Solutions of scalar mean profiles close to gas–liquid interfaces under turbulent free slip motion

Abstract

Mean profiles of scalar properties close to moving gas-liquid interfaces subjected to turbulence are quantified using Random Square Waves (RSW). The condition of stationary turbulent transfer allows reducing the third order nonlinear governing equation successively to a second order and to a first order equation, which admits theoretical integration, furnishing the set of solutions analyzed in the present study. It is shown that different solutions may apply to different parts of the calculation domain (physical domain). It is also shown that the stationary problem admits a linear profile close to the gas-liquid interface, while a nonlinear function describes the mean properties apart from the interface.

Turbulence aspects of mass transfer in the thin interfacial region of the concentration boundary layer in gas–liquid systems

“…Data of Ref [6],. presented as a grey cloud, were Experimental data of α varying along z*, and the two constant values used here.compared with the calculated profiles, and the agreement with the solution obtained for θ 1 =2 is remarkable ([16,17]). 3 STATISTICAL FUNCTIONS FOR EQUATIONS (5A) AND (5B)3.1 Central Moments: the Concentration RMS Function n, α, β, and ω 2 allow obtaining any statistical function related to mass transfer for the boundary layer situation under study.…”

“…3). For stationary turbulence and constant α the equation for n was theoretically solved ( [15] and [16]), allowing checking the behavior of the mean concentration profile. Equations (1) and 2are the 1D mass conservation equation and the nondimensional form of the turbulent mas flux for the RSW method, respectively.…”

“…The equation furnished by Ref. [16] for the mean concentration n and any constant value of A = 1-α is: . 4K is a nondimensional constant coefficient.…”

Mass Transfer Through Free Surface Boundary Layers Using a Statistical Approach

“…[15] Transient-theoretical Concentration profile obtained for a wide range of α f values. [26] Stationary-theoretical Theoretical solutions obtained for stationary regime. The partition function n (see Table 1), ranging between 0 and 1, is the portion of time that the square wave is greater than (or equals F p ).…”

“…Because divergence considers the turbulent movement of the superficial velocity components, it points to the importance of elucidating how the structure of turbulence combines with the molecular diffusion to control the mass exchange in the adjacent region of the gas-liquid interface. In a study of long maturation, Schulz and co-workers [9], [15], [16], [25][26][27] progressively presented the tool "Random Square Waves", which was applied to an interface boundary layer. The starting equation is the Reynolds averaged mass conservation equation, where the Reynolds decomposition of variables, given by a mean parcel and a fluctuating parcel, is the main assumption.…”