The wake of a heated crossbar: like grid turbulence

In 2012, while at the University of Newcastle (Australia), I presented this work at the 7th Turbulence, Heat and Mass Transfer symposium (THMT7) in Palermo, with Lyazid Djenidi and Robert Antonia. The topic: the wake of a crossbar, two heated orthogonal square cylinders, and how its large-scale structures transport the turbulent kinetic energy ⟨q²⟩ and the temperature variance ⟨θ²⟩.

My contribution: as first author, I developed the LBM code coupled with its thermal solver, ran the simulations, then handled the data post-processing and analysis.

Why a crossbar?

• In grid turbulence, the temperature field does not behave like the velocity field.
• A crossbar is the basic element of a grid: its wake may help to understand grid-generated turbulence.
• My aim: determine how this forcing affects the velocity and temperature fields (here a passive scalar, carried by the flow without affecting it).

The method

• Velocity: I solved the flow with the lattice Boltzmann method (LBM, 19-velocity lattice), which models the propagation and collision of particle distribution functions between neighbouring nodes.
• Temperature: I solve the energy equation, with transport by the velocity and thermal diffusion.
• Parameters: Reynolds number Re_D = 2000, Prandtl number Pr = 0.75.
• Domain: 110D × 12D × 12D, with D = 12 mesh points. Resolution of 5η close to the crossbar and 2η at X/D = 100 (η: Kolmogorov scale).

Decay along and away from the centreline

• Near the crossbar (X/D < 20): the flow depends strongly on the initial conditions, temperature even more than velocity.
• Further downstream (X/D > 40): ⟨q²⟩ and ⟨θ²⟩ follow power-law decays, ⟨q²⟩ ∼ x⁻ⁿ and ⟨θ²⟩ ∼ x^−m, with n = 1.15 and m = 1.30. The dissipation rates follow ⟨ε⟩ ∼ x⁻¹⁻ⁿ and ⟨χ⟩ ∼ x^−1−m.
• The exponents are similar at all three positions I studied: downstream of the crossbar, the two wakes interact strongly.
• The isotropic estimates ⟨ε_iso⟩ and ⟨χ_iso⟩ agree well with ⟨ε⟩ and ⟨χ⟩.

Scale-by-scale statistics

• ⟨(δq)²⟩ and ⟨(δθ)²⟩ behave differently: temperature reaches a scaling range more rapidly.
• Both quantities agree well with their grid turbulence counterparts: on the centreline of the wake, turbulence resembles grid turbulence.

• The temperature spectrum seems to tend towards a scaling range, which I do not clearly observe in the velocity spectrum.

Key takeaways

• On the centreline of the wake, the velocity and temperature structure functions show the same features as in grid turbulence.
• The temperature spectrum approaches a scaling range more rapidly than the velocity spectrum, as in grid turbulence.

Further reading

N. Lefeuvre, L. Djenidi, R. A. Antonia, Turbulent crossbar wake with passive scalar, 7th International Symposium on Turbulence, Heat and Mass Transfer (THMT7), Palermo (2012), PDF