Introduction Properties of a supercritical fluid: No sharp distinction between liquid and gas phases ---- considered to be a “fluid” Surface tension vanishes Density, thermal conductivity and mass diffusivity varies widely Evaporation not possible in the absence of latent heat --- surface cannot exist
Applications: Diesel engines Gas turbines Liquid fuel rocket engines Reason: Higher chamber pressures lead to a higher specific impulse for the engine, increased power and efficiency. Introduction
Detailed core information Quantitative density measurements Effects of preheating the injected fluid Changes in the core length Stability of the jet Gain insight into the fundamental features of supercritical injection into subcritical and supercritical environments for binary species systems. Expand the database of reliable experimental measurements of supercritical liquid/gas mixing. Goal of the Present Work Insufficient Data Regarding….
Experimental Setup & Technique High Pressure Chamber Test chamber schematic Overall view P max = 70 atm T max = 620 K Injector Diameter = 2 mm
Experimental Setup & Technique Image Acquisition System Continuum Surelite II (Nd:YAG) 355 nm wavelength 10 ns pulse width 10 Hz frequency Princeton Instruments (PI Max II ICCD) 1024 × 1024 resolution 150 ns exposure time 16 bit dynamic range Laser Camera Planar Laser Induced Fluorescence (PLIF) has been used to investigate the mixing characteristics
Experimental Setup & Technique Cylindrical Lenses Test Chamber Band-Pass Filter 355 nm 355 nm + 532 nm Dichroic Mirrors Continuum Surelite II Nd:YAG Laser ICCD Camera
Experimental Setup & Technique Working Fluid: Fluoroketone T boil : 322 K (49 0 C) T cr : 441 K (168 0 C) P cr : 18.4 atm. Decomposition Temperature: 820 K ( 550 0 C) Spectroscopic properties: Unique Non flammable: Safe for use in large quantities.
Laser Sheet Correction Uncorrected image Corrected image An uncorrected image can lead to incorrect density and density gradients Laser sheet absorption through the gas and liquid phases needs to be taken into account before image analysis
Test Conditions Selection of the experimental conditions. Reduced temperatures and pressures have been selected to cover the subcritical to supercritical regime. Cold injection Heated injection Critical point
Subcritical Selected Test Cases Supercritical Subcritical Supercritical Injectant Chamber
Selected Test Cases CaseT r,g T r,l P r,g P r,l 10.691.131.381.51 20.721.211.861.97 30.761.291.881.98 40.801.311.381.51 Supercritical Injection into Subcritical Environment
Injection Experiments Drops observed beyond 10 jet diameters from the injector. Drop formation decreases with increasing chamber temperature. Spreading angle increases with increasing chamber temperature. Observations…
CaseT r,g T r,l P r,g P r,l 11.041.001.261.34 21.061.081.371.47 31.08 1.411.50 41.091.181.471.67 Supercritical Injection into Supercritical Environment Selected Test Cases
Complete supercritical behavior noted. No effects of surface tension. No drops observed up to 20 jet diameters from the injector. Images resemble those of a gaseous jet injected into a gaseous environment. Spreading angle increases with increasing chamber temperature. Observations… Injection Experiments
Results and Discussion Core Length Calculation Core Using the width at the injector, individual square density matrices or blocks are created along the length of the jet (Roy and Segal 2010). The point that corresponds to the maximum density change with respect to its immediate neighbors is taken to be the core length. In this case shown, the core length is close to 20 mm (10 jet diameters).
Results and Discussion Spreading Angle Calculation Location of highest density gradients identify the gas-jet interface. A threshold intensity is used to separate the jet from its surroundings. Axial distances kept very close to the injector exit plane as the initial mixing region can be approximated as two dimensional mixing layers. Spreading Angle Jet Boundary Density Gradients
Results and Discussion Core length remains relatively constant at 11.5 jet diameters. Chamber-to-injectant density ratios vary from 0.01 to 0.12. Our data lies slightly beyond the theory predicted by Abramovich for turbulent non- isothermal submerged cold gas jets. Hence a jet injected at supercritical conditions behaves very similar to a gas jet injected into a gaseous medium. Core Lengths, plotted as a function of chamber-to- injectant density ratio, stay relatively constant at about 11.5 jet diameters.
Results and Discussion The data lies between the Dimotakis’ theory and the proposed model by Reitz and Bracco for diesel sprays. Beyond a density ratio of 0.08, the data appears to be an exact average of these two curves. Below 0.08, it is closer to that of Reitz and Bracco, which is expected since conditions are typically subcritical. Similarity exists with that obtained by Chehroudi for N 2 - N 2 injection at subcritical and supercritical conditions. Jet spreading angle plotted as a function of chamber-to-injectant density ratio.
