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JOBY BOXAll AND eEDO MAKSIMOVIC - EDITORS

Integrating Water Systems – Boxall & Maksimovic (eds)© 2010 Taylor & Francis Group, London, ISBN 978-0-415-54851-9

Mathematical modelling of a hydraulic controller for PRV flow

modulation

HossamAbdelMeguid, Piotr Skworcow & Bogumil Ulanicki

Process Control – Water Software Systems, De Montfort University, Leicester, UK

ABSTRACT: The main purpose of this paper is to describe a new experimental setup for testing static anddynamic behaviour of theAQUAI-MOD® hydraulic controller coupled with a standard PRV, as well as to developmathematical models which represent static and dynamic properties of such a system. The controller has beenexperimentally tested to assess its performance in different conditions andoperating ranges.Thedevice in all caseshas showed good performance by modulating the outlet pressure as expected between two points correspondingto the minimum and the maximum flow. The mathematical models of the controller have been implemented andsolved using the Mathematica software package to represent both steady state and dynamics conditions. Theresults of the steady state model have been compared with experimental data and showed a good agreementin the magnitude and trends. The steady state model can be used to simulate the behaviour of a PRV and theAQUAI-MOD® hydraulic controller in typical network applications. It can be also used at the design stage and tocompute the required adjustments for the minimum andmaximum head set points before installing the controllerin the field. Subsequently, a dynamic model of the PRV and theAQUAI-MOD® hydraulic controller system hasbeen developed and solved. Again the dynamic model showed a good agreement with the experimental data.The main time constant in the system model corresponds to the movement of the main element of the PRV.The research presented here has been carried out within the Neptune project (www.neptune.ac.uk) which is aStrategic Partnership between EPSRC, ABB,Yorkshire Water and United Utilities.

1 INTRODUCTION

Water utilities use pressure control to reduce back-ground leakage and the incidence of pipe bursts.Control is usually implemented across areas that aretypically supplied through pressure reducing valvesand closed at all other boundaries (Alonso et al., 2000;Ulanicki et al., 2000; Prescott et al., 2005). Single-feedPRV schemes are often adopted for ease of control andmonitoring but risk supply interruption in the eventof failure. Multi-feed systems improve the security ofsupply but are more complex and incur the risk of PRVinteraction leading to instability (Ulanicki et al., 2000;Prescott and Ulanicki, 2004). A better understandingof the dynamics of PRVs and networks will lead toimprove control strategies and reduce both instabilitiesand leakage.Dynamic models are currently available for repre-

senting behaviour of most water network components.Such models are relatively simple, accurate and canbe easily solved (Pérez et al., 1993; Andersen andPowell, 1999; Brunone and Morelli, 1999). Prescottand Ulanicki (2003) developed the PRV dynamicphenomenological, behavioural, and linear models torepresent dynamic and transient behaviours of PRVs.Prescott and Ulanicki (2008) developed a model toinvestigate the interaction between PRVs and waternetwork transients. Transient pipe network models

incorporating random demand were combined with abehavioural PRV model to demonstrate that changesin the system demand can produce large and persistentpressure variations, similar to those seen in practicalexperiments.The pressure control is more efficient if there is

a possibility of automatically adjusting a set point ofa PRV according to the PRV flow – so called flowmodulation. The PRV set point can be adjusted elec-tronically or hydraulically. The former require the useof a flow sensor, a microcontroller and solenoid valvesacting as actuators. The major disadvantages of thissolution are the necessity of providing power supplyand the exposure of the electronic equipment to harshfield conditions.A hydraulic flowmodulator is amuchmore robust and simpler solution.The AQUAI-MOD® hydraulic controller manufac-

tured by theAquavent company (Peterborough, UK) isprobably the first hydraulic flow modulator availableon the market.The AQUAI-MOD® hydraulic controller can be

used to implement optimal pressure control strategies(Vairavamoorthy and Lumbers, 1998; Ulanicki et al.,2008) by controlling the outlet pressure of the PRVsaccording to the flow. This will minimise continuousover pressurisation of the mains and therefore reduceenergy consumption on pumps and stress on the mainscausing potential leaks.

