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Showing posts with label fluid. Show all posts
Showing posts with label fluid. Show all posts

Cavitation - an Introduction

Cavitation may occur in fluid flow systems where the local static pressure is below the vapor pressure



Cavitation is a common problem in pumps and control valves - Causing serious wear and tear and damage. Under the wrong conditions, cavitation Reduces the components life time dramatically.

What is Cavitation?
Cavitation may occur when the local static pressure in a fluid reach a level below the vapor pressure of the liquid at the actual temperature.

According to the Bernoulli Equation this may Happen when the fluid accelerates in a control valve or around a pump impeller.

The vaporization itself does not cause the damage - the damage happens when the vapor almost immediately collapses after evaporation when the velocity is Decreased and Increased pressure.

Avoiding Cavitation
Cavitation can in general be avoided by

increasing the distance between the actual local static pressure in the fluid - and the vapor pressure of the fluid at the actual temperature
This can be done by:

reengineering components initiating high speed low velocities and static pressures
increasing the total or local static pressure in the system
reducing the temperature of the fluid
Reengineering of Components Initiating High Speed ​​Velocity and Low Static Pressure
Cavitation and damage can be avoided by using special components designed for the actual rough conditions.

conditions as huge pressure drops can - with limitations - be handled by the Multi Stage Control Valves
challenging pumping conditions - with fluid Temperatures close to the vaporization temperature - can be handled with   special pumps - after working principles of centrifugal pumps than

Increasing the total or Local Pressure in the System
By increasing the total or local pressure in the system the distance between the static pressure and the pressure is Increased vaporization and vaporization and cavitation can be avoided.

The ratio between the static pressure and the vaporization pressure - an indication of the possibility of vaporization, is Often Expressed by the Cavitation Number.

Unfortunately it may not always be possible to increase is due to the total static pressure systems Classifications or other limitations. Local static pressure in components may be Increased by lowering the component in the system. Control valves and pumps in general should be positioned in the and lowest part of the systems to maximize static head.

This is a common solution for boiler feeding pumps receiving hot condensate (water close to 100 ° C) from condensate receivers.

Reducing the Temperature of the Fluid
The vaporization pressure of fluid temperature depends. Vapor pressure of Water, our most common fluid, is Indicated below  :

Temperature ( ° C)
Vapor Pressure (kN / m 2 )
0
0.6
5
0.9
10
1.2
15
1.7
20
2.3
25
3.2
30
4.3
35
5.6
40
7.7
45
9.6
50
12.5
55
15.7
60
20
65
25
70
32.1
75
38.6
80
47.5
85
57.8
90
70
95
84.5
100
101.33

Note ! - The possibility of evaporation and cavitation increases dramatically with the water temperature.
Cavitation can also be avoided by locating components to the coldest part of a system. It is common to locate pumps in heating systems in the "cold" return lines.
This is the same for control valves. If it is possible control valves should be located on the cold sides of the heat exchangers.

Bernoulli Equation


Conservation of energy - non-viscous, incompressible fluid in steady flow
A statement of the conservation of energy in a form useful for solving problems involving fluids. For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point.


A special form of the Euler’s equation derived along a fluid flow streamline is often called the Bernoulli Equation:




































For steady state incompressible flow the Euler equation becomes (1). If we integrate (1) along the streamline it becomes (2). (2) can further be modified to (3) by dividing by gravity

Head of Flow
Equation (3) is often referred to the head because all elements has the unit of length.

Dynamic Pressure
(2) and (3) are two forms of the Bernoulli Equation for steady state incompressible flow. If we assume that the gravitational body force is negligible, (3) can be written as (4). Both elements in the equation have the unit of pressure and it's common to refer the flow velocity component as the dynamic pressure of the fluid flow (5).

Since energy is conserved along the streamline, (4) can be expressed as (6). Using the equation we see that increasing the velocity of the flow will reduce the pressure, decreasing the velocity will increase the pressure.

This phenomena can be observed in a venturi meter where the pressure is reduced in the constriction area and regained after. It can also be observed in a pitot tube where the stagnation pressure is measured. The stagnation pressure is where the velocity component is zero.

Example - Bernoulli Equation and Flow from a Tank through a small Orifice
Liquid flows from a tank through a orifice close to the bottom. The Bernoulli equation can be adapted to a streamline from the surface (1) to the orifice (2) as (e1) :



Since (1) and (2)'s heights from a common reference is related as (e2), and the equation of continuity can be expressed as (e3), it's possible to transform (e1) to (e4).

Vented tank
A special case of interest for equation (e4) is when the orifice area is much lesser than the surface area and when the pressure inside and outside the tank is the same - when the tank has an open surface or "vented" to the atmosphere. At this situation the (e4) can be transformed to (e5).

"The velocity out from the tank is equal to speed of a freely body falling the distance h." - also known as Torricelli's Theorem.

Example - outlet velocity from a vented tank

The outlet velocity of a tank with height 10 m can be calculated as

V2 = (2 (9.81 m/s2) (10 m))1/2
    = 14 (m/s)

Pressurized Tank
If the tanks is pressurized so that product of gravity and height (g h) is much lesser than the pressure difference divided by the density, (e4) can be transformed to (e6).

The velocity out from the tank depends mostly on the pressure difference.

Example - outlet velocity from a pressurized tank
The outlet velocity of a pressurized tank where

p1 = 0.2 (MN/m2)
p2 = 0.1 (MN/m2)
A2 / A1 = 0.01
h = 10 (m)

can be calculated as

V2 = ((2 / (1 - (0.01)2) ((0.2 106 N/m2) - (0.1 106 N/m2)) / (1000 kg/m3) + (9.81 m/s2) (10 m)))1/2
       
        = 19.9 (m/s)

Coefficient of Discharge - Friction Coefficient
Due to friction the real velocity will be somewhat lower than this theoretic examples. If we introduce a friction coefficient c (coefficient of discharge), (e5) can be expressed as (e5b)
The coefficient of discharge can be determined experimentally. For a sharp edged opening it may bee as low as 0.6. For smooth orifices it may bee between 0.95 and 1

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