong blade–vortex interaction. Predictions of two models for the local blade aerodynamics are compared with the test data. A marked improvement in accuracy of the predicted high-frequency airloads and acoustic signature is obtained when a lifting-chord model for the blade aerodynamics is used instead of a lifting-line-type approach. Errors in the amplitude and phase of the acoustic peaks are reduced, and the quality of the prediction is affected to a lesser extent by the computational resolution of the wake, with the lifting-chord model producing the best representation of the distribution of sound pressure below the rotor.

Effect of blade geometry on the aerodynamic loads produced by vertical-axis wind turbines

Accurate aerodynamic modelling of vertical-axis wind turbines poses a significant challenge. The rotation of the turbine induces large variations in the angle of attack of its blades that can manifest as dynamic stall. In addition, interactions between the blades of the turbine and the wake that they produce can result in impulsive changes to the aerodynamic loading. The Vorticity Transport Model has been used to simulate the aerodynamic performance and wake dynamics of three different vertical-axis wind turbine configurations. It is known that vertical-axis turbines with either straight or curved blades deliver torque to their shaft that fluctuates at the blade passage frequency of the rotor. In contrast, a turbine with helically twisted blades delivers a relatively steady torque to the shaft. In this article, the interactions between helically twisted blades and the vortices within their wake are shown to result in localized perturbations to the aerodynamic loading on the rotor that can disrupt the otherwise relatively smooth power output that is predicted by simplistic aerodynamic tools that do not model the wake to sufficient fidelity. Furthermore, vertical-axis wind turbines with curved blades are shown to be somewhat more susceptible to local dynamic stall than turbines with straight blades.

Influence of Blade Aerodynamic Model on the Prediction of Helicopter High-Frequency Airloads

Brown’s vorticity transport model has been used to investigate the influence of the blade aerodynamic model on the accuracy with which the high-frequency airloads associated with helicopter blade–vortex interactions can be predicted. The model yields an accurate representation of the wake structure yet allows significant flexibility in the way that the blade loading can be represented. A simple lifting-line model and a somewhat more sophisticated liftingchord model, based on unsteady thin aerofoil theory, are compared. A marked improvement in the accuracy of the predicted high-frequency airloads of the higher harmonic control aeroacoustic rotor is obtained when the liftingchord model is used instead of the lifting-line approach, and the quality of the prediction is affected less by the computational resolution of the wake. The lifting-line model overpredicts the amplitude of the lift response to blade–vortex interactions as the computational grid is refined, exposing the fundamental deficiencies in this approach when modeling the aerodynamic response of the blade to interactions with vortices that are much smaller than its chord. The airloads that are predicted using the lifting-chord model are relatively insensitive to the resolution of the computation, and there are fundamental reasons to believe that properly converged numerical solutions may be attainable using this approach.

Simulating the aerodynamic performance and wake dynamics of a vertical‐axis wind turbine

AbstractThe accurate prediction of the aerodynamics and performance of vertical‐axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high‐fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus‐type vertical‐axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade–vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright © 2010 John Wiley & Sons, Ltd.

Helicopter Tail Rotor Thrust and Main Rotor Wake Coupling in Crosswind Flight

The tail rotor of a helicopter with a single main rotor configuration can experience a significant reduction in thrust when the aircraft operates in crosswind flight. Brown’s vorticity transport model has been used to simulate a main rotor and tail rotor system translating at a sideslip angle that causes the tail rotor to interact with the main rotor tip vortices as they propagate downstream at the lateral extremities of the wake. The tail rotor is shown to exhibit a distinct directionally dependent mode during which tail rotors that are configured so that the blades travel forward at the top of the disk develop less thrust than tail rotors with the reverse sense of rotation. The range of flight speeds over which this mode exists is shown to vary considerably with the vertical location of the tail rotor. At low flight speeds, the directionally dependent mode occurs because the tail rotor is immersed within not only the downwash from the main rotor but also the rotational flow associated with clusters of largely disorganized vorticity within the main rotor wake. At higher flight speeds, however, the tail rotor is immersed within a coherent supervortex that strongly influences the velocity field surrounding the tail rotor.

