Machinery's Handbook, 31st Edition
2796 FLUID CONDITIONING AND STABILIZATION Liquid Pulsation (Water Hammer): Valves and reciprocating pumps are often the cul prits when water hammer occurs. Water hammer is a pressure spike in a fluid circuit caused by a sudden stoppage of flow. A valve closing can cause a shock wave in the liquid, resulting in noise. Reciprocating pumps cause acceleration and deceleration of the fluid that result in pressure variations. Hydraulic water hammer can be severe enough to burst pipes. Pulsation dampeners are recommended when water hammer is likely. An equation for the pressure rise that can occur due to water hammer follows: ∆ p Q 20 d 2 ------ SG b = where p is pressure in psi, Q is flow rate in GPM, SG is specific gravity, b is bulk modulus in psi, and d is pipe inside diameter, in inches, upstream of the point of interest. Accumulators and pulsation dampeners are used to store pressurized hydraulic fluid, which contains potential energy. This fluid and its energy can then be released to smooth out intermittent system cycles, dampen pulsations, absorb shocks, and compensate for leaks in the system. Accumulators: Pressurization against an accumulation of fluid can be accomplished through weight loading, spring loading, or compressed gas loading. Hydro-pneumatic, or gas loaded, accumulators are the most common. The three most common of this class are piston, bladder, and diaphragm accumulators. In these, a piston, bladder, or diaphragm separates the fluid from the compressed gas. When a hydro-pneumatic accumulator has a closed volume of gas, the change in volume of hydraulic fluid is equal to the change in volume of the gas. The equation for polytropic processes can then be used to calculate accumulator volume or pressure, depending on which values are known. The polytropic exponent, n, depends on the type of process. For slow gas expansion and compression processes which occur almost isothermally, the polytropic exponent can be assumed to be n = 1. For rapid processes, the adiabatic exponent can be taken as n = 1.4 for Nitrogen and air. For pressures above 3000 psi the real gas behavior deviates considerably from the ideal one, which reduces the effective fluid volume. In such cases the adiabatic exponent used is greater than 1.4. The equation for polytropic processes is: p 0 V 0 n p 1 V 1 n p 2 V 2 n Constant = = = where p 0 is the gas precharge pressure, p 1 is the minimum working pressure, and p 2 is the maximum working pressure. V 0 , V 1 , and V 2 are the gas volumes in each of the states. For low pressure applications of less than 150 psi, absolute gas pressures must always be used in the equation for required gas volume. These equations are assuming ideal gas behavior. Correction factors must be used to take into account real gas behavior. Those correction factors can range from 1 to 2 depending on the pressures involved. V 0 ∆ V – = ----------------- where V 0 is the precharge volume of gas, and D V = V 1 - V 2 p 0 p 1 --- 1 n -- p 0 p 2 --- 1 n -- Precharge pressure for energy storage is generally about 90 percent of system minimum working pressure. For shock absorption, precharge is usually 60 to 90 percent of median working pressure; for pulsation dampening, precharge is usually 60 to 80 percent of me- dian working pressure. A small amount of fluid should remain inside the accumulator at minimum working pressure to prevent the mechanical components from rubbing or impacting. Therefore the precharge pressure should be slightly lower than the minimum working system pressure.
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