Eindhoven University of Technology

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Modeling a control valve for periodic pressure oscillations

Hermans, S.J.M.

Award date:2002

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Modeling a control valve for periodic pressure oscillations

S.J.M. Hermans

DCT 2002.46

The use of turbo machinery in modern day Iife is widespread. The application area of these machines is limited for low mass flows by the occurrence of two physical phenomena: Surge and Stall. These phenomena cause a loss of efficiency, but in more severe forms can cause damage to the machinery and even complete breakdown. The common way of dealing with these phenomena is to avoid them altogether by defining a control line for low mass flows beyond which, operation of the machinery is not possible. A drawback of this approach is that the efficiency of the machinery is effected, and that the area in which the machinery can be operated is limited.

An alternative to the surge avoidance control is to allow the machinery to be operated in the area where surge and stall should normally occur, and deal with the phenomena by blowing of compressed medium in the same frequency as the oscillations. This active surge control would not only increase the operational area, but also limit the loss of efficiency in comparison to surge avoidance control.

This strategy requires control valves with a bandwidth higher than the highest os- cillatory mode that occurs in case of Surge or Stall, and a capacity big enough to blow off the amount of mass flow necessary to lower the pressure in the machinery with this frequency. In this report, the ASCO control valve is discussed as a possible candidate for active control of turbo machinery. A large number of measurements are presented to investigate the behavior of this valve under the process conditions dictated by this control strategy. As a result of these measurements, a model is presented that describes the behavior of the Asco control valve.

F'rom these measurement and simulation results, one can conclude that the capacity of one Asco control valve is insuiEcient for active surge control, but a number of valves mounted parallel to each other can easily overcome this issue. A second and more serious issue is raised by the limited bandwidth of the valve. The recommended way to alter the valves dynamics, is to slightly modify the mechanical operation of the valve. Since this is only a slight modification, the Asco control valve can be regarded as a suitable actuator for active surge control.

Contents

Abstract 2

1 Introduction 3

2 Surge in turbo-machinery 5 . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The operation of gas turbines 5 . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Aerodynamic flow instabilities 6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Greitzer model 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Control Strategies 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Surge measurement 11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Discussion 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Conclusions 15

3 Open loop control valve measurements 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Valve operation 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experimental setup 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Static valve characteristics 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Tuning of the valves 21 . . . . . . . . . . . . . . . . . . . . . . . 3.5 Quasi static valve characteristics 23

. . . . . . . . . . . . . . . . . . . . . . 3.6 Response to harmonic input signals 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Response to a sine-sweep 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conclusions 29

4 Modeling the control valves 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Model of the valve 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The static relation 32

. . . . . . . . . . . . . . . . . . . . . . . . 4.3 Modeling of the valve dynamics 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Discussion 38

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusions 39

5 Conclusions and recommendations 40

References 42

Samenvat ting 44

Dankwoord 45

Chapter -

Introduction

In modern life, the use of turbo-machines, pumps and turbines is widespread. The application field stretches from propulsion systems in jet aircraft to gas pressurization and transportation systems in process and chemical industries. The performance and efficiency of these compressors is limited for low mass flows by the occurrence of aerody- namic flow instabilities [I] called surge and rotating stall, which can lead to unacceptable thermal and mechanical loads to the shaft and the blades, endangering the safe operation of turbo-machines. In a mild form, the efficiency of the overall system decreases, while in extreme cases this can lead to complete failure or severe damage to the machine. Therefore the big community of users of these machines would benefit from methods that suppress these instabilities.

The common strategy to deal with these phenomena, is to avoid them altogether by imposing a control strategy based on a surge avoidance line that demarcates a "for- bidden" area in the compressor map. If mass flow through the system decreases to a level where surge may occur, the surge avoidance control system enlarges the mass flow through the compressor by opening a bleed or recycle valve behind the compressor. This prevents any damage to the system, but has a drawback: Surge avoidance control changes the operational range at the cost of the overall efficiency of the system.

This drawback can be minimized by using active surge control. Instead of demarcat- ing a "forbidden" area, in the compressor map, and preventing the turbo-machinery from entering that area, this control strategy ensures safe operation of the machinery in an area near the theoretical surge line. This results in a larger operational area and smaller bleed mass flows [2]. As [2] also shows, the requirements on the sensors and controller are relatively modest. The main challenge is to find valves with a sufficient bandwidth and capacity.

The goal of this study is to investigate the Asco control valve as a possible candi- date for active surge control. The bandwidth and capacity are the main parameters to be investigated. First, a number of measurements on surge in a laboratory scale turbo charger are presented. These provide an estimate of the surge frequency and the am- plitude of the pressure rise in the compressor during surge. These are translated into requirements on the mass flow capacity and bandwidth of the Asco control valve. The actual capacity and the bandwidth of the valve is then measured and compared to the

requirements for active surge control in turbo-machinery. With the insight gained from these measurements, a model of the dynamic behavior of the valves is derived, which is used to check the suitability of the valves for active surge control. The main focus is the modeling of the behavior of the valve.

In Chapter 2, the two aerodynamic flow instabilities, rotating stall and surge are discussed. During this discussion the choice for active surge control will be motivated and the required cqmcity and bandwidth of the valves is estimated. In Chapter 3, a number of open loop measurements on the ASCO valve are presented. These measure- ments will produce an estimate of the bandwidth and capacity of the valve and those generate the parameters for the model of the control valve, the derivation of which can be found in Chapter 4. With the insight gained by simulation results on this model, recommendations are made on how to increase the ASCO control valve capacity and bandwidth. Finally the conclusions and recommendations of this study can be found in Chapter 5 .

Chapter 2

Surge in turbo-machinery

2.1 The operation of gas turbines

In the operation of gas turbo-machines, there are three distinctive stages:

1. The compression of a gaseous fluid

2. The combustion of the compressed gasses

3. The expansion of the gasses over a turbine

In the first stage, a gaseous fluid is pressurized by the compressor. In the next stage, inflammable gasses are added and the combination of these gasses is ignited, causing a temperature rise and an increase in speed. In the third stage, this mixture of gasses expands over a turbine, delivering kinetic energy to the shaft.

Taking a close look at Figure 2.1, which shows an aircraft engine, one might notice that the compressor and the turbine are mounted on the same shaft. This way, the energy needed in the compressor stage is delivered by the expanding gasses in the turbine stage. External energy is needed to startup this process, and in steady operation a continuous compressor flow is required to keep the process of air compression, combustion and expansion going.

Figure 2.1: Aircraft engine

5

Figure 2.2: Compressor maps with speed lines (left) and stalled flow characteristics (right)

There are two main types of continuous flow compressors: the axial compressor (of which Figure 2.1 is an example), where the flow leaves the compressor in a direction parallel to the rotational axis, and the centrifugal compressor (see Figure 2.7 in Sec- tion 2.5), where the flow leaves the compressor in the direction perpendicular to the rotational axis. Rotating stall, surge and other flow instabilities occur in both types of compressors, causing a limitation of the efficiency and effectiveness of the compressor.

I \ A

2.2 Aerodynamic flow inst abilities

pressure

The operational area of compressors is limited for low mass flows by the occurrence of aerodynamic flow instabilities. Surge and rotating stall are two of these instabili- ties. The results of both rotating stall and surge cause a restriction of the performance (pressure rise) and efficiency (specific power consumption) of the compressor. More- over, the unsteady fluid-dynamic excitation results in additional periodic loads on the blades, causing blade vibrations and fatigue (and so reduces reliability and durability) and may even cause severe damage to the machine due to iinacceptable !eir& of system vibration [3, 41. In the next paragraphs rotating stall and surge are described and a classification is presented.

pressure

Rotating stall

Rotating stall is an instability phenomenon, in which a circumferentially uniform flow pattern in the compressor is disturbed. A local region (or regions) appear where the Bow is stagnant: the flow stalls. These regions propagate in the same direction as the blades at a speed of 20 to 50 percent of the blade speed (at least for fully developed stall; initial rotating stall cells move faster) [5 ] . The part of the area of the annular flow path the regions occupy may also grow with time, until a certain size is reached. Rotating stall may occur in some parts of the machine only (e.g. in some stages). The graph on the

Figure 2.3: Greitzer compressor and plenum model

right side of Figure 2.2 shows a compressor map during stall. Stall occurs if from point 1 the compressor mass flow is reduced. The compressor pressure rise drops dramatically to a new stable operation point, 2. Without further action, the system operates in this new operation point. Stall is regarded, at least for axial machines [6 ] , as an inception of a more severe and potentially dangerous flow instability problem, namely surge.

