Vorticity Confinement Research Articles

Modeling of wake features of a propeller using the vorticity confinement method

The instability and evolution mechanisms of propeller wakes are of vital significance to the development of next-generation propulsion devices with better hydrodynamic and noise performances. The temporal–spatial scales and the vortex details are important for the understanding of the vortex features and their dynamic responses to the propeller. In the present study, the vorticity confinement (VC) method was employed on the numerical simulations achieved by the improved delay detached eddy simulation with various advance coefficients to characterize the underlying features of wake flows. Comparisons were made between the results computed with and without the VC model from different perspectives. The analyses showed that the VC method captures more high-frequency power spectral density results as well as more small-scale vortical topology on the far downstream field based on the same spatial resolution and indicates the multi-scale interference on the tip vortex evolutionary trajectories. The VC method also elucidates rich small vortical structures with low advance coefficient and elliptical instability with high advance coefficient. This paper further widens our knowledge on the propeller wake evolution mechanisms and highlights the value of the VC method in the investigation of propeller wakes.

Assessment of the Vortex Feature-Based Vorticity Confinement Method Applied to Rotor Aerodynamics and Aeroacoustics

The accurate prediction of helicopter rotor aerodynamics and aeroacoustics using Computational Fluid Dynamics (CFD) techniques still remains a challenge, as the over-dissipation of numerical schemes results in a higher diffusive rate of rotor wake and vortices than what can be expected from the fluid governing equations. To alleviate this issue, a vortex feature-based vorticity confinement (FVC2-L2) method that combines the locally normalized λ2 vortex detection method with the standard second vorticity confinement (VC2) scheme is presented to counterbalance the truncation error introduced by the numerical discretization of the convective term while avoiding the over-confinement inside the boundary layer. The FVC2-L2 scheme is adopted for helicopter rotor aerodynamic and aeroacoustic predictions through its implementation in the multi-block structured grid CFD solver ROSITA and coupling with the aeroacoustic code ROCAAP based on the permeable surface Ffowcs Williams–Hawkings (PS-FWH) equation. This approach is assessed in helicopter rotor flows via three databases. Firstly, the well-documented HART-II rotor in the baseline condition is used to evaluate the capability of the presented VC scheme in blade–vortex interaction (BVI) phenomena prediction. Subsequently, the UH-1H non-lifting hovering rotor and the AH-1/OLS low-speed descending flight rotor are adopted for assessment of such a method in aeroacoustics. The benefits of the FVC2-L2 scheme in terms of aerodynamics prediction, wake preservation, and noise signal prediction are well demonstrated by comparison with the experimental data and the results obtained without VC schemes. Particularly, the FVC2-L2 scheme mainly improves the highly unsteady airloads prediction, and results in an improvement of BVI noise prediction by more than 5 dB with respect to the case without VC schemes for AH-1/OLS rotor case. Additionally, some shortcomings of the approach are noticed in engineering applications. On the basis of a simplified convective vortex, some provisional guidelines on the required εo value in terms of number of cells per vortex diameter are provided: an εo value ranging from 0.01 to 0.04 for grids which may represent the vortex core diameter with 6 to 12 cells.

Analysis of a higher-order vorticity confinement scheme in flux correction form

This article presents a detailed comparison of the classical source-term formulation of higher-order Vorticity Confinement with a flux-correction version, through an application to a series of well-documented cases. Both formulations and their numerical implementation are presented first. Then the methods are applied to the simple case of the long-time advection of an inviscid and isentropic vortex. A shock-vortex interaction case is also computed to demonstrate the compatibility of the method with the shock-capturing properties of the baseline scheme. Both methods are finally applied to a ZDES mode 3 (Wall-Modelled LES) simulation of a zero-pressure-gradient flat-plate turbulent boundary layer, showing a better preservation of smaller-scale vortical structures with respect to standard higher-order numerical schemes. Furthermore, the flux-correction form of Vorticity Confinement significantly improves the prediction of skin friction with respect to both the baseline scheme and the classical source-term formulation, thus showing that the flux-correction form of confinement is essential for a reliable prediction of this quantity.

Vorticity Confinement Technique and Blade Element Method for Accurate Propeller Modelling

Traditional CFD techniques are not effective in preserving wakes and vortices over larger distances and for longer times. Vorticity Confinement (VC) technique helps counter the numerical diffusion to preserve wakes and vortices. In the current study, VC was used to accurately model the propeller flow using two different propeller modelling techniques after being implemented into SU2, an open-source CFD solver. One resolves flow past the propeller by solving RANS equations in a rotating reference frame. Another is a simplified propeller modelling technique in which the propeller needs to be modelled as a disk, and the propeller loading is determined using the blade element method. In the first case, VC enabled tip and hub vortices to convect over larger distances from the propeller, along with an improved resolution of gradients in the tip vortex. With the latter technique, VC helped conserve the tangential velocities for longer distances.

Numerical investigations of the vortex feature-based vorticity confinement models for the assessment in three-dimensional vortex-dominated flows

In order to improve the vortex resolution in aerodynamic wakes, a locally normalized vortex feature-based vorticity confinement method is implemented into the multi-block, structured computational fluid dynamics solver (ROSITA). In this method, the second vorticity confinement (VC2) scheme with two well-known vortex feature detection methods (non-dimensional Q criterion, non-dimensional lambda _2 criterion) is employed to counterbalance the truncation error introduced by the numerical discretization of the convective term. The flow field of two benchmark three-dimensional steady vortex-dominated cases, the NACA0015 wing and the Caradonna–Tung hovering rotor, is simulated with the implemented method. The improvements in aerodynamics prediction, vorticity preservation, computational stability, and efficiency are demonstrated. From the numerical results, the vortex feature-based confinement models significantly improve the computational stability, the aerodynamic loads prediction and vorticity preservation capability, especially for the lambda _2–based VC2 model. In addition, it allows the use of higher confinement parameters on a coarse grid with a relatively higher computational efficiency to obtain better results than those of a finer grid.

Vorticity Confinement Applied to Accurate Prediction of Convection of Wing Tip Vortices and Induced Drag

The vorticity confinement (VC) method was applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined by its application to tip vortices shed by 3-D stationary and rotating wings. The VC was used with a total variation diminishing (TVD) approach to reduce the needed confinement. The TVD minmod and differentiable flux limiters were tested to evaluate their effect on the VC parameter. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for induced drag generated by 3-D wing. The VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.

Compensating the vorticity loss during advection with an adaptive vorticity confinement force

AbstractThe advection step in grid‐based fluid simulation is prone to numerical dissipation, which results in loss of detail. How to improve the advection accuracy to preserve more fluid details is still challenging. On the other hand, a common way to enhance smoke details is to use vorticity confinement. However, most of the previous methods simply used a fine‐tuned scale factor ε to adjust the strength of the confinement force, which can only amplify existing vortex details and is easy to cause instability when ε is large. In this article, we proposed an adaptive vorticity confinement method, which does not suffer from the above problems, to compensate the vorticity loss during advection with little extra cost. The main idea is to first calculate a scale factor whose value depends on the vorticity loss during advection, and then use it to adaptively control the vorticity confinement force for vorticity compensation with high stability. The experiment results show the effectiveness and efficiency of our method.

Combined Vorticity Confinement and TVD Approaches for Accurate Vortex Modelling

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to convected and stationary vortices. The optimal VC parameter was determined by application to 2-D vortices. The conservativity of the scheme is investigated in terms of kinetic energy and momentum. Grid convergence study was conducted for the range of grid steps. The log–log plot of the error shows that the second-order upwind scheme with the VC nearly reaches the 4th order of accuracy for the wide range of grid cell sizes. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method and prevention of over-confinement.

A Numerical Study on Fluid Flow and Acoustic Characteristics of a Supersonic Impinging Jet Using Vorticity Confinement

The objective of this work is to numerically study the fluid flow and acoustic field of a supersonic impinging jet by applying the vorticity confinement (VC) method. For this aim, the three-dimensional compressible Navier-Stokes equations with the incorporation of the VC method are considered and the resulting system of equations is solved by using the sixth-order compact finite-difference scheme. To eliminate the numerical instability, a low-pass high-order filter is used. The nonreflective boundary conditions are applied for all the free boundaries and the radiated sound field is obtained by the Kirchhoff surface integration. Comparisons of the present results with the experimental data and other numerical simulations show that the solution methodology adopted based on the application of the VC method with the high-order compact finite-difference scheme provides a good prediction of the fluid flow and the acoustic field of the impingement region on coarser grids than that usually required in the LESs, and thus, the calculations of coarse grid LESs are improved.

Prediction of fluid flow and acoustic field of a supersonic jet using vorticity confinement.

In this study, the numerical simulation of the fluid flow and acoustic field of a supersonic jet is performed by using high-order discretization and the vorticity confinement (VC) method on coarse grids. The three-dimensional Navier-Stokes equations are considered in the generalized curvilinear coordinate system and the high-order compact finite-difference scheme is applied for the space discretization, and the time integration is performed by the fourth-order Runge-Kutta scheme. A low-pass high-order filter is applied to stabilize the numerical solution. The non-reflecting boundary conditions are adopted for all the free boundaries, and the Kirchhoff surface integration is utilized to obtain the far-field sound pressure levels in a number of observer locations. Comparisons of the jet mean flow and jet aeroacoustics results with the other numerical and experimental data at similar flow conditions are made and show a reasonable agreement. The study shows that the proposed solution methodology based on the high-order compact finite-difference scheme in conjunction with the VC method can reasonably predict the near-field flow and the far-field noise of high Reynolds number jets with a fairly coarser grid than that used in the large eddy simulations and, thus, the computational cost can be significantly decreased.

