Operation and control of flows and transient system component design

Operation of networks is generally carried out by valves, which aims at transferring the system from one steady state to another steady state. Two main fields of problems exist related to operation of networks. First deals with transients. Second is associated with the optimal scheduling problems, which aims at determination of cost optimal pumping schedules or valve settings for the daily or weekly demand variations. This problem does not take into account transients and, in fact, is based on steady state models.

Optimal scheduling problems are not within the scope of present study. Scope of the study is limited to analysis and control of transients, both slow and rapid. Developments in this area are presented in this section for both slow and rapid transients.

Analysis and control of transients

A change from steady state flow in a piping system occurs because of a change in boundary conditions. There are many kinds of boundary conditions that may introduce transients such as changes in valve settings, accidental or planned, starting or stopping of pumps, changes in power demands in turbines etc. Transient problems in engineering practice are of significant importance because it can cause excessive pressures, vibration, cavitation and noise far beyond that indicated by steady flow analysis. Excessive pressure fluctuations caused by acceleration or deceleration of a fluid mass are the main concern in liquid system transient analysis.

With the increase of complexity and performance requirements of modern engineering network systems, the control of objectionable transients in the operation is becoming increasingly important in a number of applications such as the design of hydroelectric generating stations, water supply systems, cyclic components of otherwise continuous flow processes and hydraulic systems developed for industrial and commercial applications.

Therefore, various devices and/or control procedures such as surge tanks, air chambers, pressure reducing valves, valve stroking etc. are used to reduce or eliminate undesirable transients.

An optimal flow control is desired in hydraulic network systems due to operation and design considerations. Optimal control aims at defining a mode of operation of various appurtenances and control devices so that a desired response is obtained. A desired system response may be, for instance, to keep the maximum and minimum transient pressures within specified limits, changing the flow from one steady state to another without flow oscillations and so on. For example, a valve at the downstream end of a pipeline may be closed in such a

way that the pressure dose not exceed a specified limit and the transients are completely eliminated at the end of valve operation. Such a valve operation has been referred to as optimal valve closure or valve stroking.

Optimal flow control is a synthesis approach in which the variations of boundary conditions are determined to obtain a desired system response. This is also called transient design. This approach is different from the usual analysis approach in which the boundary conditions are specified and resulting response of the system is analysed.

The subject area of design of valve operations to control transients and more specifically transient design has not received much attention from the researchers. Scientific developments in this area are limited to control of transients in some very simple systems.

Subject area can be divided into two categories; control of pressure surges or slow transients and control of rapid transients.

Analysis and control of pressure surges using rigid model

Pressure surges or slow transients with low frequencies are analysed using rigid water column model (RWCM) which treats the fluids as an inelastic substance wherein pressure changes propagate instantaneously throughout the system and elastic properties of the pipe walls are of no consequence. The rigid water column model is a lumped approximation to the elastic column model (Watters, 1984).

A wide range of pipeline problems falls within the domain of rigid water column theory.

Transients generated in the systems consisting of surge tanks and subjected to slow valve operations are of low frequencies and can well be analysed by RWCM. The equations describing this type of flow are generally ordinary differential equations, which can be solved in closed form or with relatively straightforward numerical techniques.

Until now, RWCM has not been applied for pressure surges analysis of complicated piping systems (Watters, 1984; Streeter and Wylie, 1993). It is observed that it is difficult to derive a system of non-linear ordinary differential equations of the first order, which can be numerically integrated.

Though, approaches based on both loop and incidence method are developed for analysing pressure surges in looped networks, authors considered some very simple systems and their algorithms lack generality (Onizuka, 1986 and Shimada, 1989). It is observed that it is difficult to generate generalised model due to complexity of networks. This generally results in a set of ordinary differential equations in which it is difficult to separate independent and dependent variables..

A generalised and efficient algorithm, which can handle arbitrary topology of network and provides a minimum set of ODEs that can be numerically integrated easily, is necessary and needed.