Surge

Surge is a self-excited cyclic phenomenon, affecting the compression system as a whole, characterized by large amplitude pressure rise and annulus-averaged mass flow fluctua- tions. Even flow reversal is possible. This type of behavior is a large amplitude limit cycle oscillation. It starts to occur in a region of the compressor map where the pressure rise versus mass flow characteristics for constant speed have a positive slope that exceeds a certain value determined by characteristics of the compressor and the slope of the load line. Essentially, the slope of the mass flow versus pressure rise characteristic, and the Greitzer stability parameter B are important.

2.3 Greitzer model

Greitzer defined a lumped parameter modei to study the nonlinear behavior of systems with low pressure-ratio axial compressors. Figure 2.3 shows a schematic view of the coxpressor a d p!enum parameters in the model. This model is based on the following assumptions:

1. One-dimensional incompressible flow in the ducts.

2. Isentropic compression process in the plenum

3. In the plenum,velocity is negligible and pressure is uniformly distributed.

4. Quasi-steady compressor and throttle behavior.

5. Influence of rotor speed variations is small

6. System's overall temperature ratio is near unity.

The model produces a dimensionless momentum equation for the compressor:

Where, (b is the dimensionless mass flow, t" the dimensionless time, & the dimensionless compressor pressure rise and (b the dimensionless plenum pressure rise. The dimension- less parameter B is defined as:

1 U o r : B = --

2 WHLC

where a is the speed of sound, Ac the duct area, Vp the plenum volume, LC the compressor duct length and U the compressor blade tip speed. WH is the Helmholtz resonance frequency, which is discussed in the next paragraph. For a given compressor, the system will exhibit surge if the slope of the compressor characteristic dAP/d (b exceeds a critical value. If dAP/d (b is less than this, the compression system maintains itself at an overall equilibrium point. Linear stability analysis predicts that the system is unstable when

with T' the slope of the load line [6].

Classification of r o t a t i n g stall a n d su rge

The essential differences between rotating stall and surge are that the average flow in pure rotating stall is steady in time, but the flow has a circumferentially nonuniform mass deficit, while in pure surge the flow is unsteady but circumferentially uniform [7]. Because it is steady, rotating stall may be local to (parts of) the compressor. Surge, on the other hand, involves the entire compression system, so the phenomena can be regarded as distinct. On the other hand, both phenomena are natural oscillatory modes of the compression system (with surge corresponding to the lowest or zero order mode) and thus they are related [8, 91. There are several classifications for rotating stall:

Part-span and full-span: only a restricted region of the blade passage (most often the tip) or the complete height of the annulus is stalled.

Small (large) scale: a small (large) part of the annular flow path is blocked.

For a typical rotating stall pattern, displayed in the compressor map, see Figure 2.2: Surge has a more complex topology than rotating stall. At least four different categories of surge, with respect to the flow and pressure fluctuations, can be distinguished [lo, 6,3].

Mild Surge: a phenomenon with small pressure fluctuations and a periodicity governed by the Helmholtz resonance frequency, which is thus the inverse of the characteristic time of the compression system during this stage of surge. Flow reversal does not occur.

Figure 2.4: Compressor map with surge line (left), and one with a deep surge cycle (right)

Classic Surge: with larger oscillations and at a lower frequency than mild surge (al- though high frequency oscillations may be present also: the dynamics is nonlinear and introduces higher harmonics), but no flow reversal.

Modified Surge: where the entire annulus flow fluctuates in axial direction and rotat- ing stall is superimposed, so the flow is unsteady and non-axisymmetric. It is a mix of rotating stall and classic surge phenomena.

Deep Surge: a more severe version of classic surge, where even flow reversal is possible. This is an unsteady, but axisymmetric limit cycle for the flow. The frequency is set by the plenum emptying and filling time, which is well below the Helmholtz frequency.

Note that the terminology is not unique, e.g., in [ll] the term classic surge is used for the phenomena that are termed here modified surge. Figure 2.4 shows an example of a deep surge cycle depicted in the compressor map. The cycle starts at (I), where the flow becomes unstable. It then goes very fast to the negative flow characteristics at (2) (approximately represented by the straight line) and descends until the flow is approximately zero (3). Then it proceeds very fast to the normal characteristics at (4), where it starts to climb to point (1). Arriving at point (1) the cycle repeats, unless measures are taken to avoid that. For both axial and radial compressors, one or some of the surge categories mentioned above may occur in sequence. This means that a control strategy, in order to be robust, has to deal with all these categories simultaneously.

2.4 Control Strategies

There are mainly two ways to make sure that the safe operation of turbo-machinery with respect to surge and stall is guaranteed. Either avoid the operation of the machinery near

stall line load line with actzve surge avoidance line <

Figure 2.5: Control strategies (left) and valve capacity Q versus bandwidth wb trade-off

the surge line (surge avoidance control) or make sure that the machinery can be operated in this unstable operational area in a safe way (active surge control). This last option increases the operational area of the machinery considerably as is depicted in Figure 2.5. This is done by placing fast valves between the compressor and the combustion chamber that eliminate the pressure fluctuations behind the compressor by releasing compressed medium in phase with these fluctuations. This requires valves with a bandwidth that is at least twice the frequency of the surge frequency. The next paragraph provides some measurements on the surge frequency, which results in requirements for these valves.

Most important at this stage is to understand the major difference between active surge control and surge avoidance control. If the load mass flow requirement is too low, the first strategy uses a constant bleed mass flow to allow the overall system to operate in an operation point that would normally cause the compressor to surge. Active surge control uses control valves that prevent the system from going into surge by actively blowing off plenum gas in phase with the pressure signal in the plenum. Moreover, the operational costs for turbo-machinery using active surge control are significantly lower than for those using surge avoidance control [2]. This is due to the fact that surge avoidance control causes a larger bleed flow than active surge control.

This difference in control approach implies that the requirements on the sensors and actors used in the control loop are set accordingly. In surge avoidance control, the main issue is the maximum allowed bleed flow. This is the limiting factor on the control loop. In active control, the bandwidth of the control valve is more important. This should be large enough to deal with the plenum pressure variations which in mild surge occurs at approximately the Helmholtz frequency. Assuming that the space to install multiple valves is available, the capacity of these valves is less important. As long as it is cost effective, more valves can be installed parallel to reach the required flow. Figure 2.5 shows the classic trade-off between valve bandwidth and capacity. If bandwidth is uncompromisable, the number of installed valves need to be chosen so that the required capacity is met.

@ pressure

Orifice @ Temperamre

b Y a Valve position

blow-off - @ Number of revolutions

Turbine

Combustion chamber

'r I

Air I

Nuturul gas

I I Vessel

Turbine throttle I

I Compressed

air

Figure 2.6: Outline of the gas turbine installation

In the next paragraph, a number of measurements on a laboratory scale compressor installation are presented. The main goal in these measurements is to estimate the (Helmholtz) surge frequency of this installation. An attempt is made to produce a first order estimate of the bleed flow at surge as this will be useful in determining the valve capacity to be used for active surge control on this installation. This knowledge will be the basis of the valve selection and validation that follows in the next chapters.

2.5 Surge measurement

Up to this point, the discussion of rotating stall and surge has been purely theoretical. In order to get a grasp of the effects of surge on a compressor, measurements have been done on a laboratory scale low speed radial compressor with a vaned diffuser.

From the steady state compressor performance, a compressor map can be determined which provides the steady state mass flow versus pressure rise characteristic as well as an estimate of the surge line. This steady state performance is used to produce an estimate of the necessary controi valve capacity. This is no more than a ~oiigh impression as the dynamic mass flow through the compressor can not be measured directly (eg with the use of a flow meter).

Using dynamic measurements of the system in surge, the surge frequency is de- termined. From these measurement, a minimal bandwidth of the controller valves is determined. The next paragraph introduces the laboratory scale compressor system that is used.

