Abstract

Introduction

During the priming of a spacecraft propulsion system, the filling of an evacuated pipeline can generate severe waterhammer spikes due to the column of liquid impacting a closed thruster valve. A severe example of this occurred on the Compton Gamma Ray Observatory, on April 7, 19911. During this mission fluid components downstream were damaged during the priming event. Once in orbit an isolation valve or a pyrotechnic valve opens, creating this priming event, which can be destructive due to the large amount of energy that is released. A typical satellite propulsion system is shown in Figure 1. A Valcor Thruster Valve shown, in Figure 2, and is used to control the flow of hydrazine to the thruster. Orifice restrictions have been used to slow down the flow during the priming event2,3. A flow limiting device, commonly known as a flow fuse, will be used to replace a fixed orifice. A literature search of the use of such a device in a propulsion system yielded no previous results. The lack of use of such a device may be due to certain concerns about improper operation during use. This paper will show that if a flow device is properly sized, it can be used during a priming event with great success, and no unintended consequences.

Flow Fuse Description

The flow fuse is a check valve with its poppet spring loaded open. It is a flow sensitive device in the normal flow direction. It is a free flow element in the reverse direction. A typical commercial flow fuse is show in Figure 34. The mechanical operation is simple as the poppet is the only moving part. Under normal conditions, the poppet is spring loaded to the open position. During this condition and up to the trip point, the force differential created by the flow across the poppet is equal to or less than the spring force. If the flow increases beyond the trip point, as would occur if a downstream pipe ruptured, then a large pressure differential across the poppet will counteract the spring force, thus slamming the valve shut. The same closure would occur in the case of a priming event, when a downstream valve suddenly opens up into an evacuated line, thus having the same effect as a line rupture. A properly sized flow fuse will be designed with a flow trip point well above the nominal expected flow. This will guarantee that flow fuse will not accidentally trip, which would occur if the flow fuse was undersized. A properly sized flow fuse will also be designed with a flow trip point well below the expected surge flow that would occur in a line breakage or a priming event. This will guarantee that the flow fuse will close when needed, which would not occur if the flow fuse was oversized.

The flow fuse that will be used in this study is a 3/8″ line size, and has a trip point of 5.4 gpm of water. The proposed flow fuse will have a poppet that has an open orifice of .200 inch, and a closed (tripped) orifice of .075 inch. To accomplish reducing the flow during the priming event, the flow fuse used will have a .075 inch hole in the center of the poppet. When the flow fuse is tripped the flow will be reduced by only allowing flow through the .075 inch hole, and no longer across the .200 inch seat.

Modeling Approach

Historically water hammer was first studied for systems with instantly closing or opening valves. The first person to describe this effect was the Russian scientist Joukowski, who is responsible for the formula for pressure rise, which bears his name. The Joukowski Formula is shown in Figure 4. The system to be modeled is shown in Figure 5. The parameters of the model are listed in Table 1. Two dynamic models were created for this investigation.

For the first approach, the fluid was modeled as a rigid column accelerating upon valve opening and including both inertia and friction effects5. The model reduces the feedline to an Ordinary Differential Equation (ODE). This is done by reducing the feedline to a lumped one-dimensional model. The Lumped Model equations are shown in Figure 6. This model was used to calculate the velocity of the fluid column when it reaches the closed thruster valve. The pressure rise when then calculated from the Joukowski Formula.

For the second approach, the feedline was modeled as a Partial Differential Equation (PDE) by using the Method of Characteristics (MOC)6. This model divided the feedline into 100 segments. This second model can then provide more accurate results, by including the elastic effects of the fluid and the pipe, along with the transient pressure waves created when the flow fuse, isolation valve, and thruster valve, open and close. The MOC model used the method of Lin and Baker7, who used the Method of Characteristics (MOC) to treat one-dimensional liquid transients in liquid-full segments, and the lumped-inertia technique to model the dynamics of partially filled segments. The equations for MOC are shown in Figure 7. The equations for the partially-filled segment are shown in Figure 8.

