**Minimize Valve Cavitation by Proper System Design**

Provided By Onyx Valve Company

Textbooks address cavitation in ideal fluids. Real world process fluids are seldom ideal and valves do not always conform to textbook characteristics. This article was written to address cavitation issues related to pinch valve applications. Transposing these concepts to other valve types may be valid but might require considerable modification.

**Cavitation**

The formation of cavities in a flowing stream is a potential problem to hydraulic equipment designers. Symptoms include noise; it sounds like gravel flowing through the line, vibration, loss of efficiency, and physical damage. Valves subject to cavitation erode until components rupture or leak.

Most process equipment can tolerate some degree of cavitation without severely crippling system performance or creating an onerous maintenance burden. While it may be theoretically possible to design systems that completely eliminate cavitation, in many cases this is not really the optimum design.

For example, if calculations indicate a throttling valve will occasionally operate in the cavitation range, the pressure drop could be dissipated across two valves in series. But if the cavitation is not too frequent or too severe, and the damage is concentrated in a short section of relatively inexpensive pipe, the capital expense entailed by the second valve may not be justified. The mathematical tools proposed herein are intended to provide some rule-of-thumb guidance to anticipate the severity and the consequences of cavitation under varying conditions.

**What Causes Cavitation in Valves?**

Valves have three ways to dissipate energy:

- Turbulence: Changing direction of the fluid increases the shear rate. This extracts energy from the process liquid, converting it into non-recoverable heat and noise. The classic globe valve, due to its “tortuous path”, makes extensive use of this mechanism to reduce energy in the flow stream.
- Energy exchange. A pump imparts energy to the flow

stream. This energy has a dynamic component in the form of forward momentum and a potential component, which is pressure. After liquid leaves the pump, exchanges can occur between potential and dynamic energy but total energy cannot increase. As liquid flows through pipe it draws from this store of potential energy to overcome friction. That is why the pressure gradient through horizontal pipe slopes slightly downward. Liquid squeezing into a restriction accelerates to maintain volumetric flow. This increases kinetic energy at the expense of potential energy. Pressure falls as the liquid accelerates. These processes are considered adiabatic as there is no energy extracted during the pressure drop. The process is imperfect in that heat is generated in the fluid due to turbulence and friction that cause heat to be lost to the environment.3. Change of state. Conditions inside piping are not subject to the limitations that we experience in the outside world. The lowest pressure that we experience in our frame of reference is atmospheric, around 14.7 psi absolute. Pressure inside pipe and valves is not subject to this limitation and can drop into the vacuum range. The boiling point, the temperature at which liquid changes to gas, is a function of pressure. As pressure falls, the boiling point is depressed. As pressure ventures into the vacuum range, the boiling point can be suppressed to a point lower than room temperature. The process of boiling extracts energy from the liquid, regardless of the temperature at which the boiling occurs.

Inside a valve, the “vena contracta” is the locus of minimum cross sectional area of the flow stream. This is where the flow stream achieves its highest velocity, so this is where pressure falls to its lowest level. If pressure at the vena contracta falls below the vapor pressure, the liquid changes state from a liquid to a gas forming pockets or cavities in the flow stream.

If the fluid pressure remains below the vapor pressure a fraction of the fluid remains in the gaseous state and a froth of liquid and bubbles continues downstream. This is flashing.

Flashing erosion creates smooth gouges with a polished appearance as seen in the picture at the left.

The process reverses itself when liquid emerges from the restriction. The fluid decelerates and pressure recovers. Pressure does not recover to its original magnitude since this process is not adiabatic. If pressure recovers beyond the vapor pressure the cavities collapse and re-liquefy. This is cavitation.

The collapse of these gas pockets is accompanied by intense micro shock waves generating localized impact pressure over 200,000 psi. Cavitation is generally more destructive than flashing. Cavitation damage produces a rough surface texture even if the process fluid is a liquid with no suspended solids.

If the process fluid is abrasive you can have both abrasion and cavitation damage concurrently. It can be challenging to distinguish which demon is the larger culprit in destroying your valve.

As a general rule, abrasion damage tends to be localized in a single narrow zone right at the valve seat.

In contrast, cavitation damage frequently exhibits a sequential series of pitted areas as shown in the picture above, with observable damage occurring a considerable distance downstream of the vena contracta. Flow streams can have multiple recovery points and cavitation damage can occur in unexpected locations due to the turbulent nature of the flow stream.