Experimental set up

Surge is investigated in the gas turbine installation [12] shown in Figure 2.6. Similar to the experiments described in [6], the test turbocharger is driven by the turbine. The compressor discharges via the compressor blow-off valve, which is placed closely

Figure 2.7: (BBC VTR 160L) Compressor

Im~eller I Value I Vaned Diffuser I Value

Table 2.1: Compressor parameters BBC VTR 160L

number of blades inducer inlet diameter (casing) dl,, inducer inlet diameter (hub) dl,h impeller diameter d2 impeller exit width b2

to the compressor, and the blow-off duct into the laboratory room. Figure 2.7 shows a demonstration model of the turbocharger (BBC VTR 160L), which is used in the experiments. The turbocharger consists of a low-speed, single-stage, radial compressor with an un-shrouded, radial ending impeller without back sweep and a diffuser with straight vanes, which is mounted on the same rotational axis as the axial turbine. Due to the small plenum volume, the occurring surge oscillations are assumed to be relatively harmless to the machinery. Additionally the steady-state compressor characteristics can be determined up to relatively low mass flows. Contrary to [6], the external supplied compressed air flows into a combustion chamber where natural gas is added and burned. The hot exhaust gases expand over the turbine and deliver the power to drive the compressor. Relevant compressor parameters are incorporated in Table 2.1.

The duct between the compressor outlet and the compressor blow-off valve is small compared to the wave length of the surge oscillations. Therefore, the pressure fluctua- tions measured in the compressor outlet duct are not associated to a standing pressure wave pattern [13]. More detailed information about the experimental setup is given in [14].

The uncertainty of the measured rotational speed, the compressor outlet pressure, and the compressor mass flow, determined from the measwed noise level and expressed

20 0.106 [-] 0.054 [-I 0.180 [m] 0.007 [m]

number of vanes vanes inlet diameter ds vanes outlet diameter d4

45 0.215 [m] 0.258 [m]

Figure 2.8: Steady state compressor performance (left), and surge initiation pressure (right)

in percentages of the mean value is 0.6%, 0.4% and 4% respectively [12]. Measurements of the transients into and during surge consist of data from the high-frequency response pressure probe at the outlet of the compressor, the blow-off valve position sensor and the rotational speed transducer. Each measurement is triggered by a certain blow-off valve position. While closing the blow-off valve a "trigger point" is reached and data is acquired for 15 [s] with a sample frequency of 200 [Hz], which is far above the expected surge frequency.

Experimental results

Steady-state measurements are performed to find the mass flow where surge is initi- ated. Figure 2.8 shows the dimensionless plenum pressure rise $ (defined in the Greitzer model) versus the mass flow (in [kgls]) through the compressor. The lines represent the performance of the compressor at various constant rotational speeds. The dotted line represents a fit of the surge line. The mass flow through the compressor at surge initistion ranges from 0.15 to 0.25 [Kg/s].

The measurement points on the surge line in Figure 2.8 are determined from pressure measurements during surge initiation. Surge initiation is defined as the point where the amplitude of the pressure trace starts to grow. While the mass flow is further reduced, the amplitude of the pressure oscillations grows rapidly. Due to a constant shaft power, the reduction of the mass flow results in a slight increase of the mean rotational speed and a decrease of the mean pressure. For fully developed pressure oscillations, a frequency of about 20 [Hz] is found. Surge data is collected for different shaft powers, and so for different rotational speeds. The surge frequency has been determined from a spectral analysis of the fully-developed pressure oscillations with an accuracy better than 0.5 [Hz] . Figure 2.9 shows the obtained surge frequency versus the rotational speed. In some literature [15] and [16] it is stated that the impeller speed did not noticeably change the surge frequency. Such a conclusion can not be drawn from the results shown

Figure 2.9: Surge frequency (left), and surge frequency ver- sus the position of the blow-off valve (right)

in Figure 2.9. The surge frequency versus the position of the blow-off valve is plotted in Figure 2.9, '0' denotes a closed blow-off valve, while '1' denotes a fully opened valve. In the investigated speed range, the position of the blow-off valve appears to determine the surge frequency.

2.6 Discussion

Valve capacity

The required valve capacity for active surge control depends on how much the operational area of the compressor needs to be increased. In [2] this the most ambitious control strategy requires a valve capacity equal to 7 percent of the throttle valve capacity. Or in terms of K, : K, = 10.6 [m3/hr]. This K, factor is defined in the next chapter, when valve measurements are presented.

This seems an ambitious requirement, but bear in mind that the capacity of the control valve(s) can easily be increased by placing more valves in parallel. This gives us ail the necessary freedom to increase the number of valves if the actual required capacity turns out to be more than was estimated. Increasing the bandwidth of the valves is more difficult (if not impossible), so the calculations on the required bandwidth of the valves need to be as accurate as possible.

Valve bandwidth

The measurements on the laboratory scale compressor installation show that surge ini- tiation typically occurs at a frequency of f 20 [Hz]. This frequency does not depend on the compressor blade tip speed n, but on the compressor duct length and area (LC and A, respectively) and the plenum volume Vp. Since these parameters do not de- pend on the mass flow, the surge frequency for a certain compressor installation does not depend on the operation point. This means that this freqilency can be determined

during the design of the installation. The requirements on the bandwidth of the active surge control valves are then known. As a rule of thumb, a control valve bandwidth of 5 times the surge initiation frequency is generally accepted. This results in a control valve bandwidth requirement of 100 [Hz]. The next chapter shows some measurements on the ASCO control valve using a small test-bench. The requirements are then compared to the actual performance of this valve on the small test-bench. The results will determine

n .. . . if this is a d i d candidate foractive surge control applications on the tall laboratory scale compressor installation.

2.7 Conclusions

A number of conclusions can be drawn from the combined theoretical discussion and experimental approach of surge presented in this chapter.

1. Rotating stall and surge in a compressor are closely related, and can not be dis- cussed and treated separately. So the reader should bear in mind that both phe- nomena occur simultaneously while performing surge measurements.

2. The required control valve capacity is strongly related to the control strategy and the required increase of operational area. For the one sided bounded feedback strategy proposed in [2] on the compressor installation presented in this chapter, the required K, value is 10.6 [m3/hr] .

3. The surge frequency of the fully developed pressure oscillations is f 20 [Hz] . Applying the generally accepted rule of thumb that the control valve bandwidth should be at least 5 times this value for active surge control, this leads to a required valve bandwidth of f 100 [Hz] .

4. The amplitude of the fully developed pressure oscillations is f 0.15 [bar].

The next chapter presents measurement results for the ASCO control valve on a small scale test-bench, and determines the suitability of this valve for active surge control on our full laboratory scale compressor installation.

Chanter r - 3

Open loop control valve measurements

The previous chapter presented an overview of the processes and parameters that play a role in describing surge and stall. An approach for active surge control was sketched, and conclusions were drawn concerning the design requirements of control valves to be used for active surge control. The conclusions in Section 2.7 provide two important requirements for the selection of an appropriate valve:

1. The capacity of the valve should be at least K, value is 10.6 [m3/hr].

2. The required bandwidth for the valve is 100 [Hz] .

To check if the Asco control valve meets these requirements, a number of measure- ments on the valve are presented in section 3.2. Before addressing the experimental setup for these measurements, the valve operation is explained in Section 3.1.

3.1 Vaive operation

Figure 3.1 shews a schematic view of the wcrking principle of the A~~~ type Po~if iow SC E202.026V. The valve controls the amount of gas flowing through the orifice by the position of the core. The steady state of the valve is closed, which means that the flow area of the tube is blocked completely. The control valve is operated by an electrical signal that causes a core in a coil to move due to electro-magnetic forces. The core functions as a shutter to the orifice; by the movement of this core, the size of the orifice is adjustable. The measurements presented in this chapter show that this relationship is not linear, which means that control systems using this valve will have to deal with these non-linearities. The relation between the electrical signal to the valve and the width of the orifice can be manipulated by the use of a number of potentiometers. These potentiometers are used to set the application area of the ASCO control to meet the requirements of active surge control as closely as possible. This tuning of the valve is described in Section 3.4.

