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Gas pressure regulators are widely used in both commercial and residential applications to control the operational pressure of the gas. One common problem in these systems is the tendency for the regulating apparatus to vibrate in an unstable manner during operation. These vibrations tend to cause an auditory hum in the unit, which may cause fatigu...
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... schematic diagram of a typical gas pressure regulator (American Meter Gas Regulator, Model 1800) is shown in Fig. 1. High pressure gas flows through an inlet orifice that is opened or closed by a disk and linkage attached to a diaphragm. The diaphragm moves in response to the balance between pressure inside the reg- ulator body and the adjustment spring force. As the regulated pressure increases, the disk closes to restrict the incoming gas. When ...
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... that there is no change in volume for the body chamber, so that _ V body ¼ 0 and the mass balance for the body chamber in Fig. 1 is obtained by summing the mass flow rates in and out of this ...
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... mechanical parts of the system also contribute to the dynamic response of the system. The gas pressure regulator is represented with a simplified model as shown in Fig. 10. Free body diagrams are given in Fig. 11. A simple dynamic analysis of the free body diagrams leads to ...
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... mechanical parts of the system also contribute to the dynamic response of the system. The gas pressure regulator is represented with a simplified model as shown in Fig. 10. Free body diagrams are given in Fig. 11. A simple dynamic analysis of the free body diagrams leads to ...
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... we have used the traditional analysis for the effective mass of a spring, based on the concept of conservation of total energy in the spring [15], even though this is likely a negligible component of the total inertia. Because we make an assumption that the mechanical linkage shown in Fig. 10 is rigid, the inertia and damping are reflected by the square of the motion ratios, where L = R 2 /R 1 . Note that the diaphragm and the plunger displacements are related by x d = Lx p and that the effect of any flow forces on the plunger has been ...
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... equations are also illustrated by the block diagram shown in Fig. 12. The numbers in parenthesis in the figure correspond to equation numbers in the text. For the nonlinear model, four independent equations govern the dynamics of the system. These equations are obtained by combining Eqs. (5), (7), (9) and (22) together with Eqs. (11), (13), (15) and (20); ...
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... operation of the regulator, including the transient response to large and small changes in outlet flow rates and steady state pressure and flow conditions. Our main objective is to show that the simulations operate in a reasonable way in response to normal inputs, and in a manner consistent with observed behavior of the physical gas reg- ulator. Fig. 13 shows the simulation results for the steady state outlet pressure as a function of the outlet flow rate. The three modeling approaches are compared with the empirical data, and it is clear that there is a dif- ference in the steady state response using the linear and nonlinear models, particularly at higher flow rates. Fig. 13 also ...
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... gas reg- ulator. Fig. 13 shows the simulation results for the steady state outlet pressure as a function of the outlet flow rate. The three modeling approaches are compared with the empirical data, and it is clear that there is a dif- ference in the steady state response using the linear and nonlinear models, particularly at higher flow rates. Fig. 13 also shows the input values used to test the models: a small flow demand of 0.001 m 3 s À1 and larger demands of 0.0065, 0.0071, 0.0092 and 0.0098 m 3 s À1 , along with the outlet orifice areas used to generate these flows. First, the linear model will be compared to the nonlinear simulations to show that the linear model is valid for ...
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... First, the linear model will be compared to the nonlinear simulations to show that the linear model is valid for small amplitude response about an equilibrium point. Next, using the linear model, we will apply the powerful root locus techniques to investigate the effects of changes in various parameters on the system response and stability. Fig. 14 shows the time response of both the linear and the nonlinear models to a small step input in flow demand, corresponding to case I in Fig. 13. The initial outlet flow rate was set to Q out0 = 3.9329 · 10 À4 m 3 s À1 and the step change for the outlet orifice area was taken as e A ¼ 1:5355 Â 10 À5 m 2 . Note that the sudden change in the ...
