Effect of Ncr on VLM and LLT in XFLR5 An S5010 airfoil was solved twice by setting Ncr = 9 and Ncr = 4. The effect of Ncr on CL and CD in 3D is observed. Wing: AR = 10, Re = 70,000
Alpha-CL 1.2 1 0.8 L
C0.6
LLT N4 LLT N9
0.4
VLM N4 VLM N9
0.2 0 0
5
10
15
20
Alpha
CL Effect •
Ncr has no effect on VLM, VLM calculates inviscid C L but LLT does take 2D viscous CL into account.
•
Note that VLM doesn’t calculate stall but it stops when it reaches a local CL in the solution that doesn’t have a corresponding one in 2D to interpolate CD from.
CD-CL 1.2 1 0.8 L
C0.6
LLT N4 LLT N9
0.4
VLM N4 VLM N9
0.2 0 0
0.05
0.1
0.15
0.2
CD
CD Effect • •
Both VLM and LLT are affected by N cr and by 2D viscous results in general. CD is the same in both methods vs CL, for the same Ncr but this doesn’t mean that it is the same vs Alpha since Alpha-CL curves are different
Alpha vs CL3/2/CD
20 18
LLT N4
16
LLT N9 VLM N4
14
VLM N9
12 D
C /
10
2 / 3 L
C 8
6 4 2 0 0
5
10
15
20
Alpha
•
Although both VLM curves have same CL but they have different CD since Ncr affects CD, so the power coefficient curves are different.
Alpha-Cm 0.1 0.05
0
0
5
10
15
20
-0.05 LLT N4 m
C -0.1
LLT N9 VLM N4
-0.15
VLM N9
-0.2 -0.25 -0.3
•
Alpha
Cm in VLM is inviscid and is not affected by Ncr as in CL
Conclusion VLM: • •
CL is inviscid, CD is viscous from 2D solution Stall is not estimated. The solution just stops when local C L reaches max in any span position.
LLT: • •
CL and CD are both viscous. Stall is approximated in some way using 2D solution.
So, in a Low Re case with separation bubble present, using the VLM is equivalent of ignoring separation separa tion bubble effect on CL and treating the problem as a s a high Re. Thus, I believe that the error of LLT not taking sweep effect into account is much smaller than treating the CL as inviscid in VLM
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