化工原理课程(全英文)教学课件 7
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Relation between ������������������������ and ������
Effect of roughness Moody’s chart
Boundary layers
Understand the concept
Be able to explain Figs. 1.8, 1.9, 1.10, and 1.11
2100 and 4000 a transition region
is found where the flow may be either laminar or turbulent, The Onset of Turbulence in Pipe Flow. ������ is the mean lifetime of a puff before decaying or splitting. Avila, K. at al., Science, 333, pp.192 (2011)
Sketch for HW6-2
3 © 2015 Yanwei Wang
Today’s topic
Date: March 23, 2015
Hale Waihona Puke Baidu
Pages 29-33 and 52-56 of textbook
Turbulent flow in pipes and channels
Velocity profile
Pages 25-29 & 43-56 of textbook
Types of fluid flow and Reynolds number
Reynolds experiment Laminar vs. Turbulent flow Reynolds number Macroscopic momentum balances
Layer flow with free surface
Incompressible flow in pipes and channels Laminar flow case (Poiseuille flow)
2 © 2015 Yanwei Wang
Homework (HW-6)
HW6-1: Reynolds number and transition from laminar to turbulent flow: (a) airflow and (b) water flow. HW6-2: Incompressible flow through an inclined pipe
local values of the scale and intensity of turbulence. Difficult to
determine in practice.
9
© 2015 Yanwei Wang
Interim summary on Turbulence (4/4)
The transition from laminar to turbulent flow may occur over a wide range of Re values. In a pipe, flow is always laminar at Re < 2100, Under ordinary conditions, the flow in a pipe or tube is turbulent at Re > 4000. Between
������������ ������������ = ������������ ������������
⑩
������ = ������ + ������������
������������ ������������
where ������������ is called the eddy viscosity. Fluid viscosities (������) are true properties of the fluid, and can be measured on isolated samples of the fluid; eddy viscosity (������������ ) depends on both the fluid and also the fluid velocity and system geometry and is sensitive to location in the turbulent field and the
Fall Semester, 2014
Basic Principles of Chemical
Engineering Processes
Lecture 7
Yanwei Wang (王衍伟) Email: ywwang@suda.edu.cn
© 2015 Yanwei Wang
Previous Lecture
© 2015 Yanwei Wang
depending upon conditions at the
entrance of the tube and on the distance from the entrance.
10
Turbulent Velocity Profile (1/6)
Unlike laminar flow, the expressions for the velocity profile in a turbulent flow are based on both analysis and measurements, and thus they are semi-empirical in nature with constants determined from experimental data. The velocity profile is parabolic in laminar flow but is much flatter in turbulent flow, with a sharp drop near the pipe wall, and the difference between the average velocity and the maximum velocity is considerably less. At even higher Re number, the velocity distribution would be even flatter.
⑧
In the study of turbulence in fluids (turbulence modeling), a common practical strategy for calculation is to ignore the smallscale vortices (or eddies) in the motion and to calculate a largescale motion with an eddy viscosity, ������������ , that characterizes the transport and dissipation of energy in the smaller-scale flow.
������������������ inertial force ������������ = = ������ Viscous force
Parabolic velocity distribution, with
������ = ������������,������������������ ������ Shear stress is linear in radial distance Volumetric flow rate is given by the Hagen-Poiseuille equation The Fanning friction factor is given by ������ = ������������ ������������ ℎ������������
difficult – hence experimental measures are used.
7
© 2015 Yanwei Wang
Interim summary on Turbulence (2/4)
⑥ Turbulent flow consists of eddies of various sizes, but even the smallest eddies have diameter 10 to 100 μm, so turbulent flow is not a molecular phenomenon. ⑦ The turbulent energy cascade: The energy by external forces excites the largest possible eddies and is gradually passed to ever smaller eddies, all the way to a minimum scale where this energy is ultimately dissipated to heat by viscous dissipation.
4 © 2015 Yanwei Wang
Summary of Laminar flow in pipes
Poiseuille flow, Re < 2100
Total shear stress is the viscous stress given by Newton’s law of viscosity
6 © 2015 Yanwei Wang
Interim summary on turbulent flow (1/4)
① Occurs at high Re (Re > 4000 for flow in a pipe) ② In Reynolds experiment, dye mixes rapidly and completely – Hence, turbulent flow is important for mixing. ③ Path of fluid particles completely irregular, tends to produce chaotic eddies, vortices and other flow instabilities. ④ Deviating velocities: Average motion is in the direction of
the flow, but there are rapid fluctuations in local velocities,
often characterized by statistical analysis. ⑤ Most common type of flow, but Mathematical analysis very
8
© 2015 Yanwei Wang
Interim summary on Turbulence (3/4)
⑨ The total shear stress in a turbulent fluid is the sum of the viscous stress and the turbulent stress, ������������
5
Δ������������2 ������ ������������ ������ = 1− 4������������ ������ ������������������ ������ = Δ������ 2������
2
∆������������ 4 ������ ������ ������ 2 ������ ������ 2 = = ������������ = 4������ = ������ ������ ������ ������ ������ 2 ������ 2
������������������ 4 ������������������4 ������ = = 128������������ 8������������
© 2015 Yanwei Wang
Turbulent flow in pipes
The onset of turbulence: The top panel shows an image of a single “puff” (localized turbulent patches embedded in the surrounding laminar flow) structure, at a Reynolds number of 2000 (just below the onset of turbulence). As the Reynolds number increases, the spatial scale of the structure decreases.
