Fluid Mechanics Solutions

The Cause of Transients: Role of Valving.

 

A change from steady flow conditions in a piping system occurs when there is a change in operation of elements or facilities in the system. Quite often these are terminals or boundaries of the pipe and may be referred to as boundary conditions. There are many opportunities to introduce transients into fluid systems through active changes in operating conditions. There may also be passive or reactive changes that contribute to the transient behavior. Rather than exhaustive itemization of the causes of transients only a few different opportunities are listed.

• Changes in valve settings, accidental or planned.

• Starting or stopping pumps or compressors.

• Changes in power demand in turbines

• Action of reciprocating devices.

• Changing level or reservoir or pressure tank.

• Liquid vaporisation or vapor condensation.

• Vibration of impellers or guide vanes in turbo machines.

• Vibration of deformable appurtenances such as valves.

• Motion of pipe or other system element.

• Unstable controller or turbo machine characteristic.

 

The study of fluid transients quite often involves analyses of problems having one or more of these conditions.

Traditionally, this study has been one of analysis rather than design or synthesis.

A design is made, and then the system is analyzed to see if it is satisfactory from transient viewpoint. If not, alterations in the design are made and it is analyzed again, perhaps with such changes as an increase in the thickness of pipe walls or introduction of surge tanks, accumulators, surge suppressors, and so on.

 

Routine control of flow in a system is usually affected by adjusting the position of one or more valves. Valves, by introducing losses into a system(except for needle nozzles at the end of a line),control the rate of flow; each adjustment of the valve also sets up pressure pulse waves that traverse the system at the wave speed for the particular pipe. By making the valve adjustments very slowly, one can keep the transient pressure change under control. But slow changes may hamper the process under control, so it is desirable to know how to make rapid valve adjustments and still keep the transients within tolerable limits.

 

Column Separation: Gas Release.

 

Vapor Formation.

 

Aside from damaging equipment attached to piping systems, water hammer may cause the pipe to fail from excessive pressure or to fail by collapse due to pressure less than atmospheric. The phenomenon of column separation may occur within a piping system where boundary conditions are such that the pressure is reduced. A reduction in pressure at the upstream end of a pipe with positive flow causes a negative pulse to be transmitted down the pipe, thereby reducing its velocity; the fluid downstream continues at its steady velocity until the wave arrives. This difference in velocity between portions of the flow tends to put the liquid column into tension, which commercial fluids cannot withstand. When vapor pressure is reached, a vapor cavity forms in the pipe. With a pipeline of varying elevation, column separation usually forms near one of the high points in the profile. This cavity will tend to stay on the downstream side of the high point, with the liquid flowing below the cavity. After the cavity is formed it may continue to grow in volume until the flow velocities of the two columns become equal. Usually, the upstream column will be accelerated and the downstream column decelerated by the boundary conditions, and the upstream column overtakes the downstream column. If the difference in velocity at the instant of collapse of the vapor cavity is DV, a pressure increase of may be expected. This pressure increase may be of sufficient magnitude to rupture the pipe.

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Gas Release.

 

If the liquid in the pipeline contains dissolved air or other gases, a reduction in its pressure below saturation pressure causes gas bubble formation at the many nuclei generally present in commercial liquids. An example could be the reduction of pressure from say 2 atm to 0.5 atm. These small bubbles greatly decrease the wave speed. If the liquid has its pressure reduced to vapor pressure, the bubbles would contain also vapor. If these conditions develop in a system or if the liquid being transported contains free gas, a variable wave speed exists that is highly pressure dependent.