**How Can the Process Engineer Cope With Cavitation?**

The ideal solution is to rebalance the pressure drop across the valve, preferably by increasing pressure at the valve exit. This might be possible by relocating the valve closer to the pressure source, or installing it at a lower elevation in the piping network, or reducing the pipe size between the valve and the system exit.

The process engineer often encounters a system where there is simply no practical way to diminish the overall pressure drop across the valve. In these instances the key to minimizing cavitation damage is to stretch out the pressure recovery that occurs when the liquid emerges from the valve throat.

Accelerating the fluid gradually in a series of small steps maintains sufficient pressure to avoid cavitation. One method to accomplish this is to insert a “cavitation cage” in the valve as shown in the picture at the right. This cage consists of a maze of sieves or washers that form a labyrinth of intricate passageways. Fluid passing through the valve traverses this tortuous path which staves off the sudden pressure recovery that initiates cavitation.

Unfortunately, a lot of fluids in the real world cannot tolerate these devices without clogging. The classic example is pressure letdown on tar sand slurries where a confluence of high pressure drop and a solute mix of sand and tar make cavitation cages impractical. Flow streams such as sewerage, sludge, sand slurry and mine tailings also pose significant challenges to the use of anti-cavitation cages.

**Predicting cavitation**

Cavitation prediction evolves directly from valve sizing. Every system engineer is familiar with the basic valve sizing equation:

Where:

###### Cv = Valve Capacity

Fp = Piping geometry factor

G = Specific Gravity

N1 = Numerical constant for units of measure

###### P1 = Pressure at valve inlet

P2 = Pressure at valve exit

q = Volumetric flow rate

Valve sizing is simple. Plug numbers into equation 1, turn the crank, and calculate Cv. Then peruse catalogues and pick a valve with a published Cv greater than calculated Cv.

As long as the process does not cavitate, increasing ∆P increases flow in a linear fashion as seen in the graph, so equation #1 works fine.

But if you continue to increase the pressure drop by lowering P2, eventually the pressure drop reaches the point of incipient cavitation where bubbles start to form in the flow stream. These bubbles crowd the vena contracta obstructing the flow path. At a point called ∆Ps (max delta-P allowable) these bubbles obstruct the flow path to the point where further increases in pressure drop no longer increase the flow through the valve.

At this point, ∆P=∆Ps where the valve is in chocked flow. Further increases in the pressure drop only result in more cavitation.

To find points of incipient cavitation and choked flow, the designer returns to the valve catalogue. Associated with every valve is a second constant, “FL”. This recovery constant represents the valve’s ability to resist cavitation. Higher FL values indicate greater resistance to cavitation.

Although FL is frequently referred to as the recovery ‘constant’, in reality it is really a variable function of valve opening. In torturous path valves like the globe type the variation is slight, so FL may be listed as a constant without adverse effect; no reference is made to the fact that it varies with stem position.

High recovery valves such as ball, butterfly, and pinch types may show FL in graphical format or a table, or they may simply publish a ‘worst-case’ minimum value to simplify calculations and incorporate a safety factor.

The current trend is towards valves with a ‘straight through’ design such as ball, butterfly, diaphragm, and pinch types. These valves are less expensive than the classic globe valve and they function well on slurries and suspensions.

The bad news is that straight through designs are more prone to cavitation, which is reflected in their lower FL numbers.

Equation # 2 determines if cavitation is present:

###### ∆Ps = Delta-P max allowable

FL = Recovery coefficient

P1 = Inlet pressure to valve

Atm = atmospheric pressure = 14.7 psi

Rcrit = Critical pressure ratio= 0.93 (typical)

Pvap = Vapor pressure

Quite simply, if AP ≥ APS then your process is in choked flow cavitation.

Then :

That’s why ∆Ps is the ceiling value for AP in equation 1.

If: ∆P in equation 1 is higher than ∆Ps,

Then: go back to equation 1 throw out the original ∆P, substitute ∆Ps, recalculate Cv and, if necessary, select a larger valve.

Metal valves and rubber-lined valves respond differently to cavitation. Metal valves begin deteriorating between incipient cavitation and choked flow. Metal components with higher elastic stress limits tolerate cavitation better than softer metals.

Ironically, rubber fares better than metal under cavitation conditions. Rubber absorbs much of the shock of the imploding bubbles.

