Hybrid Vortex Method Research Articles

Aero‐hydro‐servo‐elastic coupling of a multi‐body finite‐element solver and a multi‐fidelity vortex method

AbstractThe manuscript presents a novel aero‐hydro‐servo‐elastic coupling framework, MIRAS‐HAWC2. In this coupling, the wind turbine blades and rotor‐wake aerodynamics are modeled using a modified lifting‐line theory which accounts for blade curvature, combined with a hybrid vortex method. The wind turbine structure and foundation are modeled using a finite‐element and multi‐body system approach. Last, hydrodynamics are modeled using Airy wave theory together with Morison's equation. An initial assessment of the performance of the aeroelastic coupling framework has been performed for steady rotor‐only cases, assuming laminar inflow without shear. This included a comparison against fully resolved computational fluid dynamics, for both stiff and flexible blades showing an excellent agreement. In a second stage, the aero‐hydro‐servo‐elastic coupling is used, comparing MIRAS‐HAWC2 as well as blade‐element momentum‐based simulations with selected results from the Offshore Code Comparison Collaboration projects (OC3 and OC4), which study the NREL 5 MW turbine mounted on different offshore support structures. A good agreement has been obtained for the simulations of a monopile with rigid foundation, a tripod, and jacket support structures.

Theoretical study of cryogen spray cooling with R134a, R404A and R1234yf: Comparison and clinical potential application

In laser dermatology, cryogen spray cooling has been used to protect the epidermis from unwanted thermal damage. In this work, spray characteristics and surface heat transfer dynamics were simulated by two-way coupling hybrid vortex method to evaluate the surface cooling capacity of R134a, R404A and R1234yf in terms of cooling density and effective heat flux. Simulation results reveal that R404A has the largest cooling capacity and smallest dispersion. R1234yf has similar spray characteristics but smaller dispersion compared with R134a. The maximum effective heat flux for R134a, R404A and R1234yf was determined as 262.1, 407.5 and 225.8 kW/m2 at the spray distances of 25.6, 30.8 and 25.1 mm, respectively. Substituting the environment friendly R1234yf for R134a can remarkably reduce global warming potential by over 1430 times and increase cooling density but insufficient cooling capacity. The effective heat flux of R1234yf can be enhanced by 18.8% by reducing the nozzle diameter and decreasing the back pressure (D = 0.4 mm, Pb = 0.01 MPa). This result is comparable with that of R134a under 1 atm and provides a theoretical basis for R1234yf potential application in clinics.

Numerical simulation of cryogen spray cooling by a three-dimensional hybrid vortex method

Cryogen spray cooling (CSC) can protect the epidermis from unwanted thermal damage during laser dermatological procedures. Numerical simulation of CSC can provide significant guidance for clinical implementation, but relevant research is sparse. Thus, a 3D two-way coupling hybrid vortex method is developed to simulate CSC. The two-way coupling and compressibility effects are implemented by introducing a vorticity source term into the grid. The validity of this algorithm has been confirmed in a previous simulation of the evaporating acetone spray. Comparisons between the simulation results and the R134a spray cooling experimental results demonstrate the accuracy of the present method in analyzing the complex atomization and evaporation. The simulated cooling capacity achieves the maximum experimental value at a spray distance of 26mm, which is close to the optimal spray distance of 30mm in clinical practice. Particulate count reveals that the central area with a radius of 2mm in R134a spray accounts for 74% of the total cooling capacity, which is beneficial for the precise control of the therapy area in laser surgery.

Hybrid Vortex Method for the Aerodynamic Analysis of Wind Turbine

The hybrid vortex method, in which vortex panel method is combined with the viscous-vortex particle method (HPVP), was established to model the wind turbine aerodynamic and relevant numerical procedure program was developed to solve flow equations. The panel method was used to calculate the blade surface vortex sheets and the vortex particle method was employed to simulate the blade wake vortices. As a result of numerical calculations on the flow over a wind turbine, the HPVP method shows significant advantages in accuracy and less computation resource consuming. The validation of the aerodynamic parameters against Phase VI wind turbine experimental data is performed, which shows reasonable agreement.