Coaxial Rotor Helicopter in Hover Based on Unstructured Dynamic Overset Grids

C OAXIAL rotor configuration is one of the technological solutions for increasing helicopter forward speed, maneuverability, and load-carrying ability. Since two rotors produce the net thrust instead of a single rotor in the conventional design, the diameter of the rotors can be reduced to carry the same amount of weight. Themost attractive feature of a coaxial design is the resulting compactness and safety of the vehicle. Second, the antitorsional moment generated by the two rotors would be canceled due to the opposite rotational directions, and the tail rotor and tail boom can be eliminated, resulting in a smaller and lighter vehicle. Compared to the individual-rotor helicopter, the aerodynamics and flow physics of coaxial rotor helicopter are relatively less studied and understood. The method of slipstream theory was first used to study the coaxial rotor, and then the predicted wake vortex model [1,2], free wake vortex model [3], and vorticity transport model [4,5] were applied to the coaxial rotor analysis. All the methods above carry out some approximations to the rotor, and the detailed flow feature near the blades and blade vortex in the wake cannot be simulated. Recently, the unsteady Navier–Stokes equations were used to simulate the coaxial rotor flows [6–8] to provide a detailed understanding of the flow physics of coaxial rotor. In the present Note, the three-dimensional unsteady Euler equations were solved to simulate the unsteady flows around coaxial rotor helicopter and individual-rotor helicopter in hover based on the unstructured dynamic overset grids. The aerodynamic interaction property of the coaxial rotor helicopter in hover and the effect of fuselage on the unsteady performance were studied.

A Comparison of Coaxial and Conventional Rotor Performance

The performance of a coaxial rotor in hover, in steady forward flight, and in level, coordinated turns is contrasted with that of an equivalent, conventional rotor with the same overall solidity, number of blades, and blade aerodynamic properties. Brown's vorticity transport model is used to calculate the profile, induced, and parasite contributions to the overall power consumed by the two systems, and the highly resolved representation of the rotor wake that is produced by the model is used to relate the observed differences in the performance of the two systems to the structures of their respective wakes. In all flight conditions, all else being equal, the coaxial system requires less induced power than the conventional system. In hover, the conventional rotor consumes increasingly more induced power than the coaxial rotor as thrust is increased. In forward flight, the relative advantage of the coaxial configuration is particularly evident at pretransitional advance ratios. In turning flight, the benefits of the coaxial rotor are seen at all load factors. The beneficial properties of the coaxial rotor in forward flight and maneuver, as far as induced power is concerned, are a subtle effect of rotor-wake interaction and result principally from differences between the two types of rotor in the character and strength of the localized interaction between the developing supervortices and the highly loaded blade-tips at the lateral extremities of the rotor. In hover, the increased axial convection rate of the tip vortices appears to result in a favorable redistribution of the loading slightly inboard of the tip of the upper rotor of the coaxial system.

A Rational Approach to Comparing the Performance of Coaxial and Conventional Rotors

The merit, in terms of its efficiency and performance, of the twin, contrarotating coaxial rotor configuration over the more conventional single rotor system has long been a point of contention. Previously published comparisons yield seemingly inconsistent and conflicting conclusions. In this paper, the basis for a fair, like-for-like comparison of the performance of coaxial and single rotor systems is discussed. A comparison between experimentally measured data and numerical predictions of rotor performance obtained using the vorticity transport model shows that a computational approach can be used reliably to decompose the power consumption into induced and profile constituents. These comparisons show that a somewhat stronger similarity in geometry needs to be enforced between the two types of rotor system than previously suggested in order that the systems be directly comparable. If the equivalent single rotor system is constructed to have the same disk area, blade geometry, and total number of blades as that of the coaxial rotor, then the geometric differences between the two systems are confined to the defining characteristics of the two types of rotor system, in other words to the vertical separation between the rotor blades and their relative direction of rotation. The differences in aerodynamic performance between a coaxial rotor and an equivalent single rotor defined in this way then arise solely as a result of the differences in the detailed interaction between the blades and their wakes that arise within the two types of system. Using this form of comparison, the articulated coaxial system is shown to consume marginally less induced power than the equivalent single rotor system. The difference is small enough, however, to be obscured if the profile drag of the blades is overtly sensitive to operating condition, as for instance might be the case at low Reynolds number.

Simulation of wind turbine wake interaction using the vorticity transport model

AbstractThe aerodynamic interactions that can occur within a wind farm can result in the constituent turbines generating a lower power output than would be possible if each of the turbines were operated in isolation. Tightening of the constraints on the siting of wind farms is likely to increase the scale of the problem in the future. The aerodynamic performance of turbine rotors and the mechanisms that couple the fluid dynamics of multiple rotors can be most readily understood by simplifying the problem and considering the interaction between only two rotors. The aerodynamic interaction between two rotors in both co‐axial and offset configurations has been simulated using the Vorticity Transport Model. The aerodynamic interaction is a function of the tip speed ratio, and both the streamwise and crosswind separation between the rotors. The simulations show that the momentum deficit at a turbine operating within the wake developed by the rotor of a second turbine is governed by the development of instabilities within the wake of the upwind rotor, and the ensuing structure of the wake as it impinges on the downwind rotor. If the wind farm configuration or wind conditions are such that a turbine rotor is subject to partial impingement by the wake produced by an upstream turbine, then significant unsteadiness in the aerodynamic loading on the rotor blades of the downwind turbine can result, and this unsteadiness can have considerable implications for the fatigue life of the blade structure and rotor hub. Copyright © 2009 John Wiley & Sons, Ltd.

