Controlling the cavitation phenomenon of evolution on a butterfly valve

Transcription

1 IOP Conference Series: Earth and Environmental Science Controlling the cavitation phenomenon of evolution on a butterfly valve To cite this article: G Baran et al IOP Conf. Ser.: Earth Environ. Sci. View the article online for updates and enhancements. This content was downloaded from IP address on 9//8 at 4:4

2 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// Controlling the cavitation phenomenon of evolution on a butterfly valve. Introduction G Baran, I Catana, I Magheti 3, C A Safta and M Savu 3 Department of Hydraulic and Hydraulic Machineries, University Politehnica of Bucharest, 33 Splaiul Independentei, Bucharest, 64, Romania Department of Control and Computer Science, University Politehnica of Bucharest 3 Department of Mechanical Engineering, University Politehnica of Bucharest baran_gheorghe@yahoo.co.uk Abstract. Development of the phenomenon of cavitation in cavitation behavior requires knowledge of both plant and equipment working in the facility. This paper presents a diagram of cavitational behavior for a butterfly valve with a diameter of mm at various openings, which was experimentally built. We proposed seven stages of evolution of the phenomenon of cavitation in the case of a butterfly valve. All these phases are characterized by pressure drop, noise and vibration at various flow rates and flow sections through the valve. The level of noise and vibration for the seven stages of development of the phenomenon of cavitation were measured simultaneously. The experimental measurements were comprised in a knowledge database used in training of a neural network of a neural flow controller that maintains flow rate constantly in the facility by changing the opening butterfly valve. A fuzzy position controller is used to access the valve open. This is the method proposed to provide operational supervision outside the cavitation for a butterfly valve. Three aspects are important in order to determine the stage of cavitation development or evolution in hydraulic circuits, machines and power systems: alterations in performances, noises and vibrations, cavitational damages. As a result, the monitoring procedure of hydraulic turbine behavior in cavitation is certified by CEI/IEC , 997, []. It is more difficult to monitor the cavitation development and its action in the flow through a device with complex geometry. This is the case of control valves where the procedure of the monitoring process of cavitational damage appearance is certified by ISA Recommended Practice, ISA-RP , []. Even until recent years, most control valve manufacturers used a cavitation index (between F L and K c ) based of the standard control valve pressure recovery test curve, the method proposed by ISA suggests the calculus of σ ( σ = ( p pv )/ ( p p )) and the plot of tested sigma curves which included the vibrations recording downstream pipe for different flow rates. The experimental work of monitoring the phenomenon of cavitation of control valves extended in technical papers goes back over to last decade by Koivula [4] who proposed as the cavitation monitoring methods: monitoring of steady-state flow behavior; monitoring the high-speed of pressure and vibrations; monitoring of acoustic pressure emission; detecting the cavities by flow visualization. Yang et al. [5] proposed a monitoring scheme using a feed-forward neural network called SVM (support vector machine). The neural network was trained for a knowledge database of vibrations measurements for the working regime of a butterfly valve with a large diameter. Another method to characterize and verify local effects under flow cavitating flow conditions is to determine the coefficient of local head losses and the minimum value of the cavitation number, [6], but these are not enough to control the cavitation phenomenon on a control valve. The actual theoretical researches are based on Rayleigh-Plesset mathematical and physical cavitational models and computational analysis to find not only the behavior of a control valve or a hydraulic one but also to give an optimal design of the valve, [7]. A new method of controlling the butterfly valve which operating with cavitation is proposed. Four global evolution stages of cavitation are discussed regarding the dimensionless coefficients of cavitation of a butterfly valve, [] and then seven particular stages of cavitation are identified, [4]. For a given disc open at different θ angles the pressure drop on the valve,, the level of noise and vibrations in all seven particular stages of cavitation were c Ltd