Dispersion Equation: The following dispersion relation was obtained for a subcritical jet injected into a subcritical atmosphere (Lin, S. P., ‘Breakup of Liquid sheets and Jets’, 2003): For Reynolds numbers of 10,000 and above, the fourth term in the relation can be neglected compared to the others. Hence the simplified form of the dispersion relation is: This has also been used for the same boundary conditions in subcritical cases by Ponstein (1959) and Chandrasekhar (1981). In supercritical cases when We l tends to infinity, the last term in the equation tends to zero, and no solution can be found. Linear Stability Analysis
Solution to the Dispersion Equation: Re=11,500, We =7000, and ρ g / ρ l = 6.25*10 -4 Stability curves for We from 7000 to 30000 Increasing We All the coefficients were kept fixed except the Weber number. Critical conditions were reached asymptotically. Stability curves were obtained for increasingly high Weber numbers. The trends of the most amplified disturbance were noted.
Asymptotic trend of the peak growth rate vs. We for Re=25000 Asymptote reached The Weber numbers have been increased upto one hundred million - large enough to approximate supercritical cases. Five different gas-to-injectant density ratios have been plotted separately, and all of them show a similar trend. The wave numbers increase very steeply up to Weber numbers of about 100000, and then gradually reach an asymptote after We=1000000. Since this wave number corresponds to an extremely small value of the disturbance wavelength, it indicates that in supercritical conditions, the jet is unstable to very small perturbations in the flow. Linear Stability Analysis
Summary A study of a jet at supercritical conditions injected into subcritical and supercritical chamber conditions was undertaken using PLIF. The laser intensity loss through the jet was taken into account. In the case of a supercritical jet injected into a subcritical environment, droplets were observed to form at beyond 10 jet diameters downstream of the injector at lower chamber temperatures. In the case of a supercritical jet injected into a supercritical environment, the jet surface exhibited complete supercritical behavior with no formation of droplets noted and resembled gas-gas mixing. The core length values were found to remain unaffected with density ratios ranging from 0.01 to 0.12 and was found to be 11.5 jet diameters. A model was found for the jet spreading angles which predicted that the angle was proportional to the square-root of the chamber-to-injectant density ratio, following a curve midway between the models of Dimotakis and Reitz for turbulent, gaseous, subsonic, mixing layers and diesel sprays respectively.
Laser Sheet Correction Fluorescence intensity dependence with vapor density A region very close to the window was examined where the laser sheet has not been attenuated by absorption (x=0). The plot shows a weak second-order dependence of the fluorescence signal with the vapor density. Near and above the critical point, non- linearities start to become important (Tran et. al. 2008).
Laser Sheet Correction Photophysics of Fluoroketone The general fluorescence equation can be expressed as (Roy, Gustavsson and Segal 2010): If (p x, p y ) is the pixel where the point (x, y) is imaged, then the fluorescence signal recorded for a specific laser excitation wavelength I(x,y) is: The collection optics efficiency, fractional solid angle, photon to signal count conversion factor and other constants are grouped into a factor F.. It shall also be assumed in this work that σ g + σ e ≈ σ g or simply σ. When scattering is neglected, the drop in laser intensity due to absorption should follow the Beer-Lambert’s law. Thus: Hence, the following relation is obtained for the fluorescence signal: For the linear regime of excitation (Hanson and Mungal 1996), N ph is small, and hence the above equation can be approximated as:
Laser Sheet Correction Fluorescence intensity dependence with laser power The concentration of the fluoroketone vapor inside the chamber was kept fixed. The laser intensity was gradually varied. A non-linear dependence of the signal with laser power is observed. For fixed values of density ρ, constant optics efficiency F and absorption cross-section σ, the fluorescence signal S is dependent on the incident laser intensity I(0,y) as shown below if the quantum yield φ is a constant.
Laser Sheet Correction Calibration of absorption coefficient Since φ has been shown to be a constant, the fluorescence intensity can thus be expressed as: Hence for a specific value of I(0, y), the fluorescence signal also undergoes an exponential drop in intensity across the line of propagation of the laser sheet. Laser fluorescence intensity at 14.7 atm., 165 0 C. Actual intensities have been plotted on the left and the normalized intensities have been plotted on the right.
Laser Sheet Correction An exponential curve is then fitted to the data points and the value of the absorption cross section is obtained. This value of the absorption coefficient is valid for the specified concentration of vapor at a particular chamber pressure and temperature, i.e., 14.7 atm. and 165 0 C. The higher the pressures and temperatures are, the greater is the concentration of vapor, and thus the value of the absorption coefficient. Normalized intensity points vs. the length traversed by the laser sheet in pixels.
Laser Sheet Correction Absorption coefficients for various vapor concentrations were obtained and a calibration curve was obtained. Calibration curve for the absorption coefficient plotted against density, and since it is a straight line, the slope is constant throughout the vapor phase. The absorption coefficient and cross section are related as: The slope of the calibration curve is proportional to the absorption cross section, indicating that the absorption cross section is also constant throughout the vapor phase.