Session Q37: Turbulence: Buoyancy-Driven Flows

Large Eddy Simulation of Turbulent Density Currents Over Rough Surfaces

When a heavy density fluid enters an environment with a lighter density, the interaction forms turbulent density currents, a significant type of buoyancy-driven flow. These horizontally moving density currents are critical for ocean mixing and the dispersion of atmospheric pollutants. A large-eddy simulation is conducted on a lock-exchange releasing density current over smooth and rough walls to comprehend the impact of surface roughness on drag effects of density currents. The purpose of the study is to understand the differences between uniform and random roughness elements on the drag characteristics. A previously implemented elegant, immersed boundary-based volume penalization approach where the solid regions are represented as a porous medium with vanishing permeability has been used for this study. The incompressible Navier-Stokes equations are solved with Boussinesq approximations in a finite volume implementation. Various roughness configurations have been utilized to describe the flow's behavior by altering the floor with cubical, cylindrical, and pyramidal geometries. The results have shown that the presence of roughness elements slows down the front because of enhanced drag and uniform pyramid roughness has less drag when compared to cylinders. The effect of Reynold’s number, frictional Reynolds number, and Froude’s number have been studied to provide a universal framework on the effect of roughness in density current.

    

Unveiling the signature of surface tension on Rayleigh-Taylor turbulence

The Rayleigh-Taylor instability originates when a heavier fluid is initially placed on top of a lighter fluid in the presence of gravity. The instability then evolves into a self-similar turbulent mixing layer, sustained by the continuous conversion of potential into kinetic energy. If the two fluids are not miscible, the surface tension prevents them to mix at the molecular level. Nevertheless, the turbulence fragments one fluid into the other, generating an emulsion-like state. In this state, the characteristic bubble size decreases in time according to a power law scaling that results from a balance between the rising kinetic energy and the surface energy density. In this contribution we draw a phenomenological picture that describes the Rayleigh-Taylor emulsification process following the prediction of Chertkov, Kolokolov and Lebedev (PRE 2005) and present the first experimental and numerical evidences that challenge this prediction.   

Effect of inclination angle on heat transport properties in two-dimensional Rayleigh-Bénard convection with smooth and rough boundaries

Using direct numerical simulations, two-dimensional tilted Rayleigh-Bénard convection is studied in both smooth and roughness facilitated convection cell of double-aspect-ratio for air as a working fluid. We investigate the effect of inclination angle (0^○ ≤ Φ ≤ 90^○) on heat flux (Nu), Reynolds number (Re), and flow structures. In a Rayleigh number range 10⁶ ≤ Ra ≤ 10⁹, we address the Ra dependence of Nu(Φ) trend. In the smooth case, while greater tilt results in highest heat flux below Ra=10⁸, Nu drops with Φ monotonically above it. For the smooth case, we identify the control parameters (Φ=75^○ and Ra=10⁷) which yield maximum heat flux (an increment of 18% with respect to the level case). On the other hand, among the three roughness setups, the tallest roughness configuration yields the maximum increment in heat flux (25%) in vertical convection (Φ=90^○) at Ra=10⁶. With increase in Ra, Re changes with Φ marginally in the smooth case, whereas it shows notable changes in its roughness counterpart. We find that the weakening of thermal stratification is directly related to the height of roughness peaks. While Ra delays the onset of thermal stratification (in terms of Φ) in the smooth case, an increase in roughness height plays the same role in roughness facilitated convection cells.   

Direct numerical simulation of a statistically stationary Rayleigh-Taylor mixing layer

Rayleigh-Taylor (RT) instabilities are known to show a strong dependence on the initial conditions at early stages before transiting to a self-similar turbulent regime at high Reynolds numbers. In this study, the late time self-similar nature of the RT mixing layer is exploited to enforce a statistically stationary solution at a prescribed mixing layer width. The governing equations are solved in a transformed coordinate system, where the vertical coordinate is first shifted by δ to account for flow asymmetries, then normalized by a mixing layer width, q. In the transformed coordinates, the governing transport equations resemble the original ones in physical coordinates but with additional terms involving q'/q and δ' – both of which are computed from vertically integrated, ensemble-averaged quantities that are extracted directly from the simulation. The solution is periodic and homogeneous in both horizontal directions, does not require resolution of the initial transients and exhibit statistical convergence over time. Growth rates, mean profiles, velocity anisotropy and conditional means of velocity on density are extracted and compared against other direct numerical simulation and experimental results.   

