洛阳理工学院毕业设计（论文）

38

洛阳理工学院毕业设计（论文）

外文资料翻译

Pressure transient theory

Before embarking on the analysis of pressure transient phenomena and the derivation of the appropriate wave equations,it will be usefull to describe the general mechanism of pressure propagation by reference to the events fllowing the instantaneous closure of a value postioned at the med-length point of a frictionless pipeline carrying fluid between two reservoirs.The two pipeline sections upstream and downstream of the value are identical in all respects.Transient pressure waves will be propagated in both pipes by valve operation and it will be assumed that rate of value closure precludes the use of rigid column theory.

As the valve is closed,so the fluide approaching its upstream face is retarded with a consequent compression of the flude and an expansion od the pipe cross-section.The increase in pressure at the valve results in a pressure wave being propagated upstream which conveys the retardation of flow to the column of fluid approaching the valve along the upstream pipeline.This pressure wave travels through the fluid at the appropriate sonic velocity,which will be shown to depend on the properties of the fluid and the pipe material.

Similarly,on the downstream side of the valve the retardation of flow results in a reduction in pressure at the valve,with the result that a negative pressure waves is propagated along the downstream pipe which,in turn,retards the fluid flow.It will be assumed that this pressure drop in the downstream pipe is insufficient to reduce the fluid pressure to either its vapour pressure or its dissolved gas release pressure,which may be considerable different.

Thus,closure of the valve results in propagation of pressure waves along both pipes and,although these waves are of different sign relative to the steady pressure in the pipe prior to valve operation,the effect is to retard the flow in both pipe sections.The pipe itself is affected by the wave propagation as the upstream pipe swells as the pressure rise wave passes along it,while the

39

洛阳理工学院毕业设计（论文）

downstream pipe contracts due to the passage of the pressure reducting wave.The magnitude of the deformation of the pipe cross-section depends on the pipe material and can be well demonstrated if,for example,thin-walled rubber tubing is employed.The passageof the pressure wave through the fluid is preceded,in practice,by a strain wave propagating along the pipe wall at a velocity close to the sonic velocity in the pipe material.However,this is a secondary effect and,while knowledge of its existence can explain some parts of a pressure-time trace following valve closure,it has little effect on the pressure levels generated in practical transient situations.

Following valve closure,the subsequent pressure-time history will depend on the conditions prevailing at the boundaries of the system.In order to describe the events following valve closure in the simple pipe system outlined above,it will be easier to refer to a series of diagrams illustrating conditions in the pipe at a number of time steps.

Assuming that valve closure was instantaneous,the fluid adjacent to the valve in each pipe would have been brought to rest and pressure waves conveying this information would have been propagated at each pipe at the appropriate sonic velocity c.At a later time t,the situation is as shown in fig.The wavefronts having moved a distance 1=ct,in each pipe,the deformation of the pipe cross-section will also have traveled a distancel as shown.

The pressure waves reach the reservoirs terminating the pipes at a time t=1/c.at this instant,an unbalanced situation arises at the pipe-reservior junction,as it is clearly impossible for the layer of fluid adjacent to the reservoir inlet to maintain a pressure different to that prevailing at that depth in the reservoir.Hence,a restoring pressure wave having a magnitude suffcient to bring the pipeline pressure back to its value prior to valve closure is transmitted from each reservoit at a time 1/c.For the upstream pipe,this means that a pressure wave is propagated towards the closed valve,reducing the pipe pressure to its original value and restoring the pipe cross-section.The propagation of this wave also preduces a fluid flow from the pipe into the

40

洛阳理工学院毕业设计（论文）

reservoir as the pipe ahead of the moving wave is at a higher pressure than the reservoir.Now,as the system is assumed to be frictionless,the magnitude of this reversed flow will be the exact opposite of the original flow velocity,as shown in fig.

At the downstream reservoir,the converse occurs,resulting in the propagation of a pressure rise wave towards the valve and the establishment of a flow from the downstream reservoir towards the valve.

For the simple pipe considered here,the restoring pressure waves in both pipes reach the valve at a time 21/c.The whole of the upstream pipe has,thus,been returned to its original pressure and a flow has been established out of the pipe.At time 21/c,as the wave has reached the valve,there remains no fluid ahead of the wave to support the reversed flow.A low pressure region,therefore,forms at the valve,destroying the flow and giving rise to a pressure reducing wave which is transmitted upstream from the valve,once again bringing the flow to rest along the pipe and reducing the pressure within the pipe .It is assumed that the pressure drop at the valve is insufficient to reduce the pressure to the fluid vapour pressure.As the system has been assumed to be frictionless,all the waves will have the same absolute magnitude and will be equal to the pressure increment,above steady running pressure,generated by the closure of the valve.If this pressure increment is h,then all the waves propagating will be±h,Thus,the wave propagation upstream from the valve at time 21/c has a value-h,and reduces all points along the pipe to –h below the initial pressure by the time it reachs the upstream reservoir at time 31/c.

Similarly,the restoring wave from the downstream reservoir that reached the valve at time 21/c had established a reversed flow along the downstream pipe towards the closed valve .This is brought to rest at the valve,with a consequent rise in pressure which is transmitted.downstream as a +h wave arriving at the downstream reservoir at 31/c,at which time the whole of the downstream pipe is at pressure +h above the initial pressure whth the fuid at

41