Sizing employs principle of conservation of energy. Daniel Bernoulli discovered that as the liquid flows through the orifice ,the square if fluid velocity is directly proportional to pressure difference across the orifice
& inversely proportional to specific gravity of the fluid ,therefore greater the pressure differential pressure greater the velocity.greater the density lower the velocity.logically the liquid flow rate is calculated by multiplying the fluid velocity by area of flow .There exists energy losses due to friction &
turbulence .
Now the basic liquid sizing equation can be written as follows:
Q = Cv √(▲P/G) where
Q = capacity of gallons per minute.
Cv = valve sizing coefficient .
▲P=pressure differential in psi.
G =specific gravity of fluid.
Cv is equal to number of US gallons of water flowing at 60°F through the valve in one minute when the pressure difference of one pound per square inch. Cv provides both style & size ,also provides an index for comparing liquid capacities of valves under standard test of condition.
CONTROL VALVE SIZING:
To be a good aircraft pilot it is necessary to have the seat of the pants feel of the ship. It is also important to know why the ship responds the way it does. For the same reasons, the art of valve sizing goes hand in hand with the science of fluid mechanics.
Incompressible fluids: (LIQUIDS)
A fluid flowing through control valves follows the same laws of conservation of mass & energy as expressed in the equations of fluid mechanics. First conquered the flow of liquids, which essentially are incompressible fluids. When any fluid flowing inside a pipe, passes through a narrow passage or restriction, it must
accelerate. The energy for this acceleration must be taken from the pressure of the fluid, or the static head. After passing the restriction, the fluid slows down again &
part of this head is recovered.
Neglecting friction & other non-ideal influences for a moment, Bernoulli’s theorem gives us the equation,
Where Q is flow through control valve, A2 is area at vena contracta, p1 is upstream pressure, and p2 is downstream pressure & is density at operating conditions.
After further simplification it works out to be, Q = Cv √ (▲P/G)
where Q is flow of liquid through pipeline, G is operating density & ▲P is differential pressure across control valve.
We will have to consider two important factors, which affect calculations of Cv for liquids
1)Piping geometry factor (Fp): Ideally we had considered same size of piping as that of a control valve, but in practice there are always reducers/expanders
upstream/downstream of control valves & you have to correct for this change from ideal condition.
2) Viscosity factor (F ): When flow is turbulent there is no problem & correction factor is not required. But the moment the viscosity becomes low & flow starts getting laminar, we will have to apply correction to the Cv using viscosity correction factor.
The calculation sheet enclosed gives details of these factors & also elaborates methods of calculations for these factors & their use in calculating corrected Cv.
Above we have seen the fundamentals of control valve sizing for liquids, which are non-cavitating & non-flashing.
We will now turn our attention to two important phenomena, namely Cavitation &
Flashing. These phenomena are of significant interest in any comprehensive discussion of control valves since their occurrence will affect the valve sizing procedures, may introduce noise & vibration & also may limit the life expectancy of the valve components & immediate downstream piping.
What is cavitation:
Cavitation is a two-stage phenomenon, the first step of which is the formation of voids or cavities within the liquid system. The second stage is the collapse or implosion of these cavities back into an all-liquid state.
How cavitation takes place:
For cavitation to take place, requirement in the form of nucleating agents is mandatory.
These tiny nuclei which which will contain either dissolved gases or vapors will enlarge into finite cavities within the liquid.
In short when pressure of liquid at the outlet of control valve goes below critical
pressure the nuclei discussed above tend to form cavities & when it is recovered back, these cavities try to implode back into liquid & temporary gaseous phase is eliminated.
What is Flashing:
Flashing is similar to cavitation, only difference being that in cavitation the pressure recovery is full but in flashing outlet pressure remains below critical pressure of the fluid.
Fig.1 shows the process of cavitation & flashing graphically.
In short if cavitation has to take place following criteria to be fulfilled, 1) The fluid at both inlet & outlet to be in an all liquid state
2) The liquid must be in subcooled state at the inlet.
3) The valve outlet pressure must be either at or above the vapor pressure of the liquid.
If flashing has to take place, following criteria to be fulfilled,
1)The fluid at inlet must be in all liquid condition ,while some vapor must be present at the valve outlet.
2)The fluid at the inlet may be in either a saturated or a subcooled condition
3)The valve outlet pressure must be either at or below the vapor pressure of the liquid
Cavitation evidences:
1) Noise: In a control valve the evidence of cavitation is usually a hissing sound .As cavitation intensity increases due to increasing pressure differentials, the sound level also increases.
2)Vibration: more noise due to cavitation, more vibrations emanating from control valve.
3) Material damage: due to cavitation, there is serious damage to the valve internals
Cavitation control:
1)Generally control valves with high recovery of pressure drop are more prone to
cavitation than low recovery valves. Hence globe valves are less prone to cavitation than butterfly/ ball valves.
2) Use hard trim to avoid material damage to the control valve trim. Stelliting of trim is a standard procedure to delay effects of cavitation.
3) Pressure balancing of trim is to be done to improve throttling stability.
4) 90 degree bends in flow path create a series of velocity head losses reducing pressure gradually.
5) Pressure drop may be divided across a series of orifices.
6) A combination of 4) & 5) above having multiple small differential pressures rather than one larger differential pressure to keep the liquid above its vapor pressure so that cavitation does not occur.
7) Flow may be jetted against flow & swirled to create a massive turbulence & internal friction to dissipate the energy as heat.
Cavitation & flashing phenomenon the control valve sizing also gets affected & the deviations from standard formula for control valve sizing for liquids is discussed
below,Cavitation & Flashing both produce a decrease in ability of the valve to convert pressure drop across it into a mass flow rate. Referring to basic equation for liquid sizing, it can be observed that the flow rate is proportional to the square root of
pressure drop & that the constant of this proportionality is liquid flow coefficient Cv.
It has been observed that if pressure drops of above 5~10 psi are considered while carrying out the valve capacity experiment, then it is observed that above 5~10 psi range, the flow of fluid through control valve tends to decrease rather than following standard flow & square rooted ▲ P relationship. This indicates incipient cavitation of the main flow stream.
Cavitation index:
A dimensionless ratio, experimentally determined from plot of q versus squareroot of
▲P at fixed values of inlet pressure & valve opening is used to describe the point of initial departure from a proportional relationship..This ratio is called cavitation index
& is given as below,
Kc= P1-P2/ P1-Pv = ▲P/P1-Pv
After cavitation has has begun, further decrease in in valve outlet pressure (increased pressure drops) results in increased vaporization, increased cavitation intensity &
further decreases in the apparent liquid flow coefficient. It is observed that with sufficient pressure drop the flow becomes FULLY CHOKED., so that increasing pressure drop results in no increase in flow rate. Increasing the pressure drop after choked flow has been reached will result in increased amounts of cavitation damage until the valve outlet pressure is decreased to to the value that will permit flashing.