Equation #2 yields insight into ways to reduce or eliminate cavitation. The objective is to maximize ∆Ps.

One way to manipulate ∆Ps is to reduce the fluid temperature, which reduces PV and elevates ∆Ps

Another possible manipulation is to increase P1. Installing the valve at the lowest possible elevation, as close to the pressure source as practical, increases P1, which elevates ∆Ps.

If all else fails, split the pressure drop in half, installing two valves in series, each taking half the drop.

**Reality Check**

Cavitation problems trap engineers in an infinite loop. Textbooks warn of danger but seldom propose practical solutions. Process engineers solve equations; discover potential cavitation and stop, wondering what to do next.

The situation is not as hopeless as it might appear.

The first step towards a resolution is to recognize that there are different degrees of cavitation. The second point is to remember that valves work under cavitation conditions; they just don’t work as long as you’d like.

**How much cavitation is too much?**

Because of their ability to absorb the localized shock waves generated by the cavitation process, rubber lined pinch valves tolerate fairly high levels of cavitation; much higher than metal valves. These limits can be analyzed using basic thermodynamic tools.

These mathematic tools – while not perfect – are more reliable than empirical methods like trying to estimate valve wear based on sound level. There is a disconnect between sound levels and cavitation damage. As soon as the cavitation process is initiated, the characteristic “rumble” can be heard emanating from the valve. (It sounds like gravel is going through the valve.)

However, as cavitation intensifies the sound level remains flat. Also, sound levels are unduly influenced by valve size. There is no auditory change as you cross from acceptable cavitation levels to more destructive cavitation levels. Furthermore, attempt to link the equations used to predict sound levels, to cavitation damage have been fruitless to date.

To answer this question in a rational manner, think about where the energy driving cavitation comes from: The pump.

Let’s use the example shown in figure 9.

We will make the following assumptions regarding the pump operating conditions:

**Assumptions:**

- Q (flow) = 1430 gpm
- P1 (pump discharge pressure) = 120 psi
- P2 (pressure downstream of valve) = 40 psi
- ΔP across the valve = P1 – P2 = 80 psi
- ΔPs=50psi
- The motor injects 120 Brake HP into the pump.
- The pump is 83% efficient

**Now we have to recall some fundamental concepts we learned in thermodynamics.**

- 1 On the first day of Thermodynamics class the professor goes to the blackboard and draws an amorphous shape with arrows pointing in and out. It looks like a potato stuck with toothpicks. He identifies this ‘shape’ as an energy boundary and announces: ΣE = 0, or the sum of energy entering and leaving the system = zero, where energy going into the system is positive, and energy flowing out of the system is negative. The border surrounding the picture of our pump and valve is exactly this kind of energy boundary. Electrical energy goes in to the pump motor, and a mixture of liquid horse power, heat, and noise come out
- 2 Liquid flowing through a pipe contains potential energy that can be extracted to do work. This potential energy is the product of flow and pressure, or:

- 3 Liquid Horse Power = Flow x Pressure.
- 4 In US customary-pain-in-the-butt units the equation works out to:

Equation 3

We can use equation 3 to calculate the power at every point in the pumping system shown in figure 9.

If the pump is 83% efficient, then the liquid HP at the pump discharge is:

Liquid HP (discharge) = 120 HP (in) * 0.83 = 100 HP

Or, the pump looses 20 HP due to internal friction losses inside the casing.

We know that ΔPS across the valve = 50 psi, so we can use equation 3 to calculate exactly how much energy is being dissipated here:

Now, here is the key concept behind our discussion: We know that ΔPS = 50 psi, and ΔP actual = 80 psi, but what does this mean in real physical terms? Between zero and 50 psi the increasing pressure drop causes increasing flow. Once this threshold is reached, further increases in pressure drop do not increase flow; the additional 30-psi of pressure is being used by the system to boil and collapse bubbles!

Since we know exactly what fraction of our pressure energy is driving the cavitation process and we know the flow rate, we can calculate the power involved in the cavitation transformation. This is important because this power is being used just to grind away the discharge of the valve.

In our example, we can see that 25 HP is simply generating the destructive power of cavitation. Now we can account for all of the energy entering and leaving our system.

If we know the destructive power going into cavitation and we have some idea of the surface area inside the valve that has to absorb this, we can write an equation to distributed destructive power over surface area. We need to quantify ‘cavity impacts per square inch’.

