D.1 IR thermography in Fluid Flow Visualization
The basic principles and techniques of IR thermography applied to fluid mechanics and heat transfer measurements are summarized in [7], [8], [22], [138]. The objectives of the infrared gas detection system are:
• to measure the intensity difference between background radiation that passes through the gas from radiation background that does not;
• quantitatively to determine the absorbed gas distribution of leaked gas density.
Three approaches of infrared thermographic leak testing are the following:
• infrared emission pattern techniques;
• infrared absorption techniques;
• infrared photoacoustic techniques.
The first two techniques rely on an infrared thermographic imager either to image the infrared energy emitted by leaking fluid and its effect on its surroundings (passive technique) or to image the leaking fluid as it is irradiated with specific frequency of infrared energy (active technique). Readily available infrared technology has the capability to provide detailed visualization of various flow phenomena in subsonic to hypersonic flight regimes. For example, in a NASA technical report [10] the infrared thermography was used to obtain data on the state of the boundary layer of a natural laminar flow airfoil in supersonic flight. In addition to the laminar-to-turbulent transition boundary, the infrared camera was able to detect shock waves and present a time dependent view of the flow field. A time dependent heat transfer code was developed to predict temperature distributions on the test subject and any necessary surface treatment. A commercially available infrared camera was adapted for airborne use in this application.
Using the thin foil technique and infrared thermography to visualize the thermal pattern on the wall has been presented in [48]. An image correlation method has been proposed to track the displacement of the observed thermal pattern. Detailed mean and transient surface temperature and pressure, and near wall flow measurements for a reattaching slot jet flow has been presented in [102]. The flow structure in the recirculation region was examined using low-frequency differential surface temperature measurements and time traces along specific locations on the surface. Local surface temperatures were measured non-intrusively with an 8–13 μm wavelength scanning type IR camera.
Thermal flow structures (called ‘thermal eddies’) that vary in the span-wise direction were identified in the recirculation region from low-frequency transient infrared thermographs of the heated surface. Flow visualization is an important tool for investigating turbulent flow, and, specifically, for characterizing low-speed streaks in the boundary layer. In [140] an automatic method has been developed based on edge
heated wall exposed to turbulent flow. The method presented in [140] yields not only the spacing between the low-speed steaks but also their width and separation. The experimental region was in the wall mounted 50 μm-thick constantan floor heated by a direct current source and was imaged on the dry side by an IR camera. Important element in turbulent flow investigations is the typical transition to turbulence with large-scale coherent structures, defined as persistent flow patterns with a relatively long life-time and large spatial extent. The coherent thermal structures on a heated wall have been monitored by means of infrared thermography in [52].
The idea for the above studies based on the assumption that observation of thermal patches at the wall may reflect characteristics of coherent structures of the flow. Despite its widespread usage in surface flow visualization, few researchers have visualized the free fluid flow field using IR imaging. Some examples for these off-surface measurements are the follows. The temperature and velocity distribution and droplet size have been determined with experiments in a turbulent condensing free steam jet, for varying nozzle diameters and varying initial velocities in [104]. A plate was placed vertically along the axis of the jet, in the symmetry plane of the flow. The temperature of the plate was monitored with an infrared camera. Temperature profiles along and perpendicular to the axis were obtained from these thermograms. The temperature of the plate is the wet-bulb temperature of the droplets in the jet. The increase in centreline temperature due to droplet condensation has been successfully predicted. Flow field visualization in a heated air/CO2 axisymmetric free jet using a mid-IR (3–5 μm) detector has been presented in [45]. CO2 gas was used since it has a strong emission peak in the detector bandwidth at 4.24 μm. Two images of the jet intensity – one with pure heated air, and the second with the heated air/CO2 mixture – were taken, and subtracted to isolate the radiant energy from CO2 gas. It was established that non-dimensional intensity profiles in the fully developed region of the jet collapsed onto curves of similarity. Furthermore, the irradiance data collapsed onto a common curve for different initial CO2 concentrations when the data were made non-dimensional with the detected intensity at the centreline axis of the jet at the same jet exit temperature.
A method to visualize the airflow in the long-IR (8–13 μm) region using sulphur hexafluoride (SF6) gas as a tracer has been presented in [101]. SF6 gas has a band in the far IR region centred at 10.56 μm. Scattering by this gas is considered negligible. The visualization technique involves using a background surface at a known temperature different from that of the flow and image subtraction. The technique has been demonstrated on free, impinging, and reattachment subsonic air jets, and has been shown to be an effective means of visualizing flows at both elevated and ambient temperatures.
D.2 Wavelet Threshold of Turbulent Flow Field
Wavelet analysis is a powerful tool for studying physical systems that are of unsteady and/or multiscale in nature [98]. The wavelet transform can decompose a signal into different frequency sub-bands or scales so that each component can be studied with a resolution matched its scale, resulting excellent frequency and spatial resolution [5].
