ALBERT

Description: A quasi-three-dimensional analysis has been developed for unsteady rotor-stator interaction 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 stress-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using an explicit four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing is used to increase the stability limit of the time-accurate computations. The scheme is described, and stability and accuracy analyses are given.

Description: The capability of generating 2-D unstructured triangular meshes about arbitrary geometries is demonstrated. This work uses a distribution of boundary points and triangulates the computational domain using a Delaunay triangulation algorithm. Typically, initial cells are added based on cell aspect ratios or cell areas. A resulting mesh can then be used along with the connectivity of the cells to solve either a Euler or Navier-Stokes flow problem.

Description: The topics are presented in viewgraph form and include the following: governing equations; grid generation; numerical approach; results; and conclusions.

Description: The major thrust of the computational analysis of turbomachinery to date has been the steady-state solution of isolated blades using mass-averaged inlet and exit conditions. Unsteady flows differ from the steady solution due to interaction of pressure waves and wakes between blade rows. To predict the actual complex flow conditions one must look at the time accurate solution of the entire turbomachine. Three quasi-three-dimensional Euler and thin layer Navier-Stokes equations are solved for unsteady turbomachinery flows.

Description: No abstract available

Description: The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.

Description: In the present work, the generation and radiation of acoustic waves from a 2-D shear layer problem is considered. An acoustic source inside of a 2-D jet excites an instability wave in the shear layer, resulting in sound Mach radiation. The numerical solution is obtained by solving the Euler equations using the space time conservation element and solution element (CE/SE) method. Linearization is achieved through choosing a small acoustic source amplitude. The Euler equations are nondimensionalized as instructed in the problem statement. All other conditions are the same except that the Crocco's relation has a slightly different form. In the following, after a brief sketch of the CE/SE method, the numerical results for this problem are presented.

Description: Three benchmark problems from the current and previous CAA workshops involving tone noise generated in viscous flows are investigated using the CE/SE finite volume method. The CE/SE method is first briefly reviewed. Then, the benchmark problems, namely, flow past a single cylinder (CAA Workshop II problem), flow past twin cylinders (from the current CAA Workshop IV, Category 5, Problem 1) and flow past a deep cavity with overhang (CAA Workshop III problem) are investigated. Generally good results are obtained in comparison with the experimental data.

Description: A quasi-three-dimensional analysis was developed for unsteady rotor-stator interaction 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 are integrated in time using a four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.