The growth rate of the turbulent magnetic Rayleigh-Taylor instability

The Rayleigh-Taylor instability is strongly modified in the presence of a vertical mean magnetic

field. Perturbations are firstly stretched in the vertical direction with no mixing due to the inhibition

of the small scale shear instabilities. Then, smooth elongated fingers eventually break after transition

to turbulence, and a strong anisotropy persists. For increasing Alfv`en velocities, the growth rate of

the mixing zone in the fully turbulent regime is damped due to the conversion of potential energy

into turbulent magnetic energy. A new theoretical prediction for the growth rate is proposed and

assessed with high resolution direct numerical simulations of the Boussinesq-Navier-Stokes equations

under the magnetohydrodynamics approximation.   

Spectral analysis of temperature variances in turbulent Rayleigh-Benard convection at moderate Rayleigh numbers

Temperature variances, 〈θ'²〉, in turbulent Rayleigh-Bénard convection (RBC) are studied by direct numerical simulation (DNS) combined with spectral analyses of the budget equations. DNSs of three RBC at Rayleigh number, Ra, at 1×10⁵, 6×10⁶, and 4×10⁸ with unity Prandtl number, Pr, are used for analysis. The spectral densities of each term in the budget equation of 〈θ'²〉, namely, production, inter-scale transfer, wall-normal transport by turbulence, wall-normal transport by thermal diffusion, and dissipation, are computed as functions of length-scale, λ, and wall-normal distance, z. Scale separations between large-scale structure (LSS) and small-scale structure (SSS) are observed in both production and dissipation spectra, and the size of LSS grows with Ra. The dissipation by LSS in the near-wall region exists, but its contribution reduces with Ra. Generally, the inter-scale transfer occurs from LSS to SSS except for the small amount in the near-wall region. Also, LSS transport the 〈θ'²〉 from the outer region to the near-wall region. However, SSS transport the 〈θ'²〉 from the near-wall region to the outer region when z > δ_θ where δ_θ is the thermal boundary layer thickness. Finally, we will discuss the possibility of the universality of small-scale structures in high Ra RBC flows.   

Observations of the surface thermal signature of buoyant plumes: Impacts of temperature anomaly, flow rate, and polymers

Surface thermal signatures of a buoyancy-induced flow can reveal the evolving organization of flow structures, allowing for an understanding of their role in entrainment/mixing processes. This is of utility when the flow is still transient, where its mathematical description does not follow conventional similarity variables and power-law scaling. One such aspect of a thermal buoyancy-induced transitory flow is the surfacing of ambient cold-water pockets, captured and analyzed in our experiments. To further elucidate the causality of these pockets with regards to the turbulent nature of the subsurface flow, they are analyzed with and without turbulence-inhibiting polymer additives. Consequently, these pockets are objectively identified as coherent flow-features via proper orthogonal decomposition mode analysis. Resulting modes and their rank distribution are presented. Pocket correlation length scales are then analyzed with varying volumetric flow rates and temperature difference between the ambient and the plume source. For the polymeric cases, the additional parameter of Weissenberg number is included to draw upon the influence of turbulent flow on the evolution/formation of these pockets. Differences between the polymeric and non-polymeric cases are then interpreted to attempt a scaling for the evolution of such pockets and shed light on their formation mechanics via the entrainment process.   

Turbulent pulsating flow driven convective heat transfer in the quasi-steady and low frequency regimes

The instantaneous and time-averaged dynamics of single-phase internal convective flows, driven by turbulent pulsating pipe flows is investigated experimentally over a parameter range in the quasi-steady and low frequency regimes. The heat transfer in steady flow increases with Reynolds number at a steeper rate compared to heat transfer in pulsating case. Therefore, time-averaged Nusselt number (Nu) in pulsating case is lower relative to time-averaged Nu in steady case. Also, time-averaged Nu increases with Reynolds number non-monotonically. The general observation is that, in the turbulent pulsating pipe flows, in the quasi-steady and low frequency regimes, the time-averaged heat transfer marginally increases with pulsation frequency. However, compared to steady flows, heat transfer marginally decreases.