Conservative multiblock Navier-Stokes solver for arbitrarily deforming geometries

Abstract

A new finite volume based thin-layer Navier-Stokes solver for time-dependent compressible flows is described. The implicit, temporally and spatially second-order accurate formulation facilitates the simulation of flows at high Reynolds numbers. Complex, arbitrarily deforming geometries can be handled using fully conservative multiblock structured grids. An iterative time-stepping utilizing a multigrid technique maintains the temporal and spatial accuracy of the basic scheme also at grid block interfaces and solid boundaries. Several test cases have been computed to verify the proper function of the developed code, and the simulations of a transonic buffet and an oscillating supercritical airfoil are presented here. The solver employing the three-level fully implicit time discretization scheme is found to work well in dynamic grids within the limitations of the original formulation. The new code has the desired capabilities, although there is room for improvement in computational efficiency. Nomenclaturerea l P art °f scaled unsteady pressure coefficient, 2;jsin(ft>OCp(Od'/Kr) c = airfoil chord c d , c, = drag and lift coefficients e = total energy per unit volume F = flux vector in a curvilinear grid k = reduced frequency, a>c/(2f/ ao ) M = Mach number n v , n v = Cartesian unit normal components of a cell face p = pressure R = residual Re = Reynolds number S = cell face area T = cycle period t -time U = vector of conservative variables U x -freestream velocity u = convective velocity component u, v = Cartesian velocity components u g , v g = Cartesian velocity components of the grid u n = normal velocity component of the flow V = cell volume v n = normal velocity component of the grid jc, y = spatial coordinates a = instantaneous angle of attack, a + « 0 sin(W) a = average angle of attack a () = angle-of-attack oscillation amplitude ft = parameter defining the implicitness of the temporal discretization y = parameter controlling the time levels in the temporal discretization A/ = physical time step, nondimensionalized by the freestream sonic speed and the airfoil chord AT = volume swept by a cell face during a time step AT = local pseudo-time-step 8U = change in conservative variables in an iteration cycle or a pseudo-time-step p = density a> = angular velocity Subscripts /, j = spatial indices k = summing index mod = modified expression v = viscous 1,2 = cell face endpoints Superscripts k = intermediate solution between n and n + 1 n = time level with the latest known solution n + 1 = new time level with the unknown solution n -1 = time level one step before n

Empirical Design Considerations for Industrial Centrifugal Compressors

“…With the development of computational science and computer hardware, design engineers rely on quality models to establish the physical relationships among diverse thermodynamic, geometric, and fluid dynamic parameters that govern turbomachinery performance [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Although CFD has helped to design many successful industrial compressors and has become an important tool in industrial compressor design, multidomain optimisation is still very time consuming.…”