Trailing Tip Vortices Research Articles

Numerical simulation of vortex instabilities in the wake of a preswirl pumpjet propulsor

A numerical analysis based on detached eddy simulations is conducted to investigate vortex instabilities in the wake of a preswirl pumpjet propulsor. Three models are established to separate the roles that the rotor, stator, and duct play in the vortex structure of the pumpjet propulsor. In this paper, only the vortex structure of the rotor is considered. The results show that the vortex system of the rotor is mainly composed of the tip vortices, a hub vortex, the trailing tip vortices, and the trailing root vortices. The trailing tip vortices are generated by the premature shedding of the tip vortices in the rotor model compared with a normal single propeller. The existence of trailing root vortices increases the stability of the hub vortex. Furthermore, a unique multi-inductance instability mode of the tip vortex, called the “overlap–forward” phenomenon, is found for low values of the advance coefficient J. It is found that the instability of the tip vortex depends not only on the spiral-to-spiral distance but also on the highest-efficiency point of the propeller. The instability inception point of the tip vortex moves farther downstream with increasing J, whereas when J is greater than the highest-efficiency point of the propeller, the stable length of the tip vortices drops sharply. The energy transfer process from blade harmonics to shaft harmonics of the tip vortices depends on J and is related to the spatial evolution of the tip vortices.

Numerical analysis of the effect of flaps on the tip vortex of a wind turbine blade

Two oscillating flaps located close to the tip and at mid span are used to excite the unstable modes of the tip vortex system of a wind turbine blade. The two flaps are deflected in opposite directions such that the root bending moment of the wind turbine blade remains almost unchanged. To investigate the mechanism of how and to what extent the deflection of the flaps influences the tip-vortex system, Large-Eddy Simulations in the Arbitrary Lagrangian-Eulerian formulation in a rotating frame of reference are performed at an averaged chord based Reynolds number of 300,000. Periodic boundary conditions are applied in the circumferential direction such that the flow over only one of the three blades of the wind turbine needs to be computed. A subsequent simulation of the trailing tip-vortex system is performed to analyze the evolution of the disturbed tip vortex. These simulations use a far-wake model based on the parameters obtained from the wind turbine simulation as inflow condition for the wake flow field. The comparison of the flow without and with oscillating flaps shows that the tip-vortex core is displaced by approximately 5% of the rotor radius by the flap motion. The root bending moment and torque at the root of the blade with flaps vary sinusoidally. Due to the compensation by the middle span flap, the difference of the root bending moment and torque is found to be less than 5% compared to the case without moving flaps. The simulations of trailing tip vortex show considerably earlier breakdown of the excited system, which proves the concept to excite instabilities in the vortex system by oscillating flaps successful.

Mutual inductance instability of the tip vortices behind a wind turbine

AbstractTwo modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier–Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tjæreborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120° symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360° wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\pi /2$and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

Determination of Wind Turbine Near-Wake Length Based on Stability Analysis

A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method. The wake is perturbed by applying stochastic or harmonic excitations in the neighborhood of the tips of the blades. The flow field is then analyzed to obtain the stability properties of the tip vortices in the wake of the wind turbine. As a main outcome of the study it is found that the amplification of specific waves (traveling structures) along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the pairing instability has a universal growth rate equal to π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, we provide an analytical relationship between the turbulence intensity and the stable wake length. The analysis leads to a simple expression for determining the length of the near wake. This expression shows that the near wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity.

Combined Feature-Driven Richardson-Based Adaptive Mesh Refinement for Unsteady Vortical Flows

Combined Feature-Driven Richardson-Based Adaptive Mesh Refinement for Unsteady Vortical Flows

Numerical Study of Cavitation Inception Due to Vortex/Vortex Interaction in a Ducted Propulsor

Cavitation inception in a ducted propulsor was studied numerically using Navier-Stokes computations and bubble dynamics models. Experimental observations of the propulsor model and previous numerical computations using Reynolds-averaged Navier-Stokes (RANS) codes indicated that cavitation inception occurred in the region of interaction of the leakage and trailing tip vortices. The RANS simulations failed, however, to predict correctly both the cavitation inception index value and the inception location. To improve the numerical predictions, we complemented here the RANS computations with a direct Navier-Stokes simulation in a reduced computational domain including the region of interaction of the two vortices. Initial and boundary conditions in the reduced domain were provided by the RANS solution of the full ducted propulsor flow. Bubble nuclei were released in this flow field, and spherical and nonspherical bubble dynamics models were exercised to investigate cavitation inception. This resulted in a solution in much better agreement with the experimental measurements than the original RANS solution. Both the value of the cavitation inception index and the location of the cavitation inception were very well captured. The characteristics of the emitted acoustic signals and of the bubble shapes during a cavitation event were also computed.