A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers

We present a validation study for the hybrid particle-mesh vortex method against a pseudo-spectral method for the Taylor–Green vortex at Re Γ = 1600 as well as in the collision of two antiparallel vortex tubes at Re Γ = 10,000. In this study we present diagnostics such as energy spectra and enstrophy as computed by both methods as well as point-wise comparisons of the vorticity field. Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases. For the Taylor–Green vortex, the vorticity contours computed by both methods around the time of the energy dissipation peak overlap. The energy spectrum shows that only the smallest length scales in the flow are not captured by the vortex method. In the second flow case, where we compute the collision of two anti-parallel vortex tubes at Reynolds number 10,000, the vortex method results and the pseudo-spectral method results are in very good agreement up to and including the first reconnection of the tubes. The maximum error in the effective viscosity is about 2.5% for the vortex method and about 1% for the pseudo-spectral method. At later times the flows computed with the different methods show the same qualitative features, but the quantitative agreement on vortical structures is lost.

A hybrid vortex method for the simulation of three‐dimensional flows

AbstractThis paper presents an integral vorticity method for solving three‐dimensional Navier–Stokes equations. A finite volume scheme is implemented to solve the vorticity transport equation, which is discretized on a structured hexahedral mesh. A vortex sheet algorithm is used to enforce the no‐slip boundary condition through a vorticity flux at the boundary. The Biot–Savart integral is evaluated to compute the velocity field, in conjunction with a fast algorithm based on multipole expansion. This method is applied to the simulation of uniform flow past a sphere. Copyright © 2007 John Wiley & Sons, Ltd.

Hybrid vortex method for high Reynolds number flows around three-dimensional complex boundary

The hybrid vortex method, in which the vortex particle method was combined with the vortex sheet method, was extended to flows around a three-dimensional complex geometry boundary at high Reynolds number of O(10 6). The computing domain was decomposed into an interior domain of vortex blobs and a thin numerical boundary layer of vortex sheets. The core radii of shedding blobs were related to the size of the vortex sheets. As the result of numerical experiments on the flow over a ship propeller, the hybrid vortex method was found to be acceptable for simulations of unsteady separated flows around a solid body at high Reynolds number, since the computed results showed reasonable agreement with the measured data.

Topological aspects of three-dimensional wakes behind rotary oscillating cylinders

The development of a three-dimensional viscous incompressible flow generated behind an infinitely long circular cylinder, impulsively started into rectilinear motion and rotationally oscillating, is studied computationally. The numerical scheme, an hybrid vortex method, is used to integrate the velocity–vorticity formulation of the Navier–Stokes equations. The Reynolds number considered is for which the flow becomes spontaneously three-dimensional. The numerical method is explained and its main points are developed. This scheme is then applied to solve some two-dimensional problems, both in order to validate the method and to compute a nominal two-dimensional flow, required to measure the impact of three-dimensionality. The three-dimensional flow past a steady cylinder is also compared to benchmark simulations. Once the flow has become fully three-dimensional, beyond the transient regime and saturation of instabilities, the cylinder begins a rotary oscillation around its axis. Two kinds of rotations are considered: constant amplitude and several frequencies, and constant frequency and various amplitudes. When amplitude and frequency are high enough, the whole flow comes back to its two-dimensional state. This result gives a justification for two-dimensional computations in the literature related to rotating cylinders. For the first super-harmonic frequency of the flow, a parametric study is performed in order to find the impact of the amplitude on the topology of the flow. A bifurcation is clearly identified. Finally, the mechanisms involved in the return to a two-dimensional state are explained: the interaction between transverse instabilities and von Kármán streets is quantified by means of a correlation analysis.

NUMERICAL INVESTIGATION OF A ROTATIONALLY OSCILLATING CYLINDER IN MEAN FLOW

Vortex shedding and the development of a wake behind a rotationally oscillating circular cylinder was investigated using a hybrid vortex method at a Reynolds number of 1000 over a wide range of forcing frequency and amplitude. The normalised peripheral velocity–oscillation amplitude of the cylinder ranged from 0 to 3 while the ratio of forcing frequency to the vortex-shedding frequency from a stationary cylinder varied from 0 to 10. The time-dependent pressure, lift and drag forces exerted on the cylinder were studied together with the flow patterns in the wake. Some behaviours of vortex shedding are revealed and the lock-on range for vortex shedding is obtained. It is found that, in the case of a very low frequency ratio, vortices are shed at a frequency close to that from a stationary cylinder when the amplitude is small; however, the vortices are shed at cylinder-oscillation frequency when the amplitude is large. When the frequency ratio is close to 1, the form of vortex shedding and lock-on exhibit a particularly strong resonance between the flow perturbations and the vortex wake, and the mean value of the drag coefficients increases remarkably. Its maximum value increases with increasing amplitude within the lock-on range and shifts towards the lower frequency end of the lock-on range. When the frequency ratio is greater than a certain value beyond the lock-on range, small-scale vortices are shed at the forcing frequency in the near wake. Subsequently, these vortices coalesce and result in a large-scale antisymmetrical structure in the far wake similar to the Kármán vortex street past a stationary cylinder. The mean value of the drag coefficients decreases in the post lock-on frequency range. The larger the amplitude, the more distinct is the drag coefficient decrease, and the minimum value is lower than that for flow past a stationary cylinder. After the minimum is reached, the drag coefficient increases again with further increase in cylinder-oscillation frequency and approaches the value for the stationary cylinder.

