Abstract
This article describes experiments to investigate the fluid-to-wall interaction downstream of a highly underexpanded jet, with a pressure ratio of 120, confined in a channel. Heat transfer induced by Joule-Thomson cooling, which is a real gas effect in such a configuration, has critical implications on the safety of pressurised gas components. This phenomenon is challenging to model numerically due to the requirement to implement a real gas equation of state, the large range of (subsonic and supersonic) velocities, the high turbulence levels and the near-wall behaviour. An experimental setup with simple geometry and boundary conditions, and with a wide optical access was designed and implemented. It consisted of a high-pressure gas reservoir at controlled temperature and pressure, discharging argon through a nozzle into a square channel. This facility was designed to allow for a steady-state expansion from over 120 bar to atmospheric pressure for over 1 min. The choice of fluid, pressure and temperature regulation system, and the implementation of a high pressure particle seeding system are discussed. The gas dynamics of this flow was then investigated by two separate optical techniques. Schlieren measurements were used to locate the position of the Mach disk, and planar particle image velocimetry (PIV) was used to measure the turbulent velocity field in the regions of lower velocity downstream. Mie scattering images also indicated the presence of a condensed argon phase in the supersonic region as expected from previous studies on nucleation. The observed location of the sharp interface at the Mach disk was found to be in excellent agreement with the Crist correlation. Rapid statistics were derived from the PIV measurements at 3 kHz. The recirculation zone was found to extend about 4 channel heights downstream, and in the region between 2 and 3 channel heights downstream, a continuous deceleration on the centerline velocity was observed in line with the narrowing of the recirculation zone. The first and second velocity moments as well as Reynold stresses were quantified, including pdf distributions. In addition, a sensitivity and repeatability analysis, an evaluation of the PIV random uncertainty, as well as an estimation of errors induced by particle inertia were performed to allow for a full quantitative comparison with numerical simulations.
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References
Abram C, Fond B, Heyes AL, Beyrau F (2013) High-speed planar thermometry and velocimetry using thermographic phosphor particles. Appl Phys B Lasers O 111:155–160. https://doi.org/10.1007/s00340-013-5411-8
Abram C, Fond B, Beyrau F (2015) High-precision flow temperature imaging using ZnO thermographic phosphor tracer particles. Opt Express 23:19453–19468. https://doi.org/10.1364/OE.23.019453
Abram C, Fond B, Beyrau F (2018) Temperature measurement techniques for gas and liquid flows using thermographic phosphor tracer particles. Prog Energy Combust Sci 64:93–156. https://doi.org/10.1016/j.pecs.2017.09.001
Arun Kumar R, Rajesh G (2017) Shock transformation and hysteresis in underexpanded confined jets. J Fluid Mech 823:538–561. https://doi.org/10.1017/jfm.2017.231
Baughn JW, Hoffman MA, Takahashi RK, Launder BE (1984) Local heat transfer downstream of an abrupt expansion in a circular channel with constant wall heat flux. J Heat Transf 106:131–136. https://doi.org/10.1115/1.3246753
Baab S, Lamanna G, Weigand B (2018) Two-phase disintegration of high-pressure retrograde fluid jets at near-critical injection temperature discharged into a subcritical pressure atmosphere. Int J Multiph Flow 107:116–130. https://doi.org/10.1016/j.ijmultiphaseflow.2018.04.021
Burns RA, Danehy PM (2017) Unseeded velocity measurements around a transonic airfoil using femtosecond laser tagging. AIAA J 55(12):4142–4154. https://doi.org/10.2514/1.J056154
