David W. Watt

Turbulent flow visualization by interferometric integral imaging and computed tomography

An experimental system using integral interferometric imaging and computer tomography for visualizing the structure of a turbulent, vertical helium jet is described. Integral images and tomographic integral data were obtained using a pulsed phase-shifted interferometer. The integral images revealed a sinuous overall jet structure and large-scale buckling motions in the far-field. Tomographic reconstruction of jet cross-sections at numerous axial locations were made for three turbulent jets at two different Reynols numbers, 2,800 and 4,300. Tomographic images revealed unmixed ambient fluid far inside the jet boundary and a bimodal concentration distribution. Image interpretation and experimental errors are discussed.

Quantitative visualization of high-speed 3D turbulent flow structures using holographic interferometric tomography

Abstract Using holographic interferometry the three-dimensional structure of unsteady and large-scale motions within subsonic and transonic turbulent jet flows has been studied. The instantaneous 3D flow structure is obtained by tomographic reconstruction techniques from quantitative phase maps recorded using a rapid-switching, double reference beam, double pulse laser system. The reconstruction of the jets studied here reveal a three-dimensional nature of the flow. In particular an increasing complexity can be seen in the turbulence as the flow progresses from the jet nozzle. Furthermore, a coherent three-dimensional, possibly rotating, structure can be seen to exist within these jets. The type of flow features illustrated here are not just of fundamental importance for understanding the behavior of free jet flows, but are also common to a number of industrial applications, ranging from the combustion flow within an IC engine to the transonic flow through the stages of a gas turbine.

Column-relaxed algebraic reconstruction algorithm for tomography with noisy data

A tomographic reconstruction algorithm similar to the well-known algebraic reconstruction technique (ART) is presented. Similar to ART, the approximate algebraic reconstruction technique (AART) technique consists of a sequence of displacements of the image vector based on the projection error. AART is a column-relaxation technique that is a series of vector displacements of the image vector parallel to its coordinate axes. AART is compared with ART, a standard conjugate-gradient technique, and a conjugate-gradient technique augmented by nonnegativity. The use of relaxation parameters to improve the performance of both ART and AART in the presence of noise is discussed, and the use of an iteration termination criterion based on random generalized cross validation is illustrated.

Optical and electronic design of a calibrated multichannel electronic interferometer for quantitative flow visualization

Calibrated multichannel electronic interferometry is an electro-optic technique for performing phase shifting of transient phenomena. The design of an improved system for calibrated multichannel electronic interferometry is discussed. This includes a computational method for alignment of three phase-shifted interferograms and determination of the pixel correspondence. During calibration the phase, modulation, and bias of the optical system are determined. These data are stored electronically and used to compensate for errors associated with the path differences in the interferometer, the separation of the phase-shifted interferograms, and the measurement of the phase shift.

Three-illumination-beam phase-shifted holographic interferometry study of thermally induced displacements on a printed wiring board

Spatially resolved measurement of thermally induced surface displacements of printed wiring boards using phase-shifted holographic interferometry is discussed. Three separate holograms with three linearly independent illumination beams were recorded. The interferograms were viewed in real time from a fixed detector location, and phase maps corresponding to each illumination direction were generated with the phase-shifting interferometer. The phase maps are then used to compute the displacements on a point by point basis. The measurement accuracy is estimated to be +/-0.004 microm out-of-plane and +/-0.02 microm in-plane over a temperature range of 40 degrees C. The system was tested on a through hole in a printed wiring board; the results of this test are discussed. Phase computation and unwrapping, data reduCtion, experimental geometry, surface preparation, and displacement computation are discussed.

Surface waves impinging on a vertical wall

Flow visualization experiments have been performed which consider a solitary wave impinging on a vertical wall. Several stages of motion appear as the incident wave height is increased in subsequent runs. Small amplitude incident waves reflect off the vertical wall without a significant change in shape. Higher wave amplitudes form a liquid sheet at impact, which ascends the vertical wall and has a ridge of fluid at the leading edge. Small waves form behind the ridge, and the ridge may form droplets. Large incident wave amplitudes form spilling breaking waves, which result in much more complicated motion in the ascending sheet, including the formation of spray.

An investigation of tire-wheel interface loads using ADINA

Aircraft wheels are designed to exhibit a fail-safe point so that a crack in the wheel can be detected before any catastrophic failure occurs. Presently, engineers use intrusive instrumentation to directly measure the tire-wheel interface pressure distribution. The goal of the current research is to demonstrate a nonintrusive methodology for using experimental displacement data in conjunction with the finite element method to back calculate this pressure distribution. The result is a well calibrated and credible finite element model which can be used to investigate the structural performance of the wheel.

Consistent iterative convolution: a coupled approach to tomographic reconstruction

Iterative convolution, a technique for limited-data tomographic reconstruction, is based on constrained iteration between a source function’s estimated image and its Radon transform. For certain source functions, the estimated image diverges from the source function. This divergence is shown to result from the algorithm’s failure to enforce consistency between the estimated image and its measured Radon transform. To correct for this, consistency can be enforced by using a routine based on the direct-inversion formula and on decomposing the image into components generated from its measured and missing Radon-transform integrals. This routine was used to develop a new iterative scheme that converges absolutely for three test objects for which simple iterative convolution diverges.

Theory and application of quantitative, bidirectional color schlieren for density measurement in high speed flow

This paper describes a quantitative schlieren technique called Calibrated Color Schlieren (CCS) that is capable of measuring the light deflection angle in both spatial directions simultaneously and hence is able to extract the projected density gradient of a two-dimensional flow. CCS makes use of a graded color filter in combination with a square source of size whose size may be varied to change the sensitivity. A calibration polynomial is used to obtain the deflection angle from color ratios at each pixel. The technique’s performance was assessed in terms of repeatability, sensitivity and accuracy using the Prandtl-Meyer expansion fan at the wedge-plate shoulder in a supersonic flow. From the measured deflection angles the density gradient and the density are computed. The density information agrees well with Prandtl-Meyer theory. The technique is also applied to a more complex wake flow, which required the use of a color correction based on a shadowgraph image.

Fourier-Bessel harmonic expansions for tomography of partially opaque objects.

Tomographic reconstruction from a limited amount of projection data of fields with embedded opaque objects can result in streaks and other artifacts in the reconstructed image. These artifacts result from the use of local-basis-function expansions to represent the image. I demonstrate that reconstructions by circular-harmonic expansions are largely free of these artifacts. A Fourier-Bessel expansion on a circular domain is used as the reconstruction basis; this expansion is used to compare circular-harmonic reconstructions with square-pixel reconstructions to determine qualitative differences between the local bases and the circular harmonics. Computational issues are also discussed.