3.7 R ESULTS AND D ISCUSSION
3.7.2 Inverse Analysis of IR Thermography Data
The examined cross-section of the jet is discretized by equally spaced points corresponding to the image-pixels. The path-length end points
[
x0,x1]
can be calculated from the cross-section half with radius r12, according to R=2r12, see Fig. 64. The pixel-size has to be determined from the focal-plane distant of the measurement. In this case the resolution is 0.0017 m/pixel.The inverse analysis can be executed at several cross-sections, of which I have presented some examples. Selecting the cross-section at z/ D=5.7, the detected and calculated cross-section intensities are compared in Fig. 88. In this figure the box-plot of the cross-section time-series data is shown. The box has lines at the lower quartile, median, and upper quartile values. The whiskers are lines extending from each end of the box to show the extent of the rest of the data. Outliers are data with values beyond the ends of the whiskers. A thin line represents the time-averaged data. The bold line shows the intensity curve obtained by the presented inverse algorithm. The residual norm between the averaged and the approximated data is 1.56⋅10−4. It can be seen that the approximation curve lies inside the quartile boxes close to the average values through the cross-section.
1 2 3 4 5 6 7 8 91011121314151617181920212223242526272829303132333435363738 8.05
8.1 8.15 8.2 8.25 8.3 8.35
Intensity (W/m2 )
Radial Pixel Number
Approximation Average
Fig. 88. Box-plot and average of time series data completed by the approximation of inverse analysis at cross-section of z/D=5.7
Estimated temperature and absorption coefficient distributions at two distinct cross-sections are plotted in Fig. 89 and Fig. 90, respectively.
0 0.2 0.4 0.6 0.8 1
0 0.05 0.1 0.15 0.2 0.25 0.3
Absorption Coefficient (m-1 )
300 310 320 330 340 350 360 370
y/R
Temperature (K)
α T
Fig. 89. Resulting temperature and absorption coefficient distributions at z/D=4.2
The temperature near the boundary is higher than the background temperature which agrees with the assumption that radiation intensity could be detected only if there is a temperature difference between the inspected medium and the background. It follows from this that the whole boundary layer could not be detected with passive IR techniques.
The liquid water concentration distribution depends on the effective droplet radius as well. The estimated concentration distributions of the examined cross-section with various assumed effective droplet radii can be seen in Fig. 91.
0 0.2 0.4 0.6 0.8 1 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Absorption Coefficient (m-1)
300 310 320 330 340 350 360 370
y/R
Temperature (K)
α T
Fig. 90. Resulting temperature and absorption coefficient distributions at z/D=5.7
0 0.2 0.4 0.6 0.8 1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
y/R LWC (g/m3 )
re= 2 μm re= 4 μm re= 6 μm re= 8 μm re=10 μm
Fig. 91. The estimated LWC distributions of the examined cross-section z/D=5.7 with various assumed effective droplet radii
In this study the total liquid water content (TLWC) in cross-sections between z/D=5 and z/D=8 proved to be practically identical. By assumption, the effective droplet radius is equal to 10μm (this assumption is based on the typical cloud droplet sizes at the end of the droplet formation cycle [42]), the total liquid water content in the examined jet transitional region is equal to 2.4⋅10−2g/m. This value shows that relatively low liquid water content can be detected with the suggested method.
3.8 Summary and Conclusion
In this study I have proved that thermograms of semitransparent free jets, provided by a common, high temperature resolution IR camera, are suitable not only for qualitative, but quantitative analyses as well. The long-IR imaging is a new technique for off-surface monitoring of turbulent phenomenon. The detected long-IR radiation of the
condensed water droplets in the jet represents the turbulent scalar field. I have used the instantaneous images for qualitative analysis, i.e. for visualisation of turbulent free jet flow. I have analysed the time-averaged images to estimate the liquid water content in the jet.
The fictitious jet temperature provided by the IR camera was only slightly higher than the background temperature, therefore in the instantaneous raw images the jet appears as a semitransparent, diffuse cloud. Removal of the high-frequency noise from the image requires special smoothing techniques, since the observed turbulent phenomenon contains a high frequency component as well. Smoothing of this component is not desirable. I have proved that a fuzzy-rule based diffusion filter with an intensity dependent diffusion coefficient could remove the background noise without decreasing the intensity variations in the jet area of the image. I investigated the filtered images with wavelet techniques to verify that these instantaneous images, although the frame rate of the applied imaging system was low, contain information over the turbulent phenomenon. From high frequency sub-bands reconstructed images show the instantaneous flow directions in the jet. A special wavelet transformation algorithm has been applied to extract the coherent turbulent structures. With coherent vortex filtering, the intermittence of the scalar field of the turbulent flow can now be visualized.
