Direct Numerical Simulations of turbulent heat transfer in a channel flow are presented for three different Reynolds numbers, namely Re τ = 500, 1000 and 2000. Medium and low values of the molecular Prandtl number are studied, ranging from 0.71 (air), down to 0.007 (molten metals), in order to study its effect on the thermal flow. Mixed boundary conditions at both walls are used for the thermal flow. Mean value and intensities of the thermal field were obtained. Two different behaviors were observed, depending on the Prandtl and Péclet numbers. The expected logarithmic behavior of the thermal flow completely disappears for Prandtl below 0.3. This is a direct effect of the thicker viscous thermal layer generated as the Prandtl number is reduced. Von Kármán constant was computed for cases above this Prandtl, and turbulent Prandtl and Nusselt numbers were obtained for all the cases. Finally, the turbulent budgets for heat fluxes, temperature variance and its dissipation rate are presented. As a general result, there is a scaling failure near the wall in very cases studied, which is accentuated for lower Prandtl numbers. The statistics of all simulations can be downloaded from the web page of our group.

Abstract

We present a new set of direct numerical simulation data of a passive thermal flow in a turbulent plane Poiseuille flow with constant Prandtl number P r = 0.71, and mixed boundary conditions. Simulations were performed at Re τ = 500, 1000, and 2000 for several computational domains in the range of l x = 2πh to 8πh and l z = πh to 3πh. As a first key result we found that a length of l x = 2πh and a width of l z = π is enough to accurately obtain the one-point statistics and the budgets of the thermal kinetic energy, its dissipation and the thermal fluxes. None of them collapse exactly in wall units. On the other hand, the value of the thermal Kármán constant grows very slightly with the Reynolds number with a value of κ th = 0.44 for Re τ = 2000. The statistics of all simulations can be downloaded from the web page of our group.

This Brief Report studies the linear stability of a thermoconvective problem in an annular domain for relatively low (∼1) Prandtl (viscosity effects) and Biot (heat transfer) numbers. The four possible patterns for the instabilities, namely, hydrothermal waves of first and second class, longitudinal rolls, and corotating rolls, are present in a small region of the Biot-Prandtl plane. This region can be split in four zones, depending on the sort of instability found. The boundary of these four zones is composed of codimension-two points. Authors have also found two codimension-three points, where some of the former curves intersect. Results shown in this Brief Report clarify some reported experiments, predict new instabilities, and, by giving a deeper insight into how physical parameters affect bifurcations, open a gateway to control those instabilities.

Abstract. In this article the instabilities appearing in a liquid layer are studied numerically by means of the linear stability method. The fluid is confined in an annular pool and is heated from below with a linear decreasing temperature profile from the inner to the outer wall. The top surface is open to the atmosphere and both lateral walls are adiabatic. Using the Rayleigh number as the only control parameter, many kind of bifurcations appear at moderately low Prandtl numbers, and depending on the Biot number. Several regions on the Prandtl-Biot plane are identified, their boundaries being formed from competing solutions at codimension-two bifurcation points.

Abstract:This article studies the linear stability of a thermoconvective problem in an annular domain for different Bond (capillarity or buoyancy effects) and Biot (heat transfer) numbers for two set of Prandtl numbers (viscosity effects). The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. Different kind of competing solutions appear on localized zones of the Bond-Biot plane. The boundaries of these zones are made up of codimension two points. A co-dimension four point has been found for the first time. The main result found in this work is that in the range of low Prandtl number studied and in low-gravity conditions, capillarity forces control the instabilities of the flow, independently of the Prandtl number.

A linear stability analysis of a thin liquid film flowing over a plate is performed. The analysis is performed in an annular domain when momentum diffusivity and thermal diffusivity are comparable (relatively low Prandtl number, Pr=1.2). The influence of the aspect ratio (Γ) and gravity, through the Bond number (Bo), in the linear stability of the flow are analyzed together. Two different regions in the Γ-Bo plane have been identified. In the first one the basic state presents a linear regime (in which the temperature gradient does not change sign with r). In the second one, the flow presents a nonlinear regime, also called return flow. A great diversity of bifurcations have been found just by changing the domain depth d. The results obtained in this work are in agreement with some reported experiments, and give a deeper insight into the effect of physical parameters on bifurcations.

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.