Figure 3.1: Valve operation

Compressed air

Mass flow controller

Figure 3.2: Experimental setup

3.2 Experimental setup

Design considerations

A test setup has been built as shown in Figure 3.2. Table 3.1 shows a list of the main parts of this setup and their properties. It was designed to test if the ASCO control valve can meet the requirements for active surge control. The following considerations and restraiiits have led to this design:

1. It is impossible to measure the mass flow through the valve.

2. Pressure sensors can provide a good alternative, since these sensors are capable of picking up high frequency signals without disturbing the flow.

These considerations have consequences for the design of the measurement:

A model is needed to calculate the valve mass flow from the pressure difference over the valve.

The pressure sensor should be placed as close to the valve as possible to provide maximum accuracy for the measurement.

Equipment Tank Plenum BRONKHORST mass flow controller I Type F -2O3AC- FA-55V BRONKHORST mass flow controller I1 Type F-202C-FA-44V Asco cor,',rol vdve Type Posiflow SCE202.026V

property 8.8 Ill

7.9.10-~ [zj

1250 [ l ~ / m i n ]

65 [ l ~ / m i n ]

0.72 [m3/hr]

Table 3.1: Equipment and relevant properties

The plenum before the valve should be small in order to obtain a small time constant for the measurement system (a deviation of mass flow is measured imme- diately as a deviation in plenum pressure without a significant lag time).

The mass flow into the plenum should be kept constant during the experiment. The pressure in the plenum is then only related to the valve mass flow.

Operating principle

The test-bench consists of, a mass flow controller (actually two different controllers were used during the experiments), a tank, a throttle and a control valve as well as two pressure sensors. See Table 3.1 for specifications. An external source provides the test rig with air at f 7 [bar]. The air flow is controlled by the mass flow controller. The flow is then led into a tank, to provide a buffer (which de-couples the influence of the mass flow controller from the valve effects under investigation). The tank exit is equipped with a manually adjustable valve. This valve should be set to a position that ensures a supersonic mass flow speed through the valve in case of dynamic valve tests. The mass flow into the plenum then only depends on the tank pressure, so the control valve actions do not influence the mass flow into the plenum. When performing (quasi) static valve tests, the position of the manually adjustable valve is less critical, the pressure in the p!emrn g h s a re!ia.b!e estim&,te fer the cmtra! mass flow in this case. The m ~ j m i t y of all experiments were carried out using BRONKHORST MASS FLOW CONTROLLER 1 , while BRONKHORST MASS FLOW CONTROLLER I1 was only used to determine the static flow curves for mass flows 5 1-10-~ [kgls].

Input and output parameters

There are three inputs to this system, the mass flow mmfc, the throttle position Ut, and the control valve signal U, which dictates the control valve position. Likewise, there are three system outputs, the pressure in the tank Pt, the pressure in the plenum Pp, and the mass flow through the control valve m,. Assuming isentropic compression, the mass balance for an arbitrary volume V, with mass Aow in mi,, and mass Aow out rizOut can be written as:

/ Control valve I mC = et (Kc, potl, pot3, Uc) Pp / me = ct (Kc, potl, p0t3, Uc) dPp - Po / Table 3.2: Mass flow descriptions for the throttle and the control valve

Throttle

This equation can be specified for both the tank and the plenum in the test setup, producing the following equations:

Supersonic Subsonic P P

kt = Ut Kt Pt

In these equations the input and output mass flows are not yet specified. The shape of these equations depends on whether the valve mass flow is sub- or supersonic. The mass flow depends on the ratio of the pressures on both sides of the orifice, it reaches supersonic speed in the orifice if _< 0.53 and subsonic otherwise.

In case of a subsonic speed the mass flow scales with the square root of the pressure difference over the orifice, while in case of a supersonic mass flow speed, the mass flow through the orifice scales linearly with the absolute pressure in front of the orifice. This leads to descriptions for the throttle and valve mass flows for both sub-, and supersonic mass flow speed as described in Table 3.2. In these formulae, Ut and Uc represent the (normalized) valve signal, Kt and Kc denote the valve capacity specified by the valve manufacturer, while poti and pot3 refer to settings of the valves potentiometers. These relations are described in Chapter 4, where the valve model is introduced.

3.3 Static valve characteristics

The previous sections described the function of the control valve, and the way it operates in the experimental setup. This section focuses on the static valve characteristics which are carried out on the experimental setup. The following sections elaborate on this, by describing quasi-static and dynamic valve measurement results.

The first measurements are designed to determine the static characteristics of the control valve. Point of interest in these tests is the maximal amount of air through the valves for a specific pressure drop over the valve. From the valve capacity, the required amount of valves can be calculated by simply dividing the required capacity for active surge control by the valve capacity. During these measurements, the throttle was fully opened, causing subsonic mass Sow conditions through the throttle. Only very large mass

Mass Flow vs Conuol S~gnal for different plenum pressures

Figure 3.3: Mass flow as a function of the control signal Uc

flows will cause a pressure ratio between the tank and the plenum which is large enough for supersonic mass flow to occur in the throttle. These measurements were conducted in the following manner, first the desired control valve position is set by means of the electrical signal Uc between 0 and 10 [V], after which the mass flow controller is opened to a position that causes a specified pressure level in the plenum (and a supersonic pressure ratio over the throttle). This mass flow level, which causes the required plenum pressure is drawn as a function of the control valve voltage in Figure 3.3.

The two low pressure characteristics in Figure 3.3 show clearly that the relation between the control valve signal U, and the mass flow through the valve m, is nonlinear. The characteristics for plenum pressures of 2.0 and 2.2 [bar] are less clear because these could not be continued for larger mass flows due to instrumentation limits. Since the plenum pressure is the same in all cases this cannot be the cause of the nonlinearity, so two possible causes remain:

1. The relation between the position of the coil x and the area of the orifice in the valve is nonlinear.

2. The relation between Kc and the value of the flow coefficient Cc causes the non- linear relation between Kc and m,.

The influence of both these phenomena is the subject of study in Chapter 4 where the parameter estimation for this valve is presented. The most important conclusion to be drawn from these measurements is the maximal static valve capacity. If we take a look at the characteristic for Pp = 1.5[bar], we can conclude that the static valve capacity is 3 - 1 0 - ~ [kgls]. The operational area of the valve reaches from 3 to 10 [V] incorporating the range from 0.2.10-~ to 3 - 1 0 - ~ [kgls]. The manufacturer defines the capacity of the valve in the Kv factor defined in Equation 3.4. The claim that the valve has a capacity of 0.72 [m3/hr] does not meet the measurements presented here. The resulting K, value

for the Asco valve is: Kv = 7.0 1 . 2 9 1 ~ - J"03.10-3 - C.46 [m3/hr] .

Invloed potenliometer 1

t Mmfc

10-3Mass Flow vs Convol S~gnal for d~fferent P1 settmgs. Pp=l 5 Ibal

35r

Potl = -720 [deg] Potl = -360 [degl Potl = 0 [deg] Potl = 360 [deg] Potl = 720 [deg]

Figure 3.4: Influence of potentiometer 1 on the mass flow characteristics with (left) the theoretical influence as specified by the manufacturer, and (right) the measured influence

In the next sections, the (dynamic) operational area of the valve is investigated. But first the valve is tuned to make the mass flow versus input voltage curve as linear as possible.

3.4 Tuning of the valves

In order to enable the user of these valves to adjust the relation between the electrical signal led to the valve, and the width of the orifice (and thus the mass flow through the orifice) the valves are equipped with a number of potentiometers which influence the

sC t,at,ic A m a d dynaEic behavior. The eEect of the tm pote~ttiometers that influence the valve's static behavior are depicted in Figure 3.4 and 3.5. Each figure shows the theoretical effect of the potentiometer as claimed by the manufacturer on the left-hand side, and the measured effect on the right-hand side. The measurements were performed by turning the potentiometers, one at a time, over a complete rotation clockwise (denoted by the -) or counter-clockwise (denoted by the +). The plenum pressure Pp was set to 1.5 [bar] each time, while the valve control signal U, varied between 2 and 10 [V].

