what is the cv of a valve?
Cv is the flow capacity of a valve, this value is experimentally determined in lab under some testing conditions. As per ISA standards (specifically ANSI/ISA-75.01 and 75.02), the (Valve Flow Coefficient) is defined as the volume of water in US gallons at 60 F that will flow through a fully open valve in one minute with a pressure differential of 1 psi across the valve.
The valve cv depends on two parameters, valve size and valve percentage if opening. If the valve size is high then we have a large cv and vice versa. it also depends up on the valve opening. if the valve is less open, then it has a less cv.
why sizing of control valve is important?
control valve in a system should handle minimum flow to maximum flow through the system. if the valve is under sized it could not pass maximum flow through the valve and if the valve is oversize, it could not handle low flow rate .so proper sizing of the valve is important to for the system to handle the specified minimum to maximum flow.
Pressure profile
Control valve pressure drop
Fluid pass through a control valve generally obeys the continuity and law of conservation of energy. The control valve act as a restriction to the flow stream, as the fluid pass through the control valve its velocity increase and a corresponding decrease in pressure to maintain the law of conservation of energy. The point at which velocity at its maximum and pressure at its minimum is called the vena contracta. After passing the vena contracta the fluid recovers some of its pressure. But this pressure is less than the inlet pressure. The difference between this inlet and outlet pressure is called pressure drop or delta p. This pressure drop has a important factor in selection the valve body type, trim, and the type of actuator.
When the control valve is fully open, it offers minimal resistance to flow and allows maximum flow rate through the system. As the valve begins to close, the effective flow area (orifice size) decreases. Due to the continuity principle, the fluid velocity through the restricted area increases. According to Bernoulli’s equation, this increase in velocity results in a reduction in static pressure at the vena contracta.
Consequently, the differential pressure (DP) across the control valve increases. Therefore, as the valve moves toward the closed position, the pressure drop across the valve rises. It should be noted that although local velocity increases at the restriction, the overall system flow rate will decrease as the valve continues to close due to the increased flow resistance.
Control valve sizing terminology for liquid sizing
CV- Valve sizing coefficient.
P1- valve inlet pressure.
P2- control valve outlet pressure.
ΔPchoked- Choked pressure drop.
ΔPsizing- Sizing pressure drop.
DP- pressure drop across the control valve.
Fp- piping geometry factor (dimensionless).
Q- volumetric flow rate.
Fl- Liquid recovery factor.
– Relative density of the fluid.
FF = Liquid critical pressure ratio factor.
FL = Liquid pressure recovery factor of a valve without attached fittings.
FLP = Combined liquid pressure recovery factor and piping geometry factor.
CONTROL VALVE SIZING OF LIQUID (Turbulent flow)
The standard used for control valve sizing is given below.
IEC- 60534-2-1
First, we will discuss about the manual process of performing the control valve sizing. THE EQUATIONS USED IN ISA75.1 IS BASED ON TURBULENT FLOW. FOR NON TURBULENT FLOW CORRECTION FACTORS WILL BE USED, THIS WILL BE DISCUSSED LATER.THE BASIC EQUATION TO DETERMINE THE CONTROL VALVE Cv IS
As per IEC -60534-2-1 the sizing equation under turbulent condition is given below. The below equation is used only when the fluid is single phase.
Here in Equation 1 , added two correction factors one is N1 and other is Fp. N1 is the correction factor for the units . Fp is a correction factor for the effect of reducers and other fittings adjacent to the valve. During control valve testing the valve is attached to a pipe as the same size of valve.so the capacity changes due to reducers and expanders are not calculated. If the valve size is same as of line size this value reduces to 1. During initial sizing consider there is no reducers and expanders attached to the valve inlet and out. The above equation is used only for single phase liquids. The following equation can be used for estimating the Fp. The equation for Fp is given below.
The factor is the algebraic sum of effective velocity head coefficient of all fittings attached to the inlet and outlet of the control valve. Here K1 and K2 is the resistance coefficient of inlet and outlet fittings.KB1 and KB2 are the Bernoulli’s coefficients for the inlet and outlet fittings. This Bernoulli’s coefficient drops out from the equation when the inlet and outlet fittings are of same size. If not KB1 and KB2 are calculated based on the below equation.
Step-by-Step Control Valve Sizing Procedure (Cv Calculation Guide). The following step steps are for the manual sizing of control valve. Master the sizing manually and then use the software. This will help you in master the control valve sizing. In most of the EPC companies the sizing will done by the process team and datasheet is prepared by the instrument team. Read this section for the detailed workflow.
