# Diffusing Bubble Bombs

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

By Gerald Liu, PE

Instrument technicians are often called by their instrument engineers to look at repeated control valve failure problems during plant shutdowns. From a maintenance point of view, the definition of "severe service" in control valves can be based on how long the valves last.

If the same or similar damage is observed in a control valve for two consecutive shutdowns, the service conditions experienced by that valve can be classified as severe service, and so the valve can be defined as a severe-service control valve. Of course, other definitions of severe service exist. The responding instrument engineer has two ways to tackle this problem. In general, the process conditions could be questionable, and/or the valve could be unsuitable for handling the process conditions, i.e. not sized correctly.

For any plant operating for many years while production was maintained without change, process conditions after reconfirmation can be considered valid and good. In such cases, the instrument engineers should take a closer look at how the damaged valve serving the process conditions was sized, rather than just ordering the same valve using control valve data sheets from when the plant was built. This enables instrument engineers maintaining the control valves to rewrite specifications for procuring and engineering new control valves best suited for the application. This is the best practice for eliminating repeated failures.

However, it's not unusual for the supplier of the damaged valve to try every means to discredit the instrument engineers by approaching their management to negotiate for a solution to monitor the valve problems without eliminating them. Using an asset management system to monitor control valves plant-wide while continuing to supply the same parts for the damaged valves is an unwise approach.

The relationship between the process conditions and the velocity (in the control valve in this case) is governed by this derivation of the Darcy's Equation:

P1 – P2 = f (L/D) pv2 / 2 gc

in which P1 and P2 are, respectively, the upstream and downstream process fluid pressures of the control valve, while f (L/D) is the loss coefficient or resistance (the k-factor) of the control valve trim; v and p are respectively the fluid velocity and the fluid density at the exit of the control valve trim; and gc is the universal gravitational constant of 32.2 lbmft/lbfs2.

Assuming incompressible flow, if the k-factor of the control valve trim is small, then the trim exit fluid velocity will be high because the trim can't dissipate much of the fluid energy. With kinetic energy increasing quickly according to the second order of velocity, it causes internal damage by cavitation, vibrations and/or unacceptable control valve noise. If the trim exit kinetic energy is excessive, piping and downstream equipment can be damaged (Figure 1).

Conversely, if the k-factor of the control valve is large enough to reduce the exit fluid kinetic energy to a safe value, damage to the control valve or downstream components can be eliminated. With compressible flows, for a given trim exit fluid kinetic energy, the density of the fluid at the trim outlet becomes smaller when P2 gets lower, and thus the outlet velocity becomes higher. This can cause objectionable noise problems when vent valves with very low pressure outlets are concerned. This explains why a good low-noise vent valve requires a high k-factor, such as 10, has many stages (often 30), and is expensive. In actual practice for design of gas vent valves, the trim exit fluid kinetic energy should often be less than 1 psi to meet EPA noise standards.

However, while trying to reduce cavitation in valves, a challenging question arises—why rewrite the control valve specification for in-house use when ISA already has so many established control valve specifications and standards readily available? The answer is simple—ISA standards on control valves do not consider or calculate the k-factor/loss coefficient of control valve trims. In ANSI/ISA S75.01 standard, "Flow Equations for Sizing Control Valves," paragraph 4.3, "Piping geometry factor Fp," it's stated that the factor ∑k is the algebraic sum of the four effective velocity head coefficients of all fittings attached to, but not including the valve. ANSI/ISA S75.01 calculates the flow capacity and the impact of flow choking (cavitation, flashing and sonic flow) on the Cv of control valves. It doesn't calculate the capabilities of the control valves to resist the damage from flow choking.

To calculate the capability of a control valve, one has to use a method called trim analysis. That is, one must consider the trim flow geometry, then evaluate the total k-factor/loss coefficient based on trim inlet area or trim outlet area, substitute into the Darcy's equation above for a given set of process conditions, and use 70 psi as the criteria for the trim exit outlet fluid kinetic energy. If both sides of the equation are satisfied, then the control valve with the selected trim is capable of handling the process conditions.

Other methods of calculating the k-factor of a control valve trim exist. For complicated trim geometries, or when manufacturers won't provide information about their trims, one can still do iterative calculations by assuming a value for the k-factor of the trim, calculating the Cv's to see how close the calculated Cv's will match with the Cv's published (at various valve openings) by the specific valve manufacturer. If the calculated Cv's match with the published Cv's to within 5% at various valve openings, then the assumed k-factor will become the k-factor of the trim in question.

This method is similar to reverse- engineering an unknown trim for a control valve, which challenges some control valve manufacturers, who keep producing control valves that fail repeatedly in a given set of process conditions. Often, when the sales engineers visit the instrument engineers experiencing repeated control valve failures, it's important to educate the them and request information on the k-factor/loss coefficient of the trims from their manufacturers according to in-house specifications. The important information to ask about is the k-factor/loss coefficient of the control valve trim. If assistance is required, it helps to request a third party, such as another valve manufacturer, to review and comment on the calculations of the trim k-factor/loss coefficient based on the fluid mechanics or transport phenomenon.

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