The characteristics show discontinuities for mass flows smaller than approximately 1 .10-~ [kgls]. These are the result of the fact that two different mass flow controllers were used for these experiments: BRONKHORST MASS FLOW CONTROLLER I for mass flows > l . l ~ - ~ [ k ~ / s ] BRONKHORST MASS FLOW CONTROLLER I1 for smaller mass flows. First, all measurements for one mass flow controller were conducted (over the full poten- tiometer range), and then the mass flow controllers were swapped, and the experiments

I Mmfc

Invloed potentiometer 3 10-3Mass Flow vs Control Signal for different P3 settings, Pp1 5 [bar] 3 5r

Figure 3.5: Influence of potentiometer 3 on the mass flow characteristics, (left) the theoretical influence as specified by the manufacturer, and (right) the measured influence

were repeated for all potentiometer values. This explains the discontinuities in the char- acteristics. The setting of the potentiometers is not precise enough to be reproducible.

Close examination of the measured potentiometer influence in Figure 3.5 shows that the characteristic for pot3 = -720 deg] for input signals between 2 and 3 [V] does not match with the characteristic for larger input signals. This is caused by an erroneous setting of the potentiometer. Apparently the pot3 = -360 [deg] is used during this measurement.

The right hand sides in both Figure 3.4 and Figure 3.5 show that the effects of the potentiometers on the mass flow is not as big as we are led to believe by the specifications for the Asco valve. Moreover, the effects of both potentiometers are not independent.

First, potentiometer 3 is be adjusted in such a manner that the characteristics for maximal flow and U, = 10 [V] no longer show a horizontal part. This horizontal part can be explained as saturation of the valve. Then potentiometer 1 is used to move the operating point for minimal mass flows to lower valve voltages as far as possible. .-7 . lnis operation disturbs the settings ~f potentiometer 3 (saturation is re-introduced in the characteristics for high mass flows). This means that the previous steps have to be repeated two or three times, until no more improvement is made. The relation between the input signal U, and the mass flow through the control valve is now as linear as possible over the operational area with a minimal amount of saturation. The setting of the potentiometers is validated in the next section using quasi static measurements.

The measurements described in Figures 3.4 and 3.5 show that the influence of the potentiometers as specified by the manufacturer of the valves is rather optimistic. At best, the potentiometers enable the user to influence the opening voltage and the slope of the curve over a small range. This is not sufficient to guarantee linear behavior of the valves over the full operating range. This implies that the control strategy will have to account for a non linear valve characteristic, which will be taken into account in the model that will be presented in Chapter 4 .

Asco statlc valve characteristics

. .

o 4 , : : : ' j.(.-.\,;..:::;;:;,<;.h; . . . . . . .

. .

. . . . . . . . .

0 . 2 L ' ' " ' ' ' ~ ~ 0 1 2 3 4 5 6 7 8 9

Uc(t) [vl

Figure 3.6: Quasi-static measurements on the Asco control valve

3.5 Quasi static valve characteristics

The previous section described the influence of the potentiometers on the static behavior of the valve. The effect of these proved to be less then specified. Still the valve charac- teristics are now set as linear as possible by these potentiometers. The next step is to validate these settings by investigating the quasi static behavior of the valves. The main point of interest for this measurement is to find the linear operating range, the saturation point and the amount of hysteresis. To measure these, the following conditions need to be met:

1. The tank pressure needs to be set to a level that guarantees supersonic mass flow into the plenum.

2. The control valve input signal may only be varied slowly.

3. The variation of the input signal must be the same for each cycle in order to be abk to detect hysteresis.

The first condition ensures a constant mass flow into the plenum during the mea- surement. The second condition ensures that the measured plenum pressure gives an accurate estimate of the momentary control valve mass flow (this means that no valve dynamics are measured). Figure 3.6 shows the results of three measurement runs. The plenum pressure was measured as a function of the control signal over a period of 720 [s]. This was repeated for different mass flows. Outstanding fact in these figures is the flat characteristics for large values of the control signal (for the two lowest mass flow rates). It seems like the valves saturation point is reached. Further opening the valve no longer has any effect on the amount of mass flow through the valve (and thus the pressure in the plenum). This is consistent with the fact that the potentiometers are tuned so that the mass Bow through the valve scales linear with the valve control signal for low input

Plenum Pressure response to 1 [Hz], 0.5 [V] input at various U-(cO1 levels

time [s] time [s]

Figure 3.7: Different Uco, frequency leftl, and right: 20 [Hz]

range. However, the large pressure difference over the valve at the saturation point is not well understood. The most plausible explanation is that the valve is not fully opened at this saturation point. This does not influence the dynamic measurements presented in the next sections, but should absolutely be addressed before using the valves in an active surge control loop.

The data in Figure 3.6 shows that a certain amount of hysteresis is present in the valve, but this is below 5% maximum that is specified by the manufacturer.

The influence of the nominal voltage Uco

The static valve characteristics (mass flow versus control signal), presented in Section 3.3 are not linear. Which means that the valve behaves differently to harmonic signals with different nominal voltages. This phenomena is the focus of our attention in this section.

The tests were designed using one fixed mass flow of f 2. l . l0-~ [kgls]. The nominal control valve voltage Uco was applied to the valve, and after a short period of time the system settled to a stationary state. Then a harmonic signal was added to the nominal control valve signal giving: Uc = Uc, + A sin( f 27rt). The results are printed in Figure 3.7. The left hand figure shows the resulting plenum pressure signal for f = 1 [Hz], while the right hand figure shows the plenum pressure signal around the surge resonance frequency (f = 20 [Hz]). The amplitude was 0.5 [V] for all experiments, while the nominal voltage Uco was set to 3, 4 and 5 [V]. The flat signal for low plenum pressures we encountered earlier returns here, as was to be expected because of the saturation of the valve. The high pressure peak levels for 20 [Hz] signals are bigger than we have seen before.

Plenum oressure resDonse to 1 lHzl inDut at various amuliudes Plenum pressure response to 20 [Hz] input at various ampliudes

time [s]

Figure 3.8: The influence of amplitude A, frequency f leftl, and right: 20 [Hz]

3.6 Response to harmonic input signals

The influence of amplitude A

Figure 3.8 shows the influence of the amplitude A of the control signal Uc on the plenum pressure Pp for a fixed mass flow. The control signal is:

U, = Uco + A sin (f 257t) (3-5)

The left side figure shows the results of input signals with f = 1 [Hz], while the right side figure shows the influence of different amplitudes for f = 20 [Hz] on the plenum pressure. The following procedure has been followed to obtain these results:

The control valve signal Uc was set to a nominal value of U, = 4 [V].

The controller mass flow was set to mmfC = l.88.10-~ [kgls] .

= The throttle was set,, so that ,pt = 3.38 [bar].

The frequency f is 1 (left), and 20 [Hz] (right), while the amplitude A is varied according to the data in the legend.

The figures show that this system behaves almost linear (shows a harmonic output signal as a result of a harmonic input signal) for low frequency control signals (at 1 [Hz]) up to an amplitude of 1 [V], while at a frequency of 20 [Hz] only the signal with an amplitude of 0.25 [V] shows a harmonic plenum pressure. The power spectrum density presented in Figure 3.10 also shows the two main characteristics of a linear causal system (although the second condition is only met for limited amplitudes of the input signal):

1. The response to a harmonic input signal of limited energy is a harmonic, limited energy, output signal with the szme frequency.

Plenum pressure response 5 +- 1 M inplrt a1 various fmquencies

. . . o . z 5 ~ ' " " ' r ' i

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lime [s]

Planum pressure response 5 t 1 [!Il Input at varlous frequencies

0 9

0 8

0 5

0 4

0 3

0 002 004 006 008 0 1 012 014 016 018 0 2 tlms [s]

Figure 3.9: The plenum pressure as a result of a Uc signal with an amplitude of 1 [V] and different frequency settings between 1 and 20 [Hz]

2. The response to an input signal of amplitude 2A is an output signal, with an amplitude which is 2 times the response to an input signal of amplitude A.

The higher the frequencies and amplitudes of the input signal Uc, the less these conditions are met. The response to large pressure input signals show almost a block signal as the minimal pressure is reached, while (especially at a frequency of 20 [ H z ] ) the pressure signal reaches sharp and high peak levels. During these 20 [Hz] experiments, the noise level coming from the valves is noticeably higher than during experiments at other frequencies. This, together with the high power spectrum density presented in Figure 3.10, indicates that the valves have an eigenfrequency at f 20 [Hz]. In Section 3.7 a number of transfer function measurements are presented that indeed show a maximum at f 20 [Hz] .

