Control Valve

# Choked Flow in Control Valve Applications

## What is choked flow?

The choked flow is a compressible flow effect.The choked flow is the dynamic condition of the fluid that is associated with the venturi effect.The fluid velocity will increase when the fluid at a given parameter flows through the constriction called convergent and divergent nozzle in a pipe or line into a lower pressure environment.

In control valve applications the choked flow is commonly known as critical flow.

This choked flow in the valve occurs when the pressure drop increases across the valve, so the flow rate cannot be increased. If the inlet pressure (P1) and flow area in the valve are fixed,

The flow rate through the control valve will increase as the downstream pressure (P2) decreases.  The graph below illustrates the relationship between flow Q and pressure drop across the control valve ΔP.

The Ideal line or linear in above figure indicates this point, to represent how the liquid flow will rise linearly when plotted against the square root of the differential pressure across the valve divided by its specific gravity.

Ideally the flow rate through the control valve is proportional to the pressure drop across the valve.

It means as the pressure drop across the valve increases the flow rate also increases and vice versa. Due to choked flow in the control valve the maximum flow rate through the valve will be limited.

In fact, the maximum flow rate of fluid through the control valve can never rise above the choked flow limit. But at this point the flow will not increase on reduction in pressure P2.

This condition is similar to the valves when used for gas service. If the flow area and pressure P1 are kept constant, the flow rate through the valve gets raised on reduction of pressure P2.

But at some point, the choking occurs and the flow rate  will not rise regardless of the value of P2.

In liquid applications, the control valve capacity is limited if the pressure is less enough to cause flashing and cavitation.

For gases and vapors applications, the control valve capacity is limited if the gases and vapors velocity ranges to sonic velocity.

To understand these conditions, we look at the normal pressure to flow relationship for a control valve and see when choked or critical flow conditions occur. The basic relationship between flow and pressure in a control valve is given by:

The choked flow is set for a liquid when vapor formation occurs at the point of vena contracta within the valve.The differential pressure (ΔP) across the valve is increased as the flow reaches the choked flow point where there is no increase in flow rate with a change in ΔP.

Vapor formation in liquid flow is generally termed flashing (see how flashing takes place in a control valve) and it results in a vapor stream or bubbles continuing downstream from the valve. If the vapor bubbles are again condensed, this transient effect is described as cavitation.

### Why does choked flow occur in the control valve applications?

For liquid applications, choking is a result of the reduction in pressure through the control elements. The figure below indicates the instantaneous pressure as liquid flows through the control valve.

The control area like the cage or the area around the plug and seat is lesser than the inlet and outlet cross-sectional areas of a control valve.Because the total flow rate of fluid is the same at every location of the valve.

The fluid velocity must be sufficiently large in the reduced area like vena contracta for the same flow rate.

The typical pressure curve of a cavitating liquid passing through a control valve is shown in the above graph. The expanding vapor will create a pressure drop for further reduction in P2.

Bernoulli’s law states that,

As the fluid passes through the restriction, the pressure is reduced when the fluid velocity is increased. The flow rate of the fluid is reduced when the fluid enters the wider piping and the same pressure is recovered.

When the liquid starts boiling the vapor bubbles will form. When spontaneous pressure in the vena contracta falls below the vapor pressure.The volume of the fluid is now increased when converted to a vapor state and starts to restrict the flow.

If the output pressure is again reduced, then the volume of vapor rises to some point such that the flow scalability can’t increase. Despite the reduction in downstream pressure.

In gas applications, when the gas vapor velocity through the valve increases the gas vapor will reach its sonic velocity.Due to the standing shock waveform, the flow rate is limited hence the gas vapor cannot flow faster.And the further reduction in output pressure doesn’t affect the flow rate through the valve.

In higher flow rates the choked vapor flow conditions are most common in relief and control valves.

In a vacuum system, the choked flow is most common, because air with low pressures reduces the sound speed.

### Volumetric flow and mass flow through the control valve for liquid application:

The choked flow through the valve is a limiting flow rate. When the vapor pressure of the liquid rises above the vapor pressure within the valve, choking occurs as a result of the vaporization of the liquid.Under normal flow conditions, both volumetric and mass flow through a control valve is given by:

In control valves, the choked flow is referred to as a subject of serious concern for industrial applications. The term “Choked”is typically associated with destructive or harmful process conditions that may damage the valve internals.

### Issues and misunderstandings in choked flow:

The control valve is not damaged by the choked flow alone, here are some conditions commonly associated with the choked flow.

#### 1. Noise levels:

The choked flow in the valve doesn’t create a noise directly, during choked flow the cavitation is present in liquid systems, which creates noise and damages the valve. The cavitation in the valve transforms to flashing on reduction of downstream pressure. But the flashing effect has noise reduced due to two-phase flow.

In vapor flow, the noise increases remarkably as the velocity turns to sonic. The extra energy is now transformed to sound when the downstream pressure in the valve reduces. The pressure drop in the valve generates sound levels higher than 100dB.

#### 2. Flashing and cavitation:

The flashing conditions are most required in choked flow.But the choked flow will occur only in cavitating conditions. Cavitation occurs when the pressure P2 rises above the vapor pressure of the liquid. The vapor bubbles start collapsing and turn back to the liquid state. If the pressure P2 remains below the vapor pressure, the liquid starts boiling forming vapor and it passes through the valve.

#### 3. Valve damage due to choking:

Some assumptions create that choked flow conditions may damage the valve. But sometimes the valve damage is minimum for the valve when choked, and valve damage is significant for the valve when not choked.The valve may get damaged by cavitation.

The vapor bubbles form micro jets after collapsing and create localized shock waves that destroy the valve internals and downstream side of the pipeline.

Note that the valve damage is less in flashing compared to cavitation.

The above graph shows the pressures at vena contracta for the high recovery ball valve or butterfly valve versus a low recovery globe valve for particular operating conditions.

The high recovery ball or butterfly valve creates lower internal pressures. High vibration and metal fatigue make excessive noise and damage the valve.

The rate of noise varies with process conditions. The noise is not associated with flow choking.

By specifying appropriate valve body designs the cavitation, flashing, and noise can be reduced and eliminated, using special valve trims, and materials of construction.

#### 4. Valve sizing:

The choked flow scheme for a particular position of the valve is based on the parameter of the flowing media and its process conditions.The choked valve for the unique parameters can allow for a higher flow rate by increasing the Cv of the valve.The conditions of choked flow in the valve can be predicted by some software programs. And can estimate the maximum flow rate.

### Rabert T

As an electrical engineer with 5 years of experience, I focus on transformer and circuit breaker reliability in 110/33-11kV and 33/11kV substations. I am a professional electrical engineer with experience in transformer service and maintenance. I understand electrical principles and have expertise troubleshooting, repairing, and maintaining transformers, circuit breakers, and testing them. Tweet me @Rabert_infohe