Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Figures & data

Table 1. The existing numerical studies on surface roughness effect on transition.

Authors	Flow conditions	Surface roughness	Numerical method	Grid format (Cell count, x10^6)
Zhou et al., 2016	Supersonic/Hypersonic, $\mathrm{Ma}=3.37-6.63$, $R{e}_h=4927-9525$	Isolated, square, cylinder, diamond, hemisphere	DNS with WCNS	Structured (81)
Duan & Xiao, 2017	Hypersonic, $\mathrm{Ma}=6$, $R{e}_h=16000$	Isolated, ramp, diamond, cylinder	DNS	Structured (50.7)
Duan et al., 2014	Hypersonic, $\mathrm{Ma}=6$, $R{e}_h=40000$	Isolated, cylinder	DNS	Structured (100+)
Dong et al., 2019	Hypersonic, $\mathrm{Ma}=5$, $R{e}_h=14100$	Isolated/double, cylinder	DNS	Structured (26.73)
Choudhari et al., 2010	Hypersonic, $\mathrm{Ma}=3.5$, $R{e}_h=547$	Isolated, diamond	DNS	Structured (16)
Sun et al., 2014a	Supersonic, $\mathrm{Ma}=2$, $R{e}_{\theta }=5760$	Isolated, micro-ramp	Implicit LES	Structured (42)
Zhou et al., 2010	Incompressible, $R{e}_h=332$	Isolated, hemisphere	DNS with MDF/IBM	Overset, structured (49.7)
Rizzetta & Visbal, 2006	Incompressible, $R{e}_h=202,334$	Distributed, cylinder	DNS	Overset, structured (28.8)
Citro et al., 2015	Incompressible, $R{e}_h=450$	Isolated, hemisphere	DNS	Structured (17)
Belkhou et al., 2019	Incompressible, $R{e}_h=1170$	Isolated, micro-ramp	LES + WALE	Structured (4.7)
Present	Incompressible, $R{e}_h=1170$	Isolated, micro-ramp	ELES	Structured (8)

Figure 1. Three-dimensional micro-ramp geometry (Ye et al., 2016a).

Table 2. Grid parameters for sub-zones.

Sub-zone	$\mathrm{\Delta }{\mathit{y}}_{\mathit{wall}}^{+}$	$\mathrm{\Delta }{\mathit{x}}^{+},\mathrm{\Delta }{\mathit{z}}^{+}$
LES	0.7	0.06-35
RANS-Front	0.7	7-124
RANS-Middle	0.7	1-51
RANS-Back	0.7	11-99

Figure 2. Mesh around the micro-ramp (a) and in the LES/RANS sub-zones (b).

Figure 3. Undisturbed boundary layer velocity profiles.

Table 3. Laminar boundary layer integral parameters.

	u∞ (m/s)	δ99 (mm)	δ* (mm)	θ (mm)	h/δ99	H	Rex	Reh	Reθ
Exp (Ye et al., 2016a)	10	3.26	1.14	0.44	0.61	2.59	2.13E+05	1170	302
ELES	10	3.31	1.04	0.41	0.60	2.53	2.13E+05	1170	303

Figure 4. Time-averaged streamwise velocity contours and streamlines in y-z planes (Left: present ELES; Right: experiment (Ye et al., 2016a)).

Figure 5. Iso-surface contour of time-averaged streamwise vorticity (Left: present ELES; Right: experiment Ye et al., 2016a).

Figure 6. Time-averaged streamwise velocity profiles in the symmetry plane.

Figure 7. Evolution of maximum velocity deficit.

Figure 8. Spanwise distribution of time-averaged velocity at streamwise locations $\mathit{x}/\mathit{h}=15\mathit{and}45$.

Figure 9. Spanwise distribution of velocity fluctuation at streamwise locations $\mathit{x}/\mathit{h}=15\mathit{and}45$.

Figure 10. Streamwise velocity semi-log profile in symmetry plane $\mathit{z}/\mathit{h}=0$.

Figure 11. Instantaneous vortex structure detected by the iso-surface of ${\mathit{\lambda }}_2$ criterion (Left: present ELES; Right: experiment (Ye et al., 2016a)).

Figure 12. Mean separation bubble around the micro-ramp.

Figure 13. Contours of rms streamwise velocity fluctuations in y-z planes (Left: present ELES, Right: experiment (Ye et al., 2016a)).

Figure 14. Contours of rms wall-normal velocity fluctuations in y-z planes (Left: present ELES, Right: experiment (Ye et al., 2016a)).

Figure 15. Contour of streamwise velocity fluctuations in the x-y plane at $\mathit{z}/\mathit{h}=0$ (Top: present ELES, Bottom: experiment (Ye et al., 2016a)).

Figure 16. Contours of the turbulence production in y-z planes (Left; present ELES; Right: experiment (Ye et al., 2016a)).

Figure 17. Turbulent wedge formation (Left: present ELES; Right: experiment (Ye et al., 2016a).

Figure 18. Profiles of velocity fluctuation and TKE in the turbulent wedge.

Table 4. Effect of micro-ramp roughness element on drag coefficient ${\mathit{C}}_{\mathit{d}\mathrm{\_}\mathit{t}}$.

Sub-zone	${\mathit{C}}_{\mathit{d}\mathrm{\_}\mathit{t}}$ with ramp	${\mathit{C}}_{\mathit{d}\mathrm{\_}\mathit{t}}$ without ramp	Drag increment
RANS-Front	$1.20\times {10}^{-3}$	$1.20\times {10}^{-3}$	0%
RANS-Middle	$2.14\times {10}^{-4}$	$2.14\times {10}^{-4}$	0%
RANS-Back	$5.40\times {10}^{-4}$	$3.82\times {10}^{-4}$	41%
LES	$2.58\times {10}^{-4}$	$1.43\times {10}^{-4}$	81%

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Data availability statement

The data that support the findings of this study are available from the corresponding author Y. Lin [[email protected]] upon reasonable request.