Catherine Mavriplis

Adaptive mesh strategies for the spectral element method

Abstract An adaptive spectral element method has been developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the one-dimensional viscous Burgers equation and the two-dimensional Navier—Stokes equations for driven flow in a cavity. Sharp gradients, singularities and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility and general capabilities for high order spectral methods.

Evaluation of viscous dissipation in liquid flow in microchannels

Different phenomena have been observed in various works indicating that the mechanisms of flow and heat transfer in microchannels are still not understood clearly. There is little experimental data and theoretical analysis available in the literature to elucidate the mechanisms. It is reasonable to assume that, as the dimensions of flow channels approach the micro-level, viscous dissipation could be too significant to be neglected due to a high velocity gradient in the channel. However, no evidence and analysis was presented to verify such an explanation. Therefore, in this paper, the effects of viscous dissipation in microchannel flows are analyzed and examined theoretically. A criterion to draw the limit of the significance of the viscous dissipation effects in the microchannel flows is suggested based on the present analysis.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15 % of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

Mind the Gap: Women in STEM Career Breaks

The slow advancement of women in scientific fields remains a persistent problem, especially in academia. Highly trained doctoral women in the sciences drop out of the academic pipeline for a variety of reasons that are poorly documented. This paper reports on a qualitative exploratory study based on structured interviews with 15 women who have taken career breaks after receiving their science, technology, engineering or mathematics (STEM) PhD, but wish to re-enter the academic career track. The study aims to understand the pressures that contribute to taking such breaks, how women remain connected (or not) to their field during breaks and how re-entering the field after a career break could be facilitated. Suggestions based on the interviews include career development workshops and networking opportunities for women in breaks, as well as systemic changes such as reduced fees for society membership and conferences, changes in the way resumes are reviewed by faculty search committees, and in the design and implementation of maternity and child care leave policies.

Polynomials for infinite-domain spectral elements

In this note, it is found that Laguerre-type elements may be used in conjunction with Legendre-type elements to resolve more accurately regions of outflow and infinite boundaries

A Posteriori Error Estimators for Adaptive Spectral Element Techniques

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1989.

Modeling of magnetization and demagnetization in magnetic regenerative refrigeration

A time-dependent model of temperature in magnetization and demagnetization processes is developed based on thermodynamic and heat transfer laws, material properties, and variable-field magnet parameters. Test results of a magnetic refrigeration test bed are compared with the model calculation. The model can be used to simulate optimum operating conditions and duty cycle of magnetic regenerative refrigeration. The effects of the thermal conductivity between the magnetocaloric material and the thermocouple on temperature measurements and thermal lag are presented.

Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Reθ ≃ 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ≃ 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. ...

Nonlinear receptivity to oblique vortical modes in flow past an elliptic leading edge

Nonlinear boundary-layer receptivity to pairs of unsteady oblique freestream vortical modes is studied in direct numerical simulation of flow over a flat plate with an elliptic leading edge. The freestream is perturbed by three types of oblique Fourier modes, differing in the magnitude of the three vorticity components. The vortical modes excite steady boundary-layer streaks. The associated receptivity mechanism, described in detail, is quadratic in the forcing amplitude. Elliptic leading edges with two different aspect ratios are considered. We find that – and explain why – the streak amplitudes in nonlinear receptivity are largely unaffected by the leading-edge bluntness for the types of external disturbances studied. As linear receptivity is the predominant mechanism at low forcing frequencies, the nonlinear mechanism comes into play when high-frequency vortices are present in the freestream. Nonlinear receptivity is therefore expected to contribute to the excitation of boundary-layer streaks by freest...

Micro-particle image velocimetry measurement of blood flow: validation and analysis of data pre-processing and processing methods

The intent of this paper is to investigate the application of a pre-processing method previously validated on glycerol to blood flows in microchannels and to compare the accuracy of results obtained when applied to a non-homogeneous fluid such as blood with results from previously applied processing methods for blood data. Comparisons of common processing methods are desired for a clear measure of accuracy in order to make recommendations for various flows. It is hypothesized that increasing the correlation window overlap improves the profile prediction. The amount of correlation window overlap and window shape in the processing of data have a significant effect on the results. Image pre-processing is explored to improve the correlation using the ‘image overlapping’ which is extended to the case of blood and the blood-specific pre-processing ‘base-clipping’ or ‘thresholding’ technique currently applied to blood. Both pre-processing methods are tested with multiple processing methods for two channel geometries: a straight rectangular channel and a Y-channel resulting in a controlled shear flow. The resulting profiles and calculations demonstrate that ‘image-overlapping’ is found to achieve a profile closer to the predicted theoretical profile than current blood pre-processing methods when both are applied to the same set of data and both are superior to conventional cross-correlation on its own. In all cases, pre-processing decreases the smoothness of the predicted profile. The use of ‘image-overlapping’ is shown to have greater accuracy when calculating the shear rate at the wall of the channel as well.