Experiments in Fluids

, Volume 47, Issue 1, pp 49–68 | Cite as

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

  • Wayne N. Kraft
  • Arindam Banerjee
  • Malcolm J. Andrews
Research Article

Abstract

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (At ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (At ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.

List of symbols

At

Atwood number \( ( \equiv {{\left( {\rho_{1} - \rho_{2} } \right)} \mathord{\left/ {\vphantom {{\left( {\rho_{1} - \rho_{2} } \right)} {\left( {\rho_{1} + \rho_{2} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\rho_{1} + \rho_{2} } \right)}}) \)

α

Rayleigh–Taylor growth parameter

αCL

Rayleigh–Taylor growth parameter determined using centerline v

β

Thermal diffusivity (m2/s)

cp,1, cp,2, cp,mix

Specific heat of inlet streams 1 and 2 and the mixing layer (J/kg °C)

E

Hot-wire anemometer voltage (V)

Ecw

Cold-wire anemometer voltage (V)

fm,1, fm,2

Mass fraction of streams 1 (top) and 2 (bottom) in the mixing layer

fv,1, fv,2

Volume fraction of streams 1 and 2 in the mixing layer

fv,he

Volume fraction of helium

g

Gravitational acceleration constant (m/s2)

h

Mixing layer half width (m)

k

Wave-number (m−1)

υ

Kinematic viscosity (m2/s)

ρ1, ρ2, ρmix

Fluid densities of inlet streams 1 and 2 and the mixing layer (kg/m3)

ρ

Density fluctuations inside the mixing layer (kg/m3)

Rρ′v′

Correlation coefficient for ρ′ and v

τ

Non-dimensional time

θ

Molecular mixing parameter

t

Time (s)

T1, T2, Tmix

Temperature of inlet streams 1 and 2 and the mixing layer (°C)

Ueff

Hot-wire sensor effective (normal) velocity (m/s)

u′, v′, w

Stream-wise, vertical, and cross-stream velocity fluctuations (m/s)

\( \bar{U},\bar{V},\bar{W} \)

Stream-wise, vertical, and cross-stream mean velocities (m/s)

X, Y, Z

Stream-wise, vertical, and cross-stream directions for lab coordinate system (m)

