Engineering topics

Walkington, N. J.

Publications and source records attributed to Walkington, N. J..

6 records

NASA NTRS1986

A numerical model of acoustic choking. II - Shocked solutions

The one dimensional equations of gas dynamics are used to model subsonic acoustic choking. This model can accommodate non-linear distortion of waves and the eventual formation of shock waves. Several finite differencing schemes are adapted to obtain solutions. The results obtained with the various schemes are compared with the asymptotic results available. The results suggest that no one finite differencing scheme gives solutions significantly better than the others and that most of the difference solutions are close to the asymptotic results. If the acoustic shock wave is sufficiently strong it almost annihilates the acoustic wave; in this situation numerical errors may dominate the results. Such solutions involve very large acoustic attenuations.

Walkington, N. J.↗

NASA NTRS1986

Fundamental investigations of the finite element solutions for acoustic propagation in ducts

The question of convergence of three finite element algorithms for the modelling of acoustic transmission in ducts carrying a nonuniform mean flow is addressed. The details of each algorithm are stated and example calculations in uniform and nonuniform ducts are made and assessed for accuracy and convergence. The algorithm based on the assumption of irrotationality is found to be highly convergent. This algorithm is the one used in current turbo-fan inlet acoustic radiation codes. A theoretical analysis indicating convergence is supported by example calculations. Two additional algorithms which do not require irrotationality are found to be less convergent, and perhaps not convergent at all for certain severely sheared velocity profiles. No theoretical convergence criteria can presently be established for these algorithms and convergence difficulties are shown here by example. Included in this class of algorithms is the duct analysis program ADAM which is known to display apparently nonconvergent solutions in certain cases.

Walkington, N. J.↗

NASA NTRS1983

A numerical model of acoustic choking. I - Shock free solutions

The phenomenon of acoustic choking in near sonic flows is investigated using the one-dimensional gasdynamic equations for an ideal gas. It is pointed out that this approach eliminates the need to make the classical small disturbance assumption. A finite difference scheme is elaborated to approximate these equations. Boundary conditions that correctly model the physics of the acoustics problems are chosen. The use of a fast Fourier transform routine allows the results to be compared with those obtained by using the conventional harmonic assumptions. Only solutions in which shocks have not fully developed are reported. Continuous solutions are sought, and these are compared with the Fubini solution and with certain results of Myers and Callegari (1977, 1978, 1979).

Walkington, N. J.↗

NASA NTRS1983

Finite difference solutions to shocked acoustic waves

The MacCormack, Lambda and split flux finite differencing schemes are used to solve a one dimensional acoustics problem. Two duct configurations were considered, a uniform duct and a converging-diverging nozzle. Asymptotic solutions for these two ducts are compared with the numerical solutions. When the acoustic amplitude and frequency are sufficiently high the acoustic signal shocks. This condition leads to a deterioration of the numerical solutions since viscous terms may be required if the shock is to be resolved. A continuous uniform duct solution is considered to demonstrate how the viscous terms modify the solution. These results are then compared with a shocked solution with and without viscous terms. Generally it is found that the most accurate solutions are those obtained using the minimum possible viscosity coefficients. All of the schemes considered give results accurate enough for acoustic power calculations with no one scheme performing significantly better than the others.

Walkington, N. J.↗

NASA NTRS1981

Accuracy and stability of finite element schemes for the duct transmission problem

An investigation is conducted regarding the feasibility of approaches for improving the efficiency and stability of existing finite element method (FEM) schemes, taking into account both analytical and numerical studies. Of the four schemes considered for the 'steady' problem, the Hermitian Galerkin formulation appears to be the most efficient and therefore the most suitable scheme for futher full scale implementation. The Hermitian residual least squares (RLS) scheme although comparable in accuracy for the cases considered exhibits a slight tendency to cumulative errors. The performance of both the Lagrangian element schemes considered compares poorly with that of their Hermitian element counterparts. This is particularly true of the Lagrangian RLS scheme. The presence of internal oscillatory components is an inevitable consequence of all Galerkin schemes irrespective of element type.

Astley, R. J.↗

NASA NTRS1980

Transmission in flow ducts with peripherally varying linings

A finite element Galerkin formulation is used for the calculation of acoustical modes in uniform ducts with arbitrary geometry, mean flow and lining configuration. Hermitian 'non-conforming' sub-parametric elements are used and the dimensionality of the resulting eigenmatrix is reduced by the use of a condensation scheme based on the compatible eigenvectors in the case with no mean flow. Results are presented for simple circular and rectangular configurations for which exact comparison results are readily calculable. Computer graphics routines required to interpret modal data are described and sample results shown.

Astley, R. J.↗