Improvement of Compressible Vorticity Confinement Method by Combining It with Vortex Feature Detection Methods

Improvement of Compressible Vorticity Confinement Method by Combining It with Vortex Feature Detection Methods

Real-time smoke simulation based on vorticity preserving lattice Boltzmann method

It is crucial to achieve high efficiency and to preserve fine-grid details in 3D interactive smoke simulation. In this paper, we present a vorticity preserving lattice Boltzmann method (VPLBM) to simulate high-resolution motion of smoke in real time. We design the method based on lattice Boltzmann method (LBM), which is parallelism-friendly, to ensure the efficiency on parallel computing devices such as graphic processing units (GPUs). To resolve the vorticity dissipation issue in LBM, we further propose an LBM-based vorticity transport method which tracks the magnitude of vorticity during the simulation. We apply vorticity confinement according to the tracked vorticity, and therefore, our method can preserve the detailed motion of smoke. Our method is forward-iterative and contains three weakly dependent distribution functions: two for thermal LBM and one for vorticity tracking. Finally, we show an implementation of a parallel smoke simulator integrating VPLBM method on a dual-GPU platform. Using a fast ray marching method, the simulator shows realistic visual effect and achieves 157.3 frames per second on a $$64 \times 64 \times 128$$ fine grid.

Towards unification of the Vorticity Confinement and Shock Capturing (TVD and ENO/WENO) methods

New multidimensional extensions of the TVD and finite difference ENO/WENO methods for the compressible flow equations are proposed. The novelty of the approach is in the discretization schemes that acquire by means of a single mechanism both shock-capturing and vorticity confinement capabilities. Thus, the new method can be interpreted as a unification of the two methodologies, intended initially for different purposes.

Comparison of different approaches tracking a wing-tip vortex

This paper compares the performance of different grid based and grid free modelling approaches to predict the tip vortex evolution in both near and far wing wake fields. The grid based methods cover different turbulence modelling approaches, adaptive mesh refinement and the adaptive vorticity confinement (VC) method using the OpenFOAM code. Computational vortex method (CVM) coupled with the OpenFOAM simulation of the near field is utilised to properly predict the tip vortex behaviour in the far field. All simulation results are compared to results of the wind tunnel experiments conducted by Devenport et al. (1996). The comparison is based on the analysis of the vortex core parameters: the core size, the peak tangential velocity and the axial velocity deficit. Additionally, the results are compared with another numerical study by Wells (2009, 2010). It turns out that turbulence modelling plays an important role since simple one and two-equation models overpredict the turbulence intensity in the vortex core resulting in its fast decay. The potential of the adaptive VC method depends on the underlying turbulence model. Grid free vortex method shows a good potential to improve the simulation accuracy.

On Coarse Grids Simulation of Compressible Mixing Layer Flows Using Vorticity Confinement

In this work, the capability and performance of the vorticity confinement (VC) implemented in a high-order accurate flow solver in predicting two-dimensional (2D) compressible mixing layer flows on coarse grids are investigated. Here, the system of governing equations with incorporation of the VC in the formulation is numerically solved by the fourth-order compact finite difference scheme. To stabilize the numerical solution, a low-pass high-order filter is applied, and the nonreflective boundary conditions are used at the farfield and outflow boundaries to minimize the reflections. At first, the numerical results without applying the VC are validated by available direct numerical simulations (DNSs) for a low Reynolds number mixing layer. Then, the calculations using a range of VC levels are performed for a high Reynolds number mixing layer and the results are thoroughly compared with those of available large eddy simulations (LESs). The study shows that, with applying the vortex identification method, more accurate results are obtained in the slow laminar region of the mixing layer. A sensitivity study is also performed to examine the effect of different numerical parameters to reasonably provide more accurate results. It is shown that the local VC introduced based on the artificial viscosity coefficient and the vorticity thickness can improve the accuracy of the results in the turbulent region of the mixing layer compared with those of LESs. It is found that the solution methodology proposed can reasonably preserve the vortices in the flowfield and the results are comparable with those of LESs on fairly coarser grids and thus the computational costs can be considerably decreased.

