1. TIM2011 SOSGSSD, May 17-19, 2011 Measurements of Probability Density Function in a Thermal Mixing Layer Embedded in Uniformly Sheared Turbulence Amir Behnamian and Stavros Tavoularis Department of Mechanical Engineering

2. TIM2011 Scalar Admixture Transported by Turbulence K.R. Sreenivasan (1991)

3. TIM2011 Analytical Approach - How to Model Turbulent Flow For a stationary and ergodic fluid field - Velocity field –Temperature or concentration fields

4. TIM2011 Experimental Approach - Simple Configurations Nearly homogeneous, uniformly sheared turbulence (USF) –Uniform mean temperature gradient (UTG) –Heated source line –Thermal mixing layer Tavoularis and Corrsin (1981) Ferchichi and Tavoularis (2002) Karnik and Tavoularis (1989)

5. TIM2011 Probability Density Function (PDF) Method Advantages –Feasible to write transport equation for Joint velocities PDF (Lundgren 1969) Concentration joint scalar PDF ( fuel, oxidant mass fraction-enthalpy) (Dopazo and O’Brien 1974, Pope 1976) Velocity-scalar joint PDF (Pope 1982) –No need for modeling reacting flow with large density variation and nonlinear reaction rate

6. TIM2011 Transport Equation of Joint PDF Transport equation of joint velocity and scalar for –Statistically stationary flow –Constant density

7. TIM2011 Joint PDF of Velocity-Scalar in USF with UTG Statistically stationary flow Nearly homogeneous flow Tavoularis and Corrsin (1981) Ferchichi and Tavoularis (2002)

8. TIM2011 PDF Method for Scalar Fluctuations in USF with UTG The Gaussian PDF of the temperature fluctuation is a unique solution of the temperature transport PDF equation Ferchichi and Tavoularis (2002)

9. TIM2011 Conditional Expectations Velocity fluctuations depend linearly on scalar value

10. TIM2011 Proposed Study: Thermal Mixing Layer in USF

11. TIM2011 Experimental Configuration and Instrumentation Multi-sensor cold-wire and hot-wire probes ΔT max < 2 K passive heating

12. TIM2011 Measured Parameters Fine structures of scalar and velocity field –Scalar-velocity joint statistics –Three temperature derivatives in three Cartesian directions to be measured simultaneously – Dissipation rate of temperature fluctuations, without the need to assume local isotropy Conditional expectations –Scalar dissipation rate conditioned upon the scalar – Conditional expectation of the velocity components upon the scalar value

13. TIM2011 Summary This work is an additional step toward understanding the fine structure of scalar fields in turbulent flows and will provide measurements of properties relevant to the PDF formulation.