Eulerian Simulation of the Fluid Dynamics of Helicopter Brownout

A computational model is presented that can be used to simulate the development of the dust cloud that can be entrained into the air when a helicopter is operated close to the ground in desert or dusty conditions. The physics of this problem, and the associated pathological condition known as ‘brownout’ where the pilot loses situational awareness as a result of his vision being occluded by dust suspended in the flow around the helicopter, is acknowledged to be very complex. The approach advocated here involves an approximation to the full dynamics of the coupled particulate-air system. Away from the ground, the model assumes that the suspended particles remain in near equilibrium under the action of aerodynamic forces. Close to the ground, this model is replaced by an algebraic sublayer model for the saltation and entrainment process. The origin of the model in the statistical mechanics of a distribution of particles governed by aerodynamic forces allows the validity of the method to be evaluated in context by comparing the physical properties of the suspended particulates to the local properties of the flow field surrounding the helicopter. The model applies in the Eulerian frame of reference of most conventional Computational Fluid Dynamics codes and has been coupled with Brown’s Vorticity Transport Model. Verification of the predictions of the coupled model against experimental data for particulate entrainment and transport in the flow around a model rotor are encouraging. An application of the coupled model to analyzing the differences in the geometry and extent of the dust clouds that are produced by single main rotor and tandem-rotor configurations as they decelerate to land has shown that the location of the ground vortex and the size of any regions of recirculatory flow, should they exist, play a primary role in governing the extent of the dust cloud that is created by the helicopter.

Wake Structure and Kinematics in the Vortex Ring State

High-resolution computational simulations of the vortical wake of a rotor operating both near to and within the vortex ring state have been conducted using Brown's vorticity transport model. The nonlinear vortex kinematics of the wake is exposed using three-dimensional visualizations of the simulated flow field. To reveal the vortex dynamics that underpin the highly unsteady flow within the vortex ring state, a rotor with just one blade was modeled. This blade was decoupled aerodynamically from the surrounding velocity field so that it acted merely as a source of trailed vorticity. The investigation identified a significant change in the dominant dynamics of the wake as it swapped fromthe tubular form that is characteristic of hover or very lowspeed descent into the toroidal geometry of the vortex ring state. Initial vortex 'pairing' leads to rotation of vortex filaments away from their original attitude. This phenomenon plays an important role in regulating the downwash that the rotor can produce and thus in precipitating the onset of the vortex ring state. The considerable and persistent coherence of the vortical structure of the wake when in the vortex ring state is revealed, despite these disturbances, as are themechanisms that lead to both small-scale and large-scale wake breakdown events. Simulations show the balance between the vortex pairing and short-wave instability modes to be different in the vortex ring state at high descent speed, where the wake lies above the rotor, compared to in the vortex ring state at low descent speed when the wake lies predominantly below the rotor. This yields subtle differences to the kinematics and structure of the wake in the two cases.

Interactional aerodynamics and acoustics of a hingeless coaxial helicopter with an auxiliary propeller in forward flight

AbstractThe aerodynamics and acoustics of a generic coaxial helicopter with a stiff main rotor system and a tail-mounted propulsor are investigated using Brown’s Vorticity Transport Model. In particular, the model is used to capture the aerodynamic interactions that arise between the various components of the configuration. By comparing the aerodynamics of the full configuration of the helicopter to the aerodynamics of various combinations of its sub-components, the influence of these aerodynamic interactions on the behaviour of the system can be isolated. Many of the interactions follow a simple relationship between cause and effect. For instance, ingestion of the main rotor wake produces a direct effect on the unsteadiness in the thrust produced by the propulsor. The causal relationship for other interdependencies within the system is found to be more obscure. For instance, a dependence of the acoustic signature of the aircraft on the tailplane design originates in the changes in loading on the main rotor that arise from the requirement to trim the load on the tailplane that is induced by its interaction with the main rotor wake. The traditional approach to the analysis of interactional effects on the performance of the helicopter relies on characterising the system in terms of a network of possible interactions between the separate components of its configuration. This approach, although conceptually appealing, may obscure the closed-loop nature of some of the aerodynamic interactions within the helicopter system. It is suggested that modern numerical simulation techniques may be ready to supplant any overt reliance on this reductionist type approach and hence may help to forestall future repetition of the long history of unforeseen, interaction-induced dynamic problems that have arisen in various new helicopter designs.

