Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-16T20:28:54.231Z Has data issue: false hasContentIssue false
  • English
  • Français

Real-fluid effects on standing-wave thermoacoustic instability

Published online by Cambridge University Press:  25 November 2019

Mario Tindaro Migliorino Open the ORCID record for Mario Tindaro Migliorino [Opens in a new window]  and
Carlo Scalo
Mario Tindaro Migliorino*
Affiliation:
Department of Mechanical Engineering, Purdue University, West Lafayette, IN47907, USA
Carlo Scalo
Affiliation:
Department of Mechanical Engineering, Purdue University, West Lafayette, IN47907, USA
*
†Present address: Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, 00184 Rome, Italy. Email address for correspondence: mariotindaro.migliorino@uniroma1.it
Get access Rights & Permissions [Opens in a new window]

Abstract

We have performed high-order compressible Navier–Stokes simulations of a thermoacoustically unstable resonator employing $\text{CO}_{2}$ in transcritical conditions. The parameter space spans the range of base pressures $p_{0}=1.01-1.5\,p_{cr}$ and temperature differences $\unicode[STIX]{x0394}T=T_{hot}-T_{cold}$ up to 200 K, with thermodynamic and transport properties obtained from the Peng–Robinson equation of state and Chung’s model. The set-up is a classic standing-wave thermoacoustic resonator, which has been optimized resulting in a minimum temperature difference required to sustain the instability of 23 K. Strong real-fluid effects in the thermoacoustic response in the linear regime are observed: (i) the thermoviscous functions need to depend on the complex eigenvalue (and not just the angular frequency) for linear theory to accurately predict the growth rate observed in the Navier–Stokes simulations, due to a high growth-rate-to-frequency ratio; (ii) the growth rate and frequency vary in a non-monotonic fashion with respect to $p_{0}$ and $\unicode[STIX]{x0394}T$; (iii) the pressure eigenmode amplitude tends to flatten out, and the pressure–velocity phase difference smoothly transitions from $\unicode[STIX]{x03C0}/2$ to $-\unicode[STIX]{x03C0}/2$ at the average pressure node location; and (iv) the sharp change in base acoustic impedance at transcritical conditions introduces a discontinuity in the eigenmodes’ spatial derivative. The energy budgets illustrate, for a given $\unicode[STIX]{x0394}T$, the increase of the acoustic power produced, but also of the heat input required, for thermodynamic conditions approaching the critical point. Finally, intense mass transport events at transcritical conditions are shown to entail thermodynamic and convective nonlinearities, which do not, however, govern the limit cycle physics, dominated instead by nonlinear minor losses.

