Numerical issues in higher-order accurate simulations of flows with vortex cavitation

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Abstract

This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

Original languageEnglish
Title of host publication11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
EditorsAntonio Huerta, Eugenio Onate, Xavier Oliver
PublisherInternational Center for Numerical Methods in Engineering
Pages4765-4778
Number of pages14
ISBN (Electronic)9788494284472
Publication statusPublished - 1 Jul 2014
EventJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain
Duration: 20 Jul 201425 Jul 2014
http://congress.cimne.com/iacm-eccomas2014/

Conference

ConferenceJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014
CountrySpain
CityBarcelona
Period20/07/1425/07/14
Internet address

Fingerprint

Cavitation
Limiters
Vortex flow
Thermodynamics
Hydrofoils
Compressible flow
Euler equations
Computational methods
Equations of state
Two phase flow
Phase transitions
Vapors
Fluxes
Computer simulation
Liquids
Gases
Costs

Keywords

  • Cavitation
  • Positivity-preserving
  • Vortex dynamics
  • WENO

Cite this

Khatami, F., van der Weide, E. T. A., & Hoeijmakers, H. W. M. (2014). Numerical issues in higher-order accurate simulations of flows with vortex cavitation. In A. Huerta, E. Onate, & X. Oliver (Eds.), 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 (pp. 4765-4778). International Center for Numerical Methods in Engineering.
Khatami, Faraz ; van der Weide, Edwin T.A. ; Hoeijmakers, Harry W.M. / Numerical issues in higher-order accurate simulations of flows with vortex cavitation. 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. editor / Antonio Huerta ; Eugenio Onate ; Xavier Oliver. International Center for Numerical Methods in Engineering, 2014. pp. 4765-4778
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Khatami, F, van der Weide, ETA & Hoeijmakers, HWM 2014, Numerical issues in higher-order accurate simulations of flows with vortex cavitation. in A Huerta, E Onate & X Oliver (eds), 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering, pp. 4765-4778, Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014, Barcelona, Spain, 20/07/14.

Numerical issues in higher-order accurate simulations of flows with vortex cavitation. / Khatami, Faraz; van der Weide, Edwin T.A.; Hoeijmakers, Harry W.M.

11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. ed. / Antonio Huerta; Eugenio Onate; Xavier Oliver. International Center for Numerical Methods in Engineering, 2014. p. 4765-4778.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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T1 - Numerical issues in higher-order accurate simulations of flows with vortex cavitation

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AU - van der Weide, Edwin T.A.

AU - Hoeijmakers, Harry W.M.

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N2 - This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

AB - This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

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KW - Vortex dynamics

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M3 - Conference contribution

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PB - International Center for Numerical Methods in Engineering

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Khatami F, van der Weide ETA, Hoeijmakers HWM. Numerical issues in higher-order accurate simulations of flows with vortex cavitation. In Huerta A, Onate E, Oliver X, editors, 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014. International Center for Numerical Methods in Engineering. 2014. p. 4765-4778