EXPERIMENTAL STUDY OF WATER HAMMER PRESSURE SURGE

During the start-up of the propulsion system of a satellite or space-craft, the opening of the tank isolation valve will cause the propellant to §ow into an evacuated feedline and slam against a closed thruster valve. This ¦lling process, called priming, can cause severe pressure peaks that could lead to structural failure. In the case of monopropellants such as hydrazine, also, the risk of adiabatic compression detonation must be taken into account in the design of the feedline subsystem. The phenomenon of priming involves complex two-phase §ow: the liquid entering the evacuated pipe undergoes §ash evaporation creating a vapor cush-ion in front of the liquid that mixes with the residual inert gas in the line. Moreover, the dissolved pressurizing gas in the liquid will desorb making the priming process di©cult to model. In order to study this phenomenon, a new test-bench has been built at DLR Lampoldshausen which allows §uid transient experiments in the same conditions as the operating space system. Tests are performed with water and ethanol at di¨erent conditions (tank pressure, vacuum level, pressurizing gas helium vs. nitrogen, etc.). The e¨ect of the geometry is also investigated, comparing di¨erent test-elements such as straight, tees, and elbow pipes. The pressure pro¦le is found to be dependent on the geometry and on the downstream conditions. The acoustic wave re§ection caused by the pipe geometry and §uid dynamic e¨ects such as the aforementioned des-orption and


INTRODUCTION
For safety reasons, the propellant feedlines of a satellite or spacecraft are usually evacuated prior to launch.Once in orbit, the start-up of the propulsion system of the satellite involves the opening of the tank isolation valve that will cause the propellant to §ow into the evacuated feedline and slam against a closed thruster valve.This ¦lling process, called priming, can cause severe pressure peaks that can lead to structural failure.In the case of monopropellants such as hydrazine, also, the risk of adiabatic compression detonation must be taken into account in the design of the feedline subsystem.The hazard of the adiabatic compression detonation was experimentally proved by Bunker et al. [1].They demonstrated that the explosive events observed in hydrazine experiments were caused by chemical reactions of liquid hydrazine (exothermic decomposition) not induced by water-hammer e¨ects but rather due to the rapid compression of the noncondensable gas present in the line.Hydrazine detonation accidentally occurred during the testing of the satellite propulsion system for the ISPM (International Solar Polar Mission) [2] which led to the destruction of the entire test-bench.According to the authors, the cause was (probably) a local high temperature along the pipe which caused the detonation of hydrazine.
To prevent this potential hazard, the solution is to slow down the §ow through the use of a §ow restriction device (venturi [3,4] or ori¦ce [5,6]) or by using the gas cushion e¨ect of a pre¦lled inert gas in the line.
The phenomenon of priming involves complex two-phase §ow: the liquid entering the evacuated pipe undergoes §ash evaporation creating a vapor cushion in front of the liquid that mixes with the residual inert gas, usually helium.Moreover, the dissolved pressurizing gas in the liquid will desorb making the priming process di©cult to model numerically due to the lack of understanding of these physical processes.Numerical codes available today for §uid transient calculations can give accurate predictions for single-phase water hammer, but they still need improvements while simulating two-phase/two-component §ows.The creation of an extensive experimental database is, therefore, necessary for the validation of these numerical tools.Although the aerospace industries perform water hammer tests as a part of the quali¦cation campaign of their propulsion subsystems, basic research in the ¦eld is rather limited.
Gibec and Maisonneuve [7] performed water hammer experiments with real propellants, namely, monomethyl hydrazine (MMH), nitrogen tetroxide (NTO), and hydrazine, for di¨erent pipe geometries including straight, bend, elbow, and tee pipes.They hypothesized that phenomena such as cavitation, pipe deformation, and vapor pressure may interfere with the water hammer.Lecourt and Steelant [8] performed several tests with ethanol, acetaldehyde, and MMH for straight and bend pipes.They observed a surprising multiple-step evolution of the ¦rst pressure peak and provided a possible explanation.They also demonstrated that ethanol can be used as a replacement §uid instead of toxic MMH.Lema and Steelant [9] investigated the e¨ect of a fully saturated liquid compared to a deareated one in vacuum conditions.Test results showed that for the saturated liquid, the pressure peak is slightly smaller due to the desorption of the dissolved gas which acts as a cushion in front of the liquid.This paper presents the experimental results of priming tests run with di¨erent geometry setups.Test §uids are water and ethanol.In addition, numerical simulations are also presented and results compared with experiments.

