Roger L. Davis

Cascade viscous flow analysis using the Navier-Stokes equations

A previously developed explicit, multiple-grid, time-marching Navier-Stokes solution procedure has been modified and extended for the calculation of steady-state high Reynolds number turbulent flows in cascades. Particular attention has been given to the solution accuracy of this procedure as compared with boundary-layer theory and experimental data. A new compact discretization scheme has been implemented for the viscous terms which has the same finite-difference molecule as the inviscid terms of the Navier-Stokes equations. This compact operator has been found to yield accurate and stable solutions in regions of the flow where the gradients are large and the computational mesh is relatively sparse. A modified C grid generation procedure has been developed for cascades that greatly reduces grid skewing in the midgap region. As a result, numerical errors associated with the use of numerical smoothing on skewed grids are reduced considerably. In addition, a body normal grid system has also been generated for accurately determining the eddy viscosity distribution based on an algebraic turbulence model and for comparing the results directly with boundary-layer theory. A combined second and fourth difference numerical smoothing operation has been carefully constructed to prevent oscillations in the solution for the flow over complicated geometries without contaminating the velocity profiles near the wall. Results from turbine and compressor applications are presented to demonstrate the accuracy of the present scheme through comparisons with experimental data and attached boundary-layer theory.

Rapid Aerodynamic Performance Prediction on a Cluster of Graphics Processing Units

Author(s): Phillips, Everett H.; Zhang, Yao; Davis, Roger L.; Owens, John D. | Abstract: Researchers have recently used the new programmable capabilities of the Graphics Processing Unit (GPU) to increase the performance of scientific codes. We investigate the use of a cluster of GPUs for large-scale CFD problems and show order-of-magnitude increases in performance and performance-to-price ratio. We implement two separate compressible flow solvers. First, we develop a CUDA-based solver for the 2D compressible Euler equations and verify the results against a reference multi-block code MBFLO. After demonstrating the performance of our Euler solver, we proceed to develop a new version of MBFLO by adding GPU-accelerated subroutines to the existing Fortran codebase. Using an eight-node cluster equiped with 16 NVIDIA 9800GX2 GPUs, we achieve speedups of up to 496x on our Euler Solver and 88x on MBFLO. This paper describes the numerical, hardware and software techniques that provide significant speedups.

Unsteady Interaction Between a Transonic Turbine Stage and Downstream Components

Results from a numerical simulation of the unsteady flow through one quarter of the circumference of a transonic high-pressure turbine stage, transition duct, and low-pressure turbine first vane are presented and compared with experimental data. Analysis of the unsteady pressure field resulting from the simulation shows the effects of not only the rotor/stator interaction of the high-pressure turbine stage but also new details of the interaction between the blade and the downstream transition duct and low-pressure turbine vane. Blade trailing edge shocks propagate downstream, strike, and reflect off of the transition duct hub and/or downstream vane leading to high unsteady pressure on these downstreamcomponents. The reflection of these shocks from the downstream components back into the blade itself has also been found to increase the level of unsteady pressure fluctuations on the uncovered portion of the blade suction surface. In addition, the blade tip vortex has been found to have a moderately strong interaction with the downstream vane even with the considerable axial spacing between the two blade-rows. Fourier decomposition of the unsteady surface pressure of the blade and downstream low-pressure turbine vane shows the magnitude of the various frequencies contributing to the unsteady loads. Detailed comparisons between the computed unsteady surface pressure spectrum and the experimental data are shown along with a discussion of the various interaction mechanisms between the blade, transition duct, and downstream vane. These comparisons show-overall good agreement between the simulation and experimental data and identify areas where further improvements in modeling are needed.

Prediction of Compressor Stage Performance From Choke Through Stall

The results of an investigation in which the predicted aerodynamic performance of the NASA Stage35 singlestage compressor is compared with the measured experimental data over the entire design speedline from choke through stall are presented. Particular attention has been given to the geometric model and boundary conditions in the numerical study to enable the aerodynamic performance to be predicted through stall. The total pressure ratios of both the rotor and stator as well as circumferential profiles of the total pressure and total temperature up- and downstream of the rotor are compared with experimental data. A time-accurate approach for predicting stall inception caused by both long- and short-wave length phenomena is introduced. The results from a series of Stage35 unsteady-flow simulations near stall with this approach are presented to demonstrate the flow physics responsible for stall inception.

Deterministic stress modeling of hot gas segregation in a turbine

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads. The LDS model is obtained from an unsteady inviscid calculation. The inviscid LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. The feasibility of the inviscid LDS model is demonstrated on a single-stage, three-dimensional, vane-blade turbine with a hot streak entering the vane passage at midpitch and midspan. The steady viscous solution with the LDS model is compared to the time-averaged viscous, steady viscous, and time-averaged inviscid computations. The LDS model reproduces the time-averaged viscous temperature distribution on the outer air seal to within 2.3 percent, while the steady viscous has an error of 8.4 percent, and the time-averaged inviscid calculation has an error of 17.2 percent. The solution using the LDS model is obtained at a cost in CPU time that is 26 percent of that required for a time-averaged viscous computation.

