Which Reynolds number would (most likely) correspond to a system where radial variations in velocity were negligible

Three different cases are computed to clarify the possible influence of the jet Reynolds number. The Reynolds number Re = V0e/ν is set to 3000 for case (I), 7500 for case (II) and 13500 for case (III). The nondimensional time step ΔtV0/e is fixed to a value which ensure the stability of the numerical scheme (CFL< 0.3). For the largest Reynolds number simulation (Re = 13500), we have to mention that only mean quantities are here reported since insufficient integration times are yet available for this case.
The length of the horizontal direction must be large enough to capture the two large recirculations on each side of jet and to limit the influence of the buffer domain inside of the domain of interest. Preliminary bidimensional simulations have been used to test the influence of the length of the horizontal direction. We concluded that a value of Hx/e = 40 is sufficient. In the framework of air curtain applications, the opening ratio is fixed to 10 for all cases. The choice of the length of the homogeneous direction (Oz) is less obvious. Indeed, the periodic boundary conditions along the homogeneous direction are justified only if the transverse dimension Hz is large enough to capture the largest structures of the flow. Consequently, the fluctuations must be practically decorrelated on a half-period (Hz/2). In the absence of two point correlations available in the literature for plane jets with short impingement distance, we considered successively two different transverse dimensions: Hz/e = π in accordance with the simulations of Hoffmann and Benocci (1994); Voke et al. (1995), then a double dimension Hz/e = 2π. Note that Cziesla et al. (2001) set the length of the homogeneous direction to 2. Beaubert and Viazzo (2001) note an overlapping problem on the transverse two-point correlations of the different velocity components in the plane of symmetry of the jet for the smallest width. Therefore, a width of 2π for the transverse direction is rather advised for the ratio Hy/e = 10 and in this range of Reynolds numbers. Table 1 contains the characteristics of the three simulations.