John Peddieson

Application of nonlocal continuum models to nanotechnology

A version of nonlocal elasticity theory is employed to develop a nonlocal Benoulli/Euler beam model. Some representative problems are solved to illustrate the magnitude of predicted nonlocal effects. Particular attention is paid to cantilever beams which are often used as actuators in small scale systems.

An application of the micropolar fluid model to the calculation of a turbulent shear flow

Abstract The problem of plane or axisymmetric stagnation-point flow of a micropolar fluid over a flat plate is considered. A new boundary condition, motivated by an analogy with phenomenological theories of turbulence, is proposed. Numerical solutions to the above-mentioned problem are obtained which appear to have the characteristics of turbulent shear flows.

A mathematical model of autoclave age forming

Abstract A mathematical model of autoclave age forming of aircraft wing panels is developed. The modeling process is illustrated by application to age forming of beam specimens. It is found that a closed form solution can be obtained for a mold in the shape of a circular arc. Closed form solutions are not possible for other mold shapes and a numerical method is, therefore, developed and applied to two noncircular mold shapes. Comparisons of predictions with experimental data obtained by Textron Aerostructures yield good agreement.

Non-linear response of a generalized Rijke tube

The mathematical model of unsteady velocity sensitive thermoacoustic interactions in a heated duct (generalized Rijke tube) reported by the authors in a previous publication is used to predict non-linear response. Both closed form and numerical solutions of equations derived by an approximate modal analysis are presented and employed to illustrate and investigate the bootstrapping instability mechanism observed in rocket motors.

Mathematical modeling of a generalized Rijke tube

A mathematical model of unsteady velocity sensitive thermoacoustic interactions in a heated duct (generalized Rijke tube) is developed. The model is constructed in a general way which is capable of employing any linear velocity sensitive thermoacoustic response model. A solution methodology is then constructed based on modal analysis. A number of rather general closed form solutions are presented and some of the results are used to qualitatively explain the behaviors of Rijke tubes and jet engine augmentors.

A Rotating Plug Model of Friction Stir Welding Heat Transfer

A simplified rotating plug model is employed to study the heat transfer phenomena associated with the friction stir welding process. An approximate analytical solution is obtained based on this idealized model and used both to demonstrate the qualitative influence of process parameters on predictions and estimate temperatures produced in typical friction stir welding situations.

Mathematical modeling of an age-forming process

A mathematical model of the autoclave age forming of beam specimens is developed based on the assumption of linear viscoelastic response. It is shown that the model is capable of predicting the qualitative features of the age-forming process.

Viscoelastic boundary-layer flow past a parabola and a paraboloid

Abstract The boundary-layer equations for steady flow of a nonlinear Maxwell viscoelastic fluid past a parabola and a paraboloid are solved numerically using an implicit finite-difference method. Selected results are presented in graphical form and are used to demonstrate the ways in which the non-Newtonian nature of the fluid manifests itself in these problems.

Eulerian Multiphase Population Balance Model of Atomizing, Swirling Flows

An Eulerian/Eulerian multiphase flow model coupled with a population balance model is used as the basis for numerical simulation of atomization in swirling flows. The objective of this exercise is to develop a methodology capable of predicting the local point-wise drop size distribution in a spray, such as would be measured by the Phase Doppler Particle Analyzer (PDA). Model predictions are compared to experimental measurements of particle size distributions in an air-blast atomizer spray to demonstrate good qualitative and quantitative agreement. It is observed that the dependence of velocity on drop size inherent in a multiphase description of the drop cloud appears necessary to capture some features of the experimental data. Using this model, we demonstrate the relative contributions of secondary atomization and transport to the variation observed in the downstream spray drop size distribution.

Eulerian Multi-Fluid Model of Air Blast Atomization

A fully Eulerian “multi-fluid” model of air blast atomization is discussed. The model envisions the system as consisting one carrier fluid phase and N drop phases, each having a discrete diameter. Discretization of the drop size distribution is often employed as part of numerical solutions. In the current approach, discretization is made part of the model itself in order to both take advantage of the large body of existing knowledge related to multiphase continuum mechanics and to make the resulting formulation consistent with the structures of the Eulerian multi-fluid solvers contained in contemporary commercial CFD packages. A complete formulation involving balances of mass, linear momentum, and energy for N+1 fluid-like continua (fluid phase plus N drop phases) is discussed. Some preliminary results are presented for a model problem allowing closed form solution. These are interpreted to illustrate the drop breakup concepts.