The following is a list of general modeling assumptions:

• 1D axisymmetric flow
• Wave speed is constant (density is constant)
• Mach Number <<1
• Constant pipe diameter
• Pipe is straight, no bends or tees
• Friction modeled using Darcy-Weisbach Formula
• Vaporization of propellant produces a negligible amount of gaseous propellant
• Thruster valve opening and closing time is instantaneous
• Isolation valve opening time is instantaneous
• Flow Fuse closing time is instantaneous

Priming Event Simulation Results (Lumped Model)

Three priming event simulations were run with the Lumped Model. The lumped model was run using water as the liquid propellant, to allow for ease of comparison to tests that are scheduled to be performed late Spring 2018. The results are listed in Table 2. Case 1, no flow fuse, has an extremely high flow, 15.1 gpm, and an extremely high pressure, 3,907 psi. This shows the need for a surge suppression device. Without a restriction the impact time is only .176 seconds. It can be seen from Figure 9 that the flow reaches a maximum and then decreases before impact. Cases 2 and 3 are similar since the closed flow fuse ESEO is .075 inch, which is the same as the fixed orifice in Case 3. Cases 2 and 3 have a greatly reduced velocity and pressure due to the .075 inch flow restriction. It can be seen from Figure 10 that the velocity quickly reaches a steady state value of 108 in/second, and remains constant until impact. The assumption that the liquid moves as a slug is shown to be a valid assumption, since the velocity of the liquid is much slower than the wave speed of 568,900 in/sec. This means that the lumped model should provide accurate results.

Priming Event Simulation Results (MOC Model)

Three priming event simulations were run with the MOC Model. The MOC model was run using water as the liquid propellant, to allow for ease of comparison to tests that are scheduled to be performed late Spring 2018. The simulations were run for the same scenarios that were run for the Lumped Model. The results are listed in Table 3. Case 4, without the flow fuse, has an extremely high pressure of 3,730 psi, and an extremely high flow of 14.1 gpm, as is shown in Figure 11 and Figure 12. All of the results for these cases very closely match the results for the Lumped Model. The impact time is .180 seconds, without the flow fuse. It can be seen from Figure 12, that the flow reaches a maximum and then decreases before impact. Cases 5 and 6 are similar since the closed flow fuse ESEO is .075 inch, which is the same as the fixed orifice in Case 6. The MOC model shows the slight difference between Case 5 and Case 6, which could not be seen with the Lumped Model. The max pressure for Case 5, 1098 psi, is higher than the max pressure for Case 6, which is 901 psi. The max pressure for Case 5 occurs when the flow fuse closes, at time = .01 seconds. This is shown in Figure 13 and Figure 14. This closure reduces the max flow from 5.4 gpm to 2.0 gpm, which produces the max pressure. It should be noted that this max pressure spike was upstream of the flow fuse and never traveled downstream to the thruster. The max pressure for Case 6, 901 psi, occurs when the flow impacts the closed thruster valve. This reduces the max flow from 2.0 gpm to 0 gpm. This same scenario occurs for Case 5 when the flow impacts the thruster valve. The pressure at the thruster valve for Case 5 is also 901 psi. Case 6 has the fixed orifice instead on the flow fuse, so the flow for this case never exceeds 2.0 gpm.

Thruster Firing Simulation Results (MOC Model)

