Crank-Nicolson Scheme for Solving Low Mach Number Unsteady Viscous Flows Using an Implicit Preconditioned Dual Time Stepping Technique

A set of perturbed compressible equations(PCE), based on a hydrodynamic/acoustic splitting method, is proposed for aeroacoustic noise prediction of low Mach number viscous flows. The present formulation corrects the deficiency of previous splitting methods that have no control over the coupling effects between the incompressible vorticity and the perturbed velocities. The validation test shows that the present PCE solution is in excellent agreement with those of direct acoustic numerical simulation(DaNS) and Curle's acoustic analogy for a laminar dipole tone from a 2D circular cylinder at Reynolds number based on the cylinder diameter, ReD=200 and free stream Mach number, M∞ = 0.3. Computational efficiency and accuracy requirements for PCE are also investigated for a vortex scattering noise from the trailing-edge of a thin plate at Reynolds number based on the plate thickness, Reh= 2000 and M∞ = 0.3. The test results indicate that the computational efficiency can be achieved with an acoustic grid at lower resolution, as long as the projection quality of the total derivative of the incompressible pressure, DP/Dt field is retained.

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A Global Preconditioning Method for Low Mach Number Viscous Flows in Rotating Machinery

Volume 6: Turbomachinery, Parts A and B ◽

10.1115/gt2006-91189 ◽

2006 ◽

Cited By ~ 1

Author(s):

Chunhua Sheng ◽

Xiao Wang

Keyword(s):

Mach Number ◽

Rotational Speed ◽

Stokes Equations ◽

Viscous Flows ◽

Rotating Machinery ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Low Mach Number ◽

Low Speed ◽

Preconditioning Method

A preconditioning scheme is applied to a compressible turbomachinery flow solver MSU-TURBO for simulating viscous flows at low Mach number and incompressible region. The Navier-Stokes equations are cast in a non-inertial rotating frame. A constant diagonal preconditioning matrix is applied to the conservative form of the governing equations, which contains a single parameter depending on the reference Mach number and rotational speed of the relative frame. The effect of the rotational speed on preconditioned scheme is numerically investigated for two low speed viscous flows in rotating machinery, a NASA low speed centrifugal compressor (LSCC) and a marine propeller (P5168). Computations are compared against the original MSU-TURBO solutions, and suggestions are provided for computing the low Mach number flows in rotating turbomachinery using the preconditioned TURBO solver.

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Unsteady Flow past a Combined Pitching and Plunging Aerofoil Using an Implicit RANS Solver

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.3481 ◽

2011 ◽

Vol 110-116 ◽

pp. 3481-3488 ◽

Cited By ~ 1

Author(s):

K. Siva Kumar ◽

Sharanappa V. Sajjan

Keyword(s):

Nodal Point ◽

Navier Stokes ◽

Aerodynamic Coefficients ◽

Low Mach Number ◽

Time Stepping ◽

Flow Past ◽

Dual Time Stepping ◽

Number Flow ◽

Naca 0012 ◽

Low Mach Number Flow

Unsteady Reynolds-averaged Navier-Stokes (RANS) computations are presented for low Mach number flow past a combined pitching and plunging NACA 0012 aerofoil. The Implicit RANS solver used for obtaining time-accurate solutions is based on a finite volume nodal point spatial discretization scheme with dual time stepping. The aim is to validate the unsteady solver for flapping motion of the aerofoil. Results are presented in the form of aerodynamic coefficients and compared with available literature, thus demonstrating the capability of the solver to provide useful unsteady input data for aeroelastic and aeroacoustic analysis.

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