The influence of frequency f

As we szw in the preview section, the frequency of the control signal for the control valve largely influences the amplitude of the plenum pressure. This effect is studied in detail in this section. The experimental approach is the same as in the previous tests. First a static signal UCo is applied to the valve, then the mass flow mmfC is set to a level that ensures a supersonic mass flow speed through the throttle. When the tank pressure has reached a stationary value, a harmonic input signal is sent to the control valve Uc = Uco + Asin(f2nt). This is done for different values of the control signal frequency f , and the results are incorporated in Figure 3.9.

The figures are scaled so that a representative number of complete cycles could be fitted on. This means that the x-axis scaling is different for all figures. Comparing these figures, one finds that the amplitude of the plenum pressure grows with the frequency of the input signal until a frequency of rz 20 [Hz]. For higher frequencies the amplitude of the plenum pressure becomes increasingly smaller. This is consistent with the results

in the Section 3.6 where we found that for different amplitudes of the input signal, the plenum pressure oscillated with a higher amplitude for 20 [Hz] input signals than for 1 [Hz] input signals.

Another striking fact in the figures is again the "chopped off" sinusoYda1 plenum pressure signal for low pressures. This saturation effect has also been discussed in pre- vious sections, so we will not discuss this again at this point. The sharp peaks for high pressure values for input signals around the 20 [hTz] reinforce the theory that this is a eigenfrequency of the valve.

3.7 Response t o a sine-sweep

The previous paragraphs dealt with the response in terms of the plenum pressure to different input signal variables. The purpose of these exercises was to gain insight into the influence of each of these terms independently on the plenum pressure. In this paragraph the scope is shifted towards the transfer as a whole. The transfer function is estimated on the basis of a number of so called sine-sweep experiments. These are experiments in which a harmonic input signal with a constant amplitude, and a linearly increasing frequency is being sent to the control valve during a fixed period of time. The control valve signal can be written as:

Uc = Uc(ol + A sin (2?i f t ) with: f = fmax--L Tend

Figure 3.10 shows the plenum pressure during two sine-sweep measurements. The nominal control valve voltage Uco was 4 [V] , and the amplitude A was 0.25 [V] each time. A few variables in this formula deserve some elaboration:

fmax: The maximum frequency of the input signal fmax determines the frequency range for which the measurements are valid, and a the range for which a transfer function can be estimated. Left fmax = 100 [Hz] and right fmax = 250 [Hz]

Tend: The end time Tend is the moment at which the maximum frequency is reached. This defines the length of the measurement interval. The Shannon theorem states that this limits the lowest detectable harmonic oscillation following the following definition: fmin = &. This is plausible if one realizes that two measurement points on one period of an unknown harmonic signal uniquely define that harmonic signal. In both Cases Tend = 100[S]

6t: The step size 6t determines the total number of measurements made during the measurement period T, which limits the minimum of the frequency step size. Here 6t = 1. [s]

The transfer function estimates show an increase in gain at f 20 [Hz] , and a band- width of f. 50 to 60 [Hz] . This limits the application area of this valve. The measured bandwidth is lower than the requested 100 [Hz] and the increase in gain around the surge frequency of the compressor is reason for concern about the fitness of this valve for active surge control.

Plcnum pressure response to a sinesweep . . . . . . . . . . . . . . . . . . . . . . . . Plenum pressure response tor sinesweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . .

Transfer function estimafe 0

Figure 3.10: Plenum pressure as a result of a sine-sweep control signal U,, and the corresp~nding transfer f~l.nct,ion estiaates

3.8 Conclusions

The previous sections presented a large number of measurements on the Asco control valve. The main conclusions are:

e The Asco control valve characteristics are measured at a pressure difference of 1.5 [bar] mer the v . 4 ~ . The maximxn mass flow through the valve at with this pressure diEaence is & 3.19. l g U 3 [kgls] .

0 In terms of the Kv value specified by the manufacturer, the valve capacity is 0.46 [m3/hr]

The valve has an eigenfrequency of f 20 [Hz] .

The bandwidth of the valve is limited to 31 50 - 60 [Hz] .

Chapter 4 will present a model for this control valve.

Chapter - 4

Modeling the control valves

The measurements presented in the previous chapter show, that both the capacity and the bandwidth of the Asco control valve do not meet the requirements for active surge control. The capacity of the valve of 0.46 [m3/hr] is only 4.3 percent of the required capacity (that is 10.6 [m3/hr]). The measured bandwidth of 50 to 60 [Hz] is too low compared to the rule of thumb of 100 [Hz], and the increase in the measured transfer function at f 20 [Hz] is reason for concern too. In general, the bandwidth and the capacity of a valve are related as depicted in 4.1. This graph shows that choosing a valve with a bigger capacity than the ASCO control valve will result in a lower bandwidth (and vice versa).

It is clear that more insight is needed in the operation of the Asco valve to produce a solution. This chapter presents a model of the test setup used in Chapter 3 including the Asco control valve. The model is validated using the measurements in the previous chapter. This model is then used to gain more insight in the behavior of the valve. That enables us to come up with a solution to the problem of finding a suitable control valve.

4.1 Model of the valve

Figure 3.2 shows the measurement setup used in the previous chapter. It consists of a mass flow controller, a throttle, a tank, a pressure tracsducer and the ASCG ce~trol valve. Figure 4.2 shows the model of this measurement setup. In this model, the mass

Figure 4.1: Tradeoff between valve capacity and bandwidth

Valve model Valve input

*

Figure 4.2: Simulink representation of the measurement setup

Potentiometers Dynamics Valve area ass flow

4

Figure 4.3: Physical background of the valve model

- 4

Mass flow controller

flow controller and the control valve input are simple signal generators. The mass flow is presented in [kgls] and the control valve signal in [V]. The plenum is modeled according to Equation 3.1:

Plenum model

V ~ P (in, - in,)dt P P = S %

Saturation has been added to the plenum model, which limits the plenum pressure between 1 and 5 [bar]. The lower limit equals the ambient pressure, and prevents erroneous model results. The upper limit is set equal to the range of the pressure transducer used for the measurements of the plenum pressure.

Layout of the valve

The operation of the valve can be explained as depicted in Figure 4.3. It consists of:

Input U, The control signal to the Asco valve in [V].

Input Pp The momentary plenum pressure. Necessary to calculate the momentary mass flow through the valve

Potentiometers The influence of the potentiometers 1 and 3.

Dynamics Model of the dynamic relation between the input signal to the valve and the coil displacement.

Dynamics Static valve

Figure 4.4: Valve model

A(,)-curve Model of the non-linear relation between the coil displacement x and the non-blocked area of the flow path.

Ku-value The maximal valve capacity as estimated from the measurements in the pre- vious chapter.

Output rh, The mass flow through the valve riz,.

Observe that the only dynamic relation in this model is that between the input signal to the valve U*, and the coil displacement x. All the other parts of the model are static relations. These static relations have not been investigated separately, but instead one relation between the coil displacement x and the the momentary valve capacity is presented. The mode! is thus reduced to a dynamic relation between U and x, and a static relation between x and m, as depicted in Figure 4.4.

4.2 The static relation

The static part of the valve model should include the following items:

0 A model for the influence of the potentiometers on the coil displacement.

A relation between the displacement of the coil and the valve area.

0 The capacity of the valve.

The manufacturers specification of the influence of the potentiometers as depicted in in the left side of Figwe 3.4 and 3.5 has bee^ adopted in this model. This means that the modeled settings of both potentiometers are decoupled. The valve characteristic can be moved along the x-axis using potentiometer 1. The shape of the characteristic can be altered by setting potentiometer 3. The measurements in the right side of Fig- ure 3.4 and 3.5 show that the potentiometers are not completely decoupled. Changing the shape of the valve characteristic also shifts the characteristic along the x-axis. This means that the if the potentiometer settings used in the model are set equal to the ones used for the measurements, the modeled valve characteristics will differ from the one found by the measurements.

