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Transition Regime Heat Conduction of Argon/Hydrogen and Xenon/Hydrogen

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Transition Regime Heat Conduction of Argon/Hydrogen and Xenon/Hydrogen TRANSITION REGIME HEAT CONDUCTION OF ARGON/HYDROGEN AND XENON/HYDROGEN MIXTURES IN A PARABOLIC TROUGH RECEIVER by FRANK W. BURKHOLDER B.S., Stanford University, l995 M.S., University of Wisconsin, Madison, 2004 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Civil, Environmental, and Architectural Engineering 2011 TRANSITION REGIME HEAT CONDUCTION OF ARGON/HYDROGEN AND XENON/HYDROGEN MIXTURES IN A PARABOLIC TROUGH RECEIVER This thesis entitled: Transition Regime Heat Conduction of Argon/Hydrogen and Xenon/Hydrogen Mixtures in a Parabolic Trough Receiver by Frank W. Burkholder has been approved for the Department of Civil, Environmental, and Architectural Engineering Dr. Michael Brandemuehl Dr. Chuck Kutscher Dr. Moncef Krarti Dr. Harihar Rajaram Dr. Ed Wolfrum Date The final copy of this thesis has been examined by the signatories, and we Find that both the content and the form meet acceptable presentation standards Of scholarly work in the above mentioned discipline. Burkholder, Frank W. (Ph.D., Civil, Environmental, and Architectural Engineering) Transition Regime Heat Conduction of Argon/Hydrogen and Xenon/Hydrogen Mixtures in a Parabolic Trough Receiver Thesis directed by Professor Michael Brandemuehl ABSTRACT The annulus of a parabolic trough receiver is normally evacuated to prevent heat conduction between the internal absorber pipe and the external glass envelope. In the past, this vacuum has been compromised by hydrogen permeation from the heat transfer fluid through the absorber pipe. Heat conduction is significantly increased by the presence of hydrogen in the annulus even though its final pressure – 10 to 100 Pa – is sufficiently low that the thermal conductivity and temperature difference alone cannot predict it. Heat conduction for the concentric cylinder receiver geometry at these pressures is in the transition regime, where neither free molecule nor continuum heat conduction solutions apply. Most solutions to transition regime concentric cylinder heat conduction focus on single species, monatomic gases with small temperature difference boundary conditions. Further constraints limiting their applicability to this research include their typical wire-in-tube geometry and assumption of complete thermal accommodation on the outer cylinder surface. Much experimental data focuses on validating these solutions so is similarly constrained. This study measures heat conduction across the annulus of a parabolic trough receiver in the free- molecular, transition, temperature jump, and continuum regimes for argon-hydrogen and xenon-hydrogen mixtures at an absorber temperature of 350°C. Experimental values are predicted successfully by Sherman’s interpolation formula and the Direct Simulation Monte Carlo Method. Depending on pressure, heat conduction of hydrogen in the annulus of a receiver can be greater than 500 W/m receiver length and decrease the annual net electricity production of a parabolic trough power plant by more than 50% relative to a plant with evacuated receivers. However, heat conduction can be reduced to 50-100 W/m when hydrogen is mixed with an inert gas such that the molar fraction of the inert gas is 95% or greater. iii This results in annual net electricity production penalty of 3-7% instead of more than 50%. Assuming 100 Pa of hydrogen in the annulus of a current receiver, the addition of 1900 Pa of xenon or 4900 Pa of argon will effect this reduction while avoiding natural convection in the annulus. iv DEDICATION To Mom and Dad. Thanks for being so supportive. ACKNOWLEDGMENTS I’ve received a lot of support along this long road. Thanks to the CSP team at NREL. They could have given up on me finishing a long time ago but they didn’t. Thanks to my advisors at CU-Boulder for the same reason. Thanks to Judy Netter for always having time to help, and thanks to Mike Martinez for holding that receiver steady more times than I can count. The data acquisition system would be 4 times more complicated if not for Chuck Kutscher’s timely advice. I’ve really enjoyed talking experimental uncertainty with Mark Mehos, and Reda Ibrahim’s advice on calibration and uncertainty analysis were very valuable. I’m sorry if I didn’t follow all of your advice here, Reda. But I was listening. My sincere thanks to Schott for supplying the specially modified receiver. I wouldn’t have had a dissertation topic without it. I doubt my friends will ever read this, but if they do…THANK YOU. Thanks for sticking by a friend that owes you at least 4 or 5 dinner parties and countless invites to other exciting events. I’m relieved that this chapter of my life is ending, and I’m looking forward to seeing more of you soon. vi CONTENTS CHAPTER I. Introduction .......................................................................................................... 1 Motivation ...................................................................................................... 3 Scope ............................................................................................................ 4 Arrangement of the Dissertation ................................................................... 5 II. Literature review .................................................................................................. 6 Heat conduction regimes ..............................................................................7 Free molecular regime ......................................................................... 11 Accommodation coefficients ................................................................ 12 Temperature jump regime .................................................................... 15 Continuum regime ................................................................................ 18 Transition regime .................................................................................. 19 Boltzmann transport equation ...................................................... 19 Transition regime solution methods ............................................................ 23 BGK collision model ............................................................................. 23 Lees moment method........................................................................... 23 Sherman interpolation formula ............................................................. 26 Direct Simulation Monte Carlo method (DSMC) .................................. 27 Transition regime solution methods applied to gas heat conduction in solar collectors .................................................................................. 28 Selection of models for this study ............................................................... 33 Transition regime experimental data in the literature ................................. 35 Uncertainty analysis .................................................................................... 36 Differential analysis .............................................................................. 38 vii Monte Carlo analysis ............................................................................ 39 Latin Hypercube sampling ............................................................... 44 III. Modeling ............................................................................................................ 47 Estimating accommodation coefficients .................................................... 48 Sherman Interpolation Formula ................................................................. 51 Gas mixture thermal conductivity ......................................................... 52 Sherman summary ............................................................................... 53 Direct Simulation Monte Carlo (DSMC) Method ......................................... 56 Molecule movement and collision with boundaries .............................. 57 Collisions between molecules .............................................................. 58 Collision dynamics ................................................................................ 60 Inelastic collisions ................................................................................. 61 DSMC gas inputs ................................................................................. 62 Convergence investigation ................................................................... 65 DSMC convergence summary ............................................................. 72 IV. Testing... ............................................................................................................ 74 Heat conduction test overview .................................................................... 75 Parabolic trough receiver specifications ............................................... 83 Temperature measurement .................................................................. 84 Power measurement ............................................................................ 91 Pressure measurement ........................................................................ 92 Baking out and off-gassing ................................................................... 93 The gases ............................................................................................. 94 Safety ...................................................................................................94 Heat conduction test procedure .................................................................
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