Treatment of Vortical Flow Using Vorticity Confinement

Steinhoff, John; Lynn, Nicholas

doi:10.1142/9789812703187_0010

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…Other possibilities exist besides the harmonic mean for the formulation of the confinement term [27,19], under the restriction that the function is nonlinear [16], but the investigation of such alternatives lies outside the scope of the present work.…”

Section: One-dimensional Scalar Formulationmentioning

confidence: 99%

“…17with Eq. (13), can be investigated by taking the curl of the developed scheme, which corresponds to the vorticity transport equation (16). In the case of an isolated 2D vortex in inviscid flow:…”

Section: Euler/navier-stokes Equationsmentioning

confidence: 99%

“…Such an alternative is the Vorticity Confinement (VC) method proposed by J. Steinhoff [16,17,18], designed to capture small-scale features directly on the computational grid. In the present work, we are working with the second (VC2) formulation [19,20] of the method to ensure discrete momentum conservation.…”

Section: Introductionmentioning

confidence: 99%

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Development and analysis of high-order vorticity confinement schemes

2017

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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 3 rd-and 5 th-order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1 st-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.

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Section: One-dimensional Scalar Formulationmentioning

confidence: 99%

Section: Euler/navier-stokes Equationsmentioning

confidence: 99%

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Development and analysis of high-order vorticity confinement schemes

2017

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“…Another methodology for wake conservation is the Vorticity Confinement (VC) technique of Steinhoff and Lynn (2006). It consists of introducing an additional term in the momentum equation in order to counteract the effect of numerical diffusion.…”

Section: A Rotor In Hovermentioning

confidence: 99%

Rotorcraft simulations: a challenge for CFD

Costes

Renaud

Rodriguez

2012

International Journal of Computational Fluid Dynamics

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This paper gives an overview of CFD techniques developed and used at ONERA for rotorcraft applications. First, the complex multidisciplinary environment around helicopters, in which aerodynamics, flight dynamics, aeroelasticity and aeroacoustics strongly interact, is highlighted. Rotorcraft simulations are thus performed by comprehensive codes capable of dealing with the whole system efficiently, using integrated simplified models for each discipline, e.g. the aerodynamics. However, fast aerodynamic models cannot accurately represent the full complexity of rotorcraft aerodynamics, in particular as far as nonlinear phenomena are concerned, contrary to CFD. Nevertheless, helicopter problems are particularly demanding for numerical methods, requiring efficient simulation of unsteady flows with shock waves, massive flow separation, concentrated vortex structures and deforming bodies with large amplitude relative motion, while allowing fine description and analysis of local flow phenomena impacting the vehicle behaviour. Helicopter trim in the CFD solution is obtained by iterative coupling with comprehensive analysis, so that the global multidisciplinary simulation can be achieved with an advanced aerodynamic model. The approaches taken by ONERA for the comprehensive code and the CFD solvers are outlined in the paper. Examples of applications typical of rotorcraft problems are given to illustrate current possibilities and difficulties. They include an isolated rotor in hover, the dynamic stall of an oscillating wing, an isolated rotor in descent flight with BladeVortex Interactions, the dynamic-aerodynamic coupling of a rotor in high-speed forward flight and the simulation of a complete helicopter in forward flight. Finally, expected and needed developments are reviewed in order to make CFD a more efficient tool in the design office of helicopter manufacturers.

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“…These can be solvers of the vorticity-velocity formulation of the Navier-Stokes equations 12,13 or numerical schemes ensuring that no dissipation term is introduced in the discrete vorticity transport equation. 14,15 Another technique is the Vorticity Confinement (VC) method of Steinhoff [16][17][18] designed to capture small-scale features of high-Reynolds number vortical flows by introducing a negative dissipation term in the flow equations to balance the excess dissipation in vortical regions. This method has been widely applied in the aeronautics field, its important advantage being that it is formulated independently of the baseline numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

Vortical flow calculations using a high-order Vorticity Confinement method

Petropoulos¹,

Costes²,

Cinnella

2017

23rd AIAA Computational Fluid Dynamics Conference

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A high-order Vorticity Confinement (VC) method is applied to the calculation of compressible vortical flows. High-order extensions of the VC methodology have been developed for the Navier-Stokes equations using a methodology that remains independent of the baseline numerical scheme, as the original VC formulation of Steinhoff. The VC method is primarily oriented towards the accurate calculation of cases involving the advection of vortical structures (e.g. wakes), allowing their propagation over long distances with low numerical dissipation. The present work however mainly investigates their applicability to the simulation of turbulent flows, where the improvement in the preservation of vortical structures shows great interest. High-order VC schemes were found to be consistent with complex vortical flow dynamics without the need of special treatment to accommodate the vortex interaction mechanisms characteristic of turbulent flows. Furthermore, they were found to consistently improve the resolvability of baseline FE-MUSCL schemes for reasonable values of the confinement parameter ε, close to the value of the high-order artificial dissipation coefficient. Last, the dependence of the solution on the confinement parameter µ was found to be moderate for the values and cases investigated in this paper.

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Treatment of Vortical Flow Using Vorticity Confinement

Cited by 5 publications

References 12 publications

Development and analysis of high-order vorticity confinement schemes

Development and analysis of high-order vorticity confinement schemes

Rotorcraft simulations: a challenge for CFD

Vortical flow calculations using a high-order Vorticity Confinement method

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