Numerical modal analysis of Howell Bunger valve using FEM method Farid Vakili Tahami, Mohammad Zehsaz, Mohammad Ali Saeimi Sadigh, Amin Paykani Department of Mechanical Engineering, University of Tabriz, Tabriz 51666 16471, Iran a.paykani86@ms.tabrizu.ac.ir ABSTRACT Fixed cone (Howell Bunger) valves have been in wide use for many years for flow control. These valves may face different types of damages and failures due to vibrational stresses during operation. In this study, a number of modal analyses of a Howell Bunger (DN: 1000 mm) valve made by Mechanic AB Co, are conducted using the Finite Element Method (COSMOS/Works) and its natural frequencies with vibrational mode shapes in five cases including fully opened, 20%, 40%,and 80% opening conditions were determined, then, the dimensionless coefficient "Mercer" was obtained for the valve. The result showed that the operating point of the valve is the flow rate of16 m 3 /s and valve opening degree of 40%, in this case due to reinforcement resulted from moving shell, the structure strength against vibration increases and as a result, natural frequency increases as well. Keywords: Failure, Howell Bunger valve, Modal analysis, Natural frequency. 1. Introduction Valves used in floodgate applications have different design requirements and are usually located at the base of dams. Often, the most important requirement (besides regulating flow) is energy dissipation. Since water is very heavy, it exits the base of a dam with the excessive force of water pushing from above. Unless this energy is dissipated, the flow can erode nearby rock and soil and damage structures. Other design requirements include considering pressure head operation, the flow rate, whether the valve operates above or below water, and the regulation of precision and cost. Fixed cone valves, also known as Howell Bunger valves, are designed to dissipate the energy from a water flow during reservoir discharge. They are a round pipe section with an adjustable sleeve gate and cone at the discharge end. Flow is varied by moving the sleeve away or towards its cone seat. The design allows high pressure water from the base of a dam to be released without causing erosion to the surrounding environment (Mefford, 1982). The accurate design of valve is an important factor in its future performance (Smith,2003). These valves may face damage and failure due to the vibrational stresses. The reports show that vibratioanl failure of valve can happen in presence of exciting external source when the frequency of it coincides to the natural frequency of the valve. One of the most important factors of excitation is the water stream crossing through the valve which its frequency depends on some parameters as type, condition and distance of valves, knee joints and other upstream instruments. Excessive vibration of the valve especially during resonance period causes crack creation or deformation of blades which are jointed to the cone shape part. This type of failure indicates the presence of hydro elastic defections in the valve. Therefore, it is necessary to define a parameter corresponded to the hydro elastic characteristics to investigate failure probability in a way that critical discharge flow rate is obtained for each valve in order to decrease failure risk. To obtain this parameter, modal analysis is performed for each valve to compute natural 649
frequencies. Detailed modal analysis determines the fundamental vibration mode shapes and corresponding frequencies. The results of a modal analysis help determine whether a model requires more or less damping to prevent failure. In this study, modal analysis of a Howell Bunger (DN: 1000 mm) is conducted using the Finite Element Method (COSMOS/Works) and its natural frequencies along with vibrational mode shapes in five cases including fully opened, 20%, 40%,and 80% opening conditions were determined, then, the dimensionless coefficient "Mercer" was obtained for this valve. Using this number, it would be possible to determine allowable value of flow rate range for the valve to avoid excitation risk. This valve is responsible for discharge flow of a dam designed and constructed in North of I.R IRAN, with nominal pressure head of 90 meters with 16 m 3 /h flow rate. 2. Modeling VIA Cosmos/Works The three dimensional geometric model of the Howell Bunger valve was constructed using SolidWorks for the current work. In order to perform modal analysis, COSMOS/Works FEM software was used. The aim of this approach is obtaining critical points in the model which have largest deformations and stresses as a result of resonance. The stress resulted from the vibrations in these parts would cause the fatigue failure phenomenon in a way that fatigue cracks are created and developed in critical points and if that part be in a corrosive environment, the crack development rate and its sudden failure would be increased. During valve closing and opening period the