Effect of roughness Moody’s chart
Boundary layers
Understand the concept
Be able to explain Figs. 1.8, 1.9, 1.10, and 1.11
2100 and 4000 a transition region
is found where the flow may be either laminar or turbulent, The Onset of Turbulence in Pipe Flow. ������ is the mean lifetime of a puff before decaying or splitting. Avila, K. at al., Science, 333, pp.192 (2011)
Sketch for HW6-2
3 © 2015 Yanwei Wang
Today’s topic
Date: March 23, 2015
Hale Waihona Puke Baidu
Pages 29-33 and 52-56 of textbook
Turbulent flow in pipes and channels
Velocity profile
Pages 25-29 & 43-56 of textbook
Types of fluid flow and Reynolds number
Reynolds experiment Laminar vs. Turbulent flow Reynolds number Macroscopic momentum balances
Layer flow with free surface
Incompressible flow in pipes and channels Laminar flow case (Poiseuille flow)
2 © 2015 Yanwei Wang
Homework (HW-6)
HW6-1: Reynolds number and transition from laminar to turbulent flow: (a) airflow and (b) water flow. HW6-2: Incompressible flow through an inclined pipe
local values of the scale and intensity of turbulence. Difficult to
determine in practice.
9
© 2015 Yanwei Wang
Interim summary on Turbulence (4/4)
The transition from laminar to turbulent flow may occur over a wide range of Re values. In a pipe, flow is always laminar at Re < 2100, Under ordinary conditions, the flow in a pipe or tube is turbulent at Re > 4000. Between
������������ ������������ = ������������ ������������
⑩
������ = ������ + ������������
������������ ������������
where ������������ is called the eddy viscosity. Fluid viscosities (������) are true properties of the fluid, and can be measured on isolated samples of the fluid; eddy viscosity (������������ ) depends on both the fluid and also the fluid velocity and system geometry and is sensitive to location in the turbulent field and the
Fall Semester, 2014
Basic Principles of Chemical
Engineering Processes
Lecture 7
Yanwei Wang (王衍伟) Email: ywwang@suda.edu.cn
© 2015 Yanwei Wang
Previous Lecture
© 2015 Yanwei Wang
depending upon conditions at the
entrance of the tube and on the distance from the entrance.
10
Turbulent Velocity Profile (1/6)
Unlike laminar flow, the expressions for the velocity profile in a turbulent flow are based on both analysis and measurements, and thus they are semi-empirical in nature with constants determined from experimental data. The velocity profile is parabolic in laminar flow but is much flatter in turbulent flow, with a sharp drop near the pipe wall, and the difference between the average velocity and the maximum velocity is considerably less. At even higher Re number, the velocity distribution would be even flatter.
⑧
In the study of turbulence in fluids (turbulence modeling), a common practical strategy for calculation is to ignore the smallscale vortices (or eddies) in the motion and to calculate a largescale motion with an eddy viscosity, ������������ , that characterizes the transport and dissipation of energy in the smaller-scale flow.
������������������ inertial force ������������ = = ������ Viscous force
Parabolic velocity distribution, with
������ = ������������,������������������ ������ Shear stress is linear in radial distance Volumetric flow rate is given by the Hagen-Poiseuille equation The Fanning friction factor is given by ������ = ������������ ������������ ℎ������������
difficult – hence experimental measures are used.
7
© 2015 Yanwei Wang
Interim summary on Turbulence (2/4)
⑥ Turbulent flow consists of eddies of various sizes, but even the smallest eddies have diameter 10 to 100 μm, so turbulent flow is not a molecular phenomenon. ⑦ The turbulent energy cascade: The energy by external forces excites the largest possible eddies and is gradually passed to ever smaller eddies, all the way to a minimum scale where this energy is ultimately dissipated to heat by viscous dissipation.
4 © 2015 Yanwei Wang
Summary of Laminar flow in pipes
Poiseuille flow, Re < 2100
Total shear stress is the viscous stress given by Newton’s law of viscosity
6 © 2015 Yanwei Wang
Interim summary on turbulent flow (1/4)
① Occurs at high Re (Re > 4000 for flow in a pipe) ② In Reynolds experiment, dye mixes rapidly and completely – Hence, turbulent flow is important for mixing. ③ Path of fluid particles completely irregular, tends to produce chaotic eddies, vortices and other flow instabilities. ④ Deviating velocities: Average motion is in the direction of
the flow, but there are rapid fluctuations in local velocities,
often characterized by statistical analysis. ⑤ Most common type of flow, but Mathematical analysis very
8
© 2015 Yanwei Wang
Interim summary on Turbulence (3/4)
⑨ The total shear stress in a turbulent fluid is the sum of the viscous stress and the turbulent stress, ������������
5
Δ������������2 ������ ������������ ������ = 1− 4������������ ������ ������������������ ������ = Δ������ 2������
2
∆������������ 4 ������ ������ ������ 2 ������ ������ 2 = = ������������ = 4������ = ������ ������ ������ ������ ������ 2 ������ 2
������������������ 4 ������������������4 ������ = = 128������������ 8������������
© 2015 Yanwei Wang
Turbulent flow in pipes
The onset of turbulence: The top panel shows an image of a single “puff” (localized turbulent patches embedded in the surrounding laminar flow) structure, at a Reynolds number of 2000 (just below the onset of turbulence). As the Reynolds number increases, the spatial scale of the structure decreases.