3 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// measured. The measurements were used to plot the characteristic curve of the butterfly valve and to build a knowledge database for a neural network which will train a flow rate neural controller (NQC). The NQC will change the flow rate if the user will change the requirement of pressure in installation and the valve is in danger of working in cavitation regime. A position fuzzy controller (FPC) will change the valve opening, θ, so that the valve will work without cavitation or in a permissible stage and the installation will respond to the pressure requirement asked by the user at the reference flow rate.. Coefficients and cavitational stages A pipeline with diameter D and a butterfly valve opened with θ angle, figure, are considered. Writing Bernoulli s formula on a streamline between M and M is obtained: p v pm vm + + z = + + zm + hp () ρg g ρg g with h p the pressure losses. Steady flow and incompressible fluid were considered. If p M = p v and v M = v max, equation () can be rewritten as: p h pv pmin pv vmax zm z p = () v / g v / g v v / g v / g or: σ = σ + σ (3) inst rez ic where σ inst is the cavitation number of installation, σ rez is the reserve coefficient at cavitation, σ ic is the internal coefficient of cavitation, p v (t ) saturated vapour pressure at t temperature and p min minimum pressure in the streamline. Fig. Scheme of a butterfly valve to define the cavitation coefficients Equation (3) defines four global stages of cavitation, []: σ rez >, σ inst > σic, non-cavitation stage; σ rez =, σ inst = σic, incipient stage; σ rez <, σ inst < σic, industrial developed cavitation stage; σ rez <<, σ <<, super-cavitation stage. inst σ ic The problem of what the stage is where cavitational damages are produced is not formulated in the technical literature. For M and M sections the reserve coefficients at cavitation will be: σ < σ, (4) rez M rez M that means that the phenomenon of cavitation is in M section. Replacing in equation () the pressure loss coefficient ζ is defined as: v = ζ (5) ρ g g and substituting the velocities with flow rates and sections corresponding with valve openings at θ angle is obtained: S zm z σic = + + ζ( θ) (6) S( θ) v / g

4 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// where S = π D / 4 is the valve inlet flow section and S(θ) is the flow section at the opening angle θ, [6]. Equation (6) will calculated the internal coefficient of cavitation σ ic if the pressure loss coefficient ζ(θ) is known. To determine the non-cavitation stage of a control valve the manufacturers calculate the pressure ratio, X F : X F = < Z (7) y pam pv where p am is the absolute pressure upstream of the valve and is the net pressure drop on the valve. The coefficient Z y is given in a table having the diameter D and angle θ as parameters, [3]. Regarding the development stages of the phenomenon of cavitation an old Tullis [8] proposal is resumed and seven stages of cavitation are defined: non (N), incipient (I), light (L), moderate (M), heavy (H), very heavy (VH), super-cavitation (S) stage, which could be acoustically evaluated. Figure represents the net pressure drop on the valve and the flow rate for two openings of the valve (θ=3, θ=4 ), and the stages of cavitation for a butterfly control valve which is operating in an installation. The cavitational stages are mentioned [, 4]. Fig. Stages of cavitation for a butterfly valve D, Pn6 which is working in the installation Using the experimental data from figure the cavitation coefficients (flow rate coefficient K v and cavitation number σ) were calculated, table, with Q = Kv and water as the fluid in experimental installation. It is obvious, that the evolution of the phenomenon of cavitation not seriously affect the flow rate coefficient K v. Q (m 3 /h) Table Cavitation coefficients for θ = 4 open valve (bar) K v (m 3 /h) σ (-) Stage of cavitation (-) N N I(L) M H VH VH S S 3

