哈工大李凤臣-粘弹性非牛顿流体动力学及其应用

哈尔滨工业大学/能源科学与工程学院 2008 年工程热物理暑期班
粘弹性非牛顿流体动力学及其应用
Viscoelastic fluid non-Newtonian fluid dynamics and its applications
李 凤 臣（工学博士，教授）
Feng-Chen Li (Ph.D., Professor) 哈尔滨工业大学/能源科学与工程学院
Linear Viscoelstic Fluid Kelvin-Voigt Model Maxwell Model
∂σ σ +λ = −ηγ ∂t
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描述粘弹性流体的本构方程 (3)
Linear Viscoelastic Fluid Standard Linear Solid Model
Generalized Maxwell Model
牛顿流体
τ
粘弹性流体
τ = τ s +τ p τ s = −η sγ τ p + λ1τ p(1) − α
Mobility factor
λ2
t
λ1 {τ p iτ p } = −η0γ ηp
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粘弹性流体在极端条件下的应用
Re
We
Non-linear terms 高雷诺数条件（对于牛顿流体处于湍流状态） 极低雷诺数条件（对于牛顿流体处于绝对层流状态）
τ
粘弹性流体 牛顿流体
t0
λ1 =
t
η
E
λ1
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描述粘弹性流体流动的动量方程（1）
Equation of motion: ρ
Dv = −∇ ⋅τ − ∇Φ Dt
Constant viscosity
Newtonian fluid: τ = − µγ Non-Newtonian fluid: τ yx = −η (γ )γ yx
l=e
ε ( t 2 − t1 )
x
η η =3
Elongation-rate dependent viscosity
z
For Newtonian fluid (viscoelastic fluid)
η η = 3 ~ 103 For polymer/surfactant solution
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粘弹性的产生及流变学特性 (5)
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粘弹性的产生及流变学特性 (6)
• Shear-dependent viscosity
Polymer liquids (molten plastic)
Viscosity
Temperature
Shear rate (Dynamics of Polymer Liquids, 1987)
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粘弹性的产生及流变学特性 (7) • Relaxation time（松弛时间）
1998.4 --- 2001.3 (日本)京都大学・工学研究科・原子核工学専攻（核能工程系） 工学博士 2001.4 --- 2002.3 海上技術安全研究所(日本) 2002.4 --- 2004.11 産業技術総合研究所(日本) Center for Smart Control of Turbulence 研究员（湍流控制） 2004.11 --- 2006.8 (日本)東京大学・生産技術研究所 日本学术振兴学会研究员（粘弹性流体&微流动） 2006.8 --- 至今 2007 哈尔滨工业大学/能源科学与工程学院 教授/博士生导师 入选教育部新世纪优秀人才支持计划
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粘弹性流体动力学
粘弹性的产生及流变学特性 描述粘弹性流体流动的动量方程 描述粘弹性流体的本构方程
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粘弹性的产生及流变学特性 (1)
• Formation of Rod-like micelles • Shear Induced State (Structure), SIS • Viscoelasticity imparted by SIS • Extensional viscosity as well as shear viscosity
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粘弹性的产生及流变学特性 (4)
Extensional viscosity （拉伸粘性） • Viscoelastic fluid: τ zz − τ xx = −η (ε )ε
1/ l
First normal stress difference
Elongational flow
ε >0
y
1/ l
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认识粘弹性流体（6）
• Where can you find the viscoelastic fluid? – Food products (ketchup, mayonnaise, egg white, etc.) – Molten plastic – Lubricant oil – Detergent – Biologic fluid (DNA solution, cell fluid, etc.) – In general, polymer liquids and surfactant solutions show the features of viscoelastic fluid.
– A kind of non-Newtonian fluid – It shares features of both “viscosity” and “elasticity”.Visco - elastic fluid “Viscosity”
Viscous fluid (Newtonian fluid)
}
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描述粘弹性流体的本构方程 (5)
τ
Nonlinear Viscoelastic Fluid
粘弹性流体
Oldroyd’s fluid B model (Quasi-Linear):
牛顿流体
t0
τ + λ1τ (1) = −η0 γ (1) + λ2γ ( 2)
(
)
λ1
t
Relaxation time Retardation time Giesekus model:
Barus Effect
5
认识粘弹性流体（3）
高速旋转圆柱体
粘弹性流体
Wessenberg Effect
6
认识粘弹性流体（4）
粘弹性流体流束
粘弹性流体流束反弹
Kaye Effect
7
认识粘弹性流体（5）
粘弹性流体流动的其它特殊现象
N
P
Shear-thinning
(from <<Dynamics of Polymeric Liquids: Vol. 1 Fluid Mechanics>>, R.B. Bird, R.C. Armstrong and O. Hassager)
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粘弹性的产生及流变学特性 (3)
• Viscoelasticity imparted by SIS • Extensional viscosity as well as shear viscosity
Fig. 3 Entangled networks and branches (arrows) of thread-like micelles of Arquad S-50 (5mM)/NaSal (5mM) at 20C imaged by cryo-TEM
School of Energy Science and Engineering, Harbin Institute of Technology
1
李凤臣 (LI Feng-Chen)
Email: lifch@
1989.9 --- 1993.7 天津大学・热能工程系・工程热物理专业 工学学士 1993.9 --- 1996.7 中国原子能科学研究院・反应堆工程安全研究设计所 工学硕士
• Effect of elasticity
– Apparent viscosity of fluid is dependent on shear rate.
Shear stress Shear rate (velocity gradient)
– Viscosity of Newtonian fluid is constant. – But, apparent viscosity of viscoelastic fluid is not uniform and dependent on flow field.
D † γ ( n +1) = γ ( n ) − ( ∇v ) iγ ( n ) + γ ( n ) i( ∇v ) Dt Convected Derivatives of the Stress Tensor: D † τ (1) = τ − ( ∇v ) iτ + τ i( ∇v ) Dt
{
}
{
Shear-rate dependent viscosity
Non-linear term, induces turbulent flow at high Re
Non-linear term, depending on We instead of Re, Induces elastic turbulence at high We
Fig. 8 Comparison of apparent extensional viscosity to shear viscosity ratio for Arquad S-50 (5mM)/NaSal (5mM) and Arquad S-50 (5mM)/NaSal (12.5mM).
Z. Lin et al. J. Non-Newtonian Fluid Mech. 93, pp. 363-373 (2000)
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• 粘弹性流体湍流减阻流动与换热