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CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
12

With this type of profile, the load magnitude ramps up from zero to some value, remains relatively constant for a time, and then ramps down to zero again. For rapid ramping times, this type of profile resembles a rectangle. Loads with impulse force/time profiles are best solved using time history or force spectrum methods. Major types of loads with impulse time profiles are relief valve, fluid hammer, and slug flow.

Relief Valve

When system pressure reaches a dangerous level, relief valves are set to open in order to vent fluid and reduce the internal pressure. Venting through the valve causes a jet force to act on the piping system. This force ramps up from zero to its full value over the opening time of the valve. The relief valve remains open (and the jet force remains relatively constant) until enough fluid is vented to relieve the over-pressure condition. The valve then closes, ramping down the jet force over the closing time of the valve.

Fluid Hammer

When the flow of fluid through a system is suddenly halted through valve closure or a pump trip, the fluid in the remainder of the system cannot be stopped instantaneously. As fluid continues to flow into the area of stoppage (upstream of the valve or pump), the fluid compresses causing a high-pressure situation. On the other side of the restriction, the fluid moves away from the stoppage point, creating a low pressure (vacuum) situation. Fluid at the next elbow or closure along the pipeline is still at the original operating pressure, resulting in an unbalanced pressure force acting on the valve seat or the elbow.

The fluid continues to flow, compressing (or decompressing) fluid further away from the point of flow stoppage, causing the leading edge of the pressure pulse to move through the line. As the pulse moves past the first elbow, the pressure is now equalized at each end of the pipe run, leading to a balanced (that is, zero) pressure load on the first pipe leg. The unbalanced pressure, by passing the elbow, has now shifted to the second leg. The unbalanced pressure load continues to rise and fall in sequential legs as the pressure pulse travels back to the source, or forward to the sink.

The ramp up time of the profile roughly coincides with the elapsed time from full flow to low flow, such as the closing time of the valve or trip time of the pump. Because the leading edge of the pressure pulse is not expected to change as the pulse travels through the system, the ramp-down time is the same. The duration of the load from initiation through the beginning of the down ramp is equal to the time required for the pressure pulse to travel the length of the pipe leg.

Slug Flow

Most piping systems are designed to handle single-phase fluids (that is, fluids that are uniformly liquid or gas). Under certain circumstances, a fluid may have multiple phases and is susceptible to slug flow. For example, liquid slugs may be entrained in a wet steam line. These slugs of liquid create an out-of-balance load when the slugs change direction in bends or tees.

In general, fluid changes direction in a piping system through the application of forces at elbows. This force is equal to the change in momentum with respect to time, or

Fr = dp / dt = Dr v2 A [2(1 - cos q)]1/2

Where:

dp = change in momentum

dt = change in time

Dr = liquid density - vapor density

v = fluid velocity

A = internal area of pipe

q = inclusion angle at elbow

With constant fluid density, this force is normally constant and is small enough that it can be easily absorbed through tension in the pipe wall. The force is then passed on to adjacent elbows with equal and opposite loads, zeroing the net load on the system. Therefore, these types of momentum loads are usually ignored in analysis. If the fluid velocity or density changes with time, this momentum load will also change with time, leading to a dynamic load which may not be canceled by the load at other elbows.

For example, consider a slug of liquid in a gas system. The steady state momentum load is insignificant because the fluid density of a gas is effectively zero. The liquid suddenly slug hits the elbow, increasing the momentum load by orders of magnitude. This load lasts only as long as it takes for the slug to traverse the elbow, and then suddenly drops to near zero again with the exact profile of the slug load depending upon the shape of the slug. The time duration of the load depends upon the length of the slug divided by the velocity of the fluid.

Where:

F1 = rv2 A(1 - cos q)

Fr = rv2 A [2(1 - cos q)]½

F2 = rv2 A sin q