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... about an equilibrium point. Next, using the linear model, we will apply the powerful root locus techniques to investigate the effects of changes in various parameters on the system response and stability. Fig. 14 shows the time response of both the linear and the nonlinear models to a small step input in flow demand, corresponding to case I in Fig. 13. The initial outlet flow rate was set to Q out0 = 3.9329 · 10 À4 m 3 s À1 and the step change for the outlet orifice area was taken as e A ¼ 1:5355 Â 10 À5 m 2 . Note that the sudden change in the outlet valve orifice area causes the pressure to drop, and then come back to the steady state. The sudden change first causes a drop in the ...
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... order to establish the conditions for the regulator to hum, we studied the time response of the regulator with an upper chamber volume about four times larger than the nominal value of the actual hardware, V U0 = 0.0025 m 3 , and the time response is shown in Fig. 15. This condition caused instability in both the non- linear and the linear model. The time response of both the linear and the nonlinear models at these large upper chamber initial volumes predict the frequency of oscillation at about <133 Hz. Fig. 15b also shows that the frequency is the same for both the linear and nonlinear models, ...
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... the nominal value of the actual hardware, V U0 = 0.0025 m 3 , and the time response is shown in Fig. 15. This condition caused instability in both the non- linear and the linear model. The time response of both the linear and the nonlinear models at these large upper chamber initial volumes predict the frequency of oscillation at about <133 Hz. Fig. 15b also shows that the frequency is the same for both the linear and nonlinear models, although there is a phase difference between them. This phase difference is caused by a very small difference in frequency between the nonlinear models and the linear model, which adds up over many cycles. The small lag gets larger if the initial ...
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... same for both the linear and nonlinear models, although there is a phase difference between them. This phase difference is caused by a very small difference in frequency between the nonlinear models and the linear model, which adds up over many cycles. The small lag gets larger if the initial displacement from the equilibrium is made larger [18]. Fig. 16 shows the time response of the regulator models for large and small inputs at the intermediate flow rates of cases II and III in Fig. 13. In the center plot, there are two step changes in the flow demand, a large change at time = 0 corresponding to an initial outlet flow area of A 0 = 1.6903 · 10 À5 m 2 and changing to A = 2.7493 · 10 ...
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... small difference in frequency between the nonlinear models and the linear model, which adds up over many cycles. The small lag gets larger if the initial displacement from the equilibrium is made larger [18]. Fig. 16 shows the time response of the regulator models for large and small inputs at the intermediate flow rates of cases II and III in Fig. 13. In the center plot, there are two step changes in the flow demand, a large change at time = 0 corresponding to an initial outlet flow area of A 0 = 1.6903 · 10 À5 m 2 and changing to A = 2.7493 · 10 À4 m 2 , and a small change at time = 1.0 corresponding to a change in outlet flow area from the steady state at A 0 = 2.7493 · 10 À4 m 2 ...
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... change for the first second is quite large, only the nonlinear models are used in the simulation. Once the steady state is reached, the flow and pressure values are used to update the linear model parameters and the response of the linear and nonlinear models are compared for the small amplitude input, shown in the zoomed portion on the right of Fig. 16. Thus, both the nonlinear and the linear model are com- pared after the step at 1 s in the simulation. For small amplitude inputs, the linear model dynamics closely match the nonlinear model simulations, although there are steady state errors predicted by Fig. 13. This same set of large and small inputs is shown in Fig. 17, but in this ...
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... compared for the small amplitude input, shown in the zoomed portion on the right of Fig. 16. Thus, both the nonlinear and the linear model are com- pared after the step at 1 s in the simulation. For small amplitude inputs, the linear model dynamics closely match the nonlinear model simulations, although there are steady state errors predicted by Fig. 13. This same set of large and small inputs is shown in Fig. 17, but in this case, with a large upper chamber vol- ume V U0 = 6 · 10 À3 m 3 . Again, the initial, large step input is only simulated using the nonlinear models, and the linear model is compared to the nonlinear responses for the small step input at 1.5 s. In this case, the ...