Effect of shock strength on oblique shock-wave/vortex interaction

An experimental study of the interaction between streamwise vortices and two-dimensional oblique shock waves has been conducted at Mach 2.5. The experiments involved positioning an instrumented two-dimensional wedge downstream of a semispan wing so that the trailing tip vortex from the wing interacted with the oblique shock wave formed over the wedge surface. The experiments were designed to simulate interaction of streamwise vortices with shock waves formed over aerodynamic surfaces or in supersonic inlets. The influence of oblique shock wave intensity on this inherently three-dimensional interaction was examined for vortices of variable strength. Results indicate that the interaction of a moderate strength vortex with an oblique shock wave can lead to the formation of a steady separated shock structure upstream of the oblique shock front. A significant expansion of the vortex core is observed in these cases, and the scale of the structure increases with shock wave intensity. In some instances the separated shock structure continues through the oblique shock front to strike the shock-generating wedge forming a three-dimensional shock-wave/boundary-layer interaction. The experiments indicate that significant distortion of streamwise vortices can be precipitated by oblique shock fronts with supersonic downstream conditions.

Airfoil pressure measurements during oblique shock-wave/vortex interaction in a Mach 3 stream

An experimental investigation of the interaction between streamwise discrete vortices and oblique shocks formed over a two-dimensional wedge surface was conducted in a Mach 3 blowdown wind tunnel. An instrumented two-dimensional wedge was placed downstream of a semiispan wing so that the trailing tip vortex would arbitrarily interact with the shock wave formed over the wedge surface. The experiments were designed to simulate interaction of streamwise vortices from upstream bodies with shock waves formed over aft surfaces as might be encountered in supersonic flight of aircraft and missiles. The influence of vortex strength and vortex-airfoil vertical separation distance on the interaction was examined.

Unsteady transonic flow past a quarter-plane

One of the most significant mechanisms of noise generation in prototype counter-rotation propeller systems is the unsteady interaction between the rear row and the wake and trailing tip vortices shed by the front row. A crucial part of predicting this noise is the determination of the resulting unsteady lift distribution on the rear row; since much of the interaction occurs in the vicinity of the rear-row blade tips, however, two-dimensional airfoil response theory cannot be applied exclusively, and some account of the presence of the blade tip must be taken. With this in mind, we solve the model problem of the unsteady interaction between a convected harmonic velocity gust and a quarter-plane, for the case of mean flow Mach number in the transonic range. The detailed lift distribution near the leading edge and corner is analysed, revealing the complicated nature of the lift singularity at the corner, and allowing the lift distribution throughout a narrow region along the leading edge to be determined. A closed-form expression for the practically important acoustically weighted lift is derived, which could easily be incorporated into existing noise prediction schemes in order to correct the rear-row blade response calculations for the presence of the blade tips. The radiation in this quarter-plane problem is also considered, and the field is seen to possess two components, one arising from the interaction between the gust and the semi-infinite leading edge, and the other from the interaction between the gust and the blade corner. The acoustic energy associated with this second term, corresponding to the conversion of vortical energy into sound by the corner, is considered in detail, and the directivity and parametric scaling determined. Our exact solution to this model problem is also used to assess the accuracy of a strip-theory approximation, which is seen to be accurate in this case over only a restricted range of observer positions.

Numerical Solution of Three-Dimensional Navier-Stokes Equations Showing Trailing Tip Vortices

Numerical solution of the incompressible Navier-Stokes equations in integro-differential form is applied to timedependent flow about a rectangular slab at an angle of attack. With this formulation the solution is obtained in the entire unbounded flowfield, but with actual computation required only in regions of significant vorticity. This allows considerable reduction in computer storage, since only points in regions of significant vorticity need be stored at any particular time. The computational field thus expands in time. (This method is not to be confused with vortex using discrete vortices and images.) The finite numerical calculation field in the integro-differential formulation is, in effect, infinite, and the necessity of locating infinity at a finite distance is avoided. Although it is not necessary in this numerical method to calculate the velocity at points outside the region of nonzero vorticity, the velocity at these points and, in fact, to infinity, is determined by the solution via an integral over the vorticity distribution. The method requires two orders of magnitude less computer storage than do methods based on the differential formulation. Results have been obtained for the development of trailing tip vortices and the force coefficients.