Liquid Flow in Control Valves – Choked flow, Cavitation and Flashing

Submitted by Jon Monsen, Ph.D.
on Mon, 01/30/2017
Choked Flow

The basic liquid sizing equation tells us that the liquid flow rate through a control valve is proportional to the square root of pressure drop. This simple relationship is shown graphically by the green portion of the graph in Figure 1. (Note that the scale of the horizontal axis is the square root of pressure drop.)

This linear relationship does not always hold true. As the pressure drop is increased, the flow reaches a point where it no longer increases. Once this happens, additional increases in pressure drop across the valve do not result in additional flow, and flow is said to be choked. Here we will call this limiting or choking pressure drop ΔPchoked, so as to be in agreement the latest versions of the IEC and ISA control valve sizing equation standards. Prior to the issuance of the 2011 edition of the IEC valve sizing equation standard and the 2012 version of the ISA valve sizing equation standard there was no official name given to the dividing line between non-choked flow and choked flow, so valve manufacturers made up their own names. Some of the most common ones are listed in Figure 1.
Figurine 1. Liquid flow in a control valve as a function of the pressure drop across the valve.
Let’s take a look at what is happening inside the valve to cause this choking of the flow. When the flow stream passes through the vena contracta (the point at which the cross sectional area of the stream is at a minimum), the flow velocity reaches a maximum. Conservation of energy dictates that since kinetic energy at the vena contracta has increased to a maximum, potential energy, in the form of static pressure, must decrease to a minimum. (See Figure2.) Note that in the figure, ΔP is less than ΔPchoked and flow is not choked.

Figure 2. Pressure and velocity profile in a Control Valve
As the pressure drop across the valve increases, the flow also increases, increasing the velocity at the vena contracta and decreasing the pressure at the vena contracta. If the vena contracta pressure drops to the vapor pressure of the liquid, vapor bubbles form at the vena contracta. Any additional decrease in the downstream pressure causes more bubbles to form, but the pressure at the vena contracta does not decrease below the vapor pressure. At this point it is worth noting that the flow through a control valve depends on the pressure difference between P1 and Pvc (the pressure at the vena contracta), and since the vena contracta pressure does not decrease below the vapor pressure, the flow does not increase, resulting in choked flow.

Something that is beyond the scope of this classical discussion of liquid flow in control valves is that experimentation has shown that the pressure at the vena contracta must actually drop slightly below the vapor pressure of the liquid before vaporization and choked flow begin. The amount below the vapor pressure that the vena contracta pressure must drop to for flow to choke is approximated in the IEC and ISA Standards by the Liquid critical pressure ratio factor, FF. When the vapor pressure is very low compared to the liquid’s thermodynamic critical pressure, the vena contract pressure where choked flow will begin is only about 4 percent lower than the actual liquid’s vapor pressure. This effect is taken into account in all of the modern control valve sizing softwares. You can read more about this in Valin Corporation’s book, Control Valve Application Technology.

Cavitation

Figure 3 illustrates the choking process along with the cavitation discussed in the next paragraph. Note that in the figure, ΔP is greater than ΔPchoked  and flow is choked.
Figure 3. Velocity and pressure profile in a control valve with choked flow and cavitation.
As the bubbles move down stream, the cross sectional flow area opens up, the velocity goes down and the pressure goes up. Now we have bubbles with an internal pressure equal to the vapor pressure surrounded by a higher pressure. The bubbles collapse in on themselves. This combination of bubble formation and the resulting choked flow, along with the collapse of the bubbles downstream is called CAVITATION. When the bubbles collapse they make a popping sound. The result is a noise like gravel going through the valve. This noise can be loud enough to be very annoying and even loud enough to damage the hearing of a person who is exposed to it for long periods. Also, when the bubbles collapse, they create shock waves that can cause severe damage to the valve. The appearance of cavitation damage is a rough, cinder like, look. (See the picture of a globe valve plug in the upper right side of Figure 3.) This damage can happen very quickly, sometimes in as little as a few weeks or months. Because cavitation damage happens so quickly, we try to avoid cavitation at all costs. Very hard materials give some improvement, but usually the improved performance is not enough to justify the cost.

Flashing

If we continue to decrease the downstream pressure, we reach a point where the pressure downstream of the valve is less than the vapor pressure of the liquid.

Figure 4. Velocity and pressure profile in a control valve with choked flow and flashing.
Now, instead of collapsing, the bubbles become larger and very soon transition from liquid with bubbles in it to vapor with small drops of liquid in it. This is called FLASHING. The appearance of flashing damage is quite different from cavitation damage, and appears as smooth, shiny rivers and valleys. (See the picture of a globe valve plug in the upper right side of Figure 4.)  The damage mechanism is a sand blasting effect. Downstream of the vena contracta the flow consists of a large volume of vapor with many tiny drops of liquid. Because the volume increases greatly when liquid vaporizes, the downstream velocity can be several hundred feet per second, and the high velocity liquid droplets can erode away a valve part. The damage caused by flashing does not usually happen as quickly as that caused by cavitation. The use of hard or erosion resistant materials can usually bring the damage to within tolerable limits. Trim parts made of the hard stainless steels, such as 17-4 ph, hold up quite well, and 316ss or chrome moly bodies do much better than carbon steel. The existence of flashing conditions is dictated by the system (P2 is less than Pv) and the valve selection neither causes or prevents flashing. The noise caused by flashing is usually below 85 dBA and to the author’s knowledge there is no method for calculating flashing noise.