JFM classification

Compressible Flows: Gas dynamics Acoustics: Acoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A23
Copyright
© 2019 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abgrall, R. 1996 How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125 (1), 150–160.CrossRefGoogle Scholar
Alexander, D., Migliorino, M. T., Heister, S. D. & Scalo, C. 2018 Numerical and experimental analysis of a transcritical thermoacoustic prototype. In 2018 Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics.Google Scholar
Backhaus, S. & Swift, G. W. 1999 A thermoacoustic Stirling heat engine. Nature 399 (6734), 335–338.CrossRefGoogle Scholar
Backhaus, S. & Swift, G. W. 2000 A thermoacoustic-Stirling heat engine: detailed study. J. Acoust. Soc. Am. 107, 3148–3166.CrossRefGoogle ScholarPubMed
Banuti, D. T. 2015 Crossing the Widom-line – supercritical pseudo-boiling. J. Supercrit. Fluids 98, 12–16.CrossRefGoogle Scholar
Casiano, M. J., Hulka, J. R. & Yang, V. 2010 Liquid-propellant rocket engine throttling: a comprehensive review. J. Propul. Power 26 (5), 897–923.CrossRefGoogle Scholar
Ceperley, P. H. 1979 A pistonless Stirling engine – the traveling wave heat engine. J. Acoust. Soc. Am. 66, 1239–1244.Google Scholar
Chung, T.-H., Ajlan, M., Lee, L. L. & Starling, K. E. 1988 Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Engng Chem. Res. 27 (4), 671–679.CrossRefGoogle Scholar
Elison, B. P., Mann, P. V. & Sinha, A. K.2014 Implementing microscale thermoacoustic heat and power control for processors and 3d chipstacks. US Patent App. 13/624,051.Google Scholar
Faith, L. E., Ackerman, G. H. & Henderson, H. T.1971 Heat sink capability of Jet A fuel: heat transfer and coking studies. Tech. Rep. Shell Development Company.Google Scholar
Fisher, M. E. & Widom, B. 1969 Decay of correlations in linear systems. J. Chem. Phys. 50 (20), 3756–3772.CrossRefGoogle Scholar
Gupta, P., Lodato, G. & Scalo, C. 2017 Spectral energy cascade in thermoacoustic shock waves. J. Fluid Mech. 831, 358–393.CrossRefGoogle Scholar
Herring, N. R.2007 On the development of compact, high performance heat exchangers for gas turbine applications. PhD thesis, Purdue University.CrossRefGoogle Scholar
Herring, N. R. & Heister, S. D. 2006 Review of the development of compact, high performance heat exchangers for gas turbine applications. In ASME International Mechanical Engineering Congress and Exposition. ASME.Google Scholar
Hines, W. S. & Wolf, H. 1962 Pressure oscillations associated with heat transfer to hydrocarbon fluids at supercritical pressures and temperatures. Am. Rocket Soc. J. 32 (3), 361–366.Google Scholar
Hitch, B. & Karpuk, M. 1998 Enhancement of heat transfer and elimination of flow oscillations in supercritical fuels. In 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. American Institute of Aeronautics and Astronautics.Google Scholar
Hunt, S.2016 Thermoacoustic oscillations in supercritical fluid flows. PhD thesis, Purdue University.Google Scholar
Hunt, S. & Heister, S. D. 2014 Thermoacoustic oscillations in supercritical fuel flows. In 12th International Energy Conversion Engineering Conference. American Institute of Aeronautics and Astronautics.Google Scholar
Idelchik, I. E. 2003 Handbook of Hydraulic Resistance, 3rd edn. CRC Press.Google Scholar
Karni, S. 1994 Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112 (1), 31–43.CrossRefGoogle Scholar
Kawai, S., Terashima, H. & Negishi, H. 2015 A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state. J. Comput. Phys. 300 (Supplement C), 116–135.CrossRefGoogle Scholar
Kirchhoff, G. 1868 Über den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung. Pogg. Ann. 134, 177–193.Google Scholar
Kramers, H. A. 1949 Vibrations of a gas column. Physica 15 (971), 971–984.CrossRefGoogle Scholar
Lin, J., Scalo, C. & Hesselink, L. 2016 High-fidelity simulation of a standing-wave thermoacoustic–piezoelectric engine. J. Fluid Mech. 808, 19–60.CrossRefGoogle Scholar
