An Additive Turbulent Decomposition of the Navier-Stokes Equations Implemented on Highly Parallel Computer Systems

1991 ◽  
Author(s):  
J. M. McDonough ◽  
E. C. Hylin ◽  
Tony F. Chan ◽  
Matthew T. Chan ◽  
Y. Yang ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Computer Systems ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Navier Stokes Equations

An Additive Turbulent Decomposition of the Navier-Stokes Equations Implemented on Highly Parallel Computer Systems

1990 ◽  
Author(s):  
J. M. McDonough ◽  
E. C. Hylin ◽  
Ivan Catton ◽  
Tony F. Chan ◽  
T. Mathew
Keyword(s):  
Stokes Equations ◽  
Computer Systems ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

scholarly journals Supersonic turbulent flow simulation using a scalable parallel modal discontinuous Galerkin numerical method

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tomas Houba ◽  
Arnob Dasgupta ◽  
Shivasubramanian Gopalakrishnan ◽  
Ryan Gosse ◽  
Subrata Roy
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Performance Study ◽  
Navier Stokes Equations ◽  
Flow Simulations

Abstract The scalability and efficiency of numerical methods on parallel computer architectures is of prime importance as we march towards exascale computing. Classical methods like finite difference schemes and finite volume methods have inherent roadblocks in their mathematical construction to achieve good scalability. These methods are popularly used to solve the Navier-Stokes equations for fluid flow simulations. The discontinuous Galerkin family of methods for solving continuum partial differential equations has shown promise in realizing parallel efficiency and scalability when approaching petascale computations. In this paper an explicit modal discontinuous Galerkin (DG) method utilizing Implicit Large Eddy Simulation (ILES) is proposed for unsteady turbulent flow simulations involving the three-dimensional Navier-Stokes equations. A study of the method was performed for the Taylor-Green vortex case at a Reynolds number ranging from 100 to 1600. The polynomial order P = 2 (third order accurate) was found to closely match the Direct Navier-Stokes (DNS) results for all Reynolds numbers tested outside of Re = 1600, which had a normalized RMS error of 3.43 × 10−4 in the dissipation rate for a 603 element mesh. The scalability and performance study of the method was then conducted for a Reynolds number of 1600 for polynomials orders from P = 2 to P = 6. The highest order polynomial that was tested (P = 6) was found to have the most efficient scalability using both the MPI and OpenMP implementations.

Direct Numerical Simulation of Turbulent Rayleigh-Be´nard Convection Using a Higher Order Scheme

2007 ◽  
Author(s):  
A. K. De ◽  
V. Eswaran
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Stokes Equations ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Higher Order Scheme ◽  
Velocity Variances ◽  
Boussinesq Fluid

In the present paper a Direct Numerical Simulation of turbulent Rayleigh-Be´nard convection of a Boussinesq fluid with Prandtl number 0.7 in a 6 : 6 : 1 aspect ratio box at Ra = 2.106 is attempted. The incompressible Navier-Stokes equations are solved on non-uniform cartesian grids using a finite difference method with a high resolution convective scheme and 2nd order Adams-Bashforth Crank-Nicolson (ABCN) time-stepping. The numerical simulation is conducted on a parallel computer. We observed that temperature and velocity variances lead to different length and temperature scales. Negative skewnesses of vertical velocity and its derivative are observed. A non-uniform distribution of temperature near the surface proceeds to an exponential like variation in the center via an intermediate region outside the surface layer. Instantaneous snapshots of the flow field reveal intense sheet-like structures near the surface layers becoming plumes in the middle region. In the vertical cross-sectional planes, strong shearing effect near the surfaces, horizontal spreading and induction of plumes are observed.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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