written 7.2 years ago by | modified 3.0 years ago by |
For the following velocity profiles, determine whether the flow has separated or on the verge of separation or will be attached with the surface.
uU=32(yδ)−12(yδ)2
uU=2(yδ)2−(yδ)3
uU=−2(yδ)+(yδ)2
written 7.2 years ago by | modified 3.0 years ago by |
For the following velocity profiles, determine whether the flow has separated or on the verge of separation or will be attached with the surface.
uU=32(yδ)−12(yδ)2
uU=2(yδ)2−(yδ)3
uU=−2(yδ)+(yδ)2
written 3.0 years ago by | • modified 3.0 years ago |
Solution :
Given :
1st Velocity Profile
uU=32(yδ)−12(yδ)3u=3U2(yδ)−U2(yδ)3
Differentiating w.r.t. y, ∂u∂y=3U2×1δ−U2×3(yδ)2×1δ
At y=0,
(∂u∂y)y=0=3U2δ−3U2(0δ)2×1δ=3U2δ
As (∂u∂y)y=0 is positive.
Hence flow will not separate or flow will remain attached with the surface.
2nd Velocity Profile
uU=2(yδ)2−(yδ)3u=2U(yδ)2−U(yδ)3
Differentiating w.r.t. y, ∂u∂y=4U(yδ)×1δ−3U(yδ)2×1δ
At y=0,
(∂u∂y)y=0=4U×(0δ)1δ−3U×(0δ)21δ=0
As (∂u∂y)N=0=0, the flow is on the verge of separation.
3rd Velocity Proflle
uU=−2(yδ)+(yδ)2u=−2U(yδ)+U(yδ)2
Differentiating w.r.t. y, ∂u∂y=−2U(1δ)+2U(yδ)×1δ
at y=0,
(∂u∂y)y=0=−2Uδ+2U(∂δ)×1δ=−2Uδ
As (∂u∂y)y=0 is negative the flow has separated.