A hybrid vortex method for two-dimensional flow over tube bundles

A hybrid vortex method is presented for computing flows about objects that accurately resolves the boundary layer details while keeping the number of free vortices at a reasonable level. The method uses a wall layer model close to the body surface and discrete vortex blobs in the free wake. Details of the wall layer implementation are presented, and results of sample calculations are compared with known analytical solutions and with calculations from other vortex codes. These results show that the computed boundary layer details are accurate to approximately 0.3 percent of analytical solutions while using three orders of magnitude fewer vortices than other vortex simulations.

Milu-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number Re=1000, 200 and the angular to rectilinear speed ratio a∈(0.5,3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Low Reynolds Number Flows around an Impulsively Started Two-Dimensional Circular Cylinder with Rotation by a Vortex Method.

There are two typical cases in the problem of the two-dimensional unsteady flow past a rotating circular cylinder which is impulsively started. (1) The circular cylinder is impulsively started with rotation from rest and (2) the rotating cylinder is impulsively started. The difference between these two cases is given by the far-field condition. A vortex method is powerful for these problems because the far-field condition is naturally imposed, so the hybrid vortex method combined with a panel method, whose numerical accuracy was tested on low Reynolds number flow around an impulsively started cylinder without rotation in the previous work, is used in the present paper. The detailed results of the flow around the rotating cylinder with a constant anticlockwise angular velocity are shown and we see that there is difference of flow between these initial conditions and its difference does not become clearly small with development of time in the case of high angular velocity, in particular, the difference in drag force does not become clearly small with time although it in lift force becomes small with time.

A HYBRID VORTEX METHOD FOR FLOWS OVER A BLUFF BODY

A hybrid vortex method was developed to simulate the two-dimensional viscous incompressible flows over a bluff body numerically. It is based on a combination of the diffusion–vortex method and the vortex-in-cell method by dividing the flow field into two regions. In the region near the body surface the diffusion–vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior domain. Comparison with results obtained by the finite difference method, other vortex methods and experiments shows that the present method is well adapted to calculate two-dimensional external flows at high Reynolds number. It is capable of calculating not only the global characteristics of the separated flow but also the evolution of the fine structure of the flow field with time precisely. The influence of the grid system and region decomposition on the results will also be discussed. © by 1997 John Wiley & Sons, Ltd.

Numerical study of a linear shear flow past a rotating cylinder

Abstract The effects of shear rate on flow past a rotating circular cylinder in a linear shear flow have been investigated by using a hybrid vortex method at a Reynolds number of 1000. The velocity gradient of the shear flow K ranges from −0.3 to 0.3 and the rotational to translational speed ratio α is 0.5. The results show that the form of vortex shedding is controlled by the shear parameter K . The drag coefficient decreases with increasing | K |. On the other hand, the lift coefficient and Strouhal number increase as K increases. As K increases, the separation positions shift downstream, the wake becomes narrower and the amplitude of fluctuation of the instantaneous lift and drag coefficients decreases.

Far-field condition of vortex methods on an impulsively started two-dimensional circular cylinder with rotation

The far-field condition in the problem of the steady two-dimensional flow past a rotating circular cylinder is well known, but this condition is not clear in the problem of the two-dimensional unsteady flow past a rotating circular cylinder which is impulsively started. In the latter problem, the circulation around a contour of sufficient large radius surrounding the cylinder is dependent on initial conditions: (1) The circular cylinder is impulsively started with rotation from rest and (2) the rotating cylinder is impulsively started. The hybrid vortex method combined with a panel method is used for the flow of a slightly viscous, incompressible fluid around the rotating circular cylinder in the two initial conditions mentioned above. The numerical accuracy of this hybrid method is tested on the flow around an impulsively started cylinder without rotation. The detailed results of the flow around the rotating cylinder with a constant clockwise angular velocity show: (1) The initial shedding vortex is anticlockwise in the former initial case, but it is clockwise in the latter initial case. (2) The growth of the wake depends on the initial condition. (3) The time history of the aerodynamic force is dependent on the initial condition at the early stages of the development but it is almost independent of the initial condition after the early stages.

