Thermal and Fluid Engineering - Lecture- Power Point slides - 01 PDF

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ThermalandFluidEngineering Lecture01:LaminarandTurbulentflow

SchoolofComputing,EngineeringandMathematics UniversityofWesternSydney MingZhao Emial:[email protected] Tel.:+61247360085

Viscosity of the fluid μ y

F (force)

Plate

u

Fluid

Δy x

 

du dy

u – Fluid velocity (m/s) μ – Dynamic viscosity (kg/m·s, N·s/m2) τ – Shear stress (N/m2) ν = μ/ρ, kinematic viscosity (m2/s) ρ – Fluid density (kg/m3) 2

Example 1-1: Engine oil is filled between two flat plates. Surface area of the plate is 20 cm × 20 cm. Thickness of the fluid = 1 cm. The bottom plate is stationary and the top plate moves at a velocity of u=1 cm/s. If the force for moving the top plate is 0.153 N, what is the dynamic viscosity of the oil? If the density of the oil is 980 kg/m3, what is the kinematic viscosity? (Answer: 3.825 N·s/m2, 0.0042 m2/s) y

F=0.153 N u=1cm/s

Plate u

Oil

Δy = 1 cm x

3

Laminar and turbulent flows Laminar flow

• Layers of adjacent fluid slide over each other • Streamlines are parallel to each other and smooth • Flow near wall slower than centre • Example: flow in pipes at small velocity

Turbulent flow

• • • •

Fluid particle paths irregular and chaotic Large scale mixing Flow in radial direction Example: Smoke billowing from chimney, flow in pipe at high speed

4

The velocity scale of the turbulence For a flow in a three-dimensional space, turbulent eddies create fluctuations in velocity, the velocity component in the x-, y- and z-directions are u, v, w, respectively. u mean velocity

u

u

time

The velocity is decomposed as

u (t )  u  u(t ) v(t )  v  v(t ) w(t )  w  w(t )

u ,v , w – mean velocity u, v, w – turbulent fluctuation

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Features of the turbulence •

Irregularity

•

Diffusivity – mixing of fluid mixtures

•

Mixed length scales of eddies

•

Rotationaligy. Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism.

•

Dissipation.

If a flow is laminar or turbulent depends on Reynolds number. Reynolds number a measure of the ratio of inertial forces to viscous forces.

6

How to evaluate turbulence The magnitude of the mean velocity

U  u 2  v 2  w2 Turbulence energy: the mean kinetic energy per unit mass

k



1 (u ) 2  (v)2  ( w)2 2



Standard derivation of the velocity

 





1 2 k (u) 2  (v) 2  ( w) 2  3 3

Turbulent intensity

turbulence intensity 

 U 7

Reynolds number (a) Flow in pipes

U

(b) Flow on a flat plate (boundary layer flow U Turbulent

Laminar

D

UD UD Re     U – averaged velocity D – pipe diameter • Re10,000, fully turbulent • 2,300...