Çek valflerinin dinamik davranışlarının analizi
Dynamic behaviour analysis of reflux valves
- Tez No: 46488
- Danışmanlar: PROF.DR. CAHİT ÖZGÜR
- Tez Türü: Doktora
- Konular: Enerji, Energy
- Anahtar Kelimeler: Dinamik analiz, Dinamik davranış, Vanalar, Dynamic analysis, Dynamic behavior, Valves
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Hidrolik tesis, şebeke ve sistemlerde geri dönüş akımının engellenmesi istenen hallerde kullanılan geri tepme vanaları yada kısa ismi ile“çek valfler”yapılışlarından gelen histerizis etkisi ile bu görevlerini ideal şekilde yapamazlar ve geçici bir süre ters akışa neden olurlar. Ters akışın aniye yakın bir hızla durduruluşu ise özellikle büyük tesislerde zararlı su darbeleri ve çalkantılara neden olur. İyi bir çek valf tasannu yapabilmek, belirli bir tesis için uygun olan ve izin verilen basıncı aşabilecek darbe vermeyen çek valf tip ve boyutlarını belirleyebilmek yada su darbelerini küçültecek önlemler alabilmek için, geri dönüş ve kapama olayım analiz etmek ve çek valfierin çeşitli şartlarda dinamik davranışlarını ortaya koymak gereklidir. Bu çalışmada mühendislik açısından en önemli olan Yelpaze tip (çalpara) çek valfler başta olmak üzere Tablalı çek valfler ve Eksenel çek valfierin dinamik davranışları kapsamlı şekilde ele alınmıştır. Çek valf kapağının genel hareket denklernlerinin gerçek şartları karşılayacak teorik bir çözümü yoktur. Çeşitli araştırmacılar bazı yaklaşrmlar ve yarı teorik kabullerle matematik modeller geh^irmişlerdir. Bu modeller bu çalışma kapsamında incelenmiş, düzeltmeler ve geliştirmeler ile tasarım için kullanıma daha uygun hale getirilmişlerdir. Geliştirilmiş matematik modeller kullanılarak çek valfierin kapanma davranışları etüd edilmiş ve çap, fîktif* kapak kalınlığı, özgül ağırlık ve benzeri tasarım paramelxelerinin etkileri sistematik bir şekilde ortaya konmuştur. Çek valf - sistem etkileşimleri ele alnımıştrr. Boyutsuz tam pompa karakteristiği, boyutsuz volan sayısı, boru rijitlik sayısı ve çek valf karakteristik denklemleri ilk kez birlikte laulanılarak, Karakteristikler ve Runge - Kutta yöntemleri yardımı ile komple matemetik bir model gelistirilrniştir. Bu model yardımı ile yapılan analiz sonucunda genellikle inanılanın aksine olarak belirli şartlarda salt çek valfln karakteristiğinden hareketle ortalama ters ivme ile ters hızın bulunamayacağı gösterilmiştir. Özel olarak yapılan deney düzeni ile her üç tip çek valfın çeşitli ters ivme değerlerinde yarattıkları maksimum ters hızlar ölçülmüş ve dinamik karakteristikler saptanmıştır. Bulunan karakteristikler geliştnmğuniz matematik modeller den elde edilenlerle kıyaslanmıştrr. Çalpara çek valilerde kapağı belirli bir açıda tutmak için gerekli hızı ifade eden boyutsuz“Le”sayısı tanımlanmış bu sayı sayesinde Pool - Porvvit Modelinde Kf katsayısı basitçe hesaplanmış ve genelleştirme yapılmıştır. Ayrıca Kd katsayısında yapılan genelleştirme ile geometrisi belirli bir çek valfın dinamik karakteristiğinin uzun laboratuvar deneylerine gerek kalmadan tahmin edilmesi olanağı sağlanmıştır. Deneysel sonuçların analizi, genel olarak sanılanın aksine olarak, ters hızın büyümesinin her zaman basınç darbesinin büyümesine neden olmadığını göstermiştir. Küçük valilerde kapağın sürtmeleri nedeniyle frenlenmesinin toplam kapama zamanım ve ters hızı arttırdığı ancak buna karşılık yavaş kapama yarattığı için tersine, darbeyi küçülttüğü sonucuna vanlrnıştır. XI
Özet (Çeviri)
SUMMARY DYNAMIC BEHAVIOUR ANALYSIS OF REFLUX VALVES Reflux valves, check valves or literally non-return valves are the elements which in principal have to prevent the reverse flow in the fluid systems. In fact as a result of their inherent characteristics they allow a short time back flow. Consequently at the end of delayed closure a sudden stoppage of the water column may cause very severe water hammer and pressure surges together with door skmming, depending on the rate of flow deceleration in the system and also on the valve design. In order to achieve a proper design for a specific job or to select the correct check valve satisfying the maximum allowable pressure condition in the system, it is essential to get insight into mechanism of valve closure phenomenon and to carry out an analysis of check valve dynamics and also to simulate the systems having check valves. In the present work three different types of reflux valves have been investigated with the emphasis on swing type which is most commonly used in practice. There is no exact theory representing the movement of check valve door that works in a decelerating flow during the closing period. Different approaches have been made to approximate the phenomena in swing check valves' two of which will be under consideration. D“ ~ Figure(l) Schematic representation of a Swing Type Check Valve The torque exerted on the valve door being due to weight (Mw), friction (Ms) and hydrodynamic force (Mh) The motion of rotating body is described by