Wavelets have been introduced into turbulence research by Farge et al. [38] and recently have been successfully applied in analyzing, modelling and computing turbulence [47].
Due to the similarity between the multiscale character of turbulence and the wavelet representation, wavelets allow the decompositions of turbulent flow fields and extracting most of the localized coherent structures. This technique is often named as wavelet based Coherent Vortex Simulation (CVS) or coherent vortex (CV) filtering has been developed to model of turbulent flows in [39], [40], [41]. The method extract the coherent modes by projecting the vorticity field onto a wavelet basis and subsequently thresholding the wavelet modes, therefore it is named wavelet threshold as well. This leads to a separation of the flow into coherent vortices on one hand, and an incoherent background noise on the other hand. Both parts are multi-scaled and show different, clearly distinguished statistical behaviour: the coherent vortices appear to be responsible for the shape of the vorticity probability density function (PDF), which differs from a normal distribution, whereas the incoherent background has a Gaussian vorticity PDF.
The CVS filtering has been extended to mixing problems in non-reactive and reactive two-dimensional flows in [16], by wavelet thresholding the (active or passive) scalar fields.
D.3 Inverse Methods with Transmission/Emission Measurements
In the study of radiation heat transfer, a distinction is made between radiation transfer as a surface phenomenon and as a bulk phenomenon. In the case of semitransparent materials as glass, salt, crystals and gases the emission or absorption of radiation occurs at all depths within the medium. Hence the radiation problem is considered as bulk phenomenon. Two different mechanisms cause the attenuation of radiation inside the medium: absorption corresponds to the energy transfer from the incident radiation to the electrons, atoms or molecules, yielding heat conduction in the material. Scattering corresponds to random changes in the propagation direction because of multiply reflection and refraction by small heterogeneities. Özisik and Orlande have been presented the recently most complete account of inverse heat transfer problems in [106].
The inverse analysis of radiation in a participating medium has a broad range of engineering applications, for example, the remote sensing of the atmosphere, the determination of the radiative properties of medium, and the prediction of temperature distribution in flame, and so on. A lot of work has been reported on the identification of radiative properties and the estimation of temperature or source term distribution. In the
have to be reconstructed. In literature theoretical analyses of plane-parallel, spherical, cylindrical, rectangular, axisymmetric and cubic media can be found. The inverse analysis is based on measuring the radiative intensities exiting the boundaries [86], [118], [141].
Inverse analyses of clouds or other gaseous media that can be found in literature are multi-layer approximations or polynomial approximations. In multi-layer approximations the medium is divided into several layers with constant properties [91], [92], [93]. Polynomial approximations have been presented for example in [86], [107], [143].
The inverse analyses of IR radiation of steam jets is little discussed in the literature, but a lot of work has been reported on the reconstruction of flame temperature or species concentration fields by infrared spectral measurements. The measurement of flame temperature or source term distributions is an important subject in combustion analysis.
Optical measurement approaches are especially favoured because of minimal disturbance of the medium being probed. Spectroscopic techniques require a large-scale optical system and only provide point measurements. With the development of the tuneable infrared laser, the recent trend in flame thermometry is applying infrared emission–absorption or emission–transmission methods. For example Zhang and Cheng [141] determined the temperature profile of axisymmetric combustion gas from low-resolution emission and transmission infrared data.
IR-detection of methane gas leakage has been presented in [97]. The methane gas density distribution was measured in air by passive and active IR thermography.
Experimental data have been compared to measurement with conventional gas detector.
The result shows that data obtained by the two types of measurements are quite consistent in the core area of the injected flow.
On many occasions, the absorption coefficient of medium is unknown and often changes with operating conditions. From the experimental point of view, it is desirable to avoid detectors within the medium, and in many situations, it is not suitable to use laser as external radiation source. Under this condition, the unknown temperature profile needs to be estimated simultaneously with the unknown absorption coefficient from the medium self-radiation intensities measured in the boundaries. An inverse analysis has been presented for simultaneous estimation of temperature profile and absorption coefficient for an absorbing, emitting, non-scattering, gray, one-dimensional semitransparent slab with transparent boundaries from the knowledge of the exit radiation intensities at boundary surfaces in [90]. The inverse problem is formulated as an optimization problem and solved using a mixed method of the conjugate gradient method and the one-dimensional search method. The study showed that the temperature profile and the absorption coefficient can be estimated accurately, even with noisy data.
