Adaptation of the Fourier–Hankel method for deflection tomographic reconstruction of axisymmetric field

Chehouani, H.; Fagrich, Mahfoud El

doi:10.1364/ao.52.000439

Cited by 26 publications

(20 citation statements)

References 19 publications

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“…In order to calibrate the pixel intensity of Schlieren images to absolute refraction angle, a 'weak' plano lens with radius r much smaller than its focal length f was applied, with r = 12.7 mm and f = 10 m (CVI PLCX-25.4-5151.0-C). Based on that, a field of local refractive index difference was reconstructed according to a numerical Abel inversion method of adaptive Fourier-Hankel [13]. Then the refractive index field was obtained and using the Gladstone-Dale law the neutral-species density distribution was obtained [14].…”

Section: Calibrated Schlieren Photographymentioning

confidence: 99%

Full spatial-field visualization of gas temperature in an air micro-glow discharge by calibrated Schlieren photography

Xiong

Wang

et al. 2018

J. Phys. D: Appl. Phys.

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Gas temperature is an important basic parameter for both fundamental research and applications of plasmas. In this work, efforts were made to visualize the full spatial field of gas temperature (T g ) in a microdischarge with sharp T g gradients by a method of calibrated Schlieren (CS) photography. Compared to other two typical diagnostic approaches, optical emission spectroscopy (OES) and Rayleigh scattering, the proposed CS method exhibits the ability to capture the whole field of gas temperature using a single Schlieren image, even the discharge is of non-luminous zones like Faraday dark space (FDS). The image shows that the T g field in the studied micro-glow air discharge expands quickly with the increase of discharge currents, especially in the cathode region. The two-dimensional maps of gas temperature display a 'W-shape' with sharp gradients in both areas of negative and positive glows, slightly arched distributions in the positive column, and cooling zones in the FDS. The obtained T g fields show similar patterns to that of the discharge luminance. With an increase in discharge currents, more electric energy is dissipated by heating air gas and inducing constriction of the low-temperature FDS. Except in the vicinities of electrode boundaries, due to the interference from optical diffraction, the estimated gas temperature distributions are of acceptable accuracy, confirmed by the approaches of OES and UV Rayleigh scattering.

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Section: Calibrated Schlieren Photographymentioning

confidence: 99%

Full spatial-field visualization of gas temperature in an air micro-glow discharge by calibrated Schlieren photography

Xiong

Wang

et al. 2018

J. Phys. D: Appl. Phys.

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“…To apply AFH directly, instead of ̄( r) , the deflection angle should be used. Following the derivations in Chehouani and Fagrich (2013), the following equation is found:…”

Section: Direct Vs Indirect Approachmentioning

confidence: 99%

“…Inside the discretization coefficient matrix is of the form as (Ma et al 2008;Chehouani and Fagrich 2013;Tan et al 2015):…”

Section: Direct Vs Indirect Approachmentioning

confidence: 99%

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Towards robust BOS measurements for axisymmetric flows

2020

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Accurately reconstructing a radial refractive index (n) field is challenging in axisymmetric background oriented Schlieren (BOS) measurement. In this study, we systematically investigated several widely adopted inversion algorithms in BOS applications. To quantitatively assess the performance of each algorithm, a synthetic experiment mimicking a helium jet discharged into ambient air was established to provide the reference. Relying on the necessity to solve a Poisson equation for a lineof-sight projected variable, tested algorithms were categorized into two groups: direct and indirect. In the direct approach, the algorithm is applied directly to the light deflection angle () to reconstruct the radial field, defined as = (n − n 0)∕n 0 where n 0 is the reference refractive index. In the indirect group, the Poisson equation is solved first. Then, an inversion algorithm is subsequently applied to the projected to obtain in the radial plane. The two approaches were compared with the synthetic experiment both using the adaptive Fourier-Hankel methods (AFH). The comparison showed that at the cost of introducing the additional step of solving the Poisson equation, the indirect approach performed more accurately when noises were present in the measurements. To identify the proper inversion algorithm suitable for the indirect approach, we further compared four types of algorithms in the synthetic experiments including AFH, onion peeling (OP), three-point Abel (TPA), and filtered back projection tomography (FBPT). The results showed that TPA had the best performance in terms of the reconstruction accuracy with noisy data. Finally, experiments on axisymmetric helium jets were conducted to confirm the effectiveness of the proposed TPA algorithm in the indirect approach.

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“…Smoothing the data, spline interpolation or polynomial fitting can be used to filter out noise and represent the discrete data as a continuous function. Furthermore, representing the data as Legendre polynomials or wavelets 21,22 , or using Fourier-Hankel transforms is also possible 23,24 .…”

Section: B Abel Transformationmentioning

confidence: 99%

Development of Validation Approaches for Numerical Simulation of Combustion Instability using Flame Imaging

Hardi¹,

Hallum²,

Huang³

et al. 2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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Combustion dynamics are controlled by the coupling between heat addition and gas dynamic modes, hence their direct measurement and comparisons with prediction are key to improving computational tools as well as our fundamental understanding of the problem. Whereas gas dynamic modes are relatively easy to measure and compare, measurement and characterization of heat addition are much more difficult due to its complexity and the lack of any direct means of measurement. This paper demonstrates several methods for characterizing and comparing heat release from experiment and simulation. A model rocket combustor is used for the study. Comparisons are made for two configurations, one stable and one unstable. High-speed, line-of-sight imaging of OH* emission from the experiment was first phase averaged, and then treated with an Abel inversion routine to produce a dynamic, two-dimensional field of heat addition. The field before inversion could be compared to line-integrated calculations of heat release rate from three-dimensional large eddy simulations, and after inversion to azimuthally averaged cross-sections from simulations. Modal decomposition analysis of the two-dimensional fields were performed. The applicability and limitations of each comparison approach are assessed. Nomenclature J 0 = zero-order Bessel function of the first kind L op = length of oxidizer post, mm|inch p′ = dynamic pressure, MPa P cc = chamber pressure, MPa Φ = equivalence ratio ′ = unsteady term of a variable ω = frequency, Hz

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Adaptation of the Fourier–Hankel method for deflection tomographic reconstruction of axisymmetric field

Cited by 26 publications

References 19 publications

Full spatial-field visualization of gas temperature in an air micro-glow discharge by calibrated Schlieren photography

Full spatial-field visualization of gas temperature in an air micro-glow discharge by calibrated Schlieren photography

Towards robust BOS measurements for axisymmetric flows

Development of Validation Approaches for Numerical Simulation of Combustion Instability using Flame Imaging

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