Study of coherent structures of turbulence with large wall-normal gradients in thermophysical properties using direct numerical simulation

Abstract

Forced-convection heat transfer in a heated working fluid at a thermodynamic state near its pseudocritical point is poorly predicted by correlations calibrated with data at subcritical temperatures and pressures. This is suggested to be primarily due to the influence of large wall-normal thermophysical property gradients that develop in proximity of the pseudocritical point on the concentration of coherent turbulence structures near the wall. The physical mechanisms dominating this influence remain poorly understood. In the present study, direct numerical simulation is used to study the development of coherent vortical structures within a turbulent spot under the influence of large wall-normal property gradients. A turbulent spot rather than a fully turbulent boundary layer is used for the study, for the coherent structures of turbulence in a spot tend to be in a more organized state which may allow for more effective identification of cause-and-effect relationships. Large wall-normal gradients in thermophysical properties are created by heating the working fluid which is near the pseudocritical thermodynamic state. It is found that during improved heat transfer, wall-normal gradients in density accelerate the growth of the Kelvin-Helmholtz instability mechanism in the shear layer enveloping low-speed streaks, causing it to roll up into hairpin vortices at a faster rate. It is suggested that this occurs by the baroclinic vorticity generation mechanism which accelerates the streamwise grouping of vorticity during shear layer roll-up. The increased roll-up frequency leads to reduced streamwise spacing between hairpin vortices in wave packets. The density gradients also promote the sinuous instability mode in low-speed streaks. The resulting oscillations in the streaks in the streamwise-spanwise plane lead to locally reduced spanwise spacing between hairpin vortices forming over adjacent low-speed streaks. The reduction in streamwise and spanwise spacing between hairpin vortices causes them to interact more frequently by merging together and by breaking apart into smaller turbulence structures.

Effects of spatial gradients in thermophysical properties on the topology of turbulence in heated channel flow of supercritical fluids

“…For each time step, the solution is declared as converged when the rms of the normalized residuals 45 of the governing equations is reduced to less than 10 5 , and this is realized with up to five outer-loop iterations per time step. With the same computational algorithm as that of the present study, the studies of Brinkerhoff and Yaras, 19 Dave et al, 48 and Reinink and Yaras 26 indicate that a satisfactory level of convergence is achieved with rms residuals less than 10 5 .…”

“…29 These structures may play a role in the recovery of turbulence as they may be associated with accelerated roll-up of the shear layer via the baroclinic instability mechanism as per the observations of Reinink and Yaras. 26 In heated downward flows, buoyancy forces are observed to destabilize the flow, which is evident as increased contributions of the buoyancy terms to the overall rate of turbulent kinetic energy production. 30 Thus, buoyancy forces act to enhance heat transfer in such flows.…”

“…DNS studies on heat transfer in flows of supercritical fluids have been performed by Azih et al, 25 Reinink and Yaras, 26 Bae and co-workers, 27,28 Nemati and coworkers, 29,30 Peeters et al, 31 and Zonta and co-workers. 32,33 Insight into the mechanisms through which such flows are affected by spatial gradients of the thermophysical properties may be attained by investigating the development of the coherent structures of turbulence, as well as investigating statistical turbulence quantities.…”

“…[25][26][27][28] Nemati et al 29 show that for heat transfer in the vicinity of the pseudo-critical state, a significant increase in wall-normal heat transfer due to turbulence advection occurs for iso-heat-flux walls in comparison with iso-thermal walls.…”

“…This observation is consistent with other studies of heated flows of supercritical fluids. 26,31 IHT is typically observed in flows with comparatively low values of heat flux where density gradients are expected to be milder. Azih et al 25 and Reinink and Yaras 26 observed the development of turbulence along a heated wall at fluid temperatures just above the pseudo-critical temperature under flow conditions that yielded IHT.…”