5 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// 3. Vibrations and noise The collapse of cavitational bubbles generates noise and damage of solid surfaces. Noise is a consequence of high pressure instantly developed when the content of cavitational bubbles is highly compressed. Noise is a consequence of the temporary high pressure of cavitational bubbles developed when the content of these is highly compressed. The appearance of the characteristic noise that accompanies the phenomenon of cavitation is one way in which the cavitation phenomenon makes its appearance in the system. For a spool control valve, Martin [5] has drawn the noise energy spectra for various stages of the cavitation development and has found that the lower values of cavitation number (σ =,53 for non-cavitation stage) where the phenomenon of cavitation starts developing there is a dramatic increase of noise frequencies between 5kHz and khz. The methods of studying the acoustic cavitation are governed by CEI / IEC , [6]. Noise and vibration recordings made for mm diameter butterfly valve highlighted the existence of minimum requirements of the level of vibration (mm/s ) and noise (db) in stage M, []. After, hours of operation of the plant with, starts and stops the measurements were repeated for the vibration frequency range extending from to Hz, and peaks of 5, 5, 77, 99 and 3 Hz, Fig. 3, were identified. Fig. 3. Development of the phenomenon of cavitation stages and level of vibrations. Only the frequencies of 77, 99 and 3 Hz are valid as the minimum values in figure 4. It follows that this stage may be an "evaluator" of valve maintenance, not only an "evaluator" of the cavitation behavior. Regarding the noise, it is up to the stage M and by comparing with earlier values a rise of % in stages VH and S is developed. Noise may not depend on the Strouhal number defined in the strangled flow section with equivalent diameter D e : f D K Sh e Sh = = f respectivly f = Q (8) V Q K where K is a constant that depends on the section of flow because the Reynolds numbers at which the flow in the facility are Re = ( 3) 5, so the Strouhal number is constant. States [9] that at Re = 4 5, Strouhal range is Modern method to control phenomenon of cavitation The control process of the evolution of cavitation in an industrial plant in which a butterfly valve works can be performed using a neural flow controller and a fuzzy position controller. Neural network is trained to generate static characteristics of functioning of the different valve openings. The plant operator sets a reference flow, Q ref 4

6 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// necessary in the facility. The fuzzy controller, with information regarding the pressure drop, continuously measured,, will switch to another system operation modeled on the static characteristics of neural network so that the system was out of the cavitation zone. In this way, pressure and flow perturbations in the hydraulic system are offset by the intervention of maintaining fuzzy controller valve operation outside the cavitation regime. The principle of work is shown in Fig.4. Figure 5 presents the plant and how neural and fuzzy controller intervenes in the operation of the plant. The two controllers are found in a cascade structure adjustment to compensate major perturbation. A mathematical linearized model of the plant is used to build neural and fuzzy controllers. The plant is formed by a variable speed pump, the pipeline and a butterfly valve. The pump and butterfly characteristic curves are described as P = AQ + AQ + A N and Q = Cd A( θ) P (9) with P, the pressure in the piping system, Q, the flow rate and N the shaft speed. Because P = RQ it is obtai ned R = / C A( θ) d. From the above relations, by replacing, the following, will result: R Q + = A Q + A N Q A N () Equation () is linearly developed by using Taylor series around the static operating point (P, Q, N ), with (p, q, n) the deviations so that P = P + p; Q = Q + q; N = N + n. Disregarding the second order deviations the linear equation of the pump is: p = ( AQ + A N ) q + ( AQ + A N )n () The discrete linear form of the eq. () is = α Δq + αδn with α ( ) = A Q + A N and α = A Q + A N so that Δq = ( α / α) Δn = α / α Δn and ΔP = α Δn. To obtain the linear form of the piping characteristic equation, the pressure in the piping system was written as a function of piping hydraulic resistance, R, and the flow rate, Q so that P = f ( R,Q). Piping hydraulic resistance depends on the flow openings of the butterfly valve, A(θ), with θ the angle-seated disc, Fig., and R = f ( θ). The differential form of the function piping characteristic equation around the static operation point (R, Q ) with (r, q) the deviations and R = R + r; Q = Q + q, is: P ( ) ( ) + p = R + r Q + q () Finally, the linearized form of the piping characteristic equation is p = Q r + RQq. The discrete linear form of the above equation is: where: Δr = 3 A ( θ) = Q Δr + RQΔq (3) Δθ. The linear mathematical model of the plant is: Q Δn Δq Q ( α RQ ) Δq = Δθ α Δn or = ( R Q α ) Δn (4) 3 3 A ( θ) Δθ Δθ A ( θ) A knowledge database for a neural network was built using the experimental curves of the butterfly valve, Fig.. A flow rate neural controller (NQC) was trained to change the flow rate in the plant if the butterfly valve is forced to work in a cavitation regime. To apply a fuzzy logic control so that the butterfly valve not to work in the cavitational regime, the system is identified using a pseudo-random binary signal input, Fig. 6, applied to the second order transfer function of the open loop system, eq. (5). Discrete transfer function, eq. (6) of the model was obtained and the selected sampling period (T e ) is. second. The discrete transfer function to a pseudorandom signal is shown in Fig. 7. 5

