Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbo-machinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved by a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage scheme. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool

Comparison of two- and three-dimensional flow computations with laser anemometer measurements in a transonic compressor rotor

Two and three dimensional inviscid solutions for the flow in a transonic axial compressor rotor at design speed are compared with probe and laser anemometers measurements at near-stall and maximum-flow operating points. Experimental details of the laser anemometer system and computational details of the two dimensional axisymmetric code and three dimensional Euler code are described. Comparisons are made between relative Mach number and flow angle contours, shock location, and shock strength. A procedure for using an efficient axisymmetric code to generate downstream pressure input for computationally expensive Euler codes is discussed. A film supplement shows the calculations of the two operating points with the time-marching Euler code

Finite element analysis of inviscid subsonic boattail flow

A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed

Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm

A multiple-grid algorithm for use in efficiently obtaining steady solutions to the Euler and Navier-Stokes equations is presented. The convergence of the explicit MacCormack algorithm on a fine grid is accelerated by propagating transients from the domain using a sequence of successively coarser grids. Both the fine and coarse grid schemes are readily vectorizable. The combination of multiple-gridding and vectorization results in substantially reduced computational times for the numerical solution of a wide range of flow problems. Results are presented for subsonic, transonic, and supersonic inviscid flows and for subsonic attached and separated laminar viscous flows. Work reduction factors over a scalar, single-grid algorithm range as high as 76.8

An algebraic turbulence model for three-dimensional viscous flows

An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number

Calculation of tip clearance effects in a transonic compressor rotor

The flow through the tip clearance region of a transonic compressor rotor (NASA rotor 37) was computed and compared to aerodynamic probe and laser anemometer data. Tip clearance effects were modeled both by gridding the clearance gap and by using a simple periodicity model across the ungridded gap. The simple model was run with both the full gap height, and with half the gap height to simulate a vena-contracta effect. Comparisons between computed and measured performance maps and downstream profiles were used to validate the models and to assess the effects of gap height on the simple clearance model. Recommendations were made concerning the use of the simple clearance model. Detailed comparisons were made between the gridded clearance gap solution and the laser anemometer data near the tip at two operating points. The computer results agreed fairly well with the data but overpredicted the extent of the casing separation and underpredicted the wake decay rate. The computations were then used to describe the interaction of the tip vortex, the passage shock, and the casing boundary layer

SWIFT Code Assessment for Two Similar Transonic Compressors

One goal of the NASA Fundamental Aeronautics Program is the assessment of computational fluid dynamic (CFD) codes used for the design and analysis of many aerospace systems. This paper describes the assessment of the SWIFT turbomachinery analysis code for two similar transonic compressors, NASA rotor 37 and stage 35. The two rotors have identical blade profiles on the front, transonic half of the blade but rotor 37 has more camber aft of the shock. Thus the two rotors have the same shock structure and choking flow but rotor 37 produces a higher pressure ratio. The two compressors and experimental data are described here briefly. Rotor 37 was also used for test cases organized by ASME, IGTI, and AGARD in 1994-1998. Most of the participating codes over predicted pressure and temperature ratios, and failed to predict certain features of the downstream flowfield. Since then the AUSM+ upwind scheme and the k- turbulence model have been added to SWIFT. In this work the new capabilities were assessed for the two compressors. Comparisons were made with overall performance maps and spanwise profiles of several aerodynamic parameters. The results for rotor 37 were in much better agreement with the experimental data than the original blind test case results although there were still some discrepancies. The results for stage 35 were in very good agreement with the data. The results for rotor 37 were very sensitive to turbulence model parameters but the results for stage 35 were not. Comparison of the rotor solutions showed that the main difference between the two rotors was not blade camber as expected, but shock/boundary layer interaction on the casing

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

A rapid technique is used for calculating inviscid and viscous flows in turbomachinery cascades. The Euler and thin-layer Navier-Stokes equations are solved using the original explicit MacCormack algorithm. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. Convergence to a steady state is accelerated by use of a variable time-step and a multiple-grid scheme. Computer time is reduced through vectorization. Details of the numerical method are presented along with computed results for two low-speed wind tunnel turning vanes, a space shuttle fuel pump turbine rotor, and a supersonic inflow compressor rotor. The method can predict subtle viscous flow phenomena in cascades and is fast enough to be used as a design tool

Coupled Analysis of an Inlet and Fan for a Quiet Supersonic Jet

A computational analysis of a Gulfstream isentropic external compression supersonic inlet coupled to a Rolls-Royce fan has been completed. The inlet was designed for a small, low sonic boom supersonic vehicle with a design cruise condition of M = 1.6 at 45,000 ft. The inlet design included an annular bypass duct that routed flow subsonically around an engine-mounted gearbox and diverted flow with high shock losses away from the fan tip. Two Reynolds-averaged Navier-Stokes codes were used for the analysis: an axisymmetric code called AVCS for the inlet and a three dimensional (3-D) code called SWIFT for the fan. The codes were coupled at a mixing plane boundary using a separate code for data exchange. The codes were used to determine the performance of the inlet/fan system at the design point and to predict the performance and operability of the system over the flight profile. At the design point the core inlet had a recovery of 96 percent, and the fan operated near its peak efficiency and pressure ratio. A large hub radial distortion generated in the inlet was not eliminated by the fan and could pose a challenge for subsequent booster stages. The system operated stably at all points along the flight profile. Reduced stall margin was seen at low altitude and Mach number where flow separated on the interior lips of the cowl and bypass ducts. The coupled analysis gave consistent solutions at all points on the flight profile that would be difficult or impossible to predict by analysis of isolated components

Application of advanced computational codes in the design of an experiment for a supersonic throughflow fan rotor

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes