Pankaj S. Kolhe

Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques

Abel inverse integral to obtain local field distributions from path-integrated measurements in an axisymmetric medium is an ill-posed problem with the integrant diverging at the lower integration limit. Existing methods to evaluate this integral can be broadly categorized as numerical integration techniques, semianalytical techniques, and least-squares whole-curve-fit techniques. In this study, Simpsons 1/3rd rule (a numerical integration technique), one-point and two-point formulas (semianalytical techniques), and the Guass-Hermite product polynomial method (a least-squares whole-curve-fit technique) are compared for accuracy and error propagation in Abel inversion of deflectometric data. For data acquired at equally spaced radial intervals, the deconvolved field can be expressed as a linear combination (weighted sum) of measured data. This approach permits use of the uncertainty analysis principle to compute error propagation by the integration algorithm. Least-squares curve-fit techniques should be avoided because of poor inversion accuracy with large propagation of measurement error. The two-point formula is recommended to achieve high inversion accuracy with minimum error propagation.

Density Measurements in a Supersonic Microjet Using Miniature Rainbow Schlieren Deflectometry

Understanding of the structure of complex supersonic flows requires high-resolution, nonintrusive measurements across the whole field. The measurement requirements are even more challenging when dealing with small-scale systems. In this study, we apply the miniature rainbow schlieren deflectometry system to measure the density field in underexpanded microjets from an orifice injector of 500 μm diameter. The injector is used to replicate the practical scenario of accidental leakage from a compressed gas storage facility. Experiments were conducted for a range of supply pressures P s , although the majority of the results are presented for P s = 860 kPa. Experimental schlieren images were analyzed to determine the density contours in an axisymmetric domain with a field of view of 1.5 mm radius and 7.5 mm length, at a spatial resolution of 25 μm. Pressure, temperature, and Mach number profiles (normalized by the values at the orifice) were also obtained along the jet centerline. Results show features similar to those observed in underexpanded macrojet from a sonic nozzle; multiple shock-cell structures with expansion and compression fans, freejet boundary, incident, normal, and reflected shock waves, subsonic slip strip, and outer shear layer. The miniature rainbow schlieren deflectometry technique is shown to provide high-quality quantitative data to explain the structural details of underexpanded microjets.

Miniature rainbow schlieren deflectometry system for quantitative measurements in microjets and flames

Recent interest in small-scale flow devices has created the need for miniature instruments capable of measuring scalar flow properties with high spatial resolution. We present a miniature rainbow schlieren deflectometry system to nonintrusively obtain quantitative species concentration and temperature data across the whole field. The optical layout of the miniature system is similar to that of a macroscale system, although the field of view is smaller by an order of magnitude. Employing achromatic lenses and a CCD array together with a camera lens and extension tubes, we achieved spatial resolution down to 4 mum. Quantitative measurements required a careful evaluation of the optical components. The capability of the system is demonstrated by obtaining concentration measurements in a helium microjet (diameter, d=650 microm) and temperature and concentration measurements in a hydrogen jet diffusion flame from a microinjector (d=50 microm). Further, the flow field of underexpanded nitrogen jets is visualized to reveal details of the shock structures existing downstream of the jet exit.

Measurements in a Combustor Operated on Alternative Liquid Fuels

Diminishing fossil fuel resources, ever-increasing energy cost, and the mounting concerns for environmental emissions have precipitated worldwide research on alternative fuels. Present study demonstrates low-emission combustion of diesel, biodiesel and straight vegetable oil (VO) is a dual-fuel burner employing flow blurring (FB) injector concept for fuel atomization. Measurements of temperature and CO and NOx emissions are acquired at various axial and radial locations within the combustor. A custom-designed thermocouple probe and a helium product gas sampling probe are employed to obtain the measurements. Infra-red images to depict combustor wall temperatures and visual flame images to demonstrated clean combustion are also presented. Results show that the FB injector ensured fine atomization of all three fuels irrespective of significant differences in their kinematic viscosity and surface tension properties.

A novel spectral analysis algorithm to obtain local scalar field statistics from line-of-sight measurements in turbulent flows

Statistical tomography to obtain local field variables from non-intrusive line-of-sight measurements in turbulent flows has been an intriguing subject for some time. In this study, a novel algorithm is presented to obtain statistical information on the local scalar field in axisymmetric turbulent flows. The algorithm uses line-of-sight transverse deflection angle measurements in only one view direction to greatly simplify the optical configuration. The validity of the algorithm is examined using noise-free synthetically generated scalar data that simulate the concentration field of a turbulent helium jet. Results show that the proposed algorithm provides excellent reconstruction of integral length scale and variance of refractive index difference, which can be related to scalar physical properties such as density, temperature and/or species concentrations. Good reconstruction accuracy and the need for a simple optical configuration make the proposed algorithm a promising method to characterize the scalar field in turbulent flows using path-integrated measurements.

Turbulence Measurements for Numerical Validation Acquired by Ultra High-speed Rainbow Schlieren Deflectometry

Ultra high-speed image sampling is integrated with rainbow schlieren deflectometry (RSD) to obtain spacetime cross-correlation measurements in a turbulent helium jet of diameter, d = 4 mm and Reynolds number of 4000. Rainbow schlieren apparatus was configured to cover the near field axial range of 0 to 20 diameters downstream of the injector exit at pixel resolution of 124 μm, image acquisition rate of 50,000 frames per second, and image exposure time of 20 μs to capture wide range of turbulent structures. Spacetime cross-correlations of deflectometric data yield mean convection velocity profile, axial and transverse wavenumber spectra, temporal spectrum, spectral coherence, and integral length and time scales. Such information is useful from experimental validation of large eddy simulation (LES) and a step towards creating data base for LES validation is undertaken in this study. Ultra high-speed imaging integrated with RSD can provide statistics characterization of turbulence through scalar measurements to compliment velocity field information obtained by other measurement technqiues.

Experimental Measurement of Density, Pressure and Temperature fields in a Supersonic free jet using Rainbow Schlieren Deflectometry

A supersonic free jet facility is designed and the density, static pressure and static temperature distributions are obtained using intrusive probes and non-intrusive Rainbow Schlieren Deflectometry (RSD) technique. The supersonic flow field was generated by a converging-diverging (C-D) nozzle flow (M=1.5, Dexit=26 mm) exhausting into the atmosphere. The jet stagnation pressure was varied to obtain overexpanded, underexpanded and fully expanded flow fields. Flow Mach number was measured using a conical probe while the total pressure was measured using a Pitot tube. The Mach number and the total pressure data were next used to calculate the static pressure. The RSD technique was used to obtain the distributions of density, pressure, and temperature. Comparison between probe and RSD measurements shows only qualitative agreement. Future work with focus on reducing the probe measurement uncertainties and on improving the optical setup used for the RSD measurements.

Frequency analysis of oblique shock wave boundary layer interaction

Frequency analysis has been performed for the oblique shockwave boundary layer interaction (OSWBLI). Rainbow Schlieren Deflectometry (RSD) has been used to capture the flow data at 5000 frames per second. The experimental setup produces a free stream flow of Mach 3.1. This flow upon encountering a 12 degree isoceles traingular prism attached to the roof of the test section generate the required oblique shock in the test section.

A Spectral Analysis Algorithm to Obtain Scalar Turbulence Data from Deflectometric Measurements

A novel algorithm based on spectral analysis of time-resolved deflectometric measurements is developed to obtain statistics of the local scalar field in non-reacting or reacting turbulent flows. The algorithm has been used to investigate time-averaged axisymmetric jet with statistically stationary turbulence. The paper presents the theoretical framework of the algorithm and its validation using synthetic turbulent scalar data simulating refractive index difference field. Synthetic data are used to generate line-of-sight deflectometric data, which are subsequently used to determine the local distributions of mean and root-mean square (RMS) of refractive index difference, and related turbulence parameters. A comparison of direct and reconstructed profiles shows the promise of the algorithm to determine statistics of the local scalar field from the line-of-sight measurements in turbulent flows. Nomenclature B = autocorelation function for refractive index difference (overhead dot is for the gradient field) d = jet diameter f = frequency in Fourier domain kx, ky = wave numbers or Fourier modes in X and Y direction, respectively l = integral length scale Nx, Ny = number of data points along X or Y direction. P = power spectral density (suffix x for gradient field) r = radial coordinate t = time T = time period for statistical stationarity x, y = transverse and longitudinal co-ordinates X, Y = maximum dimensions along x and y directions. α = shape factor of Gaussian spectral density function considered for data generation. δ = refractive index difference Δ = increment η = the value along y-coordinate µ = represents mean of the quantity indicated in subscript σ = represents the standard deviation of the quantity indicated in subscript. Θ = deflection angle φ = phase angle ξ = the value along x-coordinate

Crossbeam Rainbow Schlieren Deflectometry Technique for Scalar Measurements in Turbulent Flows

In the past, the rainbow schlieren deflectometry technique has been employed to obtain scalar measurements in non-reacting and reacting laminar steady or unsteady flows. The technique has been limited to laminar flows because the path integrated beam deflection angle data must be de-convulated to obtain the local flow properties. In this study, a cross beam approach, whereby two orthogonal beams are employed is explored for statistical measurements in turbulent flows. The theoretical framework of the cross beam correlation technique requiring assumptions of homogeneous and isotropic turbulence is presented. The workability of the technique is verified using numerical simulations of an unsteady laminar helium-air jet.