hydraulic pressure increases from minimum to maximum level, now if, the system vibrate due to excitation resulted from hydraulic forces and the vibrational frequency coincide to the natural frequency of the system, the resonance will occur. According to the reports, the destructive effect of fatigue failure resulted from vibrational loads would occur at internal vanes of Howell Bunger valve. Figure 1 shows a conceptual model with exerted boundary conditions. The length of 1500 mm from the external body is located in the concrete, so, the model was completely fixed here. In addition, According to the system shape and types of constraints, it is predicted that the aerate pipes would be in the most critical point jointing, due to creation of vibration. This phenomenon causes the failure of weld joints between the pipe and the body. Moreover, internal vanes will have the largest deformation due to the slight thickness of them under excitation. Figure 1: The FEM model of the Howell Bunger valve (DN: 1000 mm) 650
3. Results of Modal Analysis 3.1 Results of complete model analysis The results of modal analysis for complete model of Howell Bunger valve are summarized in Table 1, and the displacement contours for the model during the resonance are shown in Figure 2. It is obvious from the Figures that the aerate pipes have the largest displacement under vibrational excitation due to inadequate constraints which it causes an extreme stress at the joint and finally leads to failure of weldment joint. The displacement of the aerate pipe end reaches up to 160 mm as shown in Figure 2. 3.2 Results of revised model analysis According to the results presented in the previous part, the most critical point of the system is the place where aerate pipes join together. Now, in order to find the second critical point the suppress technique was employed. In the following model, the analysis was conducted ignoring the aerate pipes effects. By eliminating the aerate pipes, their vibration do not have any effect on vibration of vanes, however, appropriate boundary conditions should be defined at the joints location. Figure 3 depicts the revised model used for the modal analysis. The results of modal analysis for it are summarized in Table 2. This table accompanying Figure 4 indicate when the aerate pipes' joints are strengthen; the critical point during valve vibration would be the internal vanes of the valve. Figure 2: Displacement contour of the complete valve: a) First mode b) Second mode 651
Fixed Area Fixed Area Figure 3: The revised model of the Howell Bunger valve (DN:1000 mm) without aerate pipes. Table 1: Natural frequencies of the complete valve with aerate pipes. Number (Hz) Intermittent Time Period (s) 1 28.694 0.034851 2 28.771 0.034757 3 54.796 0.018249 4 55.121 0.018142 5 92.935 0.01076 Figure 4: Displacement contour of the revised model without aerate pipes: a) First mode b) Second mode 652
Table 2: Natural frequencies of the revised valve without aerate pipes Number (Hz) Intermittent Time Period (s) 1 92.785 0.010778 2 149.21 0.0067018 3 149.22 0.0067016 4 229.04 0.0043661 5 229.13 0.0043644 The first two modes of the valve vibration as shown in Figure 4 demonstrates that the internal vanes are the most critical point during the vibration and displacement of the vanes reaches to 76 mm at the first natural mode. 3.3 Results of model without hood The results of the previous part revealed that by eliminating or fixing the aerate pipes, the internal vanes are the most critical point in modal analysis. In order to more accurately consider the internal sections of the body which are known as critical points, the hood is temporarily omitted and the complete constraint condition (U x, U y, U z ) was applied. The new revised model with boundary conditions is shown in Figure 5. The results of modal analysis for it are summarized in Table 3. Comparing the results of 3.2 and 3.3 sections indicate that the frequency of the first mode for the model with hood and without hood is 92.785 Hz and 94.244 Hz respectively. This shows that omitting the hood was right at the hood joint location. In the second model, it is observed that the maximum displacement transferred towards the hood at higher modes and it transferred towards the moving shell in the third model. In addition, the numerical results show that the moving shell is the second critical point of system after the hood and omitting the hood has no considerable effect in the first and second modes of the valve. Figure 6 portrays the displacement contours for new revised model at the first and second mode. Figure 5: The new revised model of the Howell Bunger valve (DN:1000 mm) without aerate pipes and hood. 653
