Renata S. Engel

The Huygens principle for flow around an arbitrary body in a viscous incompressible fluid

The consequences of immersing a body in a Stokesian flow can be studied in the language employed in scattering research. After implementing the description of Stokesian flow in terms of velocity and pressure phasors, we formulate mathematical expressions delineating the Huygens principle for both phasors. Application is then made to scattering problems with special emphasis on impenetrable bodies.

Ambassador program for recruiting girls into engineering―appropriate messages, messengers, and modes of delivery

Although women make up more than half of the U.S. population, the percentage of women entering engineering is much lower. To address this discrepancy, the College of Engineering at Penn State has initiated an Engineering Ambassador Program that sends female engineering undergraduates to give talks in science and math classes within Pennsylvania high schools and middle schools. The main goal of these talks is to clarify what engineers do. What distinguishes our program are the specific messages in the talks and the presentation style of our ambassadors. The messages of our programs talks come from recommendations in the recent text Changing the Conversation [1]. The primary presentation style that our ambassadors rely on is an assertion-evidence style taught in a special presentations course [2]. Evaluations of the presentations by almost 500 students at six different schools across Pennsylvania (including two all-girls schools) indicate that the presentations are highly successful at communicating the messages. More powerful evidence for the efficacy of this program lies in the volunteered responses of girls to these presentations.

Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

Abstract We recast the time-dependent Stokesian flow about an axisymmetric body as a scattering problem, and solve the resulting boundary value problem using the point-matching method (PMM). The fluid is modeled to be viscous and incompressible. The velocity and pressure fields from the resulting linearized equations are cast as phasors in the frequency domain, and are broken up into incident and scattered components which are expressed in terms of spherical harmonic functions. For the numerical results presented, the incident velocity phasor is assumed to be a transverse plane wave progressing parallel to the symmetry axis of the body, and the PMM is applied to determine the scattered pressure and velocity phasors. Numerical results are shown for spheroids whose aspect ratios vary between 2 3 and 3 2 . Two different boundary condition cases are tackled: pure stick (i.e., no-slip) and pure slip. The extinction efficiency, a measure of the change in energy due to the presence of the scattering body, is also computed.

Pipe Flow Simulation Software: A Team Approach to Solve an Engineering Education Problem

THE STUDY OF THE MOTION OF FLUIDS is integral to many engineering disciplines. A first course in fluid mechanics introduces many types of flow, including steady flow through pipe systems. Computer simulations can play a role in the discovery of fluid engineering principles without requiring extensive laboratory facilities or the complicated mathematics associated with the theoretical development. TheFluid Flow Construction Set was developed as an educational tool to introduce engineering students to fluid flow in pipe systems. The software is an interactive tool to explore the fluid flow characteristics of a pipe system by manipulating the physical construction of the system. Both steady (time-independent) and transient (time-dependent) pipe flow can be simulated. The motivation and software design requirements are presented first, followed by specific details on how the objectives of the design tool were met.

Concerning the extinction cross section of an arbitrary body in Stokesian fluid flow

Time‐dependent Stokesian fluid flow around an arbitrary body can be analyzed in terms of time‐harmonic phasors. Analytical techniques commonly used for frequency‐domain scattering can therefore be brought to use. The scattering response of a body is often quantitated by the extinction cross section. However, the wave number for Stokesian flows is necessarily complex, so the usual interpretation of the extinction cross section is untenable in the present instance. It is shown, however, that a detector‐based interpretation of the extinction cross section is unambiguous and experimentally relevant. An almost exact formula is derived for the extinction coefficient for the far‐field, forward scattering case. Computed values of extinction cross sections are presented for spheres and spheroids.

Point‐matching technique for scattering of Stokesian flows around axisymmetric bodies

In solving for velocity and pressure fields in a slow, viscous, incompressible fluid, frequency‐domain scattering techniques can be brought into action by taking the Fourier transform of the equations describing Stokesian flows. This is exemplified by considering the scattering of a transverse plane wave by an impenetrable axisymmetric body immersed in a fluid modeled by the unsteady Stoke’s equation, the wave number in the ambient Stoke’s fluid being necessarily complex. The pressure and velocity phasors satisfy the Laplace and the Helmholtz equations, respectively, and are written as sums of incident and scattered components. These components are then expanded in terms of spherical harmonic functions. The point‐matching technique is used to satisfy boundary conditions on a discrete set of points on the surface of the scattering body. Convergence of the resulting series solutions is studied for spheroids of different aspect ratios and for varying wave numbers.