A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretization in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretize the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretization. Numerical results obtained for the rotor/stator cavity compare favorably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.
Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method
University of Surrey,
Thermo-Fluid Systems University
University of Surrey,
Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 16, 2016; final manuscript received October 7, 2016; published online February 14, 2017. Editor: David Wisler.
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Pitz, D. B., Chew, J. W., Marxen, O., and Hills, N. J. (February 14, 2017). "Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method." ASME. J. Eng. Gas Turbines Power. July 2017; 139(7): 072602. https://doi.org/10.1115/1.4035593
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