**First of Three Parts**

A pulsation dampener is a vessel with pressurized gas inside, normally nitrogen. The initial filling or inflating gas pressure inside the dampener must always be lower than the pressure of the circuit where it is installed. The inflating gas pressure of the dampener is designated P_{0}.

In all pulsation dampeners, the bellows isolate the gas from the circuit liquid. The main function is to avoid gas leaks, which can be costly. This part that separates the two fluids is most frequently made of two kinds of material:

*Rubber*—The rubber may be nitrile, ethylene propylene diene monomer (EPDM), fluoroelastomers (FPM), butyl, silicone or a thermoplastic material, often polytetrafluoroethylene (PTFE). When rubber is used, the separator element is called a bladder. If PTFE is used, the dampener can be a membrane or bellows type according to the form of the separator element.*Stainless steel*—Bellows can also be made of stainless steel. The use of one type of separator or another will generally depend on the particular characteristics of the circuit, such as the working pressure, temperature and the possible corrosive effect of the circuit liquid over the separator element.

Part One of this series covers the operation of pulsation dampeners. It also covers how to calculate the correct pulsation dampener size for an application.

## Operation

In volumetric piston or membrane pumps—such as dosing or metering pumps—a pulsation dampener’s primary function is to stabilize the variable and oscillating flow generated in a hydraulic circuit during each cycle. The main characteristic of this type of pump is the ability to deliver a constant volume of liquid in every cycle regardless of the circuit resistance or pressure.

When a pulsation dampener is installed in the circuit, the volume supplied by the pump during every impulse or work cycle is divided into two parts—one goes to the circuit, and the other goes into the pulsation dampener. This stored volume in the dampener is then returned back into the circuit flow, while the pump is in its suction or chamber filling stage. The amount of liquid going into and out of the dampener in each alternating cycle of the pump is designated as δV.

When δV flows into the dampener, the gas inside will be compressed, resulting in reduced volume and increased pressure. The final gas volume (V_{2}) will be the initial gas volume minus δV.

The initial gas volume is, to start, the total volume of the dampener or the size of the dampener. The size of the dampener is an unknown value to be calculated in every case depending on the kind of pump. This volume or size of the dampener will be called V_{0}.

From this knowledge, Equation 1 is established:

V_{2} + δV = V_{0}

Equation 1

Every dampener has a constant derived from its size and its filling or charging gas pressure:

P_{0} x V_{0} = constant

Equation 2

In working practice, dampeners should never be totally emptied of the liquid, which was previously stored in each cycle, to prevent the anti-extrusion insert of the separator element from repeatedly hammering against the internal bottom surface of the dampener. This could prematurely wear out the bladder or membrane. Equation 3 results from this principle:

V_{2} + δV + v = V_{0}

Equation 3

Where v = an unused volume of liquid inside the dampener

Normally, this volume is estimated to be 10 percent of the total dampener volume, as long as the temperature remains constant, and, therefore, Equation 4 expresses the amount.

V_{2} + δV + 0.1 V_{0} = V_{0}

Equation 4

This volume can also be determined using Equation 5.

V_{0} = (V_{2} + δV) / 0.9

Equation 5

At the initial gas charge pressure value P_{0}, no liquid is inside the dampener, and the gas fills the whole interior. The curve cuts the ordinate axis at the point that corresponds with a zero value in the abscissa axis. This axis is where the volume of liquid introduced into the dampener in each working cycle is represented.

The pressure P_{1} is the gas pressure when a volume of liquid (v) has been introduced into the dampener. The pressure P_{2} is the value reached by the gas when the additional volume (δV) enters the dampener.

From this curve, for a fixed dampener size, if the value δV increases, then the pressure value P_{2} will also increase. Also, if the dampener size is increased while keeping the value δV constant, the final gas pressure value P_{2} will be lower.

## Size Calculation

The data needed to calculate the dampener size are:

- δV—the volume of liquid that the dampener must store. The section above describing the different pumps that benefit from dampeners show the relationship between δV and the cubic capacity of each of the three most common types of pumps.
- P
_{1}and P_{2}—the minimum and maximum pressure values that are accepted in the circuit. - P
_{t}—the pressure required at the pump outlet to overcome the resistances that will arise and circulate the liquid to the end of the hydraulic circuit.