Table 3: Natural frequencies of the new revised valve without aerate pipes and hood. Number 3.3 Effect of valve closure (Hz) Intermittent Time Period (s) 1 94.244 0.010611 2 183.63 0.0054457 3 183.68 0.0054443 4 382.37 0.0026153 5 401.95 0.0024879 In this section the effect of valve closure on natural frequencies are studied. Natural frequencies for 20%, 60% and 80% of valve closure conditions are shown in Tables 4 respectively. Concentrating on the first mode in each case, shows that by closing the flowcontrolling shell the natural frequency increases, hence the probability of resonance occurrence and fatigue failure in vanes decreases. According to the technical data represented by the Mechanic AB Co, the Howell Bunger valve will not use around the 60% closure range. Figure 7 shows the first mode for each case. Figure 6: Displacement contour of the new revised model without aerate pipes and hood: a) First mode b) Second mode 654
3.4 Results of final model According to the results obtained, fixing the aerate pipes is necessary. In this section, the complete model of the valve considering connection of aerate pipes through fastener to the concrete wall was studied at 60% valve closure. It is predicted that constraining the aerate pipes can cause elimination of their vibrational problems. Figure 8 shows the locations of exerted constraints and boundary conditions. The results of modal analysis for it are summarized in Table 5. It is clear that the value of first and second natural frequency is 162.01 and 162.05 respectively. Figure 9 depicts the contours of model deformation for the first and second mode. It is obvious from figure 9 that the displacement of aerate pipes is near zero, therefore, constraining the pipes with fastener resolved the resonance problem. It is notable that the largest deformation is created in internal vanes of the valve's cone shape end during resonance which its value is 41 mm. It is the reason that even in this case the excitation of valve must be prevented at the natural frequency range; otherwise, the internal vanes will encounter the failure. According to the results of this model, the value of Mercer coefficient equals to 1.56. Consequently, the amount of flow rate which can cause resonance equals to 18.29 m 3 /s. Therefore, it would be possible for the valve to pass the nominal flow rate of 16 m 3 /s (Q<18.29) through itself. Table 4: Natural frequencies of the new revised valve without aerate pipes and hood: a)20% valve closure b) 60% valve closure c) 80% valve closure Number (Hz) Intermittent Time Period (s) 1 125.82 0.0079476 2 173.48 0.0057645 3 173.56 0.0057617 4 325.25 0.0030746 5 374.74 0.0026685 Number (c) (Hz) Number (Hz) Intermittent Time Period (s) 1 162.52 0.0061531 2 162.58 0.0061507 3 247.84 0.0040349 4 362.8 0.0027563 5 403.35 0.0024792 Intermittent Time Period (s) 1 155.98 0.0064109 2 156.06 0.006408 3 335.29 0.0029825 4 391.58 0.0025537 5 410.75 0.0024346 655
(c) Figure 7: Displacement contour of the new revised model without aerate pipes and hood: a) 20% valve closure b) 60% valve closure c) 80% valve closure Figure 8: The final model of the Howell Bunger valve (DN:1000 mm) with constraints at aerate pipes. 656
Table 5: Natural frequencies of the final valve with constraints at aerate pipes and 60% closure Intermittent Number (Hz) Time Period (s) 1 162.01 0.0061726 2 162.05 0.0061708 3 246.43 0.004058 4 258 0.0038759 5 258.44 0.0038694 Figure 9: Displacement contour of the final valve with constraints at aerate pipes and 60% closure a) First mode b) Second mode 4. Results and Discussion Since the first and second frequencies have the significant effect in vibration problems, the comparison between these two were performed in this section. A summary of results are shown in Table 6. The aerate pipes are the first points which are prone to failure arising from valve vibration as shown in Table 6. One solution for this problem is to fix these pipes which 657
were discussed in section "3.5". Comparing natural frequencies of the valve for hood and without hood exhibits that presence of it does not have considerable effect in value of complete valve natural frequency. Moreover, the results showed that the critical frequency for the valve has the lowest value in fully opened condition so it has the worst condition from this viewpoint. By closing the valve up to 60%, the first natural frequency increases from 94.24 Hz to 162.25 Hz. It would be stated that by closing the valve to 60%, if the streaming water velocity increases proportionally, the excitation frequency would be enhanced and the feasibility of the resonance occurrence is possible. Considering the second natural frequency, it was observed that the valve has the highest natural frequency in fully opened condition and it decreases with closing the valve. The variations in natural frequency with closing the valve are attributed to two main factors. Firstly, the moving shell approaches to the cone shape end with closing the valve, so, the structure would have a consistent situation. Secondly, due to movement of the moving shell, the valve's center of gravity shifts. These two factors may result in change of system's natural frequency. Regarding the high displacements of critical points during resonance (approximately 76 mm for the vanes and 166 mm for the ends of aerate pipes) it can be concluded that as the resonance happen very high stresses will produce in these points which can lead to fatigue failure of the parts. 