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Figure 1. AQUAI-MOD® controller and its connection

to PRV (Patents Pending GB 0711413.5, Int’l PCT/

GB2008/050445).

2 DESCRIPTION OF THEAQUAI-MOD®

HYDRAULIC CONTROLLER

As shown in Figure 1 the AQUAI-MOD® hydrauliccontroller consists of three main chambers separatedby rolling diaphragms. The first chamber is a Pitotchamber, which is connected to the Pitot tube atthe downstream of the main valve (PRV). The sec-ond chamber is a control chamber, connected to theupstream, and control space of the PRV through aT-junction (t1). The pipe connected the valve inlet andT-junction, t1, has a fixed orifice. The third one is a jetchamber, which is connected to the downstream of thePRV.The jet chamber is also connected to the Pitot tubethrough a T-junction (t2). As well, the control cham-ber is connected to the jet chamber through a hollowshaft, which allows the flow form control chamber tojet chamber through the discharge outlet of the jet.Theresistance of the jet and the seat of the main adjusterdepends on the gap between them, andwork like a pilotvalve.The major part of the valve is a hollow shaft

with attached discharge jet and two pistons connectedto the main body of the controller through rollingdiaphragms. The space between the two pistons iscalled the control chamber and it has the constantvolume. The control chamber is connected to the con-trol space of the PRV and the upstream flow. Waterenters the control chamber via the T-junction (t1) andleaves through the hole in the shaft. Subsequently it isconveyed to the discharge jet.The controller modulates the outlet pressure of the

PRV according to the main flow, which is sensed andconverted to dynamic pressure by a Pitot tube, whichinserted into the downstreamof thePRVand connectedto the Pitot chamber of the controller.The controller has two setting points, the first one

is the minimum pressure (corresponding to the mini-mum night flow), and this minimum pressure can beadjusted by main pressure adjuster by changing theinitial tension of the spring and the gab. The working

Figure 2. AQUAI-MOD® hydraulic controller experiment

layout.

principle of this part is similar to that of a traditionalpilot valve in a PRV (Prescott and Ulanicki, 2003).The second setting point is the maximum pressure

(corresponding to the peak of demand), which can beset by the modulation adjuster (one directional flowneedle valve).

3 TEST RIG DESCRIPTION

The design criterions for the experiment setup takesinto account the environmental consideration by usinga closed hydraulic loop test rig, which allows con-tinuous flow running to avoid water loss. As shownFigure 2, a centrifugal fixed speed pump pumpsthe water from the tank through 3′′ stainless steel pipewhich is expanded to 4′′ pipe before the fitting of thegate valve. The hydraulic loops have two gate valvesand one PRV. The first gate valve is upstream thePRV and is used to control the PRV inlet pressure,while the second gate valve is downstream the PRVand used to control the required flow, which representthe demand flow. The PRV is controlled by AQUAI-MOD® hydraulic controller.The 4′′ stainless steel pipeconnects the upstream gate valve, PRV, downstreamvalve, and exit to the tank.Figure 2 depicts the detailed instrumentation draw-

ing of the test rig and shows the position of each sensorand its connection to the data acquisition card.The testrig is equipped with two electromagnetic flow meters,one is high-flow range to measure the main flow andanother one is a low-flow range to measure the flowform T-junction to the control chamber of the con-troller and also is used to measure the flow throughthe modulation adjuster to identify its characteristics.Additionally, seven pressure transducerswere installedto measure the inlet and outlet pressures of the PRV,the pressures in Pitot, control, and jet chambers of thecontroller, the pressure in the control space of the PRVand finally the pressure at T-junction. A linear vari-able differential transformer (LVDT) was installed tomeasure the displacement of the main shaft of the con-troller. All transducers had 4–20mA output signals toprevent electro-magnetic interference.In order to automate the data collection, a data

acquisition card (DAQ) with 16 high-accuracy ana-logue input channels, was used to collect the different

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signals from the measurement transducers. It includedbuilt-in signal conditioning and an integrated connec-tor with screw terminal. DAQ of NI 9203 series.The acquisition software, LabView was installed

on a high specification laptop to monitor, record theacquired signals and save it in the CSV format.

