Probabilistic structural analysis algorithm development for computational efficiency

The PSAM (Probabilistic Structural Analysis Methods) program is developing a probabilistic structural risk assessment capability for the SSME components. An advanced probabilistic structural analysis software system, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), is being developed as part of the PSAM effort to accurately simulate stochastic structures operating under severe random loading conditions. One of the challenges in developing the NESSUS system is the development of the probabilistic algorithms that provide both efficiency and accuracy. The main probability algorithms developed and implemented in the NESSUS system are efficient, but approximate in nature. In the last six years, the algorithms have improved very significantly

A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate

In this paper, we introduce a three-dimensional numerical method for computing the wake behind a flat plate advancing perpendicular to the flow. Our numerical method is inspired by the panel method of J. Katz and A. Plotkin [J. Katz and A. Plotkin, Low-speed Aerodynamics, 2001] and the 2D vortex blob method of Krasny [R. Krasny, Lectures in Appl. Math., 28 (1991), pp. 385--402]. The accuracy of the method will be demonstrated by comparing the 3D computation at the center section of a very high aspect ratio plate with the corresponding two-dimensional computation. Furthermore, we compare the numerical results obtained by our 3D numerical method with the corresponding experimental results obtained recently by Ringuette [M. J. Ringuette, Ph.D. Thesis, 2004] in the towing tank. Our numerical results are shown to be in excellent agreement with the experimental results up to the so-called formation time

Cavity flow past a slender pointed hydrofoil

A slender-body theory for the flow past a slender, pointed hydrofoil held at a small angle of Attack to the flow, with a cavity on the upper surface, has been worked out. The approximate solution valid near the body is seen to be the sum of two components. The first consists of a distribution of two-dimensional sources located along the centroid line of the cavity to represent the variation of the cross-sectional area of the cavity. The second component represents the crossflow perpendicular to the centroid line. It is found that over the cavity boundary which envelops a constant pressure region, the magnitude of the cross-flow velocity is not constant, but varies to a moderate extent. With this variation neglected only in the neighbourhood of the hydrofoil, the cross-flow is solved by adopting the Riabouchinsky model for the two-dimensional flow. The lift is then calculated by integrating the pressure along the chord; the dependence of the lift on cavitation number and angle of attack is shown for a specific case of the triangular plan form

Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, R[sub]b = Ub/v, and the other on the semi-major axis a, R[sub]a = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of R[sub]b and arbitrary values of R[sub]a. When R[sub]a is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when R[sub]a tends to infinity. This result thus provides a clear physical picture and explanation of the 'Stokes paradox' known in viscous flow theory

Shock wave boundary layer interaction studied by high-speed schlieren

Shock wave boundary layer interactions at compression ramps have been examined by high-speed schlieren. A total of six ramps with angles ranging from 20 deg to 30 deg, the ramp angle effect on the SWBLI is thus studied. The present high-speed schlieren with a frame rate of 20 kHz generates a large ensemble of 9000 images, which secures the convergence of the statistics of the schlieren intensity. The rms of the schlieren intensity is of great interest, as it enables visualisation of the flow features that are not observable in the raw schlieren images, such as the corner separation/low momentum region, the spot of strong flow unsteadiness right after the shock wave and the location of the peak fluctuation over the ramp. Through the present systematic experimental investigation of SWBLI, the highspeed schlieren is demonstrated to be of great capability for SWBLI study

Symmetry-preserving Loop Regularization and Renormalization of QFTs

A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the lagrangian formalism or the space-time dimension of original theory. The appearance of characteristic energy scale $M_c$ and sliding energy scale $\mu_s$ offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.Comment: 13 pages, Revtex, extended modified version, more references adde