Liu et al. in [91], [93] studied the inverse radiation problem for reconstruction of temperature and absorption coefficient profiles in axisymmetric free flames by the conjugate gradient method and the iteration method. Most of the flames in engineering are turbulent. Due to the nature of turbulent flow, the physical parameters in turbulent
flames fluctuate around these mean values. For engineering application, there are often interested in the profiles of mean values. At present, the time resolution of detector used in the infrared spectral measurement of turbulent flames is usually low in comparison with the characteristic time of turbulent fluctuation; therefore the detector just shows the time-averaged value of radiation signals. The influences of the turbulent fluctuation on the reconstruction of Reynolds time-averaged temperature in turbulent axisymmetric free flames has been investigated by Liu et al. in [94]. The temperature profiles have been retrieved by the low time-resolution data of outgoing emission and transmission radiation intensities. The results show that the effects of turbulent fluctuation on the reconstruction of time-averaged absorption coefficient are not significant.
D.4 Detecting and Modelling of Free Steam Jets
The free round turbulent jet which results when fluid is issued from a circular orifice into free space is one of the classical prototypes of turbulent free shear flows. Its simple geometry makes it an attractive subject for the study of turbulence. The premise of this theory is that, when properly scaled, flow variables as the mean velocity profile can be expressed in terms of a unique function at each downstream distance along the jet axis.
Apart from its dynamics, turbulent jet flow has been also widely studied for its mixing properties. Together with the fluid flow one may also emit a substance from the orifice, which is then dispersed by the turbulence. The substance is usually taken to be passive, which means that it does not contribute to the jet dynamics. It is thus carried along passively by the flow while being dispersed by the turbulence. The mixing behaviour of various jet flows has been the subject of a great deal of research. However, mixing characteristics like concentration fields and entrainment rates have been reported mostly for non-condensing gas jets such as air-to-air jets and other ideal gas jets [12], [13], and reviewed references in they. Vatazhin et al. [129] investigated turbulent jets in the presence of condensation consisting of a gaseous phase (air and water vapour) and a condensed disperse phase (water droplets). They analyzed the possibility of controlling the condensation process by introducing foreign particles into the flow. They made axial temperature measurements using a Chromel-Alumel thermocouple, under varying initial jet temperatures. The condensation in axisymmetric turbulent air-steam jets theoretically and experimentally are investigated under bench experiment conditions in which a hot mist jet is injected from a nozzle into air in [130]. The local characteristics of the dispersed phase (mean particle size, standard deviation of the particle size, particle number and volume concentrations) and its integral characteristics (coefficient of vapour conversion into condensed phase and the optical thickness of the jet in different sections) have been determined. They found that the particle growth rate in all stages coincides with the growth rate of liquid drops. Strum and Toor [122] examined condensing turbulent fog jets generated by issuing saturated water vapour-air mixtures
the maximum condensation driving force, and the observed increase in temperature fluctuations in the fog jet over a dry jet have been observed.
Temperature measurement with special purpose thermocouple temperature probe is reported by Baskaya et al. in [13]. Steam jet centreline decay rate and radial distributions were measured and have been compared to previous measurements.
Mixing characteristics of turbulent water vapour jets was measured in [14]. Radial and axial profiles of air and steam mass flow rates and mass fractions were measured from which centreline decay and half-width spreading rates were calculated and compared with data from the literature. They found that the mixing characteristics of the condensing jets are very similar to those of non-condensing jets extensively reported in the literature. The numerical simulation of a turbulent water vapour jet discharged into ambient air was investigated in [12]. Calculations were made with a computational fluid dynamics (CFD) code. Results were very close to experimental measurements therefore I adopted this model in my study to generate a finite element model to approximate the averaged jet temperature and concentration distribution for validating and testing the inversion algorithm.
By the qualitative analysis of the jet the total liquid water content should be estimated, because the absorption coefficient depends on the concentration of the radiating particle. The relation between the liquid water content and optical properties has to be determined. With the consideration of spherical water droplet particles, the scattering of electromagnetic radiation by homogenous spheres of aerosol and cloud particles is called Mie scattering [17]. Mie theory gives the extinction, scattering and absorption cross-sections and the scattering phase matrix of a single spherical particle. To avoid the complicated Mie calculation, in my study a parameterization of the optical properties of spheres in terms of the physical quantities is applied according to [89]. The optical property of the semi-transparent media can be derived by a priory assumption of droplet sizes. Understanding the condensation process and support to the estimation of effective droplet radius, the paper of Fladerer at al. [42] could be very helpful. For calculating the radiative fluxes in an absorbing-scattering atmosphere, efforts of Wiscomb et al. [77], [120], [137] have to be mentioned. Wiscomb et al. profoundly studied the radiative heat transfer phenomenon in the semi-transparent atmosphere and make accessible the Fortran-90 codes of algorithms of the most frequently used solvers of radiative transfer equations in an anonymous ftp site [43]. Solution algorithms are the Delta-Eddington approximation [77], the two-flux approximation and the discrete ordinates method (DOM) [120].