Cavitation Cameron Fritz, John Glover, Maia Griswold

CIVE 401, Hydraulic Engineering Dr. P.Y. Julien November 19, 2014

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Table of Contents

Introduction Page 1 Theory Page 2 Failures Page 5 Prevention Page 7 Conclusion Page 11 References Page 12

Fritz, Glover, Griswold

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Cavitation

Introduction

Cavitation is the occurrence of small bubbles in a hydraulic system due to a pressure

decrease such that the pressure in the water is less than vapor pressure. When water

pressure is lower than vapor pressure, the water vaporizes within the liquid and small

bubbles are formed. Pressure of the liquid around the bubbles causes the bubbles to then

collapse which releases energy. In a hydraulic system, cavitation releases so much energy

that damage and erosion can occur on the solid aspects of the system. We can see the

negative results of cavitation in pumps, turbines and dams.

For any hydraulic system, cavitation must be taken into consideration both during the

design process as well as after the system is in place. Engineers need to routinely check for

cavitation damage during the life of the system. If cavitation occurs and is not caught

quickly colossal damage can occur. An example of this is outlined in the tunnel collapse of

1974 during the construction process of the Tarbela Dam in Pakistan. Prevention of

cavitation is essential for the success and continued operation of any hydraulic system. An

outline of theory, failures and prevention is detailed in the following report.

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Theory

Cavitation is a phenomenon that occurs when the pressure within a flowing fluid reaches

the vapor pressure of the fluid, resulting in the formation of vapor bubbles. It is generally

characterized by a loud crackling noise and a “cloud” of vapor bubbles that form where the

cavitation is initiated (see Figure 1). These audible and visible signs, along with damage to

surfaces within the pipe, are often the most recognizable aspects of cavitation. There are two

different types of cavitation, depending on the properties of the vapor voids: vaporous

cavitation when the bubbles consist of water vapor and gaseous cavitation when the bubbles

contain gasses other than water vapor. Cavitation occurs due to a pressure drop as a result

from an increase in the velocity of the fluid through a specific zone, often as a result of a

decrease in the cross sectional area of the flow. Since pressure decreases at higher altitudes

cavitation can also occur with an increase in the elevation of the hydraulic system. This

concept is explicitly expressed by Bernoulli’s Equation (Eqn. 1), in which it is evident that

an increase in velocity or elevation on either side of the equation will result in a decrease in

the associated pressure in order to maintain equilibrium (constant total head).

!!!+ !!!

!"+ z! =

!!!+ !!!

!"+ z! (1)

Cavitation is often confused with the process of boiling, which is a similar phenomenon

with several key differences. During the boiling process, the temperature of water is

increased while maintaining constant external pressure (e.g., an open pot on a stove). As

the water begins to undergo a phase change once the temperature reaches the boiling point,

with vapor bubbles forming and collapsing when they reach the surface. Cavitation is

similar in the way that it too consists of water changing from liquid to vapor state. However,

the primary difference is that boiling occurs by changing the temperature while holding the

pressure constant, and cavitation occurs by changing the pressure while holding the

temperature constant.

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http://www.cavitator-systems.com/en/images/kavitationsblaeschen2.jpg

Figure 1. Formation of Cavitation Bubbles Like many other phenomena, cavitation comes in a variety of magnitudes and intensities.

Vapor bubbles may vary in size depending on which stage of cavitation the fluid is

undergoing. The size of vapor bubbles is what affects the extent of damage and noise within

the system. Two terms used to describe the progression of the cavitation process are

incipient cavitation and desinent cavitation. The first refers to the critical state when cavitation

first begins to occur as velocity increases and pressure reaches the value of the vapor

pressure of the fluid. Desinent cavitation refers to the point at which velocity fluid is

reduced and the pressure is greater than the vapor pressure. Flow can also reach a point of

supercavitation, in which a single large bubble is present as opposed to the numerous

individual bubbles. Supercavitation is especially applicable to the study of the motion of

fast-moving objects submerged in a liquid. When a fast moving object is submerged in a

liquid, a large vapor bubble encompassing the object greatly reduce the drag and aids its

travel. The parameter commonly used to distinguish whether cavitation will occur and to

what level is called the cavitation index, 𝜎.

𝜎 = !!!!!!!!!!

! (2)

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The smaller the cavitation index, the greater the likelihood of cavitation. When 𝜎 remains

greater than 𝜎! (incipient cavitation number) cavitation will not take place.

