Experimental study on gravity currents flowing on heated walls

TL;DR

This work experimentally examines steady gravity currents of an air–CO$_2$ mixture flowing along a heated wall, using simultaneous LDV, FID, and cold-wire measurements to reconstruct local density and buoyancy and to quantify turbulent fluxes. By varying wall heating, the authors identify a convective boundary layer near the wall, enhanced turbulence, and a linear decay of buoyancy flux with distance, while key stability metrics $Ri_g$, $Ri_f$, and $Ri$ show limited sensitivity to heating. The study validates a measurement framework through integral balances of CO$_2$ mass, enthalpy, and buoyancy, and provides detailed first- and second-order statistics across three heating levels. The results offer a comprehensive dataset and a benchmark for validating numerical models of atmospheric gravity currents along heated boundaries, with implications for dispersion and mixing in urban or coastal environments.

Abstract

We present an experimental study on steady gravity currents advancing along a heated wall. The current is generated by a mixture of air and carbon dioxide continuously supplied at the channel inlet. To have a complete point-wise characterization of the flow, simultaneous high-frequency measurements of two velocity components, CO_2 concentration, and temperature are performed. An experimental protocol is presented to reconstruct the local fluid density and to estimate turbulent vertical and horizontal fluxes of CO_2, temperature, and buoyancy. The reliability of both the flow measurements and of the estimate of convective heat flux exchanged at the wall is assessed through integral balances of \textnormal{CO}$_2$ mass, enthalpy, and buoyancy, performed at different distances from the source. Three wall-heating conditions are considered: an adiabatic case, a moderately heated case, and a strongly heated case. In the heated experiments, a convectively unstable boundary layer forms near the wall, capped by a stably stratified region. The influence of this condition on the first- and second-order flow statistics profiles is examined. Although wall heating influences the vertical shear, the Brunt-Vaisala frequency, and both shear and buoyancy production of turbulent kinetic energy within the stably-stratified region characterized by an almost constant vertical gradient of streamwise velocity, neither the gradient Richardson number nor the flux Richardson number exhibits a clear trend in this region with the imposed wall heat flux.

Figures (12)

• Figure 1: (a) Schematic of the experimental set-up. (b) Detail of the heating wall.
• Figure 2: Characterization of convection above the heating surface. (b) Partition between the heat flux transferred by radiation and that transferred by convection, for both the free and mixed convection. (c) Temperature difference between the wall and the ambient. (d) Convective heat transfer coefficient, $h$. Panels (e) and (f) show the Nusselt numbers for free and mixed convection, respectively.
• Figure 3: (a) FID voltage output E times $r$ as a function of CO$_2$ volume fraction, $c$, for $r=25$ and $r=100$. The inset shows the FID voltage output as a function of the C$_2$H$_6$ ppm in the mixture. (b) Example of temperature spectrum obtained with the CCA with $d=1\mu$m. The three curves show the spectrum before and after the exposure to the seeding and after the cleaning with a jet of pure air.
• Figure 4: (a) Picture of the experimental probes' position. Panels (b) and (c) show the values of the cross-correlations $\overline{w'c'}$ and $\overline{w'T'}$ as a function of the time lag of the concentration and temperature signals with respect to the velocity one, respectively. Panel (d) shows an example of the longitudinal velocity, vertical velocity, CO$_2$ concentration, temperature, and density signals that are simultaneously recorded during the experiment.
• Figure 5: Vertical profiles measured 1$h_s$ downstream the inlet: panel (a) shows the mean streamwise velocity and the horizontal and vertical turbulent intensity, panel (b) shows the mean CO$_2$ concentration.