4 EXPERIMENT PROCEDURE

4.1 Measuring capacitance ofthe modulation adjuster

Awater tank was placed at a height of 1.5m.Themod-ulation adjuster valvewas detached from the controllerand installed on an elastic pipe.One endof the pipewasconnected to the tank bottom, another pipe end waspositioned at different heights (40 cm, 60 cm, 80 cm,100 cm and 120 cm) with respect to the water level inthe tank in order to measure flow through the pipe fordifferent pressure differences. The choice of pressuredifferences was consistent with the pressures in Pitotchamber and jet chamber of the controller observedduring initial experiments.Water was discharged from the water tank through

the pipe and modulation adjuster valve into a cylinder.Flow through the pipe was calculated as the volumeof water discharged into the cylinder during someperiod of time (approx 30s) which was measured witha stopwatch. The measurements were carried out forall possible combinations of modulation valve open-ing (from 10% to 80% in steps of 10%) and of pressuredifference (from 0.4m to 1.2m in steps of 0.2m).

4.2 Measuring capacitance of the ofpilot valve – procedure

Since the pilot valve could not be detached from thecontroller, its capacitancewas evaluated duringnormaloperation of the controller. Low-flow flow meter wasinstalled between T-junction and control chamber tomeasure flow, denoted in equations as q2, for differentgaps, denoted xr , between the jet outlet and jet seat.Note that xr cannot be directly controlled during valveoperation. To generate changes in xr the downstreamvalve opening was changed such and the main flowwas varied from 1 to 17 l/s. This was carried out fordifferent setting of the modulation valve, i.e. for 30%,40%, 50% and for 60% of maximum opening.

4.3 Measuring flow modulation characteristic

Using the main pressure adjuster of the controller, theminimal outlet pressure (for zero flow modulation,i.e. modulation adjuster fully open) was set to 26m.Measurements were carried out for different modu-lation adjuster settings: from 0% to 80% in steps of10%. For each modulation adjuster setting the down-stream valve opening was changed (according to thesequence 6, 5, 4, 3, 2.5, 2, 1.5, 1, 1.5, 2, 2.5, 3, 4, 5,6 turns from the complete closure), so that the mainflow varied over the range from 1 to 17 l/s. Between

each change of downstream valve sufficient time wasallowed (between 1 and 2 minutes) for the controllerand the PRV to reach the steady-state conditions.

4.4 Testing the dynamical properties ofthe controller

The following testswere performed to evaluate dynam-ical properties of the controller.

4.4.1 Sharp closure and opening ofdownstream valve

With modulation adjuster set at 30% and the down-stream valve initially at 6 turns from complete closure,the downstream valvewas sharply closed (1 turn left tocomplete closure). After 2 minutes downstream valvewas sharply opened to the initial opening.

4.4.2 Upstream valve closureWith themodulation adjuster set at 30%,openingof theupstream valve was changed, starting from fully open(5 turns) down to fully closed (0 turns), according tothe following sequence: 5, 4, 3, 2, 1, 0.5, 0, 0.5, 1, 2, 3,4, 5. Between each change of upstream valve openingsufficient time was allowed (between 1 and 2 minutes)for the controller and the PRV to reach the steady-stateconditions, except for complete closure which lastedonly few seconds.

4.4.3 Changes of the main adjuster settingWith modulation adjuster set at 30%, the minimal out-let pressure was changed every one minute via turningthe dial (1 turn at a time) of the main pressure adjuster.This was performed starting from the highest pressuresetting towards the lowest pressure setting.

4.4.4 Changes of modulation adjuster settingModulation adjuster valve opening was changedaccording to the sequence: 25%, 30%, 40%, 50%,60%, 70%, 80%, 70%, 60%, 50%, 40%, 30%, 25%.Between each change of modulation adjuster settingsufficient time was allowed (between 1 and 2 minutes)for the controller and the PRV to reach the steady-stateconditions.

