# Diffusing Bubble Bombs

## Proper Valve Sizing for Severe Service Can Help Lessen Wear and Damage from Cavitation

11/18/2009

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The calculations of the k-factors/loss coefficients of a control valve trim should not be considered as a substitute but rather as a compliment, to ANSI/ISA S75.01. The calculations are necessary to evaluate the capabilities of a control valve before the valve is bought and should be written in all in-house control valve specifications. To present the technical solution/control valve specification to eliminate repeated failures in control valves, it is important to use layman's terms to convince as many teams as possible.

#### Cavitation and Justifying the 70 psi Criteria

Cavitation is a process in which the liquid pressure is dropped below the vapor pressure due to a flow phenomenon. A dimensionless parameter describing flow-induced boiling is the cavitation number:

Ca = (Pa – Pv)/(0.5pV2)

in which Pa = ambient pressure; Pv = vapor pressure; and V = characteristic flow velocity. Depending upon the geometry, a given flow has a critical value of Ca, below, which the flow will begin to cavitate.

The author's search for the critical cavitation number for water in published literatures continued from November 2003 to October 2004. Then, in an old fluid mechanics text written in 1952 by Ludwig Prandtl, Essentials of Fluid Dynamics, the following cavitation number for submarine propellers in water was found on p. 315. It was 0.2.

Prandtl performed experimental onflows across a restrictive element in a closed conduit from which he produced various pressure recovery charts. He deduced that the point where the rise of pressure sets in marks the end of the region where cavitation occurs. He further deduced that the greatest practical significance of cavitation is in connection with high-speed water turbines and ships' propellers. In other words, he applied his knowledge from internal flows to external flows. If critical cavitation number is 0.2, then the surface fluid kinetic energy for onset of cavitation at the tip of the propellers in Prandtl's example would be 94 psi. The calculations are as follows:

0.2 = (Pa – Pv) / (0.5 pv2)

Therefore tip velocity, v = √ [(131000 – 2337) / 0.5 (998)(0.2)] = 35.9 m/s = 118.5 ft/s. And the surface fluid kinetic energy at the tip of the propellers = 0.5(62.4)(118.5) 2/(32.2)(144) = 94 psi > 70 psi. Hence, the 70 psi criteria can be considered as a safe-side design criteria for the design of control valves.

For example, during one plant shutdown, damage on three identical boiler feedwater recirculation valves was observed, and it showed that the damage on all three valves was due to cavitation (Figure 1). However, the damage among the three identical valves was not similar, even though the process conditions were identical. Further examinations reveal that some drilled holes were badly damaged by cavitation, some drilled holes were less damaged, even though all these holes were exposed to the same inlet pressure P1 and the same outlet pressure P2.. This shows that severe cavitation can't be easily predicted as claimed by many published theories. The cavitation damage can be explained by an uneven distribution of the surface kinetic energy at the exit of the damage holes. However, trim analysis can be applied to identify the root cause of the failure.

#### Fluid Velocity and Cavitation

As a result, numerous theories on cavitation exist in industry. However, the following facts hold true:

1. Cavitation is produced whenever a solid object moves through liquid at a speed great enough to create gas bubbles. If the solid object is stationary, cavitation is produced whenever the liquid moves at a speed great enough to create gas bubbles.
2. The onset of cavitation is related to the speed of the object in the first case, and to the speed of the fluid in the second case above.
3. A solid/liquid interface surface has to exist for cavitation to occur.

In addition, photos of cavitation damage on pump impellers indicate that cavitation first appears at the tips of impeller blades because the speed of the blade tips is greater than the speed of the impeller hub. This is known as blade-tip cavitation. And, as speed increases further, the entire face of the impeller blade starts cavitating, producing sheet cavitation. This proves that higher the fluid velocity means more cavitation damage. Therefore, controlling velocity can control cavitation. Of course, increasing the reference pressure or decreasing the Δp-value in the expression for the cavitation number at inception can reduce the chance of cavitation theoretically.  It is more difficult to control the fluid pressure than to control the fluid velocity in a control valve.

[In the author's paper, "Comparison of Pressure Control versus Discharge Energy control in Cavitation Service," written with J. Steinke, presented at 2006 Valve World Conference, the cavitation problems in two out of 17 boiler feedwater recirculation valves were eliminated successfully by reducing the trim exit fluid velocity to 28 feet/s (9 m/s) using a 24-stage letdown trim with loss coefficient of 10.35. Readers who are interested in the paper are welcome to contact the author.]

#### Increasing the Loss Coefficient

A method to increase the loss coefficient of the trim of a control valve also was presented by the author at the ISA Oil Sands Conference, 2006, at Fort McMurray, Alberta. This method uses a trim with a disk design having many right angle turns in each disk. With many right angle turns, the trim loss coefficient increases (Figure 2).

The criteria of trim exit fluid energy of 70 psi for design of control valves published in ISA's Practical Guides for Measurement and Control, Control Valves has been justified here in layman terms. The criteria were applied to perform quick checks on the capabilities of control valves. This serves as a compliment to ISA S75.01 on valve sizing.

Once again, cavitation in control valves can't be easily predicted, and trim analysis can be applied to identify the root cause of failures in control valves. Instrument engineers are advised to write in-house control valve specifications to include the requirements from valve manufacturers of the calculated trim k-factor/loss coefficient, and to include the criteria of trim exit fluid kinetic energy of 70 psi for severe service control valves sizing.

In general, in investigating control valve failures, it's advisable to check the trim exit fluid kinetic energy at all flows. Piping geometry should also be checked. Also, trends and  history of valve vibrations can recognize problems early. Objectionable valve vibrations at specific frequencies should be analyzed. When assistance is needed, a copy of the original instrument data sheet and the existing piping isometric drawing are necessary. It's advisable that, if necessary, the calculations of trim loss coefficient be reviewed and commented on by a third party based on knowledge of fluid mechanics or transport phenomenon.

Gerald Liu, PE, is chairman of the ISA 75.10 (Pinch Valve) and 96.03 (Pneumatic Actuators) subcommittees. He can be rreached at gerald.liu@shaw.ca