The results show that the proposed IR imaging technique with an appropriate image processing technique is able to visualize the various frequency components of the turbulent flow. Increasing the sample rate, for example by applying a FPA (Focal Plane Arrays) IR-camera, could increase the turbulent high frequency content of the images.
I have proposed an energy based method for determining the required minimal number of images that have to be summarized to approximate the stagnant flow pattern i.e. the time-average. Averaged images show the characteristic properties of the fully developed flow, for example half-width spreading rate, centreline decay. The main flow regions can be allocated from the centreline of the average image. The obtained results are in agreement with existing experimental data published in literature.
I have elaborated a complex inverse algorithm for simultaneous estimation of the absorption coefficient and the temperature distribution profiles in the cross-sections of the averaged flow. The proposed iterative minimization procedure utilizes the strong correlation between the temperature and the absorption coefficient fields. I have validated the proposed algorithm using FEM generated test data of 2D axisymmetric wet steam jet. Test results confirm that the function form approximation of these distributions is acceptable. The advantages of the proposed function form approximation of the temperature and the absorption coefficient profiles are that it has less unknown parameters than in multilayer approximations and the temperature and absorption coefficient profiles can be estimated simultaneously.
The quantitative analysis, i.e. in the presented examples determining the liquid water content, requires additional information over the effective droplet radius. This parameter is needed for the calculations and cannot be derived from the detected
IR-4 Further Work
The coarse level iterating multigrid algorithm has been developed for solving heat equations extended with the hysteresis operator. The idea behind the method can be used in other nonlinear multigrid solvers, in cases of large systems of equations. The fuzzy extension to the diffuse image filters can be useful in automated monitoring systems, where a well defined type of gray scale images can be expected and which can be trained with the fuzzy system. The idea of the fuzzy rule based diffusion could be extended to the smoothing of colour images but in this experiment only thermal images have been analyzed. Processing of colour images requires further examination.
In this research a new method is proposed to model the vapour-liquid first-order phase transition occurring in a flowing system, which is similar to the equation-of-state type models in its easy identification and in the macro-scale viewpoint, and similar to the statistic models, where the phase transition is described with a hysteresis function. The model can be very useful in several engineering applications, in which an expert could estimate the possible degree of supersaturation/superheating. Introducing a hysteresis model into the vapour-liquid phase transition can improve other macroscale heat transfer models as well, that are associated with boiling and condensation phenomena and have been treated until now as virtually isothermal heat transfer processes. Since the proposed hysteresis model does not contain dynamics; it is assumed that the predefined degree of supersaturation and superheating always occurs. A narrow hysteresis band can be accepted for numerical reasons and this type of model can be recommended in all cases where otherwise an equation-of-state type model would be used. Occurrence of wider hysteresis can be expected in metastable states, this type of parameterization can be acceptable if the simulation is directed towards analysis of transient heat transfer processes accompanied with metastable phase transitions. This method is recommended for simulations in engineering research.
The presented inverse method could be helpful in predicting the environmental load caused by steam jets released into the atmosphere. The inverse method can be easily modified or expanded to quantitative analysis of free gas jets with other constituents and temperature ranges, provided that the jet consists of one radiating component in the detector wave-band. The volume fraction of particles could be evaluated from the absorption coefficient providing that the complex index of refraction of particles is known. If the scattering effect has to be taken into account, then the ODE solver for the direct problem is not precise enough and has to be replaced with an appropriate radiative transfer equation solver, for example with DISORT.
Thesis
Thesis 1
I proved that the computation time and memory demands for numerically solving heat diffusion problems with hysteretic characteristics of thermal properties can be reduced by the introduction of a new, coarse level iterating multigrid method and the heat diffusion model could be applied both for the analysis of transient thermal processes in composite materials and for enhancing thermal images with properly (hysteresis or fuzzy-rule based) controlled diffusion coefficients.
[P1], [P3], [P5], [P10], [P11], [P12], [P18], [P19], [P20], [P21], [P22].
• For modelling the temperature dependence of the thermal diffusivity of composite materials, I constructed a Preisach-type hysteresis operator, [P1], [P18].