Control of pressure surges by valve operations has not received much attention by the researchers. Shimada (1992) considered the pressure surges control problem and used

procedures of optimal control theory. The objective function used was directed to achieve just final steady state valve settings. Neither control of pressures due to transients was considered as an objective nor the control of residual transients at the end of valve operations was given attention. In fact, procedure developed can not be termed as control of slow transients because with the known final steady state valve settings, any number of trajectories of valve operations can be found which will take the system to final steady state.

Control of pressure surges in pipe networks is still a novice area. Design of pressure surges or transient design has not been considered so far. Transient design envisages design of valve operation rules for the specified transients. Development of methodologies for transient design is necessary for effective control of pressures and flows and good operation of network systems.

Analysis and control of transients using elastic model

To analyse rapid transients elastic water column theory wherein the elasticity of both fluid and the pipe walls is taken into account is well developed (Streeter and Wylie, 1993; Watters, 1984; Choudhary, 1979). However, not much research has been carried out for the control of rapid transients by valve operations. Developments in this area are restricted to the works of Streeter (1963, 1967), Propson(1970) and Stoner (1968).

The first study, which succeeded in eliminating the objectionable residual transients, was that of Streeter. Considering a simple frictionless pipe and aided by the visual insight afforded by utilisation of the dependent variable graph (Allievi’s graphical method), he presented a procedure by means of which the downstream valve motion can be determined which would create a controlled transient between any desired initial and final steady-uniform flow conditions. More specifically, the flow change is accomplished in three phases: the length of the first and last phase is one round trip wave travel time and the central phase is of such duration that the change can be effected within the specified pressure limits. The head dose not decreases below initial steady state values and dose not exceeds the predetermined maximum. He restricted the valve closure to duration of twice the round trip wave travel time.

Streeter further extended the scope of valve stroking principles by taking into account frictional effects. The method was then readily extended to branching systems by apportioning the flow changes among the branches as a linear relation of the initial to the final steady-uniform values in each pipe.

Later, Propson developed procedure for valve stroking in a specified time and a more rapid closure, down to one round trip wave travel time. These procedures provide optimal control of flows, however, valve operation rules are not smooth and a sudden closure or opening is obtained at the beginning and end of operations. Procedures of valve stroking have been applied to some simple branched systems. Though these procedures are able to provide optimal flow control, it is noticed that valves have to act against a very high head.

Generally, transients control problem involve following aspects:

• Limit on valve operation time

• Limit on maximum or minimum pressure in the system

• Elimination or existence of residual transients after valves stops to operate

Valve stroking is a procedure, which eliminates residual transients, and maximum or minimum pressure in the system is governed by the valve operation time or vice versa. In many cases of network operation, presence of some residual transients dose not effects the requirements of the users. Generally, limit on maximum or minimum pressure is the main concern. If residual transients are permitted, with the same valve operation time limits on maximum or minimum pressures can be lowered. Such procedures of transients control are yet to be developed.

Transient system component design

Design of various system components used for controlling transients is carried out using trial and error procedures. Some typical examples are design of surge tank, air vessel, conveying elements etc.

Conventional procedures for the design of surge tanks consist of assuming a surge tank design and analysing the result of transients due to different planned and accidental cases. If the resulting behaviour of the system is not satisfactory, a new surge tank design is adopted.

Procedure is repeated until established criteria are satisfactorily met.

Similar procedures are used for other the design of other components also such as air vessel, conveyance element, valves etc. These trial and error procedures are very cumbersome specially if the network topology is complex.

Generally, these components are designed to meet some specified transient response in some other components. Methodologies providing direct design parameters would be effective in avoiding cumbersome and tedious trial and error procedures. Moreover, such procedures would help in providing an insight into the relationships between the mutual behaviour of different components.

In general, transient design and transient system component design are still unexplored fields.

It aims at design of boundary conditions for the specified transients. Developments in these areas can simplify the existing procedures of design and operations.