NB: valve selection and actuation is not included in this section. Selection of the characteristics is also not included in this part.
- Determine the service conditions.
- Flow- min/normal/max.
- Inlet pressure at these flowing conditions.
- Outlet pressure at these flowing conditions.
- Differential pressure at these flowing conditions.
- Density or specific gravity.
- Critical pressure.
- Vapor pressure.
- Pipe size.
- Pipe schedule.
- Initially assume valve size is same as pipe size and not fittings attached to the valve.
- Correction factors for the sizing. This can be obtained from the IEC standards based on the selected valve type.
- Determine the equation constant N
Use N1 if the flow is in volumetric units
Use N6 if the flow is in mass units.
- Determine the piping geometry factor Fp.
Assume Fp=1, as there no fittings attached to the valve and valve size is same as line size. Later, Fp must be recalculated based on the selected valve size and piping configuration.
- Determine the allowable pressure drop ΔPchoked.
Calculate the maximum allowable pressure drop (ΔPchoked) to check for choked flow conditions. The calculated ΔPchoked value is compared with the actual pressure drop specified in the service conditions and lesser of these two values is used in the sizing equations as ΔPsizing.
- Calculate the required Cv using ΔPsizing. This gives the initial required Cv.
- Check the Reynolds number (flow regime verification)
Check the flow is turbulent or not. If the flow is not turbulent apply Reynold correction factor need to added to the Equation and recalculate the Cv.
- Select the valve from the Cv table based on the calculated Cv.
Select a valve with rated Cv ≥ calculated Cv
Ensure the valve operating in the acceptable travel range. The selection range based on the client valve specification.
- Recalculate the piping geometry factor.
The selected valve size may be different from the pipe size. Recalculate the Fp and recalculate the Cv based on the updated Fp.
sizing pressure differential
DP sizing Value of pressure differential used for computing flow or flow coefficient. It is the allowable pressure drop.
If the actual DP is less than theΔPchoked used the actual DP for sizing and actual DP is greater than the DP choked use the sizing. If the actual pressure drop is greater than the DP choked the flow must not increase with constant inlet condition. Hence use the DPchoked for the sizing equation.
The condition where the further increase in pressure differential at constant upstream pressure no longer produces a corresponding increase in flow through the valve The pressure drop at which this occurs is called the choked flow. This is the maximum effective pressure differential that can increase the flow. This is the point at which the choking starts.
This scenario can be explained using a pump–control valve–storage tank system, as shown in Figure 1. This figure shows an example for the choked flow phenomenon and distinction between changes in pressure drop when the valve during the travel from 0 to 100% and changes in pressure differential with constant inlet conditions. Choked flow occurs under constant inlet conditions. Consider normal operating conditions where the control valve is 50% open and the pump discharge pressure (P₁) is 10 bar. Under these steady conditions, the system operates without choking.
Now assume the downstream pressure is reduced by lowering the liquid level in the storage tank or by emptying the tank. As the downstream pressure decreases, the differential pressure (ΔP) across the valve increases. This causes the flow rate to increase.
The higher flow rate increases the velocity through the valve orifice. As velocity increases, the static pressure at the vena contracta decreases. When the static pressure at the vena contracta drops below the liquid’s vapor pressure, vapor bubbles begin to form.
At this point, choked flow starts. This occurs because the formation of vapor within the liquid restricts the effective flow area through the valve, limiting any further increase in flow rate despite additional reductions in downstream pressure.
Figure-1
DPchoked can be calculated using the following equation.
FF = Liquid critical pressure ratio factor.
FF multiplied by the vapor pressure, predicts the theoretical vena contracta pressure at the maximum effective (choked)pressure drop across the valve. This factor is the ratio of the vapor pressure to the vena contracta pressure. This factor is usually given by the manufacturer and based on the type of valve. If we selecting a globe valve this value can be found directly from the IEC standard for calculation purpose. Liquid pressure recovery factor can be found from the below equation.
FL = Liquid pressure recovery factor of a valve without attached fittings.
Predicts the amount of pressure recovery that will occur between the vena contracta and valve outlet. This is a experimentally determined coefficient that accounts for the influence of the valve internal geometry in the max capacity of the valve. FL also varies according to valve type. This value is provided by the manufacturer. For the calculation purpose this value can be taken out from the
FLP = Combined liquid pressure recovery factor and piping geometry factor.
PV = The vapor pressure of the liquid.
Example for control valve sizing (manual) is given below.
Give the link of the spread sheet for the example.
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