SEPARATED FLOW ABOUT A TWO-DIMENSIONAL ELLIPSE IN LONGITUDINAL OSCILLATION: FORCES AND VORTEX STRUCTURES

SUMMARY Numerical analysis by a hybrid vortex method is carried out for the flow around a two-dimensional ellipse in harmonic translation at the 30°-angle relative to an oncoming stream. The Reynolds number considered is focused on 1000 and the axis ratio of the ellipse is chosen to be 8:1. The reduced amplitude λ of the harmonic translation ranges from 0.4 to 1.8, while the reduced frequency k¯ ranges from 0.1 to 0.7. The paper aims at analysing how the vortices in the wake contribute to the force and moment coefficients through the vorticity generated around the leading and trailing edges. Lift, drag and moment elements related to corresponding potential flows and the cross product of the velocity and vorticity are proposed for this purpose. Furthermore, it is shown that for a given λ the total lift coefficient averaged over a period of motion attains a maximum at λk¯ ≈ 0.43; the maximum lift coefficient increases with increasing λ. Near-wake flow patterns such as streamlines and vorticity structures co...

An analytical and numerical study of axisymmetric flow around spheroids

Axisymmetric viscous flow around ellipsoids of circular section is studied in detail by the method of matched asymptotic expansion and a deterministic hybrid vortex method. The main feature of the hybrid vortex method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection and stretching. Numerical results are presented for an ellipsoid of axis ratio 2:1 and the limiting case of a sphere at various Reynolds numbers between 100 and 3000. Special consideration is given to the evaluation of the drag coefficient which is computed with three different approaches, denoted by S, P and V respectively. Particular emphasis is placed on the numerical implications and physical significance of each of these different approaches. Comparisons between numerical and analytical results at small times show very close agreement in each case. Separation angles, wake lengths and stationary drag coefficients for the sphere are also found to be in good agreement with previous results by a finite-difference method and with the standard drag curve.

A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method

Impulsively started flow around a circular cylinder at various Reynolds numbers is studied by a deterministic hybrid vortex method. The key feature of the method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection. The vorticity is updated along the surface of the cylinder to satisfy the no-slip condition. The present method is basically different from previous applications of vortex methods, which are primarily in the context of random vortex algorithms. The Reynolds numbers of the flows under investigation range from 300 to 106. Numerical results are compared with analytical solutions at small times, and compared with finite-difference solutions and flow visualization results at relatively long times. Satisfactory agreement is found in the evolutions of the separation angles, wake lengths, surface pressure and drag coefficients, streamline patterns, and some velocities on the axis of symmetry behind the circular cylinder. The present hybrid vortex method is highly stable and suffers from little numerical diffusivity, yielding convincing numerical results for unsteady vortical flows at moderately high Reynolds numbers.

Vortex shedding from an impulsively started rotating and translating circular cylinder

A numerical study is made of the flow past an impulsively started rotating and translating circular cylinder using a hybrid vortex method. The Reynolds number (Re) ranges from 103 to 106 while the (counter-rotating) rotating-to-translating speed ratio (α) is increased from 0 to 2. It is found that three basic patterns of vortex shedding can be identified according to the behaviour of the stagnation points associated with the first upper and the first lower vortices. Depending on the parameters Re and α, the rotation may favour the shedding of the first upper vortex, or the first lower vortex (typically at high Reynolds numbers). In a transition region, strong competition for shedding exists between the first two vortices in the form of double transposition of stagnation (closure) points associated with the two vortices. Time variations of lift coefficients characterize different shedding patterns; the cylinder may first experience a substantial maximal downward lift when the first shedding vortex is from the upper wake, or a maximal upward lift otherwise.

Numerical simulation of flame propagations in circular cylinders

This paper presents a computational method for the solution of the equations for the turbulent combustion of a premixed gas. A random choice method is used for the modeling reaction-diffusion system. A hybrid vortex method is used for solving Navier-Stokes equation which governs the fluid motion. With the assumption of incompressibility, the fluid motion can be uncoupled from the chemistry. The method is applied to a flow past a circular cylinder, which demonstrates an ability to resolve turbulent effects on flame front propagation.