Massively Parallel Simulation of the Unsteady Flow in an Axial Turbine Stage

The results from two numerical simulations of the unsteady flow in a 11 stage axial-flow turbine are presented and compared with experimental data to show both the effect of blade count on the solution accuracy and the time-averaged and unsteady flow physics present. TFLO, the three-dimensional, multiblock, massively parallel turbomachinery flow solution procedure is used to simulate the flow through the Aachen 36-vane/41-blade/36-vane 1 ½-stage turbine rig. Comparisons of the time-averaged and unsteady flow solutions of 1-vane/1-blade/1-vane and 6-vane/7-blade/6-vane configurations with the available experimental data are used to show the importance of matching actual blade counts in unsteady flow simulations as closely as possible. In addition, these comparisons are used to quantify the predicted aerodynamic performance differences and highlight the different unsteady flow physics in the two simulations.

A multi-code-coupling interface for combustor/turbomachinery simulations

This paper describes the design, implementation and validation of a method to couple multiprocessor solvers whose solution domains share a common surface. Using Message Passing Interface (MPI) constructs, parallel communication pathways are established between various simulation codes. These pathways allow applications to exchange data, synchronize time integrations and reinitialize communication data structures when meshes change their relative positions. At an interface with another simulation code, applications request specific flow variables, typically for a ghost/halo layer of cells or nodes. Numerical estimates of these flow variables are provided by the simulation software on the other side of the interface through three-dimensional interpolation. With an aim at achieving conservative interfacing between applications, particular instances of the requested flow variables and interpolation stencils will be used for different problems. Communication tables are built for processes involved with the exchange of information and all exchanges occur strictly between specific processes, thereby minimizing communication bottlenecks. This paradigm has been used to build a code coupling interface for a three-dimensional combustor/turbine interaction simulation in which a new massively parallel computational fluid dynamic solution procedure for turbomachinery, called TFLO, has been coupled with an unstructured-grid, parallel procedure for combustors, called NCC. Numerical and physical issues regarding the exchange of information as well as the coupling of physics-disparate analyses will be discussed. Several development test cases have been used to ensure the soundness of the communication procedures. A multi-component simulation for a dump combustor/exit duct has been performed as a demonstration of the new interface.

Detached-Eddy Simulation Procedure Targeted for Design

A new detached-eddy simulation procedure, MBFLO, is described for the simulation of turbulent flow over/within arbitrary geometry. This new procedure represents the first step toward developing a turbulent technique that reduces the reliance on traditional turbulence modeling by directly solving for the larger-scale turbulence effects in regions where the computational grid is sufficient to resolve those scales. A goal of this effort was to develop a detached-eddy simulation procedure-for which the time-averaged solution can replace current steady simulation results for design. Because detached-eddy simulation requires the solution of the unsteady Navier-Stokes equations on computational grids that are typically an order in magnitude more dense than their Reynolds-averaged counterparts, special care was taken to make this new procedure computationally efficient. This paper describes the data structure, parallelization, and automation techniques used to produce time-averaged detached-eddy simulation predictions. Results for the turbulent flow through a turbine and compressor cascade at design and offdesign conditions, respectively, are shown to illustrate the technique.

DECOMPOSITION AND PARALLELIZATION STRATEGIES FOR ADAPTIVE GRID-EMBEDDING TECHNIQUES

SUMMARY A two and three-dimensional adaptive-grid procedure for the solution to fluid dynamic problems is presented. This procedure uses grid-embedding (h-refinement) to automatically refine the grid in regions of high gradients and high truncation error. With this adaptation approach, solutions are obtained with a guaranteed level of accuracy using minimum computer resources. For the solution of steady flows, a multiple-grid technique is used to allow disturbance waves to pass through regions of disparate grid spacing and to accelerate convergence. Domain decomposition and computer parallelization techniques are utilized to allow the solution procedure to be executed efficiently on parallel computer platforms. A discussion of these techniques along with a general description of the adaptive grid-embedding procedure is given. Results are provided demonstrating the accuracy and efficiency of the present procedure on a parallel computer.

GPGPU parallel algorithms for structured-grid CFD codes

A new high-performance general-purpose graphics processing unit (GPGPU) computational uid dynamics (CFD) library is introduced for use with structured-grid CFD algorithms. A novel set of parallel tridiagonal matrix solvers, implemented in CUDA, is included for use with structured-grid CFD algorithms. The solver library supports both scalar and block-tridiagonal matrices suitable for approximate factorization (AF) schemes. The computational routines are designed for both GPU-based CFD codes or as a GPU accelerator for CPU-based algorithms. Additionally, the library includes, among others, a collection of nite-volume calculation routines for computing local and global stable time