7 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// Distribution of experimental data.3 theta theta theta k cavitation characteristic curve theta n Pressure, deltap (bar).5..5 deltap deltap deltapk CAVITATION OPERATION ZONE. deltapn Qref Flow rate, Q (cm/h) Fig. 4. Butterfly valve characteristic curve of cavitation G () s = (5). 3s s + G ( z). 474z = (6) z 936, z Fig. 5. Technological installation s scheme 6

8 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// The fuzzy controller (FPC) is designed to have two fuzzy inputs variables and one output control variable to achieve fuzzy logic based position of the control valve. The input variables are the flow rate and the pressure variation on the butterfly valve. The output variable is θ, the angle-seated disc of the butterfly valve. The proposed fuzzy controller is designed and simulated using MATLAB software tool. For the purpose of simulation symmetric triangular fuzzy sets and mamdani fuzzy sets are used for input and output variable respectively, in addition to the rule table of 9 fuzzy rules, Fig. 8. A fuzzy signal command was obtained, Fig. 9, and the behavior of the system controlled with FPC fuzzy controller is shown in Fig. to Fig Response to the test signal Control signal u(t) n*te n*te Fig. 6. Pseudo-random binary signal input Transducer output y(t) Te =. Fig. 7. Response to a pseudo-random signal N Ze P N Ze P Membership degree Membership degree The error Derivative error NM Nm Ze Pm PM Membership degree Control Fig. 8. Membership functions of inputs and output of fuzzy controller (FPC) 7

9 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// Uc ( Volti ) Pressure ( bar ) KI = [, 5, 7, ] Time ( s ) 4 Fig. 9. Fuzzy command 5 5 Number of sampling periods Fig.. Butterfly valve pressure variation (K l the fuzzy controller parameter) 3 5 Flow rate ( mc/h ) KI =, 5, 7, ] Speed revolution ( rpm ) 5 5 KI = [, 5, 7, ] 5 5 Number of sampling periods Fig.. Flow rate variation 5 5 Number of sampling periods Fig.. Pump speed variation 5. Conclusion In hydraulic circuits the phenomenon of cavitation is not allowed or else a degree of development is accepted that, for valves, do not change its performance (i.e. flow coefficient, K v ) and do not cause damage downstream, such as a valve with, hours of operation (except for small prominences in the downstream pipe at the bottom, [4]). To control the evolution of phenomenon of cavitation it is necessary to calibrate the plant by building the valve operation diagram, figure. On that basis one determines the level of noise and vibration. It selects the allowable state, identified by three parameters: pressure drop, vibration and noise level. A method to monitor the cavitation behavior of the valve is proposed so that its operation in the facility can be done without cavitation. A neural flow controller is used to generate static characteristics of functioning of the different valve openings and a fuzzy position controller is used to change valve opening position so that the valve will operate without cavitation, in terms of a constant flow rate and a pressure required by the consumer. Nomenclature A, A, A D D e K K v N N P P R Q Linearization coefficients [-] Pipeline diameter [m] Equivalent diameter [m] Constant depending of the S(θ) [-] Flow rate coefficient Pump rotation speed [rpm] Pump s rotation speed in operating point [rpm] Pressure pump [Pa] Pressure in the operating point [Pa] Hydraulic resistance [kg m -7 s - ] Flow rate [m 3 /s] p am p, p M p min p v p, p v v M v max z M, z Δn Absolute pressure upstream the valve [Pa] Pressure in the point M, pressure in point M [Pa] Minimum pressure in the flow [Pa] Saturated vapours pressure at t C [Pa] Upstream and downstream pressure valve [Pa] Flow velocity in M [m/s] Flow velocity in M [m/s] Maximum flow velocity in point M (m/s) Heght of the point M, M [m] Net pressure drop on the valve [Pa] Variation of rotational speed in linear model [rpm] 8