Main Rotor-Tail Rotor Interaction and Its Implications for Helicopter Directional Control

Aerodynamic interference between the main and tail rotor can have a strong negative influence on the flight mechanics of a conventional helicopter. Significant unsteadiness in the tail rotor loading is encountered under certain flight conditions, but the character of the unsteadiness can depend on the direction of rotation of the tail rotor. Numerical simulations, using Brown's vorticity transport model, of the aerodynamic interaction between the main and tail rotors of a helicopter are presented for a range of forward and lateral flight trajectories. Distinct differences are predicted in the behavior of the system in left and right sideward flight that are consistent with flight experience that the greatest fluctuations in loading or control input are required in left sideways flight (for a counterclockwise rotating main rotor). These fluctuations are generally more extreme for a system with tail rotor rotating top-forward than top-aft. Differences are also exposed in the character of the lateral excitation of the system as forward flight speed is varied. The observed behavior appears to originate in the disruption of the tail rotor wake that is induced by its entrainment into the wake of the main rotor. The extent of the disruption is dependent on flight condition, and the unsteadiness of the process depends on the direction of rotation of the tail rotor. In intermediate-speed forward flight and right sideward flight, the free stream delays the entrainment of the tail rotor wake far enough downstream for the perturbations to the rotor loading to be slight. Conversely, in left sideward and quartering flight, the free stream confines the entrainment process close to the rotors, where it causes significant unsteadiness in the loads produced by the system.

Modelling the interaction of helicopter main rotor and tail rotor wakes

AbstractThe mutual interaction between the main rotor and tail rotor wakes is central to some of the most problematic dynamic phenomena experienced by helicopters. Yet achieving the ability to model the growth and propagation of helicopter rotor wakes with sufficient realism to capture the details of this interaction has been a significant challenge to rotorcraft aerodynamicists for many decades. A novel computational fluid dynamics code tailored specifically for rotorcraft applications, the vorticity transport model, has been used to simulate the interaction of the rotors of a helicopter with a single main rotor and tail rotor in both hover and low-speed quartering flight, and with the tail rotor rotating both top-forward and top-aft. The simulations indicate a significant level of unsteadiness in the performance of both main and tail rotors, especially in quartering flight, and a sensitivity to the direction of rotation of the tail rotor. Although the model thus captures behaviour that is similar to that observed in practice, the challenge still remains to integrate the information from high fidelity simulations such as these into routine calculations of the flight dynamics of helicopters.

Efficient High-Resolution Wake Modeling Using the Vorticity Transport Equation

Computational fluid dynamic models, through their fundamental treatment of the flow physics, present a unique and powerful tool for analyzing the aerodynamics of helicopter rotors. Their effectiveness is often limited though by difficulties in retaining the structure and form of the rotor wake that result from their tendency to dissipate vorticity. The vorticity transport model, developed some years ago, addresses the problem of vorticity diffusion by solving the fundamental fluid dynamic equations in vorticity conservation form. A development of the original model is described that results in a more efficient computational implementation. The new model uses an adaptive grid system to increase grid resolution significantly, with minimal impact on computational cost. The new grid system is effectively boundary free, thus eliminating the need for numerical boundary conditions at the edges of the computational domain. In addition, the new grid system allows very efficient evaluation of the velocity field using a technique based on the Cartesian fast multipole method. The implementation of both the grid system and the velocity calculation is described

Influence of Arctic polar ozone depletion on lower stratospheric ozone amounts at Haute‐Provence Observatory (43.92°N, 5.71°E)

Lidar and ozone sonde measurements performed at Haute‐Provence Observatory are used together with a high‐resolution potential vorticity (PV) transport model to study the influence of Arctic polar vortex ozone depletion on ozone amounts at this location prior to vortex dilution. The study focuses on four Arctic winters from 1996 to 2000. The transport model is used to investigate the presence of polar air masses above the station. These air masses, which are characterized by high PV values, can extend toward midlatitude regions during winter. Polar air masses are detected using a daily threshold value defined from the PV fields. The monthly average fraction of polar air generally increases with altitude from a few percent in the lower stratosphere to 10% or more above 500 K. The source of presence of polar air is largely dominated by filament events in the lower stratosphere and is equally divided between filaments and vortex excursions above the station in the middle stratosphere. The presence of polar air above the station shows high interannual variability. In the winter of 1999/2000 the least amount of polar air was detected above the station. However, vortex excursions above the station from January to March 2000 led to a significant average ozone reduction, estimated to 1.6% in the 400–650 K potential temperature range using a chemical transport model (CTM) evaluation of ozone loss at the vortex edge. Cold vortex, such as observed in 1999/2000, results in less transport toward midlatitude, but strong ozone depletion within the vortex combined with transient excursions of polar air can have a significant impact on ozone amounts in the midlatitude regions.