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... portion on the right of Fig. 16. Thus, both the nonlinear and the linear model are com- pared after the step at 1 s in the simulation. For small amplitude inputs, the linear model dynamics closely match the nonlinear model simulations, although there are steady state errors predicted by Fig. 13. This same set of large and small inputs is shown in Fig. 17, but in this case, with a large upper chamber vol- ume V U0 = 6 · 10 À3 m 3 . Again, the initial, large step input is only simulated using the nonlinear models, and the linear model is compared to the nonlinear responses for the small step input at 1.5 s. In this case, the linear model response still follows the nonlinear dynamics, ...
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... models, and the linear model is compared to the nonlinear responses for the small step input at 1.5 s. In this case, the linear model response still follows the nonlinear dynamics, although for both linear and nonlinear cases we see that the increase in the upper chamber volume has the effect of slowing the settling time of the regulator. Fig. 18 shows the time response of the regulator for very high flow rates corresponding to cases IV and V from Fig. 13. These step changes in the outlet orifice area from A 0 = 1.6903 · 10 À5 m 2 to A = 3.93 · 10 À4 m 2 in the first 1 s and A = 3.93 · 10 À4 m 2 to A = 4.2344 · 10 À4 m 2 at 1.5 s correspond to steady state flow rates of Q out = ...
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... In this case, the linear model response still follows the nonlinear dynamics, although for both linear and nonlinear cases we see that the increase in the upper chamber volume has the effect of slowing the settling time of the regulator. Fig. 18 shows the time response of the regulator for very high flow rates corresponding to cases IV and V from Fig. 13. These step changes in the outlet orifice area from A 0 = 1.6903 · 10 À5 m 2 to A = 3.93 · 10 À4 m 2 in the first 1 s and A = 3.93 · 10 À4 m 2 to A = 4.2344 · 10 À4 m 2 at 1.5 s correspond to steady state flow rates of Q out = 0.0092 m 3 s À1 and to Q out = 0.0098 m 3 s À1 respectively. Again, the steady state values of the nonlinear ...
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... large step input are used update the linear model parameters. Thus, both the nonlinear and the linear models are compared in the second part of the simulation, shown in the right of the figure. Note that during the initial response for the large step input, the system is very under damped, as shown by the oscillations in the left-hand portion of Fig. 18. For the smaller input at the higher flow rate, however, the dynamics show considerably more damping, indicating that higher flow rates tend to stabilize the system. Fig. 19 shows the response for this same set of inputs with the larger upper chamber volume, V U0 = 6 · 10 À3 m 3 . Here again, it is clear that the higher flow rates tend ...
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... right of the figure. Note that during the initial response for the large step input, the system is very under damped, as shown by the oscillations in the left-hand portion of Fig. 18. For the smaller input at the higher flow rate, however, the dynamics show considerably more damping, indicating that higher flow rates tend to stabilize the system. Fig. 19 shows the response for this same set of inputs with the larger upper chamber volume, V U0 = 6 · 10 À3 m 3 . Here again, it is clear that the higher flow rates tend to stabilize the system ...
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... the system with nominal parameter values, the system was stable, although there are roots close to the right half plane. The roots of the characteristic equation for the transfer function of the block diagram in Fig. 12 are À7306.4, À27.7 ± 801.9i, À62.7 ± 41.1i when V U0 = 6 · 10 À4 m 3 , and À7306.3, À92.3, À21.9, 1.9 ± 655.7i with V U0 = 0.0025 m 3 ...
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... are two plots shown, one for a small upper cham- ber volume, V U0 , and one for a large upper chamber volume. While increasing the damping reduces the ten- dency toward unstable behavior, excessive increases in damping tends to increase the transient response time of the system, and lead to undesirable steady state effects such as dead-band. Fig. 19. Time response to step changes in outlet area, V U0 = 6 · 10 À3 m 3 . Table 1 Nominal values of parameters used in the linear ...
