Investigation of the Wall Scalar Fluctuations Effect on Passive Scalar Turbulent Fields at Several Prandtl Numbers by Means of Direct Numerical Simulations

Abstract

We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall θ′w≠0 with q′w=0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field ⟨θ⟩ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

Energy Partitioning Control in the PITM Hybrid RANS/LES Method for the Simulation of Turbulent Flows

“…PITM numerical simulations are performed for the Reynolds number R τ = u τ δ/ν = 395 where u τ denotes the friction velocity and δ is the half channel width. The present results are then compared with reference DNS [46].…”

“…The DNS simulation performed by Chaouat and Peyret [46] on a very refined mesh for the same Reynolds number R τ = 395 is considered in the following for computing the ratio r DN S = k (s) /k. The dimension of the channel is identical as the one chosen for the PITM simulation, L 1 = 6.4δ, L 2 = 3.2δ and L 3 = 2δ and the equations were integrated in time using an explicit Runge-Kutta scheme of fourth order accuracy in time and solved in space by means of a centered scheme of fourth order accuracy in space.…”

Extension of the partially integrated transport modeling method to the simulation of passive scalar turbulent fluctuations at various Prandtl numbers

“…But this is a physical consequence and does not mean at all that the grid is too fine. In terms of an order of resolution purely for information purposes, the grid-point and the spacings associated with the direct numerical simulation performed by Chaouat and Peyret (2019) are also indicated in Table 3. As a result of interest, the ratio of the DNS grid-points over the PITM grid-points R(P r ) = N DN S /N P IT M varies from 113 for P r = 0.1 to 2378 for P r = 10.…”

“…( 50) and ( 54) associated with the scalar variance. A constant pressure gradient term is included in the momentum equation to balance the viscous effects at the walls and an extra source term is added in the transport equation of the scalar variable aiming to get a periodic condition between the inlet and outlet plane sections of the channel (Chaouat, 2018;Chaouat and Peyret, 2019). The boundary conditions imposed at the lower and upper walls located at x 3 = 0 and 2δ of the channel are no slip velocity conditions ūi = 0.…”

“…Present PITM simulations performed at the Reynolds number R τ = u τ δ/ν = 395. DNS(Chaouat and Peyret, 2019).…”