Linne, D., Meyer, M., Edwards, T. & Eitman, D. 1997 Evaluation of heat transfer and thermal stability of supercritical JP-7 fuel. In 33rd Joint Propulsion Conference and Exhibit. American Institute of Aeronautics and Astronautics.Google Scholar
Malone, J. F. J. 1931 A new prime mover. J. R. Soc. Arts 79 (4099), 679–709.Google Scholar
Migliori, A. & Swift, G. W. 1988 Liquid sodium thermoacoustic engine. Appl. Phys. Lett. 53 (5), 355–357.CrossRefGoogle Scholar
Migliorino, M. T., Chapelier, J.-B., Scalo, C. & Lodato, G. 2018 Assessment of spurious numerical oscillations in high-order spectral difference solvers for supercritical flows. In 2018 Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics.Google Scholar
Migliorino, M. T., Gupta, P. & Scalo, C. 2017 Real fluid effects on thermoacoustic standing-wave resonance in supercritical CO2. In 8th AIAA Theoretical Fluid Mechanics Conference. American Institute of Aeronautics and Astronautics.Google Scholar
Migliorino, M. T. & Scalo, C. 2017 Dimensionless scaling of heat-release-induced planar shock waves in near-critical CO2. In 55th AIAA Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics.Google Scholar
O’Neill, L. E. & Mudawar, I. 2018 Mechanistic model to predict frequency and amplitude of density wave oscillations in vertical upflow boiling. Intl J. Heat Mass Transfer 123, 143–171.CrossRefGoogle ScholarPubMed
Palumbo, M.2009 Predicting the onset of thermoacoustic oscillations in supercritical fluids. Master’s thesis, Purdue University, West Lafayette, IN.Google Scholar
Pantano, C., Saurel, R. & Schmitt, T. 2017 An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows. J. Comput. Phys. 335, 780–811.CrossRefGoogle Scholar
Peng, D.-Y. & Robinson, D. B. 1976 A new two-constant equation of state. Ind. Engng Chem. Fundam. 15 (1), 59–64.CrossRefGoogle Scholar
Petach, M., Tward, E. & Backhaus, S.2004 Design of a High Efficiency Power Source (HEPS) based on thermoacoustic technology. NASA Tech. Rep.Google Scholar
Poinsot, T. & Veynante, D. 2011 Theoretical and Numerical Combustion, 3rd edn. R.T. Edwards, Inc.Google Scholar
Rayleigh, 1878 The explanation of certain acoustical phenomena. Nature 18, 319–321.CrossRefGoogle Scholar
Rott, N. 1969 Damped and thermally driven acoustic oscillations in wide and narrow tubes. Z. Angew. Math. Phys. 20, 230–243.CrossRefGoogle Scholar
Scalo, C., Lele, S. K. & Hesselink, L. 2015 Linear and nonlinear modeling of a theoretical traveling-wave thermoacoustic heat engine. J. Fluid Mech. 766, 368–404.CrossRefGoogle Scholar
Soave, G. 1972 Equilibrium constants from a modified Redlich–Kwong equation of state. Chem. Engng Sci. 27, 1197–1203.CrossRefGoogle Scholar
Swift, G. W. 1988 Thermoacoustic engines. J. Acoust. Soc. Am. 84 (4), 1145–1181.CrossRefGoogle Scholar
Swift, G. W. 1992 Analysis and performance of a large thermoacoustic engine. J. Acoust. Soc. Am. 92 (3), 1551–1563.CrossRefGoogle Scholar
Swift, G. W., Migliori, A., Hofler, T. & Wheatley, J. 1985 Theory and calculations for an intrinsically irreversible acoustic prime mover using liquid sodium as primary working fluid. J. Acoust. Soc. Am. 78 (2), 767–781.CrossRefGoogle Scholar
Tijani, M. E. H. & Spoelstra, S. 2011 A high performance thermoacoustic engine. J. Appl. Phys. 110, 093519.CrossRefGoogle Scholar
Toro, E. F. 2002 Anomalies of conservative methods: analysis, numerical evidence and possible cures. Comput. Fluid Dyn. J. 11 (1), 128–143.Google Scholar
Tucker, S. C. 1999 Solvent density inhomogeneities in supercritical fluids. Chem. Rev. 99, 391–418.CrossRefGoogle ScholarPubMed
Wang, H., Zhou, J., Pan, Y. & Wang, N. 2015 Experimental investigation on the onset of thermo-acoustic instability of supercritical hydrocarbon fuel flowing in a small-scale channel. Acta Astron. 117, 296–304.CrossRefGoogle Scholar
Ward, B., Clark, J. & Swift, G. 2012 Design Environment for Low-Amplitude Thermoacoustic Energy Conversion: Users Guide. Los Alamos National Laboratory.Google Scholar
Yazaki, T., Iwata, A., Maekawa, T. & Tominaga, A. 1998 Traveling wave thermoacoustic engine in a looped tube. Phys. Rev. Lett. 81 (15), 3128–3131.CrossRefGoogle Scholar