The left side of Figure 4.5 shows some possible dimensionless relations between the displacement of the coil and the valve area. The shape of these graphs depends on the geometry and working principle of the valve. Graph a shows a quadratic relationship that occurs if the valve opens Eke the diaphragm of a camera. The linear graph b car, be

Figure 4.5: Dimensionless valve area versus coil displacement (left) and shutter in cylin- drical flow path (right)

seen as the graph of a flat shutter in a rectangular shaped flow path, while graph c shows the relationship between x and A for a cone in line with a cylindrical flow path. The measurements in Figure 3.3 indicate that graph d matches best with the ASCO control valve. This can be seen as a straight shutter in a cylindrical flow path as depicted in the right side of Figure 4.5. It is modeled by an arctan function.

The capacity of the valve is modeled linear with the valve area. The maximal capacity measured in the previous chapter is used. This leads to the following relation between x and the valve capacity C,:

arctan [ (a + bP0"3"&720) . (25 + c + d w ) ] ( t ) = ( a )

2 arctan [a + bP0"3";720]

The coefficients in this equation are fitted to the static valve characteristics. The resulting values are: a = 1.15, b = 0.75, c = -0.86, and d = -0.1. The resulting valve characteristics for different potentiometer settings are presented in the right hand side of Figure 4.6 for potentiometer 1 and 4.7 for potentiometer 3. The left hand sides of these figures show the measured potentiometer influence. Figure 4.6 shows that changing the setting of potentiometer 1 with one full rotation indeed results in a shift of the valve characteristic that is consistent with the measured data. The effect is equal to changing the value of x by 0.5.

The modeled data for potentiometer 3 is validated by comparing the change in x that results in an increase of mC from 1.5 to 2 [kgls]. The model shows that if potentiometer 3 is varied from -360 [deg] to $720 [deg] the increase in x that provides the 0.5 [kgls] increase in m, changes from 0.5 to 1.2. This corresponds with the measured increase, that ranges from 0.5 to 1.1.

Figure 4.6: Modeled (left) versus measured (right) influence of potentiometer 1

, t i l M m Flow vs Co$~trnl Slgual fur different P3 settings, @=1.5 [bar] . . . . . . . . . . . . .

Figure 4.7: Modeled (left) versus measured (right) influence of potentiometer 3

Figure 4.8: Modeled (left) versus measured (right) characteristic at different plenum pressures

The flow curve at different pressure levels

In the previous experiments, the plenum pressure is kept constant while measuring and estimating the C, parameters and potentiometer influences. To investigate if the pre- sented model holds for other plenum pressures, the valve characteristic is simulated for various plenum pressures. The potentiometers in both the measurement and the model are set to PI = -720 [deg] and P3 = 720 [deg]. This setting is also used in all the dy- namic measurements presented in the previous chapter. It provides the least saturation, and the most linear relation between x and m c possible. The results are presented in the right side graph of Figure 4.8. The left side graph shows the corresponding measure- ments already discussed in the previous chapter. The measurements are only performed using P1 = 0 [deg] and P3 = 0 [deg]. That means that the two can only be compared on qualitatively. The data shows an almost linear curve for Pp = 2.0 [bar] in both the model and the measurement. For the two curves at lower plenum pressures saturation occurs at U, = f 8 [V]. This is consistent with the measured data presented in the left side graph. That leads to the conclusion that the model and parameters presented in ti^^ 4.2 a d eyuob~~y. - . .n+-~- describe the static Seha~vior of the &co c~~tturo! d v e .

4.3 Modeling of the valve dynamics

The mechanics of the valve

This section describes the dynamic relation between the valve input signal U, and the coil displacement x. In order to understand how this relationship will become important for the dynamic description of the valve characteristics, one has to bear in mind that the input signal is translated into a magnetic force on a coil that operates as a shutter to valve. This is explained in Figure 3.1 in Section 3.1. This magnetic force has to balance the force that the spring asserts on the coil. The steady state of the valve is closed. The equation of motion can be written as:

Where Mcoil is the mass of the coil, 1 is the length (at least the part of the coil that is in the magnetic field). B is the Lorentz constant, b is the viscose damping, k is the spring stiffness, and x is the displacement of the coil from the steady state position. From this eqiiation, the transfer hc t io r ; can then deducted as:

K If Equation 4.4 is written in the standard form Hs = s2-2Bwos+wo2 , only three param- eters need to be estimated. The static gain has already been included in the fit of the static model. So for the dynamic model K equals wo2. The damping should be smaller than ;A, otherwise the measured increase in gain around 20 [Hz] would not occur. The relation between the eigenfrequency w, the damping ,L? and the undamped eigenfrequency wo (in [rodls]) for a linear second order system is given as: w = w o J m . Taking this relation into account the undamped eigenfreq~ency and damping are estimated as: wo = 50 and ,L? = 0.6.

Model of the sine-sweep response

Figure 4.9 shows the results of a sine-sweep on this model. The parameters are set equal to the ones used in the sine-sweep measurement presented in the previous chapter. The resulting transfer function estimates produce accurate results for frequencies around the damped eigenfrequency and up, but the modeled gain for frequencies between 0 and 20 H z is substantially higher than the measured gain. To investigate if this is due to errors in the sine-sweep measurement or flaws in the model, some of the harmonic tests on the Asco valve presented in Chapter 3 have been done on the model as well. The input parameters are chosen equal to the ones used in the measurement, so they will not be discussed here again.

Influence of the static input signal U,(O)

Figure 4.10 shows the influence of the static input signal Uc(o) on the plenum pressure. The graphs for Uc(o) = 4 and 5 [V] are in agreement with the measured data, but for

Uc(o) = 3[V] the plenum pressure is estimated too high. This can be explained by the settings of the potentiometer. As already stated, the settings of the potentiometer are not modeled as being coupled, so the combined result of setting potentiometer 1 to -720 [deg] and potentiometer 3 to 720 [deg] degrees leads to a mismatch in the static gain between the model and the measurements.

Influence of the amplitude A

The influence of the amplitude, as presented in 4.11 shows similar results. For small amplitudes of 0.25 [V], the modeled plenum pressure is in agreement with the data. For

Modeled Plenum pressure response to sinesweep

. . . . Modeled Plenum pressure response fo sinesweep

l ! ' l " " ' a l , . . . , . . .

time [r]

Figure 4.9: Modeled response to a sine-sweep at 100 [Hz] and 250 [Hz] and the corre- sponding Transfer Function Estimate

Model ofmnuence of U_(cOJon bs plenum pressure at20 [Hz1

Uc(0) = 4 M

Figure 4.10: Modeled influence of the static valve signals for 1 (left) and 20 [Hz] (right)

Model of influence of me amplitude of UlcO] on me plenum pressure at20 [Hz] 2.3r - . . . . . . . , . . . . . . . . . . . . . . . . .

Figure 4.11: Modeled influence of the valve amplitude for 1 (left) and 20 [Hz] (right)

larger amplitudes, the mass flow is modeled too low. That causes the difference between the measured and the modeled plenum pressure.

4.4 Discussion

The simulations presented in this chapter show that it is possible to produce a model for the behavior of the Asco control valve that consists of a static and a dynamic part. The predominant factor in the static model is the setting of the potentiometers. The decoupled potentiometer influence presented in this model is easy to use, but does not match with the actual potentiometer setting. The way to use this model is to first determine the characteristic to be modeled and then set the potentiometers. This results in different potentiometer settings between the model and the measurement, but provides a valid valve characteristic.

The dynamic behavior of the model agrees with the measurement data. That makes this model useful for investigating if the Asco control valve is a suitable candidate for active surge control on the compressor installation under investigation. Two possible applications for this model are:

1. Use this model as part of a model of the compressor installation and try to de- termine a more exact requirement for the valves bandwidth. Remember that the bandwidth requirement of 100 [Hz] used in this study is based on a general rule of thumb.