Chauveau C, Davidenko DM, Sarh B, Gökalp I, Avrashkov V, Fabre C (2006) PIV measurements in an underexpanded hot free jet. In: 13th international symposium on the application of laser and imaging techniques to fluid mechanics, Lisbon, Portugal, 26–29 June
Chuech SG, Lai M-C, Faeth GM (1989) Structure of turbulent sonic underexpanded free jets. AIAA J 27(5):549–559. https://doi.org/10.2514/3.10145
Clancy PS, Samimy MO (1997) Two-component planar doppler velocimetry in high speed flows. AIAA J 35(11):1729–1738. https://doi.org/10.2514/2.42
Crist S, Glass DR, Sherman PM (1966) Study of the highly underexpanded sonic jet. AIAA J 4(1):68–71. https://doi.org/10.2514/3.3386
Dawson DM, Books BJ (1999) The Esso Longford gas plant accident—report of the Longford Royal Commission, Tech. rep. https://www.parliament.vic.gov.au/papers/govpub/VPARL1998-99No61.pdf
DeLuca NJ, Miles RB, Jiang N, Kulatilaka WD, Patnaik AK, Gord JR (2017) Fleet velocimetry for combustion and flow diagnostics. Appl Opt 56(31):8632–8638. https://doi.org/10.1364/AO.56.008632
Forkey JN, Finkelstein ND, Lempert WR, Miles RB (1996) Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements. AIAA J 34(3):442–448. https://doi.org/10.2514/3.13087
Förster FJ, Baab S, Steinhausen C, Lamanna G, Ewart P, Weigand B (2018) Mixing characterization of highly underexpanded fluid jets with real gas expansion. Exp Fluids 59(3):44. https://doi.org/10.1007/s00348-018-2488-1
Hwang C, Chow WL, Moslemian D (1993) Base pressure of a sudden expansion from a conical converging nozzle. AIAA J 31(4):657–662. https://doi.org/10.2514/3.11600
Koppenwallner G, Dankert C (1987) Homogeneous condensation in N2, Ar, and H2O free jets. J Phys Chem 91:2482–2486. https://doi.org/10.1021/j100294a008
Krall KM, Sparrow EM (1966) Turbulent heat transfer in the separated, reattached, and redevelopment regions of a circular tube. J Heat Transf 88:131–136. https://doi.org/10.1115/1.3691456
Hahn DW, Necati Özisik M (2012) Heat conduction, 3rd edn. Wiley, Hoboken
Lijo V, Kim HD, Setoguchi T (2012) Numerical investigation of the effects of base size on supersonic flow through a sudden duct enlargement. Proc Inst Mech Eng Part G J Aerosp Eng 226(12):1562–1572. https://doi.org/10.1177/0954410011424984
Matthew MW, Steinwandel J (1983) An experimental study of argon condensation in cryogenic shock tubes. J Aerosol Sci 14(6):755–763. https://doi.org/10.1016/0021-8502(83)90059-9
McMillin BK, Palmer JL, Hanson RK (1993) Temporally resolved, two-line fluorescence imaging of NO temperature in a transverse jet in a supersonic cross flow. Appl Opt 32:7532–7545. https://doi.org/10.1364/AO.32.007532
Meier GEA, Grabitz G, Jungowski WM, Witczak KJ, Anderson JS (1980) Oscillations of the supersonic flow downstream of an abrupt increase in duct cross section. AIAA J 18:394–395. https://doi.org/10.2514/3.50770
Melling A (1997) Tracer particles and seeding for particle image velocimetry. Meas Sci Technol 8:1406–1416. https://doi.org/10.1088/0957-0233/8/12/005
Michael JB, Edwards MR, Dogariu A, Miles RB (2011) Femtosecond laser electronic excitation tagging for quantitative velocity imaging in air. Appl Opt 50(26):5158–5162. https://doi.org/10.1364/AO.50.005158
Miles RB, Connors JJ, Markovitz EC, Howard PJ, Roth GJ (1989) Instantaneous profiles and turbulence statistics of supersonic free shear layers by Raman excitation plus laser-induced electronic fluorescence (relief) velocity tagging of oxygen. Exp Fluids 8(1):17–24. https://doi.org/10.1007/BF00203060
Naik SV, Kulatilaka WD, Venkatesan KK, Lucht RP (2009) Pressure, temperature and velocity measurements in underexpanded free jets using laser-induced fluorescence. AIAA J 47:839–849. https://doi.org/10.2514/1.37343
Paul PH, Lee MP, Hanson RK (1989) Molecular velocity imaging of supersonic flows using pulsed planar laser-induced fluorescence of NO. Opt Lett 14(9):417–419. https://doi.org/10.1364/OL.14.000417.