5 EXPERIMENTAL DATA OF THE PRVANDAQUAI-MOD® CONTROLLER

As an initial assessment of the AQUAI-MOD®

hydraulic controller a number of steady state charac-teristics weremeasured. Figure 3 depicts themeasuredmodulation curve, as the main flow increases the out-let pressure of the PRV increases. The head drop atthe high flows is due to the test rig arrangement, theinlet head to the PRV is decreasing due to the pumpcharacteristics.Figure 4 shows the effect of the number of opening

turns of the modulation adjuster on the maximum out-let head. The modulation adjuster is a one-directionalflow needle valve, and is fully open at 8 turns. Asshown in the figure, as the number of turns increase

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Figure 3. Modulation curve of the AQUAI-MOD®

controller.

Figure 4. Effect of modulation adjuster opening on the

maximum outlet head.

Figure 5. Effect of main pressure adjuster on the minimum

outlet head.

from 2.5 to 6 the maximum outlet head decrease lin-early from linearly from 45 to 28m with high rateof change of −4.4m per each opening turn, but in therange of 6 to 8 turns the rate of change of themaximumoutlet pressure decrease to −0.8m for each openingturn.Figure 5 shows how the number of opening turns of

the main pressure adjuster affects the minimum outletpressure. The main pressure adjuster is a screw usedto set the minimum outlet head according to the mini-mum night flow and depends on the minimum allowed

Figure 6. Dynamic effect of quick drop and rise in the main

flow.

operating pressure across the network.As shown in thefigure there is no effect from 0–3 turns, and the outlethead is the same as inlet head of the PRV, this meansthe PRV is fully opened. After that, the minimum out-let pressure decrease with increase of the number ofopening turns .To test the dynamic and transient effect of chang-

ing the main flow on the outlet pressure, a sharpclosure and opening of downstream valve with themodulation adjuster set at 30% and the downstreamvalve initially at 6 turns from complete closure, thedownstream valve was sharply closed (1 turn left tocomplete closure), after 2 minutes downstream valvewas sharply opened to the initial opening. Figure 6shows the effects of the fast drop and rise in the mainflow. By closing the down stream valve, the main flowdecreased from 17 to 1.75 l/s in 15ms, and the outlethead dramatically increased to its maximum valueof 77.5m in 10 s, and then dropped to its nominalvalue of 24.6m. However, the sharp opening, or rapidflow increasing, did not have any serious dynamic ortransient effect on the outlet pressure. The dynamicbehaviour is explained for each interval as marked inthe figure below.In interval (1) the main flow is very high which

causes the inlet head to be very low due to thepump characteristic. The desired outlet head cannotbe maintained and the PRV is almost fully open.In interval (2) the main flow is decreasing and this

has the following effects: (a) The inlet head is increas-ing due to the pump characteristic. (b) The PRV isstill fully open and the outlet head is almost equal tothe inlet head (increasing). (c) The modulating shaftmoves to the left because of decreasing dynamic pres-sure. (d) The pilot shaft is moving to the right becauseof the increasing outlet pressure.In interval (3) the main flow is still decreasing but:

(a) The jet outlet of the modulating shaft is engagedwith the seat of the pilot shaft thus themodulating shaftstops. (b)The PRV is still fully open and the outlet headis almost equal to the inlet head (increasing).In interval (4) the main flow is now constant and

this has the following consequences: (a) Inlet head isconstant. (b) Since the gap between the jet outlet and

