## 3

40 deg.

TABLE 9 The effect of change in C on variations in capacity from the mean for a triplex pump

TABLE 9 The effect of change in C on variations in capacity from the mean for a triplex pump

FIGURE 8 Force balance of a typical valve

approximately 6:1. This shows that pumps with an even number of cylinders have a higher flow variation than pumps with an odd number of cylinders. Table 9 shows the variations in a triplex with changes in C = L/R.

Valves A pump valve in its simplest form is a free-moving plug that is opened when the force of the liquid below the valve exceeds the force of the liquid above it. When the force above the valve becomes greater than the lower, the plug closes and forms an effective seal to fluid "backflow" and pressure loss. If the valve does not perform this function efficiently, the performance of the pump can be degraded to the point where no flow is produced.

A valve will be in equilibrium when the forces above and below the valve are balanced (see Figure 8):

Equilibrium = P1 X A1 = P2 X A2 + Sf + M where P = the pressure below the valve

A = the area below the valve exposed to P

P = the pressure above the valve

A = the area above the valve exposed to P

Sf = the force of the valve spring ( if any)

M = the mass of the valve and half the mass of the spring

The significance of this simple equation becomes apparent when you remember that the valve is operating in a dynamic environment of constantly changing pressures in a time frame that is measured in tenths of a second. Add to that the requirement that the valve must pass a volume of fluid in each opening cycle with minimal pressure drop, and it becomes clear that the pump valve is the most critical component in the fluid end in terms of pump operability.

The pump designer will size the valves to provide a flow area, called the spill area, that prevents pre-established velocity limits from being exceeded. The spill area of various valve types is given in Table 10. The velocity of the fluid flowing through the spill area is called the spill velocity, V, shown in Table 11:

TABLE 10 Types of valves and their applications (Flowserve Corporation)

TABLE 10 Types of valves and their applications (Flowserve Corporation)

 TABLE 11 Valve spill velocities Valve Spill velocity, ft/s (m/s) Clean liquid suction valve 3-8 (0.9-2.4) Clean liquid discharge valve 6-20 (1.8-6) Slurry suction and discharge valve 6-12 (1.8-3.7)

In USCS units V (ft/sec) = gpm through the valve X 0.642/spill area of the valve, in2 In SI units V (m/s) = m3/h through valve X 555.6/spill area of the valve, mm2

The quantity 0.642 (555.6) is used because all the liquid passes through the valve in half the stroke.

Valve Dynamics Valve dynamics is the mechanical response of the valve to the changes of pressure across the valve. Using a suction valve as an example, the valve starts its cycle when the valve is closed and the plunger is at the start of its suction stroke (maximum insertion into the cylinder). As the plunger starts withdrawing from the cylinder, the internal volume in the cylinder starts to increase. This increasing volume results in decreasing cylinder pressure that, in turn, hydraulically unbalances the valve and the valve begins to open. There is usually a slight lag in the valve opening versus the start of the plunger motion of about 5 to 20 degrees of crankshaft rotation. Traditionally, the opening valve lag is attributed solely to the inertia required to set the valve in motion and the preload of the valve spring. In the last few years, the theory of valve stiction has been proposed as an additional cause of valve opening lag.

Valve stiction, as the name implies, can be an additional force to overcome when the valve is trying to lift off its seat. One version of the theory is that a cohesive force exists between the fluid molecules and the sealing surfaces of the valve and seat. This can be demonstrated by trying to separate two wet, highly machined plates. The second stiction theory focuses on possible fluid dynamic conditions that may occur as fluid starts to flow across the valve seat. Valve seats do not have "knife edge" sealing surfaces; they have a width that distributes the stresses in the valve and seat. The stiction theory postulates that the flow of fluid from the smaller area at the center of the seat to the larger area around the seat causes a pressure drop across the seat. The pressure drop is the result of the radial divergence of the fluid and is strong enough to momentarily prevent the valve from opening. Extreme cases have even resulted in a circumferential ring of cavitation located at the center of the sealing areas of the seat and valve.

Field testing valves with special grooves and radial slots in the sealing face has proven successful in reducing stiction and opening valve lag in some cases. Narrowing the sealing faces may also prove effective, although part life may decrease due to increased stress and decreased wear area. Additional computer modeling and testing is required before the stiction theory can be completely validated.

As the valve continues to open, the spill area increases proportionally. It must be remembered that fluid is now flowing through the valve at an increasing rate while trying to fill the expanding cylinder volume created by the plunger withdrawal. Ideally, the motion of the valve will exactly correspond to the flow rate of the fluid through the valve, and the valve follows a smooth trajectory to a full open position (see Figure 9).