4.1 Prediction of permissible flow rate Based on the Mercer dimensionless coefficient [5], it can be possible to obtain the approximate allowable passing flow rate through the valve which leads to resonance. According to this coefficient natural frequency defined by: f E T V = c (1) 2 ρ D Using the equation (1) and the definition of characteristic length "S" as stated in equation (2), the approximate allowable passing flow rate through the valve can be obtained during resonance as: V S = (2) f Q π S C. D. T V = (3) 4 D E ρ Where all of the parameters are known for the valve through the data from Mechanic AB Co. Assuming that the critical velocity and rupture due to the resonance occur at the same kinematics conditions, the rupture should take place at an equal value of term π S / 4 D. Mercer investigated various Howell Bunger valves with different diameters and flow rates, finally, he found that the value of π S / 4 D should not exceed 0.113 [5]. The results of Mercer coefficient computations and flow rates for the first and second natural frequency are summarized in Table 7. 658
Table 6: The results of numerical study for Howell Bunger valve made by Mechanic AB Co in each case Valve The type of Maximum Mode condition Model ( mm ) displacement Critical point Complete 1 28.7 166 Aerate pipes 2 28.7 166 Aerate pipes 1 92.7 76.1 Controller vane pipes 2 149.2 39.36 Controller vane 1 94.24 76.20 Controller vane pipes and hood 2 183 48.50 Controller vane 20% closure 1 125.8 77.20 Controller vane pipes and hood 2 173.5 44.80 Controller vane 60% closure 80% closure pipes and hood pipes and hood 1 2 1 2 162.25 162.58 155.98 156.06 41.3 41.7 38.81 38.81 Controller vane Controller vane Controller vane Controller vane Table 7: The Mercer coefficient for the Howell Bunger valve: a) first natural frequency b) second natural frequency Valve condition 20% closure 60% closure 80% closure Model type Complete pipes pipes and hood pipes and hood pipes and hood pipes and hood 28.7 92.7 94.24 125.8 162.25 155.98 Mercer 0.28 0. 89 0. 91 1.21 1.56 1.50 Allowable head (m 3 /s) 3.26 10.36 10.59 14.09 18.29 17.46 Valve condition Model type Complete pipes pipes and hood 28.7 149.2 183 Mercer 0.28 1.44 1.76 Allowable head (m 3 /s) 3.26 16.88 20.72 20% closure pipes and hood 173.5 1.67 19.56 60% closure pipes and hood 162.58 1.57 18.29 80% closure pipes and hood 156.06 1.50 17.58 659
5. Conclusion A number of modal analyses of a Howell Bunger (DN: 1000 mm) in different cases were conducted using the Finite Element Method (COSMOS/Works) to optimize its vibrational characteristics. Based on the results and considering the design features, the operating point of the valve is the flow rate of 16 m 3 /s and valve opening degree of 40%. The following conclusions can be drawn from this study: 1) The aerate pipes must be certainly fixed to prevent their failure during function. 2) The passing flow rate through the valve mostly adjusted in a way that the exciting frequency created due to passage of stream would not be more than first frequency and lower than second frequency. So, for the model without fixed aerate pipes and fully opened condition it can be possible to pass the approximate flow rate of 13.6 m 3 /s or (10.36<Q<16.88) through the valve, provided that it pass from the low flow rate condition of 10 m 3 /s quickly and does not stop anyway. 3) Given based on design, the operating point of the valve is the flow rate of16 m 3 /s and valve opening degree of 40%, in this case due to reinforcement from moving shell, the structure strength against vibration increases and as result, natural frequency increases as well. This is why the 40% opening condition is the best status for the valve and it would be able to pass head of16 m 3 /s or (Q<18.29). Acknowledgement The authors are grateful for technical and financial support provided by the Mechanic AB Co. References 1. US Army Corps of Engineers. Engineering manual 1110 2 2607, Planning and Design of Navigation Dams, Chapter 5, Overview of gate types. Retrieved 2008 04 14. 2. Mefford B.W., 1982. Submerged operation of the fixed cone valve, Hydraulics branch official copy. PAP 560. 3. Skousen L. Philip., 2004. Valve Handbook McGraw Hill Professional Publishing, ISBN 9780071437738. 4. Smith P., R.W. Zappe R.W., 2003. Valve Selection Handbook, Fifth Edition: Engineering Fundamentals for Selecting the Right Valve Design for Every Industrial Flow Application, Gulf Professional Publishing. 5. Mercer A.G., 1962. Turbulent boundary layer flow over a flat plate vibrating with transverse standing waves, ST. Anthony falls hydraulic laboratory, University of Minnesota, Technical paper number 41B. 660