I-9 = MW+Mh+MB (1) where I is the mass moment of inertia of the rotating parts. (Mw) and (Ms) are relatively easy to evaluate but for (Mh) assumptions have to be made. Assuming uniform pressure over each face of the valve, neglecting the friction torque we arrive at the following equation for the body movement. Xlle = 16-g.L s-(l + 4-(l + m)2)-D: (s-l)-cose-- - - - (2) where m = k/L, s the ratio of body material density to fluid density and (Hu - H<j) upstream and downstream pressure head difference. ELLIS assumed the pressure difference to be H.. - Hj =.0 Ik 2.g-A2-(l-sin9): (3) qk being the flow trough valve door which is given in the form qk = Q+ 7C-D^ L-0 (4) The last two equations are the bases of what we call ELLIS Model. It is obvious that equation (3) and (4) can not represent the extreme positions correctly and they give only an approximation for the positions corresponding to 9 other than 90°. The author proposes the following relations to replace (3) and (4) AH = W^ 2-g-(sinGmax. -sine)”Wn = L-9 + V-sin6 (5) (6) W representing the relative velocity of water at the door center with W“ its projection on the door symmetry axes. Equations (2), (5), and (6) are taken as the boundary conditions for the check valve in a hydraulic system where the flow and pressure variation are computed with the method of characteristics. In this respect Runge-Kutta method was also to be used. A computer code was developed for the simulation of a system with swing check valve working under different conditions and which also serve to determine the dynamic characteristics of the valve that is maximum reverse velocity Vt versus flow deceleration dV/dt. With the help of above mentioned simulation we were able to investigate the effects of different design parameters such as m, s, 9max, 0min, D, etc. Figure(2) Forces acting on the valve door XIIIPOOL et al.(1962) proposed a more sophisticated model in which hydrodynamic torque was composed of a flow induced moment and a fluid damping moment, latter resulting from the motion of the valve through the fluid. The coefficients of these moments have to be found with experiment. After tedious calculations we arrive at the following equation of motion where the bearing friction is omitted for simplicity. B-G -L-cosG-G, ?y-VH+ö* C^+G”2 K B-C. p ^E2+B2 K2.V2=0 (7) B, C, G and E are the constants that are related to the geometry of the swing check valve. For m = 0 they have the following values : B = 1.723 R3/2 C = 2.279 R5/2 E = 0.416 R 3/2 G = 0.550 R- 5/2 In order to obtain the coefficients Kf and Kd two separate tests were carried out in the test set up namely a steady state test with 9 = 9=0 giving 9 versus V relationship, and a free fall test with V = 0 giving 9 = f(t) relation. Using the result of the first test and the main equation under the test conditions, the coefficient Kf may be determined as a function of 9. Similarly with the help of 9 versus t curve obtained from the second test and considering the equation (7) written for V = 0, it was possible to determine Kd in relation to 9. After carefully examining the experimental curves of a 50 mm.(2“) swing check valve we came to the conclusion that these can be generalized in the following forms Kf =Lv fimax ~ ö 17 ° ft - A °max °min + m (8) KD=0.58 1- flmax ~ Ö - S \2 J (9) where Lv is newly proposed nou dimensional (position) number and Lv0 is its value corresponding to the full opening. Lv0 defined as Lvn = UB ^2-g-e-(s-l)-cos90 Id; (10) where V0 denotes the fluid velocity corresponding to the full opening. It is also called ”velocity open". Db is the pipe diameter. The validity of this generalization was checked by comparing the results obtained with the proposed relations and that XIVobtained with the experimental curves. It is concluded that, the proposed method can be used for the estimation of the pressure surges without having to run laborious tests. In order to simulate simple plug type check valves the main assumptions made by KUBIE(1982) were adopted, leading to the equation of motion in the following form D} s-X = (s-l)-g -T-Z- 32-Cj e V4 vDky V2 (lWX)' vDky (v+x): (11) Dk <s/;///////sz İ ~Te Do Figure(3) Schematic representation of a Plug Type Check Valve. C<j being the discharge coefficient of the orifice under the valve shutter. This coefficient was taken as constant and equal to 0.82 by Kubie which according to our experimental findings must be drastically altered and corrected. A second consideration of Kubie with whom we do not agree is that the last term of the equation (11) was omitted for W = V + X < 0. We have theoretically shown that the last term is not nil and it stands as it is in the case of reverse relative flow. A computer model was built based on the considerations and methods used for swing valves. By the aid of this model the theoretical prediction of dynamic behavior was made for two plug type check valves which were also tested. §^S5SÜ^ IpSSS^g! Figure(4) Cross