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the seat of the pilot shaft is zero, thus the pressure inthe control chamber and T-junction rapidly increases.This results in flow q3 going into the control spaceof the PRV and forces the main element of the PRVto move down, i.e. the PRV is closing. (c) The outletpressure is decreasing and so is the pressure acting onthe pilot shaft diaphragm. (d) The pilot shaft movesvery slowly to the left and so does the modulatingshaft; both of them are still engaged.In interval (5) the main flow is constant and

the PRV+ controller undertakes normal operation:(a) The main element of the PRV continues to movedown (flow q3 keeps going into the control space ofthe PRV). (b)The outlet pressure is decreasing. (c)Thepilot shaft moves to the left and so does the modulat-ing shaft driven by the spring; the gap between thejet outlet and the seat of the pilot shaft is close tozero. (d) At the end of this period the steady-state isachieved: (i) the modulating shaft stops at the positionwhere forces from the dynamic pressure and spring 1are balanced, (ii) the pilot shaft stops at the positionwhere forces from outlet pressure and spring 2 are bal-anced, (iii) the gap between the jet outlet and the seatof the pilot shaft is such that the pressure in T-junctionequals the pressure in the PRV control space: flow q3is thus zero and the PRV stops closing.In interval (6) the main flow is constant and the

PRV+ controller are in steady state.In interval (7) the main flow is increasing rapidly

and this causes the following: (a)Themodulating shaftmoves to the right due to increase in the flowand result-ing increase in the dynamic pressure. It stops whenthe dynamic pressure is balanced by the force of thespring 1. (b)The inlet and outlet pressures are decreas-ing rapidly due to the pump characteristic and so is thepressure acting on the pilot shaft diaphragm, hence thepilot shaft moves to the left. (c)The gap between the jetoutlet and the seat of the pilot shaft is large thus hassmall resistance, therefore the pressure in the controlchamber andT-junction rapidly decreases. This resultsin flow q3 going out of the control space of the PRVand forces the main element of the PRV to move up,i.e. the PRV is opening.In interval (8) the main flow becomes constant and

has a very high value causes: (a)The dynamic pressureis constant and the modulating shaft stops balancedby the force from the spring 1. (b) The PRV is stillopening trying to maintain the outlet pressure andsubsequently the inlet pressure is decreasing due todistribution of the head between the upstream checkvalve and the PRV. (c) Finally the PRV+ controllerreach steady state and the PRV is almost completelyopen.

6 THE MATHEMATICAL MODEL OF THE PRVAND ITS CONTROLLER

To provide a good understanding of the static anddynamic behaviour of the PRV and itsAQUAI-MOD®

hydraulic controller, a full phenomenological modelis developed to describe the effect of all variables

on the PRV and the controller. The phenomenologi-cal model of standard PRV, which was developed by(Prescott and Ulanicki, 2003) is used to model thePRV behaviour, while the mathematical model of thecontroller is developed here.In this model, three moving parts are considered,

the first part is main element of the PRV, while theother two parts are the main and secondary shafts ofthe controller (Figure 1). The displacement of eachmoving part is described by a second order differen-tial equation, equation (1) for the main element of thePRV, and equations (2) and (3) for the main and thesecondary shaft of the controller respectively.

The scripts,m, x, f and h denote themass, the displace-ment, the friction coefficient opposing the movementof the element and pressure, respectively; k and �sare the stiffness coefficient and the deflection of thespring; qm, q1 and q2 are the main flow through thePRV, the flow from the PRV inlet to the T-junction (t1)and the flow from the control space of the PRV toT-junction (t1); a1 and a2 are the areas of the bottomand top of the moving element of the PRV; A1, A5 andAj are the internal cross sectional areas of the large andsmall cylinders of the controller and the discharge areaof the jet; ρ and g are the density of water and the grav-itational acceleration. The subscripts, m, sh1 and sh2refer the main valve, main and secondary shaft of theAQUAI-MOD® hydraulic controller, respectively; inand out refer the inlet and outlet of the PRV; cpt,cc and cj refer the Pitot chamber, control chamberand jet chamber of the controller; sp1 and sp2 denotethe springs on the main and secondary shafts of thecontroller.The PRV under consideration is diaphragm oper-

ated so the area of the top of the main valve elementchanges with the opening of the valve according to theequation a2 = 1/3700(0.02732−xm). The force termsof equation (1) are from left to right, inlet pressureacting on the base of the main valve, outlet pressureacting on the region of the diaphragm around the topof the main valve, control space pressure acting on theother side of this diaphragm, weight of the main valve,friction acting on the main valve, and force caused bychange of momentum of water as its velocity goes tozero as it hits the base of the main valve.The force terms of equations (2) and (3) are from

