STATISTICALLY STEADY MEASUREMENTS OF RAYLEIGH-TAYLOR MIXING IN A GAS CHANNEL A Dissertation by ARINDAM BANERJEE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 2006 Major Subject: Mechanical Engineering STATISTICALLY STEADY MEASUREMENTS OF RAYLEIGH-TAYLOR MIXING IN A GAS CHANNEL A Dissertation by ARINDAM BANERJEE Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Chair of Committee, Malcolm J. Andrews Committee Members, Ali Beskok Gerald Morrison Othon Rediniotis Head of Department, Dennis O’Neal August 2006 Major Subject: Mechanical Engineering iii ABSTRACT Statistically Steady Measurements of Rayleigh-Taylor Mixing in a Gas Channel. (August 2006) Arindam Banerjee, B.E., Jadavpur University; M.S., Florida Institute of Technology Chair of Advisory Committee: Dr. Malcolm J. Andrews A novel gas channel experiment was constructed to study the development of high Atwood number Rayleigh-Taylor mixing. Two gas streams, one containing air and the other containing helium–air mixture, flow parallel to each other separated by a thin splitter plate. The streams meet at the end of a splitter plate leading to the formation of an unstable interface and of buoyancy driven mixing. This buoyancy driven mixing experiment allows for long data collection times, short transients and was statistically steady. The facility was designed to be capable of large Atwood number studies of AtB B ~ 0.75. We describe work to measure the self similar evolution of mixing at density differences corresponding to 0.035 < AtB B < 0.25. Diagnostics include a constant temperature hot-wire anemometer, and high resolution digital image analysis. The hot-wire probe gives velocity, density and velocity-density statistics of the mixing layer. Two different multi-position single-wire techniques were used to measure the velocity fluctuations in three mutually perpendicular directions. Analysis of the measured data was used to explain the mixing as it develops to a self-similar regime in this flow. These measurements are to our iv knowledge, the first use of hot-wire anemometry in the Rayleigh-Taylor community. Since the measurement involved extensive calibration of the probes in a binary gas mixture of air and helium, a new convective heat transfer correlation was formulated to account for variable-density low Reynolds number flows past a heated cylinder. In addition to the hot-wire measurements, a digital image analysis procedure was used to characterize various properties of the flow and also to validate the hot-wire measurements. A test of statistical convergence was performed and the study revealed that the statistical convergence was a direct consequence of the number of different large three-dimensional structures that were averaged over the duration of the run. v ACKNOWLEDGEMENTS I would like to thank my research advisor, Prof. Malcolm J. Andrews, for his guidance, support and advice during the course of this work. This work has been funded by the US Department of Energy under contract number DE-FG03-02NA00060. I also wish to thank Wayne Kraft for his help in running the experiments and our numerous discussions about the various diagnostics used in this work. Special thanks are also due to Nicholas Mueschke, Michael Peart and Gopinath Subramanian for their help in construction of the facility. I would also like to thank my parents for giving me the love, values and virtues in life. Their encouragement over the years has been the motivation in getting a doctoral degree. Special thanks, love and appreciation are also due to my wife, Atrayee, for her love, encouragement, support and being a part of this roller coaster life of a graduate student. I wish her all the best for her dissertation work. I am also thankful to my parents-in-law for being supportive over the years. Lastly and most importantly, I would like to thank Dr. Kunal Mitra at Florida Tech for giving me the opportunity to pursue higher studies in the United States and motivating me to pursue a career in research and teaching. vi TABLE OF CONTENTS Page ABSTRACT……………………………………………………………………………..iiiT ACKNOWLEDGEMENTSU U ...............................................................................................v TABLE OF CONTENTS..................................................................................................vi LIST OF FIGURES...........................................................................................................ix LIST OF TABLES ......................................................................................................... xiii 1.U INTRODUCTIONU ..........................................................................................................1 1.1U BackgroundU ............................................................................................................1 1.2U Previous Rayleigh-Taylor ExperimentsU .................................................................5 1.3U Rayleigh-Taylor Experiments at Texas A&MU .....................................................10 1.4U Hot-Wire Anemometry - Advantages and LimitationsU ........................................17 1.5U Objectives of Present ResearchU ............................................................................20 2.U EXPERIMENTAL DESIGNU ........................................................................................21 2.1U Experimental ApparatusU .......................................................................................21 2.2U Mass Flow Rate CalibrationU .................................................................................26 3.U VISUALIZATION DIAGNOSTICSU ...........................................................................32 3.1U Visualization Technique – CalibrationU ................................................................32 3.2U Correction for Non-Uniform BacklightU ...............................................................35 3.3U Steps in Image Processing DiagnosticsU ...............................................................39 3.4U Qualitative MeasurementsU ...................................................................................41 4.U HOT-WIRE DIAGNOSTICSU ......................................................................................45 4.1U Constant Temperature Anemometry (CTA) for Measuring Velocity FluctuationsU ..............................................................................................45 4.1.1U Calibration of a Single-Normal Hot-Wire ProbeU .....................................48 4.1.2U Hot-Wire Calibration EquationsU ..............................................................51 4.2U Constant Current Anemometry (CCA) for Measuring Temperature FluctuationsU .............................................................................................57 vii Page 4.2.1U The Need for a CCA UnitU ........................................................................57 4.2.2U The Cold (Resistance) Wire ProbeU ...........................................................59 4.3U Single Wire MeasurementsU ..................................................................................61 4.3.1U Multi-Position Single Wire TechniqueU ..................................................61 4.3.2U Multi-Position Multi-Overheat Single Wire TechniqueU .........................66 5.U CONVECTION CORRELATIONS FOR A HEATED WIREU ....................................84 5.1U Heat Transfer Correlations from Heated Wires at Low Reynolds NumberU .........84 5.2U Behavior of Hot-Wire/Film in Gas MixturesU .......................................................90 5.3U Effect of Temperature Jump on the Heat Transfer CoefficientU ............................91 5.4U Convective Correlations for Binary Air-Helium MixtureU ....................................94 5.4.1U Properties of Gas MixturesU .......................................................................97 5.4.2U Effect of Binary Air-Helium MixtureU ......................................................99 6.U EXPERIMENTAL RESULTSU ...................................................................................104 6.1U PreliminariesU .......................................................................................................104 6.2U Measurements with Visualization AnalysisU .......................................................106 6.2.1U Mixture Fraction MeasurementU ..............................................................106 6.2.2U Mix Width MeasurementU .......................................................................109 6.2.3U Test of ConvergenceU ...............................................................................113 6.2.4U Growth Constant (α) MeasurementU........................................................116 6.3U Hot-Wire MeasurementsU ....................................................................................120 6.3.1U Measurements with Multi-Position SN-Wire TechniqueU .......................120 6.3.2U Measurements with Multi-Position Multi-Overheat TechniqueU ............124 6.4U Energy BudgetU ....................................................................................................138 7.CONCLUSIONSU U .........................................................................................................140 LITERATUREU CITEDU ..................................................................................................144