2. Predict the effect of changing the valves bandwidth (by changing either the spring stiffness or the mass of the coil), and try to find the optimal way of increasing the valves bandwidth

4.5 Conclusions

The following conclusions can be drawn from the calculations and modeled data pre- sented in this chapter:

1. The behavior of the Asco control valve can be explained by a combination of a static and a dptimic mode!.

2. The setting of the potentiometers has a large influence on the modeled valve char- acteristic.

3. The model adequately describes the dynamic behavior of the ASCO control valve.

Conclusions and recommendat ions

Conclusions

In this thesis, the Asco control valve has been investigated as a possible actuator in surge control systems. The maximum flow capacity of the valve has been determined, as well as the dynamic behavior. These measurements are the basis of the model described in this thesis. The following conclusions can be drawn from the measurements and the derivation of the model:

1. Active surge control of the compressor described in Chapter 2 requires a mass flow of 10.6 [m3/hr] and a bandwidth of f 100 [Hz].

2. The Asco control valve has a capacity of 0.46 [m3/hr].

3. The required valve capacity can be reached by placing 24 control valves parallel to each other.

4. The ASCO control valve shows an eigenfrequency at f 20 - 25 [Hz] and a bandwidth of 50 to 60 [Hz] . This bandwidth does not meet the required bandwidth that is estimated by using a general rule of thumb.

5. The presented valve model adequately describes the dynamic behavior of the ASCO control valve.

Recommendat ions

When implementing active surge control on a compressor, the following recommenda- tions should be observed:

1. The eigenfrequency and bandwidth of the Asco control valve is governed by the coil mass versus spring stiffness ratio. The dynamical behavior could therefor be increased if the spring is swapped by one with a higher stiffness, or the coil is replaced by one that is lighter.

2. The model presented in this thesis should be incorporated in a compressor model to derive an improved estimate for the required valve bandwidth.

Bibliography

[I] E.M. Greitzer, The stability of pumping sytems, The 1980 Freman scholar lec- ture, ASME J . Fluid Dynamics, 103(2):193-242, June 1981.

[2] F. Willems, Modelling and bounded feedback stabilization of centrifugal compres- sor surge Technische Universiteit Eindhoven, Proefschrift, ISBN 90-386-2931-1, 2000.

[3] K.H.Kim and S.Fleeter, Compressor unsteady aerodynamic response to rotating stall and surge excitations, 3. Propulsion and Power, vol. 10, pp. 698-708, Sepi.- Oct. 1994.

[4] J.E. Pinsley, G.R. Guenette, A.H. Epstein and E.M. Greitzer, Active stabiliza- tion of centrifugal compressor surge, J. Turbomachinery, vol. 113, pp.723-732, Nov. 1991.

[5] I.J. Day, Stall inception in axial flow compressors, J. Turbomachinery, vol. 115, pp. 1-9, Jan. 1993.

[6] D.A. Fink, N.A. Cumpsty and E.M. Greitzer, Surge dynamics in a free-spool centrifugal compressor system, J. Turbomachinery, vol. 114, pp. 321-332, Apr. 1992.

[7] Frank Willems and Bram de Jager, Modeling and control of rotating stall and surge: An overview, Proc. of the 1998 IEEE Int. Conference on Control Appli- cations, pp331-335, 1998.

[8] J.D.Paduano, A.H. Epstein, L. Valavani, J.P. Longley, E.M. Greitzer and G.R. Guenette, Active control of rotating stall in a low-speed axial compressor, J. Turbomachinery, vol. 115, pp.48-56, Jan. 1993

[9] J.S. Simon, L. Valavani, A.H. Epstein and E.M. Greitzer Evaluation of ap- proaches to active compressor surge stabilization, J. Turbomachinery, vol. 115, pp. 57-67, Jan. 1993

[lo] I.J. Day, Axial compressor performance during surge, J . Propulsion and Power, vol. 10, pp. 329-336, May-June 1994.

[ll] J.E. Ffowcs Williams, M.F.L. Harper and D. J. Allwright , Active stabilization of compressor instability and surge in a working engine, J. Turbomachinery, vol. 115, pp. 68-75, Jan. 1993.

[12] C. Meuleman, F. Willems, R. de. Lange and B. de Jager, Surge in a low-speed radial compressor ASME paper no. 98-GT-426

[13] B. Ribi and G. Gyarmathy The behavicur cf a centrifugal compressor stage during mild surge, VDI Berichte no. 1186, 1995.

[14] H.A. van Essen Design of a laboratory gas turbine installation, Technical Report WOC- WET 95.012, Fac. of Mechanical Engineering, Eindhoven University of Technology.

[15] K. Toyama, P.W. Rundstadler Jr., R.C. Dean Jr., An experimental study of surge in centrifugal compressors ASME Journal of Fluids Engineering, Vol. 99, pp. 115-131, 1977.

[16] B. Ribi and G. Gyarmathy Impeller rotating stall as a trigger for the transition from mild to deep surge in a subsonic centifugal compressor, ASME paper no. 93-GT-234

samenvatt ing

Het gebruik van compressors en turbines is wijd verspreid in het moderne leven. Het toepassingsgebied van deze apparaten wordt voor kleine massa stromen beperkt door het optreden van twee fysische fenomenen: Surge en Stall. Deze fenomenen leiden tot een beperking van de efficientie, maar kunnen in een ernstigere vorm ook leiden tot schade en zeifs compieet faien van de machines. De gebrui~elijke iiiaiiier om deze fsnomeneii aan te pak~en, is ze te vermijden door een regel gens te definieren voor lage massa stromen. Voorbij deze grens is het niet mogelijk om de machine te laten werken. Een nadeel van deze manier van aanpak is dat de efficientie van de machine aangetast wordt, en dat het toepassingsgebied beperkt wordt.

Een alternatief voor deze regeling waarbij Surge compleet vermeden wordt, is het toestaan van het bedrijven van de machine in een werkpunt waarbij normaliter Surge op zou treden, en het aanpakken van dit fenomeen door het af'blazen van gecomprimeerd medium met dezelfde frequentie als de oscillaties. Deze actieve Surge regeling zou niet alleen het toepassingsgebied uitbreiden, maar ook een kleinere aantasting van de ef- ficientie betekenen.

Deze strategie vereist regelkleppen met een bandbreedte hoger dan de hoogst optre- dende trillingsfrequentie die optreedt tijdens Surge en Stall, en een capaciteit die volstaat om de hoeveelheid massa stroom af te blazen die nodig is om met de gewenste frequentie de druk in de machine af te doen nemen. In dit rapport wordt de ASCO regelklep bespro- ken als mogelijke kandidaat voor actieve Surge regeling van een compressor. Een groot aantal meetresultaten wordt gepresenteerd, waarbij een beeld ontstaat van het gedrag van deze klep onder de proces condities die door actieve Surge regeling worden opgelegd. Dit resulteert in een model dat het gedrag van de ASCO regelklep beschrijft.

Uit de meetresultaten en simulaties kan geconcludeerd worden dat de capaciteit van de ASCO regelklep niet voldoende is. Het gebruik van een aantal parallel geplaatste kleppen kan dit probleem eenvoudig verhelpen. De beperkte bandbreedte van de klep vormt een serieuzer probleem. De aanbevolen manier om hiermee om te gaan is het licht aanpassen van de mechanische werking van de klep. Omdat dit slechts een kleine aan- passing betreft, kan de ASCO regelklep beschouwd worden als een bruikbare kandidaat voor actieve Surge regeling.

Dankwoord Graag wil ik de volgende mensen danken voor hun bijdrage in dit afstudeerproject. Dankzij jullie kan ik met recht zeggen een studie genoten te hebben:

In de eerste plaats Jan Kok, die a1 vroeg in mijn studie mijn belangstelling wist te wekken voor het vakgebied meet- en regeltechniek. Voor de mogelijkheid om in dit gebied in een prettige sfeer af te stilderen.

Mijn begeleiders Bram de Jager en Frank Willems, voor de vrijheid die ze me hebben ge- boden in de manier van aanpak van dit project. Voor de prettige wijze van samenwerking en de waardevolle discussies die vorm hebben gegeven aan dit afstudeerverslag.

Mijn broers Pascal en Mattie, die me in de weekends hielpen de accu weer op te laden en Petra voor haar niet aflatende liefde en de ruimte die ze me heeft geboden.

Tenslotte mijn ouders Jessie en Ton, aan wie ik eenvoudigweg alles te danken heb. Zonder jullie steun, hulp, liefde en vertrouwen . . .

Hartelijk dank!

Stephan Hermans