Cavitation is a critical issue in hydraulic design due to the extreme damage that may

transpire in pipes that experience such an occurrence. As the voids reach higher-pressure

regions within the conduit they begin to collapse, releasing significant amounts of energy in

a violent fashion that can damage the structure of the hydraulic system, as shown in Figure

2. Damage from cavitation will always take place downstream of where the bubbles initially

formed, with the maximum damage arising near the end of the cloud of cavitation bubbles.

Thus, the following equation for the length of the cavitation cloud (Eqn. 3) can also be used

to determine the distance downstream to the areas experiencing maximum damage:

!!!= 2 !!

!

!.!" (3)

where: H = characteristic dimension (radius of conduit, etc.) Lk = length of cavitation cloud 𝜎 = cavitation index 𝜎! = cavitation index where damage begins (Lk/H = 1)

http://khia.belzona.com/en/view.aspx?id=1259

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Figure 2. Water Pump Severely Damaged by Cavitation

Failures

Failures due to cavitation are common in pump systems and impellers, especially on a small

scale (Figure 3). Pumps in large, high profile systems are checked continually for cavitation

damage and therefore failure within pumps is often avoided. Cavitation that occurs in

spillways and on structures involving large bodies of water is more challenging to check for

and therefore damage due to cavitation on large structures such as spillways and dams is

more visible since cavitation continues to effect the structure.

Figure 3. Failure of impeller due to cavitation

One major failure incident in history due to cavitation took place at the Tarbela Dam on the

Indus River in Tarbela, Pakistan. This hydraulic plant was once the largest man-made

structure in the world, and still stands today as the largest earth filled dam in the world. The

dam currently holds water from flooding an area that is home to millions of people. Due to

its high profile, a failure in this dam would be a catastrophic event. In 1974, the same year

of the dam completion, one of the tunnels (tunnel No. 2) used to temporarily route water

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throughout construction collapsed due to cavitation damage. Forensic engineering,

performed by Imperial College London, later determined the cause of failure and stressed

the damage that water can cause on dams. Cavitation occurred in the tunnel due to one of

the water gates, which controlled flow, being held in a half open position. Decrease in the

cross-sectional area of flow caused on increase in water velocity at the bottom of the tunnel

inlet and outlet. This increase in velocity caused a decrease in pressure great enough that

cavitation occurred and began to wear down the structural supports of the tunnel. In

September of 1974 the tunnel intake gate collapsed from erosion on both piers and gate as

shown in figure 4. The collapse of tunnel No. 2 also caused the partial collapse to tunnel

No. 1, which also had cavitation damage (Figure 5). After the collapse, an emergency

draining of water was ordered and construction of the dam was continued so that the dam

was in working operation for the summer flood season of 1975.

Although a full failure of the dam did not

occur; failure of the tunnels at the Tarbela

Dam was an indicator of the damage that

water can cause on structures. Since this

incident, dams have been monitored more

heavily to ensure that future failures do not

occur in the future.

Figure 4. Failure of piers and gate at tunnel No. 2

Figure 5. Cavitation damage at intake of tunnel No. 1

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Prevention

Cavitation can be very damaging to various structures that facilitate the passage of water

including pipes, dams, and spillways. In order to preserve the integrity of the structure, steps

should be taken to avoid cavitation throughout the entire length of the structure. Any

damage can shorten the life of a structure and add additional cost of maintenance. If

enough damage has occurred to the structure, failure could ensue and result in damage to

surrounding property and even loss of life.

There have been many studies conducted in order to understand cavitation and how to

prevent it. One study, published in 2001, written by Meng-Xi Nie in the American Society

of Civil Engineering in the Journal of Hydraulic Engineering entitled “Cavitation

Prevention with Roughened Surface,” examined the cavitation on the Zhexi dam.

Measurements taken from the Zhexi dam spillway indicated that a manually roughened

section of the dam surface was affecting occurrence of cavitation. Engineers noticed that an

irregularity directly downstream of the roughened surface did not cause cavitation, while

irregularities behind the original smooth surface had cavitation occur.

According to Nie, based on his earlier studies back in 1984, “single irregularities caused the

maximum negative pressure when they are placed near the downstream tangential point of

the curve.” This can be seen in Fig. 6 below.

