Starting laminar plumes: Comparison of laboratory and numerical modeling

Abstract

[1] A detailed comparison of starting laminar plumes in viscous fluids is provided using the complementary approaches of laboratory modeling and numerical simulation. In the laboratory experiments the plumes are started in a nearly isoviscous silicone oil with heat supplied through a fixed circular source. The temperature field is measured by differential interferometry and thermochromic liquid crystals. The velocity field is determined by particle image velocimetry. Numerical simulations of the laboratory experiments are performed using a finite element method that employs the measured properties of the physical oil and the heating history. No further adjustments are made to match the laboratory results. For fluids at two different viscosities and for variable power supplied to the plume there is excellent agreement in the temporal evolution and fine spatial detail of the plume. Minor differences remain, particulary in the transient stage of the plume in the low-viscosity fluid, but the differences are within the experimental uncertainties. In contrast, the assumption of constant viscosity in the numerical models leads to differences that are larger than the experimental uncertainties, demonstrating that these near-isoviscous fluids should not be considered to have constant viscosity.

Dynamics of a laminar plume in a cavity: The influence of boundaries on the steady state stem structure

“…It follows up on Vatteville et al . [] and is a companion to Vatteville et al . (J. Vatteville et al, Development of a laminar thermal plume in a cavity, paper II, in preparation, Journal of Fluid Mechanics ).…”

“…We will first review the theory of the velocity and thermal structure of thermal plumes at high Prandtl number Pr ( Pr = ν / κ , where ν is the kinematic viscosity and κ is the thermal conductivity). We will confirm the good comparison between laboratory models and numerical simulations [ Vatteville et al ., ]. We then use the numerical models to scale the models to much larger domains that would resemble laboratory experiments in very large tanks, with a viscous fluid filling a cavity that has no‐slip (zero velocity) boundary conditions at the base and the sides, and a free‐slip (zero normal velocity, zero tangential stress) boundary at the top.…”

“…The fluid dynamical experiments described in Vatteville et al . [] and used here are for finite Pr (5000–50,000) fluids in a confined tank. Whittaker and Lister [] describe that inertial effects introduce secondary corrections to their theory, which become important at a radius of .…”

Effect of boundary conditions on thermal plume growth

“…Within the studied range of radii, the calculated points are described by Eq. (15) with an error of 6 %. Approximation of the numerical results shows that the influence of the heater dimensions is underestimated by the equation used.…”

“…this purpose [10][11][12][13] proved to be unsuitable for the small thickness of the liquid layer and weak optical density gradients. The use of heat-sensitive liquid crystals [14][15][16] seems to be more reasonable in this situation. However, the sensitivity of this method is much lower than that of optical methods.…”