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... parameter that is a candidate for design change is the diaphragm area. The root locus for A d , shown in Fig. 21, shows some interesting trends. While the root locus shows that the diaphragm could be made very small and result in stable performance of the regulator, this size diaphragm is not large enough to counteract plunger flow forces or even allow mechanical connections necessary for the physical ...
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... of Fig. 25, and the effective lower chamber flow diameter has been decreased by a factor of ten, based on the root locus of Fig. 23. Recall that with the nominal values for the flow diameters, an upper cham- ber volume of 0.0025 m 2 was sufficient to cause instability at low output flow rates using both the linear and nonlinear models as shown in Fig. 15a. Fig. 26 shows that these two simple changes the upper and lower dis- charge coefficients are sufficient to stabilize the system response for smaller output flow rates regardless of the size of the upper chamber volume. Larger output flow rates tend to stabilize the system as shown in Figs. 17-19. However, even at the low flow rates ...
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Citations
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... A rising amount of experimental data indicates to microscale vortex cavitation as a primary event in the origin of life. [22] 2006 This study examines the research done to better understand cavitation damage. The study also examines the work done on cavitation damage in liquid sodium, and it finishes with a discussion of the reasons for the report's poor effectiveness in predicting damage. ...
... Cavitation results in pitting & its reduces the strength of pressure vessel & may lead to an accident. The work discusses the theoretical formulation of cavitation bubble collapse and the estimation of bubble collapse pressure, as well as experimental methodologies for measuring cavitation damage [22]. ...
Pressure regulators have been part of industries to address various requirement related to pressure settings. Being in industry since long time, lot of research's have already been done to address issues & improve performance. The published research papers had addressed the performance issues like cavitation (that happens due to sudden pressure drop causing the bubble formation at localized area which in term results in cavitation), high pressure, high-pressure differential(which is normally achieved by multistage of regulator as single stage regulator cannot work above certain pressure differential), pressure stability (by adding sensitive diaphragm & high precision controlled orifice seat),corrosion (by using high grade NACE complain material like 316L & duplex stainless steel),various failures (like galling, mushroom formation, pitting, diaphragm rupture) & safety (by designing regulator as per various internal standard like PED, ASME BPVC). Ergonomic aspect of pressure regulator considering the human comfort found missing. This paper addresses the ergonomic aspects pressure regulator to ease setting downstream pressure with non-stretching & frictionless material. Research will also address to make pressure regulator setting uniform torque across the pressure range making regulator more sensitive for precise pressure setting. It also addresses the requirement of high flow through controlled orifice by introducing a bypass system working in parallel with controlled regulator to achieve fast volume filling at high pressure.
... A rising amount of experimental data indicates to microscale vortex cavitation as a primary event in the origin of life. [22] 2006 This study examines the research done to better understand cavitation damage. The study also examines the work done on cavitation damage in liquid sodium, and it finishes with a discussion of the reasons for the report's poor effectiveness in predicting damage. ...
... Cavitation results in pitting & its reduces the strength of pressure vessel & may lead to an accident. The work discusses the theoretical formulation of cavitation bubble collapse and the estimation of bubble collapse pressure, as well as experimental methodologies for measuring cavitation damage [22]. ...
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... Zafer and Luecke proposed a nonlinear model and analyzed the behavior of a self-regulating high-pressure gas regulator [8]. A linear version of the model was also developed, which made it possible to analyze the stability of the system with changes in various design parameters using the root locus techniques. ...
... Taking into account the throttle block, the energy equations for variable mass of gas in cavities A and E can be written as: , (8) , (9) As a feedback pipeline, we consider a pipeline of constant cross-section with a gas flow model in lumped parameters neglecting heat exchange with the environment. Then, the mass flow equation taking into account active and reactive resistances is: , To obtain more general solutions, it is expedient to represent the system of Equations (1)-(10) in dimensionless form. ...
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2
, the mainspring stiffness is 166.76N/mm, and the leakage area of spool seal is 0.06 mm
2
.
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