Pfadler S, Dinkelacker F, Beyrau F, Leipertz A (2009) High resolution dual-plane stereo-PIV for validation of subgrid scale models in large-eddy simulations of turbulent premixed flames. Combust Flame 156(8):1552–1564. https://doi.org/10.1016/j.combustflame.2009.02.010
Raffel M, Willert CE, Wereley ST, Kompenhans J (2007) Particle image velocimetry: a practical guide. Springer, Berlin
Ragni D, Schrijer F, Oudheusden BW, Scarano F (2011) Particle tracer response across schocks measured by PIV. Exp Fluids 50:53–64. https://doi.org/10.1007/s00348-010-0892-2
Rahimi M, Owen I, Mistry J (2003) Heat transfer between an under-expanded jet and a cylindrical surface. Int J Heat Mass Transf 46(17):3135–3142. https://doi.org/10.1016/S0017-9310(03)00116-9
Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol 24(1):012001. https://doi.org/10.1088/0957-0233/24/1/012001
Schreivogel P, Abram C, Fond B, Straußwald M, Beyrau F, Pfitzner M (2016) Simultaneous kHz-rate temperature and velocity field measurements in the flow emanating from angled and trenched film cooling holes. Int J Heat Mass Transf 103:390–400. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.092
Sciacchitano A, Neal DR, Smith BL, Warner SO, Vlachos PP, Wieneke B, Scarano F (2015) Collaborative framework for PIV uncertainty quantification: comparative assessment of methods. Meas Sci Technol 26(7):074004. https://doi.org/10.1088/0957-0233/26/7/074004
Sinha S, Bhabhe A, Laksmono H, Wölk J, Strey R, Wyslouzil B (2010) Argon nucleation in a cryogenic supersonic nozzle. J Chem Phys 132(6):064304. https://doi.org/10.1063/1.3299273
Vinze R, Chandel S, Limaye MD, Prabhu SV (2017) Heat transfer distribution and shadowgraph study for impinging underexpanded jets. Appl Therm Eng 115:41–52. https://doi.org/10.1016/j.applthermaleng.2016.12.046
Wieneke B (2015) PIV uncertainty quantification from correlation statistics. Meas Sci Technol 26(7):074002. https://doi.org/10.1088/0957-0233/26/7/074002
Wilkes Inman J, Danehy P, Nowak R, Alderfer D (2008) Fluorescence imaging study of impinging underexpanded jets. In: 46th AIAA aerospace sciences meeting and exhibit. Reno, Nevada, 7–10 Jan 2008. https://doi.org/10.2514/6.2008-619
Xiao C-N, Fond B, Beyrau F, T’Joen C, Henkes R, Veenstra P, van Wachem BGM (2018) Numerical and experimental investigation of the gas dynamics in a highly underexpanded confined real gas jet. Flow Turbul Combust (submitted)
Yüceil KB (2017) A comparison of PIV and interferometric Rayleigh scattering measurements in the near field of underexpanded sonic jets. Aerosp Sci Technol 67:31–40. https://doi.org/10.1016/j.ast.2017.03.034
Yu J, Vuorinen V, Kaario O, Sarjovaara T, Larmi M (2013) Visualization and analysis of the characteristics of transitional underexpanded jets. Int J Heat Fluid Flow 44:140–154. https://doi.org/10.1016/j.ijheatfluidflow.2013.05.015
Acknowledgements
The authors are grateful to Paul Bruce (Imperial College London) for discussion on the implementation of the Schlieren measurements, and to Christopher Abram (Universität Magdeburg, currently at Princeton University) for his support in implementing the high speed PIV system.
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Fond, B., Xiao, CN., T’Joen, C. et al. Investigation of a highly underexpanded jet with real gas effects confined in a channel: flow field measurements. Exp Fluids 59, 160 (2018). https://doi.org/10.1007/s00348-018-2614-0
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DOI: https://doi.org/10.1007/s00348-018-2614-0