# On hot-wire diagnostics in Rayleigh–Taylor mixing layers

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- Accepted:

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

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## 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 (*A*_{t} ≤ 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 (*A*_{t} ≤ 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

*A*_{t}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

- α
_{CL} Rayleigh–Taylor growth parameter determined using centerline

*v*′*β*Thermal diffusivity (m

^{2}/s)*c*_{p,1},*c*_{p,2},*c*_{p,mix}Specific heat of inlet streams 1 and 2 and the mixing layer (J/kg °C)

*E*Hot-wire anemometer voltage (V)

*E*_{cw}Cold-wire anemometer voltage (V)

*f*_{m,1},*f*_{m,2}Mass fraction of streams 1 (top) and 2 (bottom) in the mixing layer

*f*_{v,1},*f*_{v,2}Volume fraction of streams 1 and 2 in the mixing layer

*f*_{v,he}Volume fraction of helium

*g*Gravitational acceleration constant (m/s

^{2})*h*Mixing layer half width (m)

*k*Wave-number (m

^{−1})*υ*Kinematic viscosity (m

^{2}/s)*ρ*_{1},*ρ*_{2},*ρ*_{mix}Fluid densities of inlet streams 1 and 2 and the mixing layer (kg/m

^{3})*ρ*′Density fluctuations inside the mixing layer (kg/m

^{3})*R*_{ρ′v′}Correlation coefficient for

*ρ*′ and*v*′*τ*Non-dimensional time

*θ*Molecular mixing parameter

*t*Time (s)

*T*_{1},*T*_{2},*T*_{mix}Temperature of inlet streams 1 and 2 and the mixing layer (°C)

*U*_{eff}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)