This idyllic situation only occurs in very slow running pumps that are fitted with oversized valves. In modern higher speed pumps, the valve often accelerates at a rate fast enough to create a spill area greater than that required to maintain a constant flow velocity. At this point, the valve motion momentarily stops, and the valve may even start to close before the fluid flow once again matches the spill area. The valve then returns to the smooth trajectory until the maximum valve lift occurs.

After the plunger passes the mid point of its stroke, it starts decelerating. The flow of fluid through the valve is high enough to start to build pressure in the cylinder and unbalance the valve and start the valve closing. The valve spring has reached its maximum compression and, if properly designed, will help accelerate the valve back toward the seat. When the plunger reaches the end of the suction stroke, the valve should also be closing. The amount of crankshaft rotation that occurs between the time when the plunger reaches the end of its stroke and when the valve is completely closed is called the delayed valve closing and is normally 2 to 12 degrees of crank rotation. Although a delayed valve opening may have little effect on overall pump performance, a delayed valve closing certainly will. A valve that is partially open when the plunger reverses direction will result in back-flow. Backflow, as the name implies, is the reverse flow of fluid back across the valve and results in lower pump volumetric efficiency.

FIGURE 9 Valve lift versus crank angle (in X 2.54 = cm)

FIGURE 10 Valve lift versus crank angle for a valve with a mechanical stop (in X 2.54 = cm)

Crank Angle (deg)

FIGURE 10 Valve lift versus crank angle for a valve with a mechanical stop (in X 2.54 = cm)

Many pump valves are designed with mechanical limits to the distance that the valve is allowed to open or lift. This is normally done to avoid overstressing the valve spring and to minimize the overall height of the valve assembly. Valve motion for a valve designed with a mechanical stop is shown in Figure 10. Another advantage of this design is that the valve does not have to travel as far during its closing cycle, compared to valves with no mechanical limits. The disadvantage is the potential for impact damage to the valve if it strikes the stop with excessive force.

The importance of valve mass to overall valve dynamics has been the subject of much debate among pump designers over the years. There is no question that the mass of the valve must be overcome in order to open the valve. Test data is also available that shows no appreciable difference in the performance of pumps fitted with hollow ball valves versus identical pumps with solid ball valves. This apparent contradiction can be explained by studying valve acceleration at various parts of the valve cycle using advanced computer modeling.

It has already been explained above why a valve can hesitate, or stop opening, during the opening portion of its cycle. It's also been stated that when the valve spill area is large enough to establish a hydraulic balance, the valve will stop opening. What actually occurs is the valve starts decelerating as it comes closer to hydraulic equilibrium. If the valve is properly designed, it will contact its mechanical stop just as its acceleration/deceleration is very low. In that case, the valve mass has little significance on the impact force of the valve on the stop. The same holds true of the impact force of the valve on the seat as it closes. If the valve is properly designed, a 62-lb (28 kg) solid ball valve operating at 100 cycles per minute can strike the seat with less than 20 lbs (9 kg) of force.

Although pump valves operate in a liquid medium, the shape of the valve is not an important design consideration for most applications. The relatively small distance that a valve travels is not sufficient for the fluid dynamics of a shape to have a measurable effect on valve dynamics. The only exception to this is valves in pumps handling high-viscosity liquids. For these applications, the ball valve, often spring-loaded, has proven to reduce closing valve lag and increase volumetric efficiency better than any other type of valve.

The most critical component in the optimization of valve dynamics is the valve spring. The pump designer normally selects a valve spring that will exert a certain amount of "pre-load" on the valve when it is closed. This pre-load helps the valve to close smoothly on the seat and avoid rebound (and possible backflow). Too high a preload in the suction valve may result in higher net positive suction head required (NPSHR). In the discharge valve, excessive preload can cause abnormally high pressure spikes in the fluid cylinder just before the valve opens.

The other valve spring design criterion is the spring rate. Every compression spring develops a predetermined resistance per unit length. This value is expressed in pounds per inch (kg per cm). As the valve is opening, the increasing spring force helps the valve obtain hydraulic balance faster. It also helps to limit the impact force of the valve on the stop. At the start of the closing cycle, the stored energy in the compressed spring helps the valve respond faster to the pressure changes in the fluid cylinder as the plunger starts to decelerate. Again, if the spring is properly designed, the closing valve lag will be minimized.

No published guidelines exist for the proper amount of valve spring pre-load or spring rate. Most pump designers use proprietary values, generated through a combination of in-house and field testing. However, although these values produce low NPSHR and high volumetric efficiency in most cases, the valve dynamics may not be close to being optimized. It should also come as no surprise that pumps fitted with "off-the-shelf" commercially available valves do not operate as well as pumps having optimized valve dynamics.

With the recent advent of advanced computer modeling of pump valves, it is now possible to optimize valve dynamics for a specific set of pump operating parameters. We may also see valve designs in the near future having variable rate valve springs, hydraulic dampening, and mechanisms that induce rotation as the valve opens and closes.

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