The question arises concerning the length over which cavitation occurs. As you saw in figure 7, cavitation damage occurs in a narrow hand, forming a ‘bath tub’ ring in the exit of the valve.

The width of this hand is fairly consistent regardless of valve size, so we can distribute cavitation power over circumference of the valve, treating the width of this band as a constant. We have used this technique for several years and empirical results correlate with predictions fairly well.

(The choice of ‘G’ as the dependent variable was strictly arbitrary.) The decimal point in the denominator was shifted two places to yield more convenient units, so the final equation is:

Where:

P = pressure in psi

D = pipe size in inches

In our example if the valve size is 8 inches then:

**Interpreting the Results**

This “G” number provides a means of comparing different valves, or operation of the same valve in different locations. On the basis of our experience with rubber lined pinch valves, we have developed the following ‘rules of thumb’ for rubber valves operating beyond choked flow conditions. Higher ‘G’ numbers indicate faster erosion.

**Minimize Damage from Cavitation:**

When dealing with fluids like slurries, abrasives, or pigments that preclude conventional cavitation trim such as strainers it is possible to delay the initiation of cavitation by other means.

One method is to use an orifice plate downstream of the valve. This builds up backpressure on the valve so that AP is below the cavitation threshold. For orifice plates:

Where Q is flow and “C” is a constant associated with the orifice and depends on the shape and size of the opening in the orifice.

These devices are non linear. Reducing the flow by 1/2 reduces the pressure drop to 1⁄4 of its original value. Orifice plates are useful in processes with fairly constant flow, with no more than a 2: 1 turn down.

Another alternative: Brute force!

Install two (or more) valves in series and take half the pressure drop across each valve. This is a highly effective, albeit expensive solution.

A better way to deal with severe cavitation is to export it from the piping completely. Cavitation does not start at the throat of the valve. As mentioned earlier it develops past the throat where pressure begins to recover.

As a result, cavitation damage occurs downstream of the valve throat. Cavitation damage in pinch valves destroys the sleeve between the pinch point and the valve exit.

Modulating pinch valves are usually supplied with a reduced port sleeve. The sleeve is molded with a Venturri shape that tapers down to a small diameter in the center of the valve. The sleeve is normally symmetric, tapered on both inlet and outlet so the valve can be installed with flow going in either direction. This design is vulnerable to cavitation damage.

Revising the sleeve design to an asymmetric shape enables the valve to withstand high levels of cavitation. This is called a “trumpet mouth” design or a “cone sleeve”. The thicker rubber at the valve outlet absorbs the pounding from the cavities. There are several ways to exploit this feature to tolerate even higher levels of cavitation with minimum sleeve damage.

One method is to install the valve at or near the end of the piping run allowing the pressure to recover as the fluid emerges from the piping system. Here the cavities form after they have emerged from the piping system, where they cascade harmlessly into the open tank.

In our example we have a 4” x 2” pinch valve installed in a 4” pipeline. Notice that we have added a short section of 2” pipe with a reducer flange at the valve exit in order to delay the pressure recovery until the end of the run.

If it is not practical to install the valve at the end of the pipe run, there is another variation to this approach that is very effective. This approach again starts with a trumpet mouth design sleeve. Our example uses a 4” x 2” valve but it works equally well with any size valve and sleeve port. This approach uses a short spool piece of pipe equal to the valve port size, 2” diameter in the example. A reducer flange is used to attach the 2” pipe to the 4” valve. The minimum spool piece length is typically 10 times nominal diameter or 20 inches. This connects to the remainder of the 4” pipe run with a second reducer flange creating a sudden expansion at the inlet to the 4” pipe. Do not use a tapered expander here; you want a sharp sudden expansion.

This design pushes the pressure recovery and its accompanying cavitation out of the valve. The obvious question is “what about the 4” pipe at the sudden expansion?” Well, yes, this is going to

take a certain amount of pounding, but first of all this can be a rubber pipe joint to absorb the noise and wear, and secondly it is easier and less expensive to replace a section of 4” hose once or twice a year than to have to service the valve.

**References:**

- G. F. Stiles, “Cavitation in Control Valves”, Instruments and Control Systems,
- Hans Baumanu, “Control Valve Primer”, 2nd ed, ISA, 1995
- Bela G Liptak, “Instrument Engineers’ Handbook’, 1970.