Marie-Christine Duluc

Transient natural convection and conjugate transients around a line heat source

Abstract Transient natural convection in liquid nitrogen around a heated wire is studied experimentally and numerically. A thin bronze wire of 40 μm in diameter and 5.1 cm in length heated by Joule effect is used in experiments and time evolutions of the wire temperature are measured through its electrical resistance. Numerical simulations of such flows are performed by using velocity–pressure formulation, spectral methods and domain decomposition technique. Experimental data and numerical results are compared and show that although the wire is extremely thin its thermal inertia plays an important role during early transients. Scaling analyses performed for the convection set-up and transients yield t∼q−1/2 and ΔT∼q3/4, which are confirmed by numerical simulations. For wires heated by Joule effect hybrid thermal conditions––combined Dirichlet and Neumann conditions are proposed on the wire surface and validated by numerical simulations. On the other hand flow conditions to be imposed on the outer artificial boundary are not well known and the answer to the question remains still open: two types of flow conditions are tested and yield different velocity fields.

Numerical simulations of natural convection around a line‐source

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

Steady-state transition boiling on thin wires in liquid nitrogen. The role of Taylor wavelength

Transition boiling on a thin wire in liquid nitrogen is investigated. Results presented in the form of a classical boiling curve exhibit some discontinuous branches in the mixed boiling region, located between the negative slope area and the film boiling regime. A model is proposed in order to explain this new feature. It is based on steady coexistence of two areas, one in nucleate and one in film boiling. The main hypothesis concerns the wire length covered with film boiling which is supposed to be a multiple of the Taylor wavelength, this last quantity being commonly regarded as the interval separating two neighbouring vapour pockets in the film boiling regime. The temperature of each area is allowed to vary in a range compatible with the respective regime. The comparison with experimental results shows that some branches develop with a constant proportion of each regime. Furthermore, this model shows that no steady branch is observed when the wire length covered with film boiling is less than one Taylor wavelength. The only experimental points occurring in this case are those located in the negative slope area.

Numerical Simulation of Thermo-Pneumatic Effects for Gas-Liquid Flows in Heated Microchannels

Numerical simulations of an air bubble flowing in a micro-channel filled with liquid water and heated on the walls are presented. Due to the small channel size, pressure changes may be induced by a heat supply on the walls. The aim is to quantify these pressure changes. A numerical model, allowing for the description of an incompressible liquid and a compressible gas bubble is presented. Air in the bubble is modeled as a perfect gas, under the low Mach approximation while the liquid is modeled as an incompressible fluid. The Navier Stokes equations and the energy equation are solved. The interface description is performed combining front tracking techniques and a Heaviside step function. A first validation test-case is presented. Then, various heating conditions are examined including uniform and non uniform heating conditions, constant and time dependent heating conditions. It is shown that pressure oscillations in the bubble may be induced by an appropriate thermal actuation.Copyright