• To reduce the computation time and the memory demands of the hysteresis operator attached to the grid, I introduced a semi-implicit discretization scheme and I developed a coarse level iterating multigrid algorithm, [P3], [P5], [P10], [P19].
• I introduced a nonlinear diffusion filter, which offers a new pre-processing technique in the enhancement of thermal images. With the hysteretic diffusion coefficient function relevant hot or cold regions can be outlined and the other areas degraded in the thermal image, [P11], [P20], [P21].
• I extended the nonlinear diffusion algorithm with a fuzzy-rule based system for the diffusion coefficient, which results in a new approach to thermal image processing and could be very useful not only in enhancement for visual inspection but for pre-processing of images for thresholding or clustering by removing noise and/or smoothing only the predefined intensity region(s) without blurring and moving edges,. The diffusion coefficient field can be the basis of automated segmentation or object detection processes, [P6], [P11], [P12], [P20], [P21], [P22].
Thesis 2
I developed a new, phenomenological, hysteresis type, PDE based vapour-liquid phase transition model that is capable of describing both equilibrium and non-equilibrium temperature driven phase transitions in the frame of homogenous two-phase flow models, which means improvement to the equation-of-state type phase transition models and can be more easily parameterised for engineering applications than the kinetic type models.
[P2], [P4], [P8], [P9], [P13], [P14], [P23], [P24], [P25], [P26], [P27].
• I developed a model fluid conception based statistical description of the isobaric vapour-liquid phase transition. The implemented hysteresis operator describes the probability of the occurrence of temperature dependent phase transformations in the ensemble of bistable water clusters. I treated the vapour-liquid phase transitions on a macro-scale without having to define the free energy functions of phases in advance, [P2], [P8], [P9], [P23].
• I introduced a saturation temperature dependent upper limit of allowable supersaturation to avoid the occurrence of unstable states, [P2], [P8], [P9], [P23].
• I proved that the PDE-based hysteresis phase transition model can be coupled to conservation equations of homogenous non-isothermal two phase flow models, [P2], [P4], [P8], [P13], [P14], [P23], [P24], [P25], [P26], [P27].
• I proved that a narrow hysteresis band corresponds to an equilibrium phase transition model, in which the occurrence of phase transitions before saturation is not allowed. Therefore the smoothing of the order parameter due to numerical reasons is shifted below and over the saturation temperature with the hysteresis function, [P8], [P23].
Thesis 3
I verified that long waveband infrared images of condensing free steam jets are suitable for qualitative and quantitative analysis of instantaneous and averaged turbulent phenomena with the developed image processing techniques based on the fuzzy rule based diffusion filter and wavelet decomposition and with the elaborated complex inverse radiation method.
[P6], [P7], [P12], [P15], [P16], [P22], [P28], [P29], [P30], [P31].
• I proposed the IR sensing of condensing free steam jets. [P15], [P28].
• The instantaneous images of the jet contain high frequency components due to the turbulent characteristics and due to noise. I developed a fuzzy rule based diffusion filter that removes the background noise from the image without considerable decreases in the turbulent components, [P6], [P12], [P22].
• I proved that IR images of the steam jet could be analysed by wavelet decomposition. Wavelet coherent vortex filtering reflects the intermittent character of the free jet, [P7], [P15], [P28], [P29].
• I introduced an energy based method for determination of the required minimal number of images that have to be summarized to approximate the stagnant flow pattern. The parameters of the averaged flow, show good correlation with experimental data in literature, [P7], [P15], [P28], [P29].
• I developed a complex inversion algorithm for simultaneously estimating the temperature and absorption coefficient profiles. Test results with FEM generated data confirm that the function form approximation of temperature and absorption coefficient distributions is acceptable, [P16], [P30], [P31].
Publications Related to Thesis Journal with IF
[P1] Jancskar, I., Ivanyi, A. (2006) Preisach Hysteresis Model for Non-linear 2D Heat Diffusion, Physica B, 372, pp. 222-225. (IF=0.872)
[P2] Jancskar, I., Sari, Z., Szakonyi, L., Ivanyi, A. (2008) Diffuse Interface Modeling of Liquid-Vapor Phase Transition with Hysteresis, Physica B, 403, pp. 505–508. (IF=0.872)
Referred Journal
[P3] Jancskar, I., Ivanyi, A. (2005) Full Multigrid Solver for 2D Steady-State Diffusion, Przeglad Elektrotechniczny, 6, pp. 37-41.
