Bayliss, A. — Page 2 | Engineering Papers

NASA NTRS1986

On the interaction of a sound pulse with the shear layer on an axisymmetric jet. III - Non-linear effects

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected, and the effect of nonlinearity is studied. A high order numerical method is used to compute the solution. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales.

Bayliss, A.↗

NASA NTRS1986

A fourth order accurate finite difference scheme for the computation of elastic waves

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Bayliss, A.↗

NASA NTRS1986

Non-reflecting boundary conditions for the compressible Navier-Stokes equations

A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results.

Abarbanel, S.↗

NASA NTRS1985

Active control of compressible flows on a curved surface

The effect of localized, time periodic surface heating and cooling over a curved surface is studied. This is a mechanism for the active control of unstable disturbances by phase cancellation and reinforcement. It is shown that the pressure gradient induced by the curvature significantly enhances the effectiveness of this form of active control. In particular, by appropriate choice of phase, active surface heating can completely stabilize and unstable wave.

Maestrello, L.↗

NASA NTRS1985

Wave phenomena in a high Reynolds number compressible boundary layer

Growth of unstable disturbances in a high Reynolds number compressible boundary layer is numerically simulated. Localized periodic surface heating and cooling as a means of active control of these disturbances is studied. It is shown that compressibility in itself stabilizes the flow but at a lower Mach number, significant nonlinear distortions are produced. Phase cancellation is shown to be an effective mechanism for active boundary layer control.

Bayliss, A.↗

NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

A computational scheme is described which is second-order accurate in time and fourth-order accurate in space (2-4). This method is applied to study the stability of compressible boundary layers. The laminar compressible Navier-Stokes equations are solved with a time harmonic inflow superimposed on the steady state solution. This results in spatially unstable modes. It is shown that the second-order methods are inefficient for calculating the growth rates and phases of the unstable modes. In contrast the fourth-order method yields accurate results on relatively course meshes.

Bayliss, A.↗

NASA NTRS1985

Active control of compressible flows on a curved surface

The effect of localized, time periodic surface heating and cooling over a curved surface is studied. This is a mechanism for the active control of unstable disturbances by phase cancellation and reinforcement. It is shown that the pressure gradient induced by the curvature significantly enhances the effectiveness of this form of active control. In particular, by appropriate choice of phase, active surface heating can completely stabilize an unstable wave.

Maestrello, L.↗

NASA NTRS1985

A fourth-order scheme for the unsteady compressible Navier-Stokes equations

A computational scheme is described which is second-order accurate in time and fourth-order accurate in space (2-4). This method is applied to study the stability of compressible boundary layers. The laminar compressible Navier-Stokes equations are solved with a time harmonic inflow superimposed on the steady state solution. This results in spatially unstable modes. It is shown that the second-order methods are inefficient for calculating the growth rates and phases of the unstable modes. In contrast the fourth-order method yields accurate results on relatively coarse meshes.

Bayliss, A.↗

NASA NTRS1985

On accuracy conditions for the numerical computation of waves

The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.

Bayliss, A.↗

NASA NTRS1985

Numerical simulation of boundary layer excitation by surface heating/cooling

The concept of active control of growing disturbances in an unstable compressible flow by using time periodic, localized surface heating is studied numerically. The simulations are calculated by a fourth-order accurate solution of the compressible, laminar Navier-Stokes equations. Fourth-order accuracy is particularly important for this problem because the solution must be computed over many wavelengths. The numerical results demonstrate the growth of an initially small fluctuation into the nonlinear regime where a local breakdown into smaller scale disturbances can be observed. It is shown that periodic surface heating over a small strip can reduce the level of the fluctuation provided that the phase of the heating current is properly chosen.

Bayliss, A.↗

NASA NTRS1985

On the interaction of a sound pulse with the shear layer of an axisymmetric jet. Part 3: Nonlinear effects

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected, and the effect of nonlinearity was studied. A high order numerical method is used to compute the solution. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales.

Bayliss, A.↗

NASA NTRS1984

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

Bayliss, A.↗

NASA NTRS1984

On accuracy conditions for the numerical computation of waves

The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.

Bayliss, A.↗

NASA NTRS1983

Radiation of sound from unflanged cylindrical ducts

Calculations of sound radiated from unflanged cylindrical ducts are presented. The numerical simulation models the problem of an aero-engine inlet. The time dependent linearized Euler equations are solved from a state of rest until a harmonic solution is attained. A fourth order accurate finite difference scheme is used and solutions are obtained from a fully vectorized Cyber-203 computer program. Cases of both plane waves and spin modes are treated. Spin modes model the sound generated by a turbofan engine. Boundary conditions for both plane waves and spin modes are treated. Solutions obtained are compared with experiments conducted at NASA Langley Research Center.

Hartharan, S. L.↗

NASA NTRS1983

An iterative method for the Helmholtz equation

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Bayliss, A.↗

NASA NTRS1983

On the interaction of a sound pulse with the shear layer of an axisymmetric jet. II - Heated jets

The fluctuating field of a heated jet excited by a sound pulse is simulated numerically. The fluctuations in both the flow field and the far field are studied. The flow field results depend crucially on the stability properties of the heated jet. The altered stability properties due to the heating cause a reduction in the overall fluctuations and a shift of the instability waves into lower frequencies. These changes cause a similar downward shift in the far field spectrum and a reduction in the total far field noise. The results provide a partial explanation in terms of stability theory of experimentally observed properties of the noise of heated jets.

Bayliss, A.↗

NASA NTRS1982

Far field boundary conditions for compressible flows

Previously announced in STAR as N81-33857

Bayliss, A.↗

NASA NTRS1982

Simulation of the fluctuating field of a forced jet

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected and the effect of nonlinearity is studied. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales.

Bayliss, A.↗