The Real Situation

Figure 1 and the associated discussion of liquid choked flow is the classical discussion, and implies that there is a sudden transition from non-choked flow to fully choked flow. In reality, at pressure drops approaching, but below the calculated value of ΔPchoked, there is usually some formation of vapor bubbles and some degree of cavitation. Figure 5 shows what really happens as flow transitions from non-choked to fully choked flow.

Figure 5. Actual transition between non-choked and choked flow.
It is interesting to note that current control valve sizing methods do not include a method of calculating where the transition from non-choked to fully choked flow begins and ends. The current ISA and IEC control valve sizing standards only give formulas for calculating the red and green lines in Figures 1 and 5.

Preventing Cavitation and Cavitation Damage

The value of ΔPchoked  is a function of both the process conditions (P1, the pressure upstream of the valve and Pv, the vapor pressure of the liquid) and the valve’s internal geometry represented by the experimentally determined Liquid Pressure Recovery Factor, FL. Typical values of FL are shown in Figure 6. Note that FL is a function of both valve style and the percentage of valve opening. Higher values of FL are associated with valves that have a lower potential for cavitation, and smaller values of FL are associated with valves that have a greater potential for cavitation.


Figure 6. Typical values of the Liquid Pressure Recovery factor, FL.
There are several methods of increasing the value of ΔPchoked and thus reducing the potential for cavitation and the associated noise and damage: (1) The value of P1 can be increased while keeping ΔP the same by moving the control valve to a location further upstream, or to a location at a lower elevation. (2) The vapor pressure can be decreased by installing the valve where the liquid temperature is lower, such as the cool side of a heat exchanger. (3) A valve style with a higher value of FL can be selected. It is interesting to note that in general, as the FL increases, so does the price of the valve. There are special cavitation resistant adaptations of many of the valve styles that have larger values of FL than those shown in Figure 6, yet which retain the other desirable features of that style.

Because noise and damage often begin before ΔP reaches ΔPchoked, there can be considerable risk in simply applying the old rule of not allowing ΔP to exceed ΔPchoked. A more reliable method of preventing cavitation damage in control valves, according to one major control valve manufacturer, is to avoid valve applications where the calculated noise exceeds limits based on a broad range of application experience. This method works because both the noise and the damage are caused by the same thing, the collapse of vapor bubbles. This manufacturer’s experience has shown that for valves 3 inches and smaller in nominal size, cavitation damage will be kept to a minimum if the calculated Sound Pressure Level, SPL, based on un-insulated schedule 40 pipe, does not exceed 80 dBA. For 4 inch and 6 inch valves this limit can be increased to 85 dBA, and for valves 8 inches and larger the limit is 90 dBA.

Other valve manufacturers predict the beginning of cavitation damage by defining an incipient damage pressure drop, which is sometimes referred to as ΔPID as shown in the formula in Figure 7 below.

Figure 7. Cavitation damage prediction
These manufacturers evaluate actual application experience with cavitation damage and assign what they believe to be meaningful values of KC to their valves. One manufacturer, for example, uses a KC for stem guided globe valves that is equal to 0.7. There are other manufacturers who, based on the recommended practice, ISA–RP75.23–1995, use sigma (σ) to represent various levels of cavitation. These valve manufacturers publish values of either σmr (the manufacturers recommended value of sigma) or σdamage. Sigma is defined as “(P1 – PV)/ ΔP.” σmr and KC are reciprocals of each other and thus convey similar information. Higher values of KC move the point of incipient damage closer to ΔPchoked, where lower values of σmr do the same.

In the past valve manufacturers determined KC by simply noting the pressure drop at which the flow curve deviated from a straight line by 2%. Using this method is unreliable because experience has shown that unacceptable levels of damage can begin even before the flow curve deviates from a straight line.

It is also important to understand that FL is NOT a cavitation parameter. It is a choked flow parameter and its only use is to determine the theoretical choked flow point based on the assumption that the choked flow point, ΔPchoked, is the intersection of the two straight dashed lines shown above in red and green. Using FL as a cavitation parameter is almost sure to result in unacceptable levels of cavitation damage.

A more extensive discussion of liquid flow in control valves can be found in Chapter 4 of Valin Corporation’s book, Control Valve Application Technology.

Before actually purchasing a control valve, it is always a good idea to ask for the manufacturer’s or the manufacturer’s representative’s comments regarding your selection.

Here are links to white papers that may be of interest:

Pressure at the Vena Contracta with Liquid Flow in a Control Valve
Installed Gain as a Control Valve Sizing Criterion
Aerodynamic Noise in Control Valves
Valve Aerodynamic Noise Reduction Strategies
Determining the Pressure Drop to be Used in a Control Valve Sizing Calculation
Size Matters: Control Valve Sizing 101

The content of these white papers are just a small portion of what you will learn in Dr. Monsen's book: Control Valve Application Technology

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