We use direct numerical simulations (DNS) to investigate the turbulent modulation due to the presence of bubbles in vertical channels flowing downward. The Reynolds number for single-phase flow based on half channel height h^* and friction velocity is Re_τ= 180. A density and viscosity ratio of ρ_d^*/ρ_c^*=0.01 and μ_d^*/μ_c^*=0.018 is chosen for two void fractions of ϵ=1.2% and ϵ=2.4%. For each void fraction three different bubble sizes are simulated: D/h=0.2130, 0.2684 and 0.3382, where D denotes the diameter of the bubbles. Numerical simulations are based on multiple markers Coupled Level-Set/Volume-of-Fluid (CLSVOF) method. To improve the efficiency of this method, a fast pressure-correction method is used in order to enable the simulation to exploit a constant coefficient Poisson equation which can be solved with FFT-based technique. Extensive verification and validation were performed and perfect accuracy and agreement are obtained. In all the simulations performed in this work, the new Poisson solver showed a minimum speedup of 22 times. Accumulation of bubbles in the core region of the channel for all cases is observed, which forms a bubble-free layer in the near-wall region. The presence of bubbles resulted in considerable modification in the mean velocity profile compared to single-phase flow. Another common observation is that all the components of velocity fluctuations in the near-wall region decrease with increasing void fraction and decreasing wall layer thickness. The opposite happens in the core region, where the presence of bubbles favours turbulence. With respect to the bubble size, the wall-normal and spanwise velocity fluctuations decrease in the near-wall region for smaller bubbles, however, the streamwise velocity fluctuations remained almost unaffected. The investigation of turbulent kinetic budgets shows that, unlike single-phase flow, the dissipation terms rises to large values in the core region of the channel. This behaviour is referred to the presence of bubbles and hence enhancement of turbulent kinetic energy in the core region.

Bubbly turbulent flow in a channel is investigated using interface-resolved direct numerical simulation. An efficient coupled level-set volume-of-fluid solver based on a fast Fourier transform algorithm is implemented to enable a high resolution and fast computation at the same time. Up to 384 bubbles are seeded in the turbulent channel flow corresponding to 5.4% gas volume fraction. Bubbles are clustered in the channel center due to the downward flow direction. The bubbles induce additional pseudo-turbulence in the channel center and are also able to attenuate the energy in the boundary layer by reducing the shear production. Turbulent kinetic energy budget indicates a significant buoyancy production in the channel center. A local equilibrium between buoyancy production and dissipation is observed here besides the shear production peak in the boundary layer. Comparing the local production and dissipation indicates a coexistence of boundary layer turbulence near the wall and bubble-induced pseudo-turbulence in the channel center. The liquid phase and gas phase are coupled through the complex liquid-gas interface. Local flow topology analysis is depicted in the liquid phase around the bubbles as well as in the gas phase. The flow topology of the liquid phase and the gas phase differs from each other significantly. Local dissipation is more dominant in the liquid phase near the bubble interface, whereas local enstrophy is preferred in the gas phase. In the liquid phase, a high dissipation event is preferred close to the interface, whereas a high enstrophy event is dominant away from the interface.

Direct numerical simulations have been adopted to study the turbulent heat transfer in forced convections of supercritical water at two different supercritical pressures P=23 MPa and P=25 MPa in a heated pipe with constant wall heat flux and a bulk Reynolds number of Re₀=5400. The present study aims to reveal the mechanisms of turbulent heat transfer of superciritical fluids at different pressures in a spatial-developing flow. The results show that at the smaller pressure ratio P_r=P/P_c, where P_c is the critical pressure, the property variations become more drastic, and both the skin friction coefficient and Nusselt number become smaller. The decompositions of skin friction and Nusselt number show that it is mainly due to the large turbulence reduction along the streamwise direction. The analyses of turbulent kinetic energy (TKE), the turbulent shear stress, and the production of TKE confirm this point. Moreover, it was found that the thermophysical property fluctuations are very large and significantly influence the turbulent statistics in the supercritical fluid flows. Due to the large property fluctuations, it was found that the density-fluctuation-related terms are significant and their values are actually comparable to the mean-density-related terms. Due to their negative contributions to turbulent shear stress and turbulent heat flux, the turbulence and heat transfer are severely attenuated by the large thermophysical property fluctuations. For near-wall scaling in spatial-developing flows at supercritical pressures, the semi-local velocity transformation with a semi-local coordinate shows a better agreement in the logarithmic region. However, a clear deviation still exists, especially for mean temperature because all the transformations only incorporate the local mean property variations and cannot consider their fluctuations.

Flow and heat transfer of merging and bouncing droplets are studied for different Weber and Reynolds numbers and eccentricities of droplets by means of direct numerical simulation. Droplets are allowed to deform under the hydrodynamic forces of the surrounding flow. A coupled level-set and volume of fluid (CLSVOF) method is used to capture the highly deformable topology of the droplets. The method is coupled with a fast pressure solver, developed by Dodd and Ferrante, 2014, in order to circumvent the expensive iterative solvers commonly used. The temperature distribution inside the droplet and its consequent effect on the Nusselt number is studied. The results show that the Reynolds number and the initial configuration of droplets is of more important than the effect of the surface tension which governs the extent of deformations.

This work investigates fully developed turbulent flows of carbon-dioxide close to its vapour-liquid critical point in a channel with a hot and a cold wall. Two direct numerical simulations are performed at low Mach numbers, with the trans-critical transition near the channel centre and the cold wall, respectively. An additional simulation with constant transport properties is used to selectively investigate the effect of the non-linear equation of state on turbulence. Compared to the case where the pseudo-critical transition occurs in the channel center, the case with the pseudo-critical transition close to the cold wall reveals that compressibility effects can exist in the near-wall region even at low Mach numbers. An analysis of the velocity streaks near the hot and the cold walls also indicates a greater degree of streak coherence near the cold wall. A comparison between the constant and variable viscosity cases at the same Reynolds number, Mach number and having the same isothermal wall boundary conditions reveals that variable viscosity increases turbulence near the cold wall and also causes higher velocity gradients near the hot wall. We also show that the extended van Driest transformation results in a better agreement of the velocity profile with the log-law of the wall compared to the standard van Driest transformation. The semi-locally scaled turbulent velocity fluctuations and the turbulent kinetic energy budgets on the hot and the cold sides of the channel collapse on top of each other, thereby establishing the validity of Morkovin’s hypothesis.