# Summary

Restriction orifices and control valves are commonly used for pressure reduction and measurement of flow rates, however for a liquid system, excessive pressure drop across these items of equipment may result in cavitation. This article describes methods of predicting cavitation across restriction orifices and valves and proposes designs which may be used to avoid cavitation.

# Definitions

 $$C_{i}$$ : Cavitation Index (often σ) $$P_{1}$$ : Upstream Pressure (absolute) $$P_{2}$$ : Downstream Pressure (absolute) $$P_{v}$$ : Fluid Vapour Pressure $$\Delta P_{p}$$ : Permanent Pressure Loss $$\Delta P_{r}$$ : Recoverable Pressure Loss

# Introduction

Cavitation occurs in liquid systems and is the result of rapid formation and collapse of vapour bubbles in the liquid. Cavitation must be avoided or controlled as the collapse of vapour bubbles releases significant energy at the location of the bubble collapse. The consequences of this energy release are typically loud noise and pitting damage to contact surfaces, which over time may result in significant damage to or failure of equipment such as pumps or valves.

Cavitation occurs at a region where the pressure is lower than the fluid vapour pressure, such as the pump suction, or where a large pressure reduction takes place. In this article we consider control valves and restriction orifices, which are commonly used as pressure reduction steps in a liquid system.

Cavitation may occur in a pressure reduction system even if the final system pressure is the above vapour pressure of the liquid. This is because the intermediate pressures may fall below the final pressure.

In the case of a simple concentric restriction orifice the fluid is accelerated as it passes through the orifice, reaching the maximum velocity a short distance downstream of the orifice itself (the Vena Contracta). The increase in velocity comes at the expense of fluid pressure resulting in low pressures in the Vena Contracta. Downstream of the Vena Contracta in the recovery zone, the fluid decelerates converting excess kinetic energy into pressure energy as it slows. Therefore the intermediate pressure in the Vena Contracta is lower than the final system pressure and thus the highest chance of experiencing cavitation as demonstrated in the figures below.

It is difficult or often impossible to measure the lowest pressure of the system, for example in the Vena Contracta, particularly for complex designs of control valves. Additionally, variability in flow stability, system vibration and other external factors can all influence the whether cavitation occurs.

Due to the difficulty in predicting or measuring the systems lowest pressure equipment may be placed in a test rig where the cavitation through the device may be characterised in terms of a Cavitation Index.

# Predicting Cavitation and the Cavitation Index

The cavitation index is the ratio of the pressure differential between the equipment inlet pressure and the fluid vapour pressure to the pressure differential pressure across the equipment. The equation for calculating the cavitation index is shown below:

$C_{i}= \frac{P_{1}-P_{v}}{P_{1}-P_{2}}$

The above equation allows the cavitation index for a particular device and application to be determined. The value of Ci above is compared against acceptable values for particular equipment and applications to indicate the likelihood of cavitation occurring. For example in the case of a typical square-edged concentric orifice plate a Ci of 2 or above would be unlikely to cause cavitation, whereas values below 2 would indicate cavitation or incipient cavitation are likely.

The cavitation index is a heuristic method for analysis of restriction orifice plates and valves, and the acceptable Ci will depend on the several factors including, flow stability, piping geometry near the orifice and the particulars of the orifice design. Some typical Ci values for restriction orifice and valves are presented in the table below:

 Restriction Type CiTypical CiRange Square-edged Concentric 2 1.8 - 6 Multi-hole orifice plate - 1.2 - 4 Globe Valve 2 1.7 - 2.0 Globe Valve with anti-cavitation trim - 1.2 - 1.7 Globe Valve with multi-stage anti-cavitation control trim - 1 - 1.3 Butterfly Valve 4 >2.5 Ball Valve 3.5 -

# Avoiding Cavitation

Avoiding cavitation for pressure reduction in liquid is achieved in one of three ways: multiple steps, tortuous paths, or controlled cavitation. Alternatively designers may choose to accept some cavitation and use hardened trim control valves. Each method has pros and cons, such as turn-down, costs, minimum Ci achievable and physical size of equipment.

## Multiple Steps

Multiple step reductions may involve multiple restriction orifices, control valves or combinations of both. A typical set up may include a control valve with a restriction orifice downstream. The restriction orifice then provides the back pressure on the control valve to prevent cavitation through the valve. However the restriction orifice itself must also be correctly sized to prevent cavitation.

The advantages of this arrangement is that it is relatively cheap, particularly if multiple restriction orifices are used in series. Disadvantages of this arrangement are a larger physical size and poor turn-down performance, particularly for orifice only arrangements.

## Controlled Cavitation

Controlled cavitation arrangements generally work by allowing cavitation to occur and controlling the location of the cavitation. this may be achieved via a control valve which directs jets of fluid at each other, allowing them to combine and cavitate away from the metal surfaces of the valves.

The disadvantages of this design are that narrow pathways are normally used and they will be susceptible to plugging. Additionally these valves are not suitable for use in systems with very low Ci values.

## Tortuous Path

Tortuous path control elements may use a variety of designs such as zig-zags, bends, etc, to reduce the pressure of the fluid over a longer path and thereby reduce the likely hood of cavitation. The long path allows the pressure loss and recovery steps to be essentially simultaneous, removing the pressure dip of the vena contracta.

Tortuous path arrangements can achieve very low Ci values, with some manufacturers advertising values as low as 1.001. This allows for a single compact valve to perform large pressure reductions steps.

The disadvantages of this technology are plugging and cost. The small pathways of the valve are susceptible to plugging unless the fluid is clean. Complicated manufacture and proprietary design mean these valves will also have a relatively high cost.

## Hardened Trim

Using hardened trim control valves does not attempt to avoid cavitation, but instead attempts to provide equipment better protected against the damage resulting from cavitation. This may be suitable for situations where cavitation is infrequent or very mild. It is not usually suitable for sustained or violent cavitation as even hardened trim valves will be rapidly damaged in these situations. Furthermore the use of these control valves will not mitigate any other symptoms of cavitation such as noise and vibration.

Using this type of valve may be appropriate where fluid is fouling (preventing the use of tortuous path designs) and turn-down or space considerations prevent the use of a multiple stage pressure reduction.