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# Evolution of the mixing layer growth rate over the convective Mach number for air and for FC-70. Comparison is made with available DNS results in literature and experimental results in Rossmann et al. (2001).

Source publication

The present article investigates the effects of a BZT (Bethe-Zel'dovich-Thompson) dense gas (FC-70) on the development of turbulent compressible mixing layers at three different convective Mach numbers Mc = 0,1; 1,1 and 2,2. This study extends previous analysis conducted at Mc = 1,1 (Vadrot et al. 2020). Several 3D direct numerical simulation (DNS)...

## Contexts in source publication

**Context 1**

... example, Pantano & Sarkar (2002) use a simulation at M c = 0.3 as a reference case. There is no consensus on this choice, which can partly explain the spreading of PG results observed in figure 8 -where the same literature results used in figure 5 are reported. DG mixing layer results are added with their corresponding error bars coloured in black, which length is equal to twice the standard deviation computed over the self-similar range. ...

**Context 2**

... remains to check whether this reduction of normalised pressure fluctuations is also observed for DGB, DGC and DGD. Figure 18 shows the normalised growth rate as a function of the normalised pressure fluctuations computed at the center of the mixing layer. For PG flow, the reduction is significant. ...

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... where stands for ensemble average. The largest integral length scales of l x /L x = 0.60 is obtained at the end of the self-similar region at M c = 1.8, and it is nearly 3 times larger than the largest value in the previous numerical studies by Pantano & Sarkar (2002) and Vadrot, Giauque & Corre (2021), and comparable to that by Pirozzoli et al. (2015). The size of the computational domain is twice as large than those in previous numerical simulations (Pantano & Sarkar 2002;Arun et al. 2019;Vadrot, Giauque & Corre 2020;Matsuno & Lele 2021). ...

... This observation indicates that the current computational domain is large enough to solve the large-scale turbulence. Otherwise, the growth of large-scale structures would be restricted resulting in the decrease of integral length scale (Vreman et al. 1996;Vadrot et al. 2021). In the self-similar region, the streamwise length scale l x /δ ω increases significantly with the convective Mach number, indicating that the large-scale structures of R uu became increasingly elongated in the streamwise direction. ...

The effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer are studied using numerical simulations at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. As the convective Mach number increases, the streamwise dissipation becomes more effective to suppress the turbulent kinetic energy. At $M_c=1.8$ , the streamwise dissipation increases much faster than the other two components in the transition region, even larger than pressure–strain redistribution, correlating with the streamwise elongated vortical structures at a higher level of compressibility. We confirm the existence of the large-scale high- and low-speed structures in the mixing layers, which accompany the spanwise Kelvin–Helmholtz rollers at low convective Mach number and dominate the mixing layer at higher convective Mach number. Conditional statistics demonstrate that the large-scale low-speed structures are lifted upwards by a pair of counter-rotating quasi-streamwise rollers flanking the structures. The small-scale vortical structures have an apparent preference for clustering into the top of the low-speed regions, which is directly associated with high-shearing motions on top of the low-speed structures. The high-speed structures statistically exhibit central symmetry with the low-speed structures. The statistics and dynamics of large-scale high- and low-speed structures in the compressible mixing layers resemble those in the outer region of the turbulent boundary layers, which reveals the universality of the large-scale structures in free shear and wall-bounded turbulence. A conceptual model is introduced for the large-scale high- and low-speed structures in turbulent mixing layers.

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