[P4] Szakonyi, L., Jancskar, I., Sari, Z. (2006) Energetic Model for an Elementary Unit of a Steam Network, Pollack Periodica, 1, (3), pp. 91-102.
[P5] Jancskár I., Iványi, A. (2006) Hiszterézises Hődiffúziós Probléma Megoldása Multigrid Módszerrel, Acta Agraria Kaposváriensis, 10(1), pp. 143-155.
[P6] Jancskar, I., Ivanyi, A. (2006) Fuzzy-Rule Based Diffusion in Thermal Image Processing, Pollack Periodica, 1, (1) pp. 115-129.
[P7] Jancskar, I., Ivanyi, A. (2006) Analysis of Free Turbulent Steam Jet by Processing of IR-Images, Pollack Periodica, 2, (2), pp. 13-26.
[P8] Jancskar, I., Ivanyi, A. (2008) Phenomenological Hysteresis Model for Vapor-Liquid Phase Transitions, Pollack Periodica, 3, (1), pp. 5-28.
[P9] Jancskar, I., Sari, Z., Ivanyi, A. (2008) Application of hysteresis in FEM modeling of vapor-liquid phase transitions, Journal of Physics: Conference Series 138, pp.1-18, doi:10.1088/1742-6596/138/1/012008, http://www.iop.org/EJ/toc/1742-6596/138/1 Proceedings of Conference Full Papers
[P10] Jancskar, I., Ivanyi, A. (2005) Solution of a Transient 2D Nonlinear Heat Diffusion Problem with the Multigrid Method, Proceedings of The Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Rome, Italy, 30 August – 2 September, 2005, paper 138, pp. 1-16. (CD-ROM)
[P11] Jancskar, I., Ivanyi, A. (2006) The Effect of the Diffusivity Hysteresis on the Smoothing Properties of Heat Equation Applied to Thermal Images, Proceedings of the 10th International Conference on Optimisation of Electrical and Electronic Equipment, Brassó, May.18-19, 2006, pp. 121-122.
[P12] Jancskar, I., Ivanyi, A. (2006) Fuzzy Rule Based Smoothing of Thermal Images, Proceedings of the Fifth International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain, 12-15 September 2006, paper 140, pp. 1-14. (CD-ROM), ISBN 1-905088-01-9
[P13] Sari, Z., Jancskar, I., Szakonyi, L., Ivanyi, A. (2007) Phenomenological Transient FEM Modelling of a Two-phase Flow with Dynamic Phase Change, Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, St. Julians, Malta, 18-21 September 2007, paper: 217, pp.1-10. (CD-ROM), ISBN 978-1-905088-16-4
[P14] Szakonyi, L., Jancskar, I., Sari, Z. (2006) A Numerical Study of Condensation in a wet Steam Flow under Dynamic Loading, Proceedings of the Fifth International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain, 12-15 September 2006, paper 180. (CD-ROM), ISBN 1-905088-01-9
[P15] Jancskar, I., Ivanyi, A. (2006) Wavelet Analysis of IR-images of a Turbulent Steam Flow, Proceedings of the Fifth International Symposium on Turbulence, Heat and Mass Transfer, Dubrovnik, Croatia, 25 - 29 September, 2006, pp.1-12. (CD-ROM)
[P16] Jancskar, I., Ivanyi, A. (2007) Inverse Analysis for Radiating Components in a Free Turbulent Steam Jet, Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, St. Julians, Malta, 18-21 September 2007, paper: 80, pp.1-22. (CD-ROM), ISBN 978-1-905088-16-4
[P17] Sári Z., Jancskárné A. I., Sipeky A. (2008) Fázisváltozással Járó Kétfázisú Áramlás Modellezése COMSOL – MATLAB _ .NET Környezetben. Konferencia kiadvány, Informatika a Felsőoktatásban 2008, szerk.: Pethő A., Herdon M., Debrecen, 2008. aug. 27-29. pp.1-6. (CD_ROM)
Conference Short Paper or Abstract Books
[P18] Jancskar, I., Ivanyi, A. (2005) Preisach Hysteresis Model for Non-linear 2D Heat Diffusion, Book of Abstracts 5th International Symposium on Hysteresis Modeling and Micromagnetics, 30. May - 1. June, 2005, Budapest, Hungary, pp. 122-123. ISBN 963 420 834 7
[P19] Jancskar, I., Ivanyi, A. (2005) Solution of a Transient 2D Nonlinear Heat Diffusion Problem with the Multigrid Method, Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Rome, Italy, 30 August – 2 September, 2005, pp. 337-338.