left to right, the net pressure force acting on the both

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sides of the rolling diaphragms, the spring force dueto the deflection of the springs, friction acting on themoving parts of the controller, and force caused bychange of momentum of water which enter the hole ofthe hollow and exit from the jet.There are a set of algebraic and differential equa-

tions to represent flows through the controller, the PRV,and the connecting pipes. The flow through the fixedorifice, needle valve, pilot valve, and main valveare given by equations of the form q = Cv(|�h|)1/2sgn(�h) where q, �h, Cv represent the flow throughthe element, the pressure loss across the element, andthe discharge capacity of the element, respectively.Thevalve capacity is the flow per root of pressure loss andis expressed as a function of opening and sgn(�h) isthe sign of the�h to indicate the direction of the flow.The valve capacity is usually given in the manufactur-ers’ literature for the main valve, and can be obtainedexperimentally for the others.Equation (4) represents the flow through the main

valve, where the valve capacitance, Cvmv(xm) dependson the valve opening xm.

where

The flow through the fixed orifice between the PRVinlet and the T-junction (t1), q1, is calibrated bythe experimental results, and can be described byequation (5)

Equation (6) describes the flow from control chamberto jet chamber through the discharge opening of the jet,q2. The flow is measured, and the capacitance of thissystem, Cvj(xr), is calibrated against the gap betweenthe discharge opening of the jet and the seat of themain adjuster shaft, xr .

where

where xr in [mm], Lc3 depends on the controller setpoints (number of opening turns of the main pres-sure adjuster,Nmpadj), and they aremeasured for eachexperiment setting.

The flow from/to the valve control space throughbi-directional needle valve, q3, can be expressed byequation (7),

and the valve capacitance, Cvnv, is taken from(Prescott and Ulanicki, 2003). The characteristics ofthe valve shows that the valve closing is approximately10 time faster than valve opening. Equations (8–9)describe the relation between the needle valve open-ing n, and the valve capacitance and the saturation flowin case of the flow going out of the control space ofthe PRV.

In the case of flow going into the PRV control space,PRV closure, the needle valve capacitance is constantand equal to 0.11× 10−3 m3/(s ·m1/2).The same flow, q3, can also be expressed as a func-

tion of the displacement of the main valve (PRV)element, xm, as shown in equation (10).

The flow into the jet chamber through the modulationadjuster, q6, is described by equation (11), themodula-tion adjuster is a one-directional (into the jet chamberdirection) needle valve, and the flow is present if thepressure difference (ht2 − hcj) is greater than zero, oth-erwise the valve is closed. Capacitance, Cvma(n) iscalibrated for the number of opening, n, and is validfor 0≤ n ≤ 8.

where

The relation between the head drop and the flow, q4,in the pipe between the Pitot tube and T-junction, t2,is described by Darcy–Weisbach equation (12). wherethe total head, hout,t is equal the PRV outlet pressureplus the dynamic pressure in the Pitot tube.

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where

Finally, The flow from/to the Pitot chamber can beexpressed as differential equation (13)

The mass balance equations (14–15) for junctions t1and t2 respectively complete the algebraic part of themodel

The pump curve is measured, and the delivered head,hin, can be expressed as a cubic function of the mainflow

where qm is in [l/s] and hin in [m].The described model can be simplified by ignor-

ing the inertia and friction terms (the second andfirst derivatives of x’s) in equations (1, 2, and 3), andlooking at the experimental data, we can assume thatht1 = hcc, ht2 = hcpt , and hcj = hout..

7 RESULTS OF THE MATHEMATICAL MODELAND MEASUREMENT DATA

7.1 Steady state results

Initially, all dynamics and transient effects are ignoredand steady state equations are solved using the Math-ematica package. Effects of flow modulation adjusterare tested in steady state to evaluate the performanceof the controller.