10 5th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science () doi:.88/755-35/// Q Re S S(θ) Sh V f g h p Flow rate in the operation point [m 3 /s] Reynolds number [-] Valve inlet flow section [m ] Flow section at the opening angle θ [m ]. Strouhal number [-] Velocity of the flow [m/s] Frequency of vortex shedding [s - ] Gravitational acceleration [m/s ] Pressure losses between M and M [m] Δr Δq, α, α ρ θ σ ic σ inst σ rez σ rezm σ rezm ζ Pressure drop variation in linear model [Pa] Variation of hydraulic resistance [kg m -7 s - ] Flow rate variation in linear model [m 3 /s] Coefficients in linear model Density [kg/m 3 ] Butterfly valve opening angle [deg.] Internal coefficient of cavitation [-] Cavitation coefficient of the installation [-] Reserve coefficient at cavitation [-] Reserve coefficient at cavitation in the point M [-] Reserve coefficient at cavitation in the point M(-) Coefficient of the local pressure drop [-] References [] Anton I Cavitatia 985 vol II (Timisoara: Editura Academiei) [] Baran Gh, Safta C A, Bunea F and Oprina G 8 Stages of noises and vibrations to a butterfly valve in working with cavitation U.P.B. Sci. Bull. (series D ISSN ) 7(4) 5- [3] Safta C A, Catana I and Baran Gh 8 Control fuzzy of hydrodinamic parameters of industrial valve working without cavitation Proc. of the H.M.E. U.P.T.Sci. (Bull. ISSN 4-677) vol 53 (67) pp [4] Baran Gh, Bunea F and Oprina G 7 On cavitation and cavitational damage of butterfly valves Proc. of nd IAHR-WG U.P.T. Sci. Bull.(ISSN 4-677) vol 5(66) pp 4-46 [5] Yang B-S, Hwang W-W, Ko M-H and Lee S-J 5 Cavitation detection of butterfly valve using support vector machines J. of Sound and Vibration [6] Sanchez R., Juana L, Laguna F and Rodriguez-Sinobas L 8 Estimation of cavitation limits from local head loss coefficient J. Fluids Eng. (ISSN 98-) 3() [7] Bernad S, Susan-Resiga R, Muntean S and Anton I 7 Cavitation phenomena in hydraulic valves, numerical modelling Proc. of Romanian Academy (Series A, ISSN ) vol 8() [8] Tullis P 978 Choking and supercavitation valves (ASCE) J. of Hydraulic Devision [9] Rusu I 988 Fenomene in hidroelasticitate (Iasi: Junimea) [] ISA-RP Considerations for evaluating control valve cavitation (recommended Practice, June) [] CEI/IEC Industrial-process control valves, part.., Flow capacity-sizing equations for fluid flow under installed condition [] SR-EN Evaluarea eroziunii datorita cavitatiei la turbine, pompe de acumulare si turbine - pompe. Partea : Evaluarea la turbine cu reactiune, pompe de acumulare si turbine pompe [3] *** EBRO Armaturen Product Programme [4] Koivula T On cavitation in fluid power Proc. Of st FPNI-PhD Symp. Hamburg pp [5] Martin C S, Medlarz H, Wiggert D C and Brennen C 98 Cavitation inception in spool valve (ASME) J. Of Fluids Eng [6] CEI/IEC Prediction of Noise Generated by Hydrodinamic Flow 9