GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 1.3 257 heat capacity assumed constant so that the thermal diffusivity is constant too. The thermal solid boundaries are modeled imposing a constant heat flux q c =1000 Wm -2 . The top surface is treated as a thermal boundary by imposing a cooling for thermal radiation and as a dynamic boundary imposing the free surface condition. The differential equations are transformed into algebraic equations through the use of the finite volume method (Patankar, 1980; Filippucci et al. , 2010, 2013) and the algebraic equations are then solved iteratively. The solution takes into account the coupling between the dynamic and the thermal equations due to both the temperature dependence of the viscosity in the dynamic equation and to the viscous term in the heat equation. The results indicate that the Reynolds number Re increases in very limited areas of the channel compared to total domain. The areas in which the Reynolds number exceeds the critical threshold Re c correspond to areas of the domain that heat up, due to the viscous dissipation effect, that lies on the lateral and basal boundaries (Fig. 1). Using this numerical model we could see that the temperature and the velocity growth is not uncontrolled but in a short time interval, which in our case study is about 30 minutes, the temperature reaches a stationary value (Fig. 2). This result implies that inside the fluid, that flows in the channel, areas in which the flow is in the laminar regime and areas in which the flow is in the turbulent regime can coexist. The local turbulent state can bring the fluid to develop local vortex. This result is in agreement with other numerical models (Costa and Macedonio, 2003, 2005) who found out that viscous friction causes a local increase in temperature near the walls that, added to the strong coupling between viscosity and temperature, causes viscosity decrease that can lead to the formation of local flow instabilities similar to vortex which cannot be predicted by simple isothermal Newtonian models. From the observations of basaltic lava flow emplacement, the concept of laminar flow in which all fluid particles move in parallel is certainly not always valid but it cannot even be said that a lava flow is turbulent in the classical sense (Baloga et al. , 1995), and the transition from purely laminar flow to turbulence is observed to occur at low values of the Fig. 2 – Temperature T as a function of time t in six monitoring points P for T e =1000 °C and α =20° for the case study with viscous dissipation (solid line) and without viscous dissipation (dashed line). a) T vs t in the monitoring point P 1 ( x = L , y ±a/2, z =- 0.5 m); b) T vs t in the monitoring point P 2 ( x = L , y =\pm a\over 2, z =0); c) T vs t in the monitoring point P 3 ( x = L , y =0, z =0); d) T vs t in the monitoring point P 4 ( x = L , y =0, z =- h /2); e) T vs t in the monitoring point P 5 ( x = L , y =0, z=-h ); f) T vs t in the monitoring point P 6 ( x=L , y ±a/ 2, z = -h ); g) sketch of the channel cross section with details of the monitoring points.