Three thruster firing simulations were run with the MOC Model. The MOC model was run using water as the liquid propellant, to allow for ease of comparison to tests that are scheduled to be performed late Spring 2018. The simulations were run to determine the pressure transients that occur during the thruster firing in a fully primed system. The thruster valve ESEO is .075 inch. The thruster valve will cause a waterhammer spike when the thruster valve is closed. Since the flow fuse should not close during the thruster firing, Case 8 was run to prove this out. The thruster valve was opened at time = 0 second, and closed at time = .2 seconds for all three cases. During this time a steady state flow was established that was used to determine the pressure drop in the feedline for all three cases. The results are listed in Table 4. Case 7, without the flow fuse, has the lowest pressure drop of 10 psi, and the highest closing pressure of 931 psi. Cases 7 and 8 are similar since the open flow fuse ESEO is similar to the no flow fuse ESEO. The highest pressure loss, 75 psi, is for Case 9 with the fixed orifice of .075 inch. The Case 9 flow is only 1.5 gpm, which is less than the required 2.0 gpm flow, due to the .075 inch orifice. The flow fuse stayed open as expected, and the flow never exceeded 2.0 gpm, which is well below the flow fuse trip point of 5.4 gpm. It should be noted that maximum pressure for the thruster valve closing for Case 8 (with flow fuse), is very similar to the maximum pressure for the priming event for Case 5 (with flow fuse). This is because the same flow rate of 2.0 gpm is stopped at the thruster valve for both events.

Conclusions

These simulation models provided an ideal tool for evaluating waterhammer effects in propellant tank feedlines during the priming event and during normal thruster operation. The results from the simple Lumped Model closely matched the MOC model results. As a rule of thumb, waterhammer spikes should not exceed the proof pressure rating of both the pressurization lines and the flow control components. The advantage of the flow fuse is that it provides the needed flow restriction only during the priming event, and not during normal operation. The results from this investigation show that the use of a flow fuse will greatly reduce waterhammer. A properly sized flow fuse will produce the same pressure rise when closing as does the thruster valve when closing, thus not putting any more stress on the system than the thruster would. The margins for the flow fuse operation are listed in Table 5. The margin for the priming event is intended to show how much flow the system would demand above the trip flow, since the flow fuse is intended to close during this event. The margin for the thruster firing event is intended to show how much less flow the system would demand below the trip flow, since the flow fuse is intended to stay open during this event. The margins for closing and staying open are both approximately 171%. This means that the flow fuse will reliably perform its intended task with confidence. A fixed orifice of the same size as the flow fuse, would not be as efficient as the flow fuse since it would cause additional pressure loss during the thrusting firing events.

It is unknown why flow fuses have not been previously used in propellant systems. Some engineers may have misgivings about using these devices due to stories about unintended flow fuse closings, which cause other problems. Almost all flow fuse problems can be traced to improperly sized devices. Flow fuses are also available with dashpots, which eliminate unintended closures caused by short duration pressure spikes, thus providing more protection against unintended closures.

As of recently the natural gas industry has become more comfortable with installing flow fuses in gas lines8. Initially flow fuses were installed in gas lines, during the ’60s and ’70s, when there weren’t any guidelines for flow fuses. This lead to lots of unwanted flow fuse closures, since they were installed in lines with unknown flow demands. In 2015 the Pipeline and Hazardous Materials Safety Administration (PHMSA) proposed requiring all utilities to install flow fuses in all pipe lines that have a capacity of 1,000 cfh or less. It is estimated that by the end of 2018, there will be over 12 million flow fuses in service in gas pipe lines.

References

• 1) Dressler, G., “Compton Gamma Ray Observatory” JPC AIAA 2001-3631.
• 2) Morgan, Michael J, “Pressure Transient Characterization Test for Star-2 Propulsion System Fuel Manifold” JPC AIAA 2004-3666.
• 3) Netwall, Christopher, “Transient Pressure Analysis and Verification Testing for the Micro-Satellite Technology Experiment (MiTEx) Upper Stage Propulsion System” JPC AIAA 2007-5523
• 4) Swagelok Excess Flow Valve, P/N SS-XS6 Series
• 5) Hearn, Henry C, “Development and Application of a Priming Surge Analysis Methodology” JPC AIAA 2005-3738.
• 6) Wylie, E. B. and Streeter, V.L., “Applications of Fluid Mechanics,” pp 500-514.
• 7) Lin, T.Y., “Analysis and Testing of Propellant Feed System Priming Process” Journal of Propulsion and Power, Vol. II, No. 3, May-June 1995
• 8) Erickson, John, “Industry Becoming More Comfortable with Excess Flow Valves”, Pipeline and Gas Journal, January 2016, Vol. 243, No 1.