76
P. Liu
0.46 m/s, and the dissipative rate is ε = 3112 m 2 /s 3 ; if V t = 1.46 m/s,
l t = 0.1 mm, Ret = 10, the length scale of dissipative vortices is η =
0.0178 mm = 17.8 μm, the velocity scale of dissipative vortices is 0.82 m/s,
and the dissipative rate is ε = 31121 m 2 /s 3 . If V t = 1.46 m/s, l t =
0.01 mm, Ret = 1, the length scale of dissipative vortices is η = 0.01 mm =
10 μm, the velocity scale of dissipative vortices is 1.46 m/s, and the dissipative rate is ε = 311214 m 2 /s 3 . It can be seen that the scale of the minimum
vortices is 10 times larger than that of the minimum macro-scale of 1 μ,
which means that the turbulence satisfies the continuity condition and that
the turbulence is the result of Macro-motion of particles.
If the minimum length scale of dissipative vortices (the requirement of
continuity) is taken as η = 1 μm, and from ηv/ν = 1, the maximum velocity
scale of dissipative vortices is ν = 14.6 m/s, the minimum time scale τ = 6.8
× 10 −8 s, and the maximum dissipation rate of dissipative vortices is ε = 3.1
× 10 9 m 2 /s 3 . For ease of comparison, the relationship between the scale ratio
of energy-carrying vortices and dissipative vortices and turbulent Reynolds
number is given in Fig. 1.91, the scale relationship between energy-carrying
vortices and dissipative vortices in Fig. 1.92, and the relationship between the
scale of energy-carrying vortices and dissipative rate in Fig. 1.93.
According to the definition of turbulent energy dissipation rate,
ε = ν
∂u
i
∂ x j
∂u
i
∂ x j
≈
V 3
t
l t
Fig. 1.91 Relation between scale ratio of energy-carrying eddies and dissipative
eddies and turbulent Reynolds number
P. Liu
0.46 m/s, and the dissipative rate is ε = 3112 m 2 /s 3 ; if V t = 1.46 m/s,
l t = 0.1 mm, Ret = 10, the length scale of dissipative vortices is η =
0.0178 mm = 17.8 μm, the velocity scale of dissipative vortices is 0.82 m/s,
and the dissipative rate is ε = 31121 m 2 /s 3 . If V t = 1.46 m/s, l t =
0.01 mm, Ret = 1, the length scale of dissipative vortices is η = 0.01 mm =
10 μm, the velocity scale of dissipative vortices is 1.46 m/s, and the dissipative rate is ε = 311214 m 2 /s 3 . It can be seen that the scale of the minimum
vortices is 10 times larger than that of the minimum macro-scale of 1 μ,
which means that the turbulence satisfies the continuity condition and that
the turbulence is the result of Macro-motion of particles.
If the minimum length scale of dissipative vortices (the requirement of
continuity) is taken as η = 1 μm, and from ηv/ν = 1, the maximum velocity
scale of dissipative vortices is ν = 14.6 m/s, the minimum time scale τ = 6.8
× 10 −8 s, and the maximum dissipation rate of dissipative vortices is ε = 3.1
× 10 9 m 2 /s 3 . For ease of comparison, the relationship between the scale ratio
of energy-carrying vortices and dissipative vortices and turbulent Reynolds
number is given in Fig. 1.91, the scale relationship between energy-carrying
vortices and dissipative vortices in Fig. 1.92, and the relationship between the
scale of energy-carrying vortices and dissipative rate in Fig. 1.93.
According to the definition of turbulent energy dissipation rate,
ε = ν
∂u
i
∂ x j
∂u
i
∂ x j
≈
V 3
t
l t
Fig. 1.91 Relation between scale ratio of energy-carrying eddies and dissipative
eddies and turbulent Reynolds number