A pulsation dampener does not eliminate 100 percent of the pressure oscillation produced in volumetric or dosing pump circuits. Its function is to regulate or control the variations of pressure so that the flow remains within previously set limits. This variation, as a plus or minus percentage of the theoretical pressure (P_{t}), and the value of δV are what determine the pulsation dampener’s size.

If the theoretical or work pressure in a circuit is P_{t} and the residual pulsation admitted is plus or minus 5 percent of this pressure, values P_{1} and P_{2} are shown in Equation 6.

P_{1} = P_{t} – (5/100) x P_{t}

P_{2} = P_{t} + (5/100) x P_{t}

Equation 6

With the known data for δV, P_{1} and P_{2}, the dampener size V_{0} can be calculated using a variation of Equation 7.

The ideal gas law in isothermal conditions (Boyle’s law) provides Equation 7.

P_{0} x V_{0} = P_{1} x V_{1} = P_{2} x V_{2} = constant

Equation 7

If V1 = V0 – v and v = 0.1 x V0, then Equations 8 through 10 can be derived.

V_{1} = 0.9 x V_{0}

Equation 8

V_{2} = V_{1} – δV

Equation 9

P_{0} = 0.9 x P_{1}

Equation 10

Then using Equations 7, 8, 9 and 10, Equation 11 can be derived.

P_{0} x V_{0} = P_{2} x V_{2}

0.9 P_{1} x V_{0} = P_{2} x (V_{1} – δV) = P_{2} (0.9 V_{0} – δV)

Equation 11

From the underlined ends of the equalities, Equation 12 is obtained.

V_{0} = P_{2} x δV / 0.9 ( P_{2} – P_{1} )

Equation 12

Equation 12 is the simplified theoretical formula to calculate the pulsation dampener volume as a function of δV, P_{1} and P_{2}.

As already stated, the fact that charging gas pressure, P_{0}, is 0.9 P_{1} is commonly accepted as a norm. This difference between P_{0} and P_{1} prevents the complete evacuation of liquid from the dampener in each work cycle. Having this extra quantity of liquid, v, stored in the dampener between P_{0} and P_{1} can also be used to compensate for, in some instances, the potential changes in the gas pressure produced by variations in the exterior temperature that would modify the calculated theoretical volume of liquid that the dampener must store, δV. In that case, this volume could not be completely introduced into or discharged from the dampener.

The former equality shown in Equation 7 does not comply in practice because, when a volume of gas is compressed quickly, the temperature rises, which increases the pressure. When a gas expands, its pressure drops an extra value because the temperature is reduced (refrigerator effect). This effect happens with the majority of gases, included nitrogen and air, which are the commonly used to charge the dampeners. Atmospheric air can be used for pressures below 10 bar, providing that no risk of chemical reaction between the oxygen in the air and the pumped liquid exists.

Equation 7 is converted to Equation 13.

P_{0} x V_{0}^{γ} = P_{1} x V_{1}^{γ} = … = P_{n} x V_{n}^{γ}

Equation 13

Where γ = the specific heat ratio of the gas at constant pressure and volume, respectively

For the majority of gases, γ = 1.41. This constant is also theoretical. In the practice, the value that can be used is γ = 1.25. However, not to complicate the formula for dampener size calculation, a new constant (0.8) is used that will provides the same result (see Equation 14).

V_{0} = P_{2} x δV / 0.8 x 0.9 x ( P_{2} – P_{1} )

Equation 14

Equation 14 can be used in practice for nearly all industrial applications. The volumes given by this formula will unlikely fit any standard dampener volume size from a manufacturer. Except for very exigent applications, using the manufacturer’s standard closest lower size, favoring cost efficiency, is recommended.

Note that these equations and techniques do not consider possible temperature variations of the fluid or the environment. This would change the charging gas pressure value at 20 C. For each 10 C variation in temperature, the gas pressure will change by approximately 3 percent.

Read the second part of this series here.

Read the third part of this series here.