Nie

Figure 6. Layout out of Roughness and Irregularity Elements along Curve of Open Channel

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used various diameters of cooper wires ranging from 0.24 mm, 0.38 mm, and 0.58 mm on a

Plexiglass model to simulate roughness elements. A copper wire with a diameter of 0.78

mm was used to represent the downstream irregularity. Other parameters of the model

were: a width of 17 cm, working heads ranging from 219, 249, and 284 cm, a velocity of 7

m/s, and a discharge of 130 L/s. With these parameters, spacing of roughness elements

were varied as well with distances of 2, 4, and 8 cm.

In order to evaluate the study more efficiently, Nie created two dimensionless parameters,

one for the pressure drop caused by the irregularity, 𝐶!, and one for the ratio between

kinetic and potential energies, η. The equations for each of these parameters can be seen

below.

𝐶! =ℎ − ℎ!𝐻

Where:

ℎ! = Pressure at the point with no irregularity

h = Pressure at the point with the irregularity

H = Total pressure at that point.

𝜂 =𝑞

𝑔  𝐻!!

Where:

q = Discharge rate

g = Gravitational acceleration.

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Using these dimensionless parameters, Nie tested three different conditions to see how

changing different aspects affected the pressure drop at the downstream irregularity. In each

of these cases two parameters were kept constant and one was varied. The three conditions

tested were:

1. Same curve radius and roughness, but different downstream heights

2. Same roughness and irregularity height, but different curve radii

3. Same curve radius and irregularity height, but different roughness

Nie found that the maximum 𝐶! always occurred when η = 0.015. Once this was establish

nine groups of roughness combinations were tested at this discharge condition.

A unique set of results was found for the d = 0.24 mm at s = 2 cm and the results were

approximated to be

𝐶!,!"# = 𝑎∆𝑅

!

Where:

Δ = irregularity height

R = curve radius

A least squares regression analysis of the values a and b for each roughness group showed

that they could be correlated by

𝑎 = 0.42𝑒!.!"(!!∗!"")

𝑏 = 0.12+ 0.19(𝑑𝑠 ∗ 100)

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Using these coefficients, the critical irregularity height for different working heads, curve

radii, and roughness conditions were compared in Fig. 7 below.

Nie’s results concluded that the critical height of irregularities located at the end of a curve

of a spillway is greatly increased with an increased roughness located upstream. The

pressure drop caused by the roughness is able to reduce the velocity of the water enough so

that cavitation is not allowed to occur. In fact, with the increased roughness, the irregularity

height was allowed to increase from 2 to 3 mm for a smooth upstream surface, up to 10 or

even 20 mm if the curve region is properly roughened. An additional benefit of using Nie’s

technique beyond reducing the damage caused by cavitation is that the quality control is

reduced during construction.

Figure 7. Critical Irregularity Heights (H = 100 m)

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Conclusion

Cavitation is a well-understood phenomenon in fluid dynamics that must be considered in

all design where water or some other fluid undergoes some pressure drop. Without properly

considering cavitation while designing a structure that transports fluid undesired damage

may occur, reducing the lifetime of the design, and producing additional expenses.

Significant damage to a structure can also lead to property damage outside of the structure.

Fortunately, the theory and equations governing cavitation are well known and understood.

Additionally, there have been many studies on how to reduce and even prevent cavitation

from occurring. Some of these found practices can even produce additional benefits, for

example reduction in quality control. Cavitation can be detrimental to any water structure

design but with careful consideration and calculation there should be no reason that

cavitation is allowed to occur.

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References

Information, pictures and figures used are sited below, used without permission for educational purposes only.

Campbell, Peter, ed. Learning from Construction Failures: Applied Forensic Engineering. Scotland, UK: Whittles Publishing, 2001. Print.

Chiarugi, V. "Sinmast Divers At Tarbela." sinitworks (1976): n. pag. Print.

"Solving a cavitation problem." Centrifugal Pump Help-John Anspach Consulting. Wordpress, 17 Apr. 2011. Web. 2014.

Nie, Meng-Xi. "Cavitation Prevention with Roughened Surface." Journal of Hydraulic Engineering 127.10 (2001): 878. Web.

“Fundamentals” Cavitation and Bubbly Flows Group at St. Anthony Falls Laboratory. N.p.,n.d. Web. 8 Nov. 2014 Falvey, Henry T. “Cavitation in Chutes and Spillways.” (1990): n. pag. United States Department of the Interior, Bureau of Reclamation. Web. 8 Nov. 2014