Development and analysis of high-order vorticity confinement schemes

Abstract High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate computation of vortical flows, following the VC2 conservative formulation of Steinhoff. First, a high-order formulation of VC is presented for the case of the linear transport equation for decoupled schemes in space and time. A spectral analysis shows that the new nonlinear schemes have improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. For the Euler and Navier–Stokes equations, the original VC method is extended to 3rd- and 5th-order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1st-order method and is suitable for application to high-order numerical simulations. The high-order extensions remain both independent of the choice of baseline numerical scheme and rotationally invariant since they are based on the Laplace operator. Numerical tests validate the increased order of accuracy, vorticity-preserving capability and compatibility of the VC extensions with high-order methods.

A vorticity confinement model applied to URANS and LES simulations of a wing-tip vortex in the near-field

In this study, the near-field (up to three chord lengths) development of a wing-tip vortex is numerically investigated at two angles of attack (five and ten degrees). The application of a vorticity confinement model to an Unsteady Reynolds averaged Navier–Stokes (URANS) model and Large Eddy Simulation (LES) is examined with the focus of preventing the rapid dissipation of vorticity in a wing-tip vortex. Vortex core size and trajectory were predicted well by the LES model, whereas the URANS model predicted a large vortex core, which remained constant with downstream distance. The LES model correctly predicted the jet-like axial velocity for an angle of attack of ten degrees and the LES and experimental axial velocity excess had the same value of 111% of free-stream velocity at two chord lengths downstream. The LES model predicted the turbulence in the vortex reasonably well as the maximum turbulent root mean square (rms) velocities were within 15% and 35% of experimental values at two and three chord lengths downstream for angles of attack of ten and five degrees respectively. The URANS model predicted the mean flow for an angle of attack of five degrees reasonably well but greatly under-predicted the mean flow for an angle of attack of ten degrees and the turbulence levels at all downstream locations.

Development of a third-order accurate vorticity confinement scheme

A new 3rd-order Vorticity Confinement scheme is presented as an extension of the original VC2 scheme developed by Steinhoff for the resolution of the fluid dynamic equations. The theoretical developments are explained, and the method is tested. The results obtained show that the new scheme combines the accuracy of the underlying higher order scheme and the confinement capability of the original VC2 method.

Tracking a Tip Vortex with Adaptive Vorticity Confinement and Hybrid RANS-LES

The prediction of coherent vortices with standard RANS solvers suffers especially from discretisation and modelling errors which both introduce numerical diffusion. The adaptive Vorticity Confinement (VC) method targets to counteract one part of the discretisation error: the one due to the discretisation of the convection term. This method is applied in conjunction with a hybrid RANS-LES turbulence model to overcome the overprediction of turbulence intensity inside vortex cores which is a typical deficiency of common RANS solvers. The third main source for numerical diffusion originates from the spatial discretisation of the solution domain in the vicinity of the vortex core. The corresponding error is analysed within a grid convergence study. A modification of the adaptive VC method used in conjunction with a high-order discretisation of the convection term is presented and proves to be superior. The simulations of a wing tip vortex flow are validated in terms of vortex velocity profiles using the results of a wind tunnel experiment performed by Devenport and colleagues (1996). Besides, the results are compared with another numerical study by Wells (2009) who uses a Reynolds Stress turbulence model. It turns out that the application of the modified adaptive VC method on the one hand reinforces the tip vortex, and on the other hand accelerates the axial flow which leads to a slight degradation compared to the experimental results. The result of Wells is more accurate close to the wing, but the result obtained here is superior further downstream as no excessive diffusion of the tip vortex occurs.

On application of high-order compact finite-difference schemes to compressible vorticity confinement method

The main goal of this study is to assess the application of high-order compact finite-difference schemes for the solution of the Euler equations in conjunction with the compressible vorticity confinement method on both uniform Cartesian and curvilinear grids. Here, the spatial discretization of the governing equations is performed by the fourth-order compact finite-difference scheme and the temporal term is discretized by the fourth-order Runge–Kutta method. To stabilize the numerical solution, appropriate dissipation terms are applied and a detail assessment is performed to study the effects of the values of confinement and dissipation coefficients on the solution to reasonably preserve the structure of vortical flows. The accuracy and performance of the proposed solution procedure by applying the fourth-order compact finite-difference scheme are also examined by comparison with the solution obtained by the second-order central finite-difference scheme. Low-pass high-order filters are also applied to the fourth-order compact finite-difference scheme to investigate the performance of the vorticity confinement with the filtering scheme. The advection of a 2D isentropic vortex and a shock–vortex interaction problem are two test cases simulated for the assessment of the present solution methodology. The study shows that the high-order compact finite-difference schemes in conjunction with the vorticity confinement method can reasonably preserve the structure of vortical flows in coarse uniform Cartesian and curvilinear grids. Indications are that the present solution methodology is accurate and effective for solving compressible flow problems with vortical structures when coarse grids are used.