Section of a Axial Type Reflux Valve Adopting similar considerations the equation of motion of valve body for the axial type reflux valves was obtained as follows XVs-X = F0-k-X 1 D? p-e tc-dJ 32-Cd e Id v-lvl ^DrV k/ (lw-x)2 ^ (v+x)' e (12) where F0 denotes spring force for full opening and k represent spring coefficient. This equation was used for the development of the appropriate model in a similar way employed for the previous models. To compare the three models mentioned above, computed dynamic characteristics are presented in Figure(5) in non-dimensional form. Experimental results are also shown on the same diagram. It is clearly seen that Pool-Porwit model gives the best results and simple Ellis model gives the poorest one. It is interesting to see that the Ellis-Kavurmacıoğlu model brings considerable improvement over the Ellis Model despite its simplicity. 1.2 O.B S 0.4 U.B ı ir i-Oirnen OH 1.0 1.2 sluriMl DeL:eleratian 1.4 1.6 Figure(5) Comperative results of the experimental non-dimensional dynamic characteristics and the computed ones. The experimental work was earned out on a test rig specially build for the purpose which is shown schematically in Figure(6). In this stand, in order to eliminate the effect of pump's inertia the flow deceleration was created by an air pressure tank and its action is applied to a pressure tank located at the initial downstream of the check valve, by a solenoid valve. During the test initial flow rate is maintained by the control valve adjustment then with the aid of a quick-action valve, the pressure at the initial downstream side is elevated to a predetermined value. This action creates a sudden difference of pressure over the test section leading to almost linearly decelerating flow until the valve is closed. Time dependent flow was measured by a fast acting flowmeter build by author. XVICOMPRESSOR TS HEAD RESERVOİR Hi h H, (E2r 1 AIR VESSEL SOLENOID VALVE AS | ^VENT P,Cfl O^-,D NONRETURN VALVE TO BE TESTED FAST ACTING FLOW METER B, VALVE CONTROL VALVE -*** HIGH PRESSURE TANK Pi. R, PRESSURE CONNECTIONS BASEMENT TANK Figure(6) Test rig for non-return valves. The three numerical models described above for the three different types of check valves were used to simulate the valve closures under decelerating flow of any desired rate. Figure(7) represents the computed dynamic characteristics of the three check valves having the same nominal dimensions. The dynamic characteristics being the measure of the check valve performance, it may concluded that the best suited one for the job is the axial type and that one must expect the strongest water hammer effect from the swing type check valve as it has very steep characteristics. 1.0 0.8 ^0.6 o CD > CD en CD Dt 0.4 0.2 0.0 10 20 30 40 Deceleration (rn/sz) 50 60 Figure(7) Comparison of various types of check valve's dynamic characteristics. Pump systems with check valves attract a special interest and this was investigated in the present work in order to give clear picture to design engineers. It is XVIIgenerally accepted, and also confirmed by our experiment that check valve has almost no influence on systems' deceleration until it closes. Therefore if the deceleration in the system and the dynamic characteristics of the valve were known it would be easy to estimate the maximum reverse velocity and consequently the water hammer. In order to determine the deceleration imposed by the pump either a special computer program matching to the system has to be prepared or an already developed computer code has to be used. For a systematic analysis the second way had to be followed. Then the computer code developed by ÖZGÜR and KAVURMACIOGLU(1992) was used with the help of which it was possible to determine the flow rate and pressure head at the outlet of the pump at any time following a pump trip and to draw the diagrams showing flow versus time in non-dimensional form. A close examination of these diagrams showed that after the power failure the flow decreases until a certain critical time after which it starts to increases again. If the valve closes before the critical time one can use the existing characteristics together with the average deceleration depicted from the diagram and calculate the reverse velocity, otherwise it will be necessaiy to run a program based on complete simulation that takes into account the effect of check valve. This processes is time consuming and such a program may not be available. For this reason a method was developed to see when a system and check valve are under critical conditions and a simple diagram was obtained indicating the border line of the critical zone. The effectiveness of the method was verified by two examples and was found to be quite satisfactory. XV1U
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ERGUN KÖSE
Yüksek Lisans
Türkçe
1986
Gıda MühendisliğiEge ÜniversitesiGıda Mühendisliği Ana Bilim Dalı
DOÇ. DR. S. SEZGİN ÜNAL