Intro4u2u

PRESSURE RECOVERY (REFER FIG. A)

As a fluid traverses the path from the valve inlet through the valve orifice and to the valve outlet it experiences those three key pressure levels:
P1     - The Valve inlet pressure (Up stream pressure)
PVC  - The Vena contract a pressure (Orifice air pressure)
P2.   - The valve outlet pressure (Down stream pressure)

The vena contract a is a physical point immediately past the orifice where the fluid experiences its highest velocity and lowest pressure while inside the valve. In essence, the fluid pressure is highest at P1 (inlet) lowest at PVC (vena contract a) and then rises to an intermediate value at P2 (out let). It is this final phenomenon which is called “pressure recovery” and is experienced to differing degrees by all control valves.

II. PRESSURE RECOVERY FACTOR FL (CRITICAL FLOW CF) 

The degree to which a given control valve experiences pressure recovery abc vena contract a pressure is primarily determined by the valve’s internal geometry is mathematically expressed by the formula.

Values for Cf (FL) are experimentally determined for each type of control and are further dependent upon the trim size (full or reduced), percent of valve open and fluid flow direction through the valve . Streamlined valves experience high pressure recovery. More restrictive valves experience low pressure recovery.

The more torturous turbulent flow path products low pressure recovery from the formula “That the higher the pressure recovery, the larger the P2 value, gives a smaller numerator and smaller Cf (FL) value.”

Restrictive Valves    -  Low Pressure recovery High Cf (FL)

The inverse relationship is significant to later discussion in view of the fact that streamlined valves with low Cf values are more susceptible to critical flow, cavitation, flashing and noise problems.

For a given P1 there is a physical limit to the quantity of fluid (Liquid or gas) can pass through a given Control Value. As that limit further increases in Delta P the valve (decrease in P2) will not result in any increased flow. This condition is called critical or choked flow and the Delta P at which it occurs is called Delta P critical.

A. LIQUIDS  : Critical flow results from the cavitation and flashing phenomena are
defined as:

Under Delta P critical conditions valve is fully cavitating if P2 > Pv or flashing if P2< Pv. Further increase in Delta across the valve will not result in flow increase.

B. GASES    : Critical flow results from the gas obtaining sonic velocity inside the valve is
defined as :

Under Delta P critical conditions the gas flow can generate high noise levels.

Note : Critical flow requires adjustment in the Cv calculation which is the function of the second column of equations in figure 1, page 1.

IV. CAVITATION 

A. Explanation  – Fluid enters the valve as a liquid at an inlet pressure P1. It then experiences a decrease in pressure to a minimum, PVC at the orifice area. If PVC < Pv then vapour bubbles (Cavities) form at the orifice area.

The liquid/vapour mixture then experiences an increase in pressure to P2 at the valve outlet. If P₂ > Pv then the vapour bubbles are collapsed and the liquid-to-vapour, vapour-to-liquid cycle is established. This is cavitation.

B. Prediction - There are two equations pertinent of cavitation
when P₂ > Pv and Pv < 0.5 P1.

1. Incipient cavitation  - The valve Delta P which brings the on set of cavitation is
defined as:

Where   KC - coefficient of incipient cavitation and may be determined using the Cf factor
for the given valve.
If no cavitation can be toler tee Delta P must be kept less than Delta P incipient.

2. Full cavitation - The valve Delta P resulting in full cavitation is defined in part III A
above as:

C. Detection - Unusual sounds on the downstream side of the valve body ranging from:
Incipient - Hissing or whistling, sometime intermittent full - loud rattling, like gravel in flow stream.

D. Effects

3. Noise  -  Can reach unacceptable levels above 90 db.

4. Inefficiency - Lower flow increase to Delta P increase ratio.

5. Vibration - Severe cavitation can cause serious vibration.

6. Erosion - Collapsing vapour bubbles can cause localized pressure on the order of 100,000 psi resulting in a distinct, pitted, cinder-like erosion unique to cavitation and occurring in the valve trim orifice area, downstream body wall, and even downstream piping.  

D. Treatment:

1. Elimination - refer to Delta P incipient, part IV - B(1)

a. Decrease Delta P such that Delta P < Delta P incipient.
b. Increase P1 such that Delta P < Delta P incipient.
c. Increase Kc such that Delta P < Delta P incipient.

. by selecting a high Cf valve (Low pressure recovery).
. by selecting flow direction with higher Cf turning valve around in line can sometimes eliminate cavitation.
. by installing two identical control valves in series with resultant increase of Cf (series) = Ö Cf (of single valve).

3. CONTAINMENT

a. Use flow-to-close cage trim designed to focus the imploding bubbles in the container of the cage void area thus controlling cavitation damage and lowering noise level.

b. Fluid mixtures with multiple vapour pressure levels do not cause serious cavitation damage. Pure fluids (especially water) with a well defined vapour pressure tens products cavitation damage.

c. Harder materials are more cavitation damage resistant.

d. Cavitation damage is generally not significant if the fluid energy level is less 70 horsepower per nominal inch of valve size. According to the following formula.

  Where: Q = Liquid flow rate, gallons per minute

            Gf = Specific gravity at flowing temperature

            Delta P = Actual pressure drop, P1 - P2, psi

a. Explanation - Flashing follows the same mechanism as out lined in part IV- cavitation until it reaches the valve outlet. If P2 < Pv then the vapor bubbles remaining stream.

b. Prediction - The same two equations in part IV-B apply with the revised constant that P2