Experiments in Fluids

, Volume 47, Issue 1, pp 49–68

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

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

DOI: 10.1007/s00348-009-0636-3

Cite this article as:
Kraft, W.N., Banerjee, A. & Andrews, M.J. Exp Fluids (2009) 47: 49. doi:10.1007/s00348-009-0636-3


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


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


Rayleigh–Taylor growth parameter


Rayleigh–Taylor growth parameter determined using centerline v


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)


Hot-wire anemometer voltage (V)


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


Volume fraction of helium


Gravitational acceleration constant (m/s2)


Mixing layer half width (m)


Wave-number (m−1)


Kinematic viscosity (m2/s)

ρ1, ρ2, ρmix

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


Density fluctuations inside the mixing layer (kg/m3)


Correlation coefficient for ρ′ and v


Non-dimensional time


Molecular mixing parameter


Time (s)

T1, T2, Tmix

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


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)

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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