Engineering topics

Himansu, A.

Publications and source records attributed to Himansu, A..

6 records

NASA NTRS2005

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations - A New Approach based on the Space-Time CE/SE Method

This paper reports on a significant advance in the area of nonreflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of t he development of t he space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics- based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains t heir unique robustness and accuracy in terms of t he conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Chang, S.-C.↗

NASA NTRS2004

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

NASA NTRS2003

Gust Acoustic Response of a Single Airfoil Using the Space-Time CE/SE Method

A 2D parallel Euler code based on the space-time conservation element and solution element (CE/SE) method is validated by solving the benchmark problem I in Category 3 of the Third CAA Workshop. This problem concerns the acoustic field generated by the interaction of a convected harmonic vortical gust with a single airfoil. Three gust frequencies, two gust configurations, and three airfoil geometries are considered. Numerical results at both near and far fields are presented and compared with the analytical solutions, a frequency-domain solver GUST3D solutions, and a time-domain high-order Discontinuous Spectral Element Method (DSEM) solutions. It is shown that the CE/SE solutions agree well with the GUST3D solution for the lowest frequency, while there are discrepancies between CE/SE and GUST3D solutions for higher frequencies. However, the CE/SE solution is in good agreement with the DSEM solution for these higher frequencies. It demonstrates that the CE/SE method can produce accurate results of CAA problems involving complex geometries by using unstructured meshes.

Scott, James↗

NASA NTRS2002

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

Wang, X. Y.↗

NASA NTRS2001

Gust Acoustic Response of a Swept Rectilinear Cascade Using The Space-Time CE/SE Method

The benchmark problem 3 in Category 3 of the third Computational Aero-Acoustics (CAA) Workshop sponsored by NASA Glenn Research Center is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of a rectilinear swept cascade to an incident gust. The acoustic field generated by the interaction of the gust with swept at plates in the cascade is computed by solving the 3D nonlinear Euler equations using the space-time CE/SE method. A parallel version of the 3D CE/SE Euler solver is employed to obtain numerical solutions for several sweep angles. Numerical solutions are presented and compared with the analytical solutions.

Wang, X. Y.↗

NASA NTRS1995

The Method of Space-time Conservation Element and Solution Element: Development of a New Implicit Solver

The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, S. C.↗