References

  1. Andreopoulos J (1983) Statistical errors associated with probe geometry and turbulence intensity in triple hot-wire anemometry. J Phys E Sci Instrum 16:1264–1271CrossRefGoogle Scholar
  2. Banerjee A (2006) Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. PhD dissertation, Texas A&M UniversityGoogle Scholar
  3. Banerjee A, Andrews MJ (2006) Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. Phys Fluids 18:035107CrossRefGoogle Scholar
  4. Banerjee A, Andrews MJ (2007) Convective heat transfer correlation for a binary air-helium mixture at low Reynolds number. J Heat Transf 129(11):1–12CrossRefGoogle Scholar
  5. Bell JH, Mehta RD (1990) Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J 28:2034–2042CrossRefGoogle Scholar
  6. Benedict LH, Gould RD (1996) Towards better uncertainty estimates in turbulent statistics. Exps Fluids 22:129–136CrossRefGoogle Scholar
  7. Besnard DC, Harlow FH, Rauenzahn RM, Zemach C (1992) Turbulence transport equations for variable-density turbulence and their relationship to two-field models. Los Alamos National Laboratory Report, LAUR-12303Google Scholar
  8. Brown GL, Roshko A (1974) On density effects and large structures in turbulent mixing layers. J Fluid Mech 64:775–816CrossRefGoogle Scholar
  9. Bruun HH (1995) Hot-wire anemometry: principles and signal analysis. Oxford University Press, Oxford, pp 197–207Google Scholar
  10. Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Dover Publications, New York, pp 428–457MATHGoogle Scholar
  11. Chassaing P, Antonia F, Anselmet L, Joly L, Sarkar S (2002) Variable density fluid turbulence. Kluwer, Dordrecht, pp 119–143MATHGoogle Scholar
  12. Cook AW, Cabot W, Miller PL (2004) The mixing transition in Rayleigh–Taylor instability. J Fluid Mech 511:333–362MATHCrossRefMathSciNetGoogle Scholar
  13. Corrsin S (1949) Extended applications of the hot-wire anemometer. Rev Sci Instr 18:469–471Google Scholar
  14. Dalziel SB, Linden PF, Youngs DL (1999) Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability. J Fluid Mech 399:1–48Google Scholar
  15. Danckwerts PV (1952) The definition and measurement of some characteristics of mixtures. Appl Sci Res A 3(4):279–296Google Scholar
  16. Fabris G (1979) Conditional sampling study of the turbulent wake of a cylinder. J Fluid Mech 94:673–709CrossRefGoogle Scholar
  17. Frota MN, Moffat RJ (1983) Effect of combined roll and pitch angles on triple hot-wire measurements of mean and turbulence structure. DISA Inf 28:15–23Google Scholar
  18. Gaulier C (1977) Measurements of air velocity by means of a triple hot-wire probe. DISA Inf 21:16–20Google Scholar
  19. Gull SF (1975) The X-ray, optical and radio properties of young supernova remnants. R Astron Soc Mon Not 171:263–278Google Scholar
  20. Harion JL, Marinot MF, Camano B (1996) An improved method for measuring velocity and concentration by thermo-anemometry in turbulent helium-air mixtures. Exp Fluids 22:174–182CrossRefGoogle Scholar
  21. Hishida M, Nagano Y (1978) Simultaneous measurements of velocity and temperature in nonisothermal flows. Trans ASME J Heat Transf 100:340–345Google Scholar
  22. Jorgensen FE (1971) Directional sensitivity of wire and fibre-film probes. DISA Inf 11:31–37Google Scholar
  23. King LV (1914) On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot-wire anemometry. Philos Trans R Soc A 214:373–432CrossRefGoogle Scholar
  24. Kline SJ, McClintock FA (1953) Describing uncertainties in single-sample measurements. Mech Eng 75:3–8Google Scholar
  25. Koop GK (1976) Instability and turbulence in a stratified shear layer. PhD dissertation, University of Southern CaliforniaGoogle Scholar
  26. Kraft (2008) Simultaneous and instantaneous measurement of velocity and density in Rayleigh–Taylor mixing layers. PhD dissertation, Texas A&M UniversityGoogle Scholar
  27. LaRue JC, Libby PA (1977) Measurements in the turbulent boundary layer with slot injection of helium. Phys Fluids 20(2):192–202CrossRefGoogle Scholar
  28. LaRue JC, Deaton T, Gibson CH (1975) Measurement of high-frequency turbulent temperature. Rev Sci Instr 46:757–764CrossRefGoogle Scholar
  29. Lindl JD (1998) Inertial confinement fusion: the quest for ignition and energy gain using indirect drive. Springer, BerlinGoogle Scholar
  30. Marmottant P, Villermaux E (2004) On spray formation. J Fluid Mech 498:73–111MATHCrossRefGoogle Scholar
  31. McQuaid J, Wright W (1973) The response of a hot-wire anemometer in flows of gas mixtures. Int J Heat Mass Transf 16:819–828CrossRefGoogle Scholar
  32. Moffat RJ (1988) Describing the uncertainties in experimental results. Exp Therm Fluid Sci 1:3–17CrossRefGoogle Scholar
  33. Molchanov OA (2004) On the origin of low- and middle-latitude ionospheric turbulence. Phys Chem Earth 29:559–567Google Scholar
  34. Mueschke NJ, Andrews MJ (2006) Investigation of scalar measurement error in diffusion and mixing processes. Exp Fluids 40:165–175; Erratum 40:176CrossRefGoogle Scholar
  35. Mueschke NJ, Andrews MJ, Schilling O (2006) Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer. J Fluid Mech 567:27–63MATHCrossRefGoogle Scholar
  36. Panchapakasen NR, Lumley JL (1993) Turbulence measurements in axisymmetric jets of air and helium. Part 2: Helium jet. J Fluid Mech 246:225–247CrossRefGoogle Scholar
  37. Ramaprabhu P, Andrews MJ (2004) Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers. J Fluid Mech 502:233–271MATHCrossRefGoogle Scholar
  38. Rose WC (1973) The behavior of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient. PhD dissertation, University of WashingtonGoogle Scholar
  39. Snider DM, Andrews MJ (1994) Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification. Phys Fluids 6:3324–3334CrossRefGoogle Scholar
  40. Vukoslavcevic PV, Radulovic IM, Wallace JM (2005) Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow. Exp Fluids 39:703–711CrossRefGoogle Scholar
  41. Wilson PN, Andrews MJ (2002) Spectral measurements of Rayleigh–Taylor mixing at low-Atwood number. Phys Fluids A 14:938–945CrossRefGoogle Scholar
  42. Youngs DL (1984) Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12:32–44CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Wayne N. Kraft
    • 1
  • Arindam Banerjee
    • 2
  • Malcolm J. Andrews
    • 1
    • 3
  1. 1.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Mechanical and Aerospace EngineeringMissouri University of Science and TechnologyRollaUSA
  3. 3.Los Alamos National LaboratoryLos AlamosUSA

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