Numerical Simulation of N-S equations in Cylindrical Coordinate

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Presentation transcript:

Numerical Simulation of N-S equations in Cylindrical Coordinate Kyongmin Yeo

Introduction Flows in Annular pipe Centrifugal Instability Chung & Sung 2005 Flows in Annular pipe Basic Instability pattern in geophysical flows Engineering Application Centrifugal Instability Couette flow Flow around cylinder Marcus & Lee 1998

Governing Equation Continuity equation Momentum equation

Spatial Discretization Spectral Method in θ and z directions Spectral Element Method in r direction

Discretized equations

Temporal Discretization: Nonlinear step Higher-order dual splitting scheme Nonlinear step

Pressure step Galerkin approximation

Pressure Step Pressure boundary condition Velocity correction

Viscous step Galerkin approximation

Fourier Transform 3/2 rule is used for dealiasing 2-dimensional backward transform complex to complex transform in θ direction complex to real transform in z-direction cpu 1 2 3 … cpu 1 2 3 …

Computation Mesh

Centrifugal Couette Flow

Taylor-Couette Instability

Azimuthal Vorticity at Re=500

Azimuthal Vorticity

Azimuthal Vorticity at Re=1000

Azimuthal Vorticity

Couette flow with Moving wall

Re = 400

Oscillating Wall Stokes Layer

Z - Vorticity at Re = 400 & 800

Flow around a cylinder Stokes flow solution

Flow around a cylinder at Re = 10

Flow around a cylinder at Re = 200

Thank you!