Capabilities and limitations of 3D flame measurements based on computed tomography of chemiluminescence

Abstract This work investigated the fundamental capabilities and limitations of three-dimensional (3D) combustion measurements based on computed tomography of chemiluminescence (CTC). Experimental, computational, and analytical studies were conducted to map out the fundamental relationship of several parameters important to 3D measurements, including the achievable spatial resolution, the dimension of the measurement volume, and the signal level. The spatial resolution was analyzed both from the Fourier Slice Theorem (FST) and from linear algebraic (LA) considerations, and two limits (the FST and LA limits) were obtained to predict the achievable spatial resolution in tomographic measurements. The achievable signal level and measurement volume were also analyzed under different conditions. These results suggest that it is advantageous to implement tomographic diagnostic such that the projection image fills the camera chip completely. Under such an implementation, the average signal level increases linearly with respect to the size of the measurement volume, and the spatial resolution under the LA limits degrades linearly with respect to the measurement volume if the chemiluminescence emission intensity remains constant. We expect these results to be valuable not only for CTC, but also for tomography diagnostics based on other types of signals because the mathematical formulation in this work is not specific to chemiluminescence signals.

[1]  Michel Defrise,et al.  Interest of the ordered subsets expectation maximization (OS-EM) algorithm in pinhole single-photon emission tomography reconstruction: a phantom study , 2000, European Journal of Nuclear Medicine.

[2]  Lin Ma,et al.  Volumetric imaging of turbulent reactive flows at kHz based on computed tomography. , 2014, Optics express.

[3]  Weiwei Cai,et al.  Information content of scattering measurements and characterization of spheroids , 2008 .

[4]  Christian B Allen,et al.  48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition , 2010 .

[5]  J. Driscoll.  Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities , 2008 .

[6]  Fulvio Scarano,et al.  Tomographic PIV: principles and practice , 2012 .

[7]  Lin Ma,et al.  Application of simulated annealing for multispectral tomography , 2008, Comput. Phys. Commun..

[8]  T. Nonn,et al.  Generation and visualization of volumetric PIV data fields , 2011 .

[9]  Nicholas A. Worth,et al.  Tomographic reconstruction of OH* chemiluminescence in two interacting turbulent flames , 2013 .

[10]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[11]  Sébastien Candel,et al.  Tomographic reconstruction of heat release rate perturbations induced by helical modes in turbulent swirl flames , 2013 .

[12]  Clemens F. Kaminski,et al.  Quantitative three-dimensional imaging of soot volume fraction in turbulent non-premixed flames , 2002 .

[13]  G T Herman,et al.  Resolution in ART. An experimental investigation of the resolving power of an algebraic picture reconstruction technique. , 1971, Journal of theoretical biology.

[14]  Robert S. Barlow,et al.  Laser diagnostics and their interplay with computations to understand turbulent combustion , 2007 .

[15]  Richard Gordon,et al.  Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography. , 2004, Physics in medicine and biology.

[16]  Yojiro Ishino,et al.  Three-Dimensional Computerized Tomographic Reconstruction of Instantaneous Distribution of Chemiluminescence of a Turbulent Premixed Flame , 2005 .

[17]  Xuesong Li,et al.  Practical aspects of implementing three-dimensional tomography inversion for volumetric flame imaging. , 2013, Applied optics.

[18]  Dimitris Mihailidis,et al.  Computed Tomography: From Photon Statistics to Modern Cone-Beam CT , 2008 .

[19]  Jerry Seitzman,et al.  CH∗ chemiluminescence modeling for combustion diagnostics , 2009 .

[20]  Gabor T. Herman,et al.  Image reconstruction from projections : the fundamentals of computerized tomography , 1980 .

[21]  Lin Ma,et al.  Determination of the optimal regularization parameters in hyperspectral tomography. , 2008, Applied optics.

[22]  N. Denisova,et al.  Emission tomography in flame diagnostics , 2013 .

[23]  Lin Ma,et al.  Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography , 2011, Appl. Math. Comput..

[24]  Lin Ma,et al.  Characterization of composite nanoparticles using an improved light scattering program for coated spheres , 2010, Comput. Phys. Commun..

[25]  Sukesh Roy,et al.  50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography. , 2013, Optics express.

[26]  M. Long,et al.  Instantaneous three-dimensional concentration measurements in turbulent jets and flames. , 1988, Optics Letters.

[27]  Andreas Kempf,et al.  Computed Tomography of Chemiluminescence (CTC): High resolution and instantaneous 3-D measurements of a Matrix burner , 2011 .

[28]  Lin Ma.  Measurement of aerosol size distribution function using Mie scattering—Mathematical considerations , 2007 .

[29]  A. Eckbreth.  Laser Diagnostics for Combustion Temperature and Species , 1988 .

[30]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[31]  M. Long,et al.  Time-Resolved Three-Dimensional Concentration Measurements in a Gas Jet , 1987, Science.

[32]  Klaus D. Hinsch.  REVIEW ARTICLE: Holographic particle image velocimetry , 2002 .

[33]  Robert J. Santoro,et al.  Multiangular Absorption Diagnostics of a Turbulent Argon-Methane Jet , 1980 .

[34]  Weiwei Cai,et al.  Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows. , 2010, Applied optics.

[35]  Qing Nian Chan,et al.  Recent advances in the measurement of strongly radiating, turbulent reacting flows , 2012 .

[36]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[37]  Fei Li,et al.  Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence. , 2013, Optics express.

[38]  Gregory Beylkin,et al.  Discrete radon transform , 1987, IEEE Trans. Acoust. Speech Signal Process..

[39]  E. Sidky,et al.  Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT , 2009, 0904.4495.