7.1.1 Modulation adjuster effectThe modulation adjuster is a one-directional flow nee-dle valve, and is fully opened at 8 turns, and is used toset the maximum outlet head corresponding to max-imum main flow. Figure 7 shows the effect of thenumber of opening turns of the modulation adjustervalve on the modulation of the outlet head with flowrate for a variable inlet head according to the pumpcharacteristic. As shown in Figure 7 below as thenumber of turns increase the maximum outlet headdecrease linearly from 57 to 26m from completelyclosed to fully opened respectively, the opening turns0 and 1 have slight effect on the modulation, due tothe small variation in capacitance of the modulationadjuster valve from 0 to 1, as well the effect of open-ing turns 7 is same as opening 8. The rate of changeof the maximum outlet head decreases by about 8mfor each one opening turn from opening (2–6) and 4mfrom opening (1–2 and 6–7).

Figure 7. The effect ofmodulation adjuster on themaximum

outlet head.

Figure 8. Steady state model results compared with exper-

imental data for step decreasing followed by step increasing

of inlet flow.

7.2 Validation of steady state model

The steady state model, which is used to test theAQUAI-MOD® hydraulic controller performance andadjustment setting, is validated by comparing theresults of the model and the experimental data. Theexperimental main flow and the inlet head are used asinputs to the mathematical model with the same min-imum and maximum pressure adjustment settings. Inall cases the steady model results show a very goodagreement with experimental data in trends and mag-nitudes. Figure 8 shows the experimental inlet flow,inlet head and outlet head as well the results of themodel. In this case, the minimum pressure is adjustedby main pressure adjuster (6.5 opening turns) to be25m corresponding to the minimum flow of 2 l/s,and the maximum pressure is adjusted by modulationadjuster (4 opening turns) to be 37m correspondingto flow of 15 l/s. Minimum and maximum flow rateare chosen to be in the normal operating range for thePRV. A very good agreement of the results of steadystate model and experimental data is observed.

7.3 Dynamic and transient results

A full model including dynamics and transient effectof the controller and the PRV is also solved.The results

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Figure 9. Results of dynamic model compared with exper-

imental data for step decreasing followed by step increasing

of inlet flow.

of the full model are compared with the experimentaldata, and showed an excellent agreement in the valuesand trends as shown in Figure 9.Figure 9 shows the results of dynamic model com-

pared with experimental data for step decreasing fol-lowed by step increasing of inlet flow, with 3 openingturns of modulation adjuster and 6.5 of main pressureadjuster.

8 CONCLUSIONS

The AQUAI-MOD® hydraulic controller is a deviceto control and modulate the outlet head of the pres-sure reducing valve according to the flow velocity.Thecontroller is experimentally tested to assess its per-formance in different conditions and operating range.The controller in all cases show good performanceas it modulates the outlet pressure as expected. Ithas two adjustment set points for the minimum andmaximum head corresponding to the minimum andmaximum flow, respectively. The outlet head is mod-ulated between these two points. The mathematicalmodel of the controller has been developed and solvedwith the Mathematica package, in both steady stateand dynamic conditions. The results of steady statemode were compared with the experimental data andit showed a good agreement in the magnitude andtrends. The steady state model can be used to computethe required adjustment for the minimum and maxi-mum head set points before installing the controller inthe field. The full model of the PRV and the AQUAI-MOD® hydraulic controller including dynamic effectshas also been solved and the results showed again agood agreementwith the experimental data. In the caseof rapid decrease in the flow rate combined with rapidincrease in the inlet head, the PRV is fully opened,and the outlet is the same as the inlet for a few sec-onds then the controller closes the valve to the desired

outlet head. Such a situation should not arise duringthe normal operation of a water distribution system.In all other cases of flow changes the outlet head issmoothly modulated to the desired values.

ACKNOWLEDGEMENTS

The authors would like express their thanks to theAquavent company and Messrs Mark Lock and DavidHurley for the provided information about theAQUAI-MOD® controller and the collaboration during the testrig experiments.

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