[P20] Jancskar, I., Ivanyi, A. (2005) Non-linear Multigrid Diffusion in Thermal Image Processing, 12th International Symposium on Interdisciplinary Electromagnetic, Mechanic &
Biomedical Problems, 12-14 Sept. 2005, Bad Gastein, Austria, pp. 186-187.
[P21] Jancskar, I., Ivanyi, A. (2005) Coarse-level Iterating Multigrid Diffusion in Thermal Image Processing, Abstracts of the First International PhD Symposium in Engineering, October 20-21, 2005, Pécs, Hungary, p.28. ISBN: 963 642 063 7
[P22] Jancskar, I., Ivanyi, A. (2006) Fuzzy Rule Based Smoothing of Thermal Images, Proceedings of the Fifth International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain, 12-15 September 2006, pp. 317-318. ISBN 1-905088-00-0
[P23] Jancskar, I., Sari, Z., Szakonyi, L., Ivanyi, A. (2007) Diffuse Interface Modeling of Liquid-Vapor Phase Transition with Hysteresis, Abstract Book of 6th International Symposium on Hysteresis Modeling and Micromagnetics, 4-6. june 2007, Naples, Italy, p.136.
[P24] Sari, Z., Jancskar, I., Szakonyi, L., Ivanyi, A. (2007) Phenomenological Transient FEM Modelling of a Two-phase Flow with Dynamic Phase Change, Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, St. Julians, Malta, 18-21 September 2007, p.217. ISBN 978-1-905088-15-7
[P25] Sari, Z., Jancskar, I., Szakonyi, L., Ivanyi, A. (2007) Application of Hysteresis in FEM Modelling of Dynamic Phase Transition in Two-Phase Flow, Abstracts of the third International PhD Symposium in Engineering, October 25-26 2007, Pécs, Hungary, p.42.
[P26] Szakonyi, L., Jancskar, I., Sari, Z. (2006) Numerical Study of Condensation in a Wet Steam Flow under Dynamic Loading, Proceedings of the Fifth International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain, 12-15 September 2006, pp. 417-418. ISBN 1-905088-00-0
[P27] Szakonyi, L., Jancskar, I., Sari, Z. (2006) Identification and Modeling of a Steam Network under Wet Steam Flow Conditions, Abstracts of the Second International PhD Symposium in Engineering, October 26-27 2006, Pécs, Hungary, p.52.
[P28] Jancskar, I., Ivanyi, A. (2006) Wavelet Analysis of IR-images of a Turbulent Steam Flow, Turbulence, Heat and Mass Transfer 5, Proceedings of the Fifth International Symposium on Turbulence, Heat and Mass Transfer, Dubrovnik, Croatia, 25 - 29 September, 2006, pp.
251-254.
[P29] Jancskar, I., Ivanyi, A. (2006) Analysis of Free Turbulent Steam Jet by Processing of IR-images, Abstracts of the Second International PhD Symposium in Engineering, Pécs, Hungary, October 26-27 2006, p.29. ISBN: 978-963-642-118-2
Structural and Environmental Engineering Computing, St. Julians, Malta, 18-21 September 2007, p.80. ISBN 978-1-905088-15-7
[P31] Jancskar, I., Ivanyi, A. (2007) IR Image Based Liquid Water Content Estimation, Abstracts of the third International PhD Symposium in Engineering, Pécs, Hungary, October 25-26 2007, p.21.
[P32] Sári Z., Jancskárné A. I., Sipeky A. (2008) Fázisváltozással Járó Kétfázisú Áramlás Modellezése COMSOL – MATLAB _ .NET Környezetben. Konferencia kiadvány, Informatika a Felsőoktatásban 2008, szerk.: Pethő A., Herdon M., Debrecen, 2008. aug. 27-29. p.160. ISBN 978-963-473-129-0
[P33] Jancskar, I., Ivanyi, A. 82008) IR Imaging of Free Turbulent Steam Jets, Abstracts of the fourth International PhD, DLA Symposium, oct. 22-21 2008, M. Ivanyi (Ed.), Pécs, Hungary, p.27. ISBN 978-963-7298-27-1.
Appendix
A. Analysis of Full Multigrid Algorithm on a Steady-State Heat