Test Bench Description
To investigate and gain detailed insight into the ¦lling process of feedlines, a new test bench has been built at DLR Lampoldshausen.The test bench features a 80-liter run tank pressurized up to 50 bar, a §exible pressurization system (gaseous nitrogen (GN 2 ) or gaseous helium (GHe) as a pressurizing gas) as well as a modular test section with its own conditioning system.This modularity ensures that the test bench is not limited to one test section but it can reproduce a real spacecraft feedline system geometry.Conditioning of the test section can be either done via evacuation or pressurization.The test bench is equipped with a fast opening valve (FOV), pneumatically actuated, mounted on a rigid support to limit vibrations during the opening (Fig. 1).Its opening time is only 6 ms.As reported in previous papers [810], the valve opening time should be faster than the travel time of the liquid front to the dead-end.The impact time, as will be shown later, is in the range 140150 ms.
The valve opening transient is an important boundary condition for numerical validation.A requirement for the experimental setup was, therefore, to have a position measurement sensor not only to ensure reproducibility of the valve opening transient but also to provide the necessary input for numerical simulations.The valve features a position encoder and its opening pro¦le (an example in Fig. 1) was perfectly reproducible over all the tests performed.The wall thickness of the test section is 1.25 mm (ID 16.56 mm).At 5 points, it is ¦xed onto a support structure by means of clamps to limit its movements.The test section is mounted with a downward slope of about 1 • to facilitate the purging procedure.The upstream segment, from the tank to the valve, is a 22×1.5-millimeterstraight stainless steel pipe with a tee piece inserted 550 mm downstream the tank to allow purging and evacuation.The detailed geometry of the test bench is given in Table 1.
When di¨erent con¦gurations are to be tested, the test-element is removed and replaced by the desired geometry.In the experiments presented in this paper, four setups are tested: straight, tees (T, T2), and elbow (L) con¦gurations.The part upstream of the FOV is kept the same.The T geometry has a 1000-millimeter straight pipe followed by two branches of 500 mm each, in a left/right arrangement.Similarly, the T2 geometry has a 1000-millimeter straight pipe but with asymmetrical branches, respectively, 1000 and 500 mm.The ¦nal geometry is an elbow (L), a 1000-millimeter straight pipe followed by another 1000-millimeter straight pipe at 90 • .The T and L setups with their measurement stations are shown in Fig. 3.The T and L con¦gurations have been sized so that the ¦lling volume is the same as the 2000-millimeter straight pipe in order to quantitatively compare the pressure peak and the impact time.The di¨erent branches are connected via Swagelok screw connectors shown in Fig. 4.

Sensors
Measurement of pressure and temperature is performed at 6 di¨erent stations as shown in Fig. 2. Each measurement station consists of three transducers: one thermocouple type k, 1-kilohertz sampling rate; one absolute piezoresistive pressure sensor type 4043A200 from Kistler, 10-kilohertz sampling rate; and one dynamic piezoelectric pressure sensor type 601A from Kistler, 150-kilohertz sampling rate.
To avoid aliasing and high-frequency noise, the ¦lter of the dynamic pressure sensors has been set to 30 kHz.
Sensors are screwed in a 20-millimeter thick disk with the same inner diameter of the pipe to avoid §ow disturbances.Dynamic pressure sensors (5.5-millimeter diameter) and thermocouple are §ush mounted, while the absolute pressure sensor is 2 mm beneath the surface through a 1-millimeter hole.The measurement stations are located as follows: In the case of T and L geometries, an additional dynamic pressure sensor is placed at the junction (Fig. 4) named Pd-6B.For T and T2 con¦gurations, the dead-end of the second branch is also provided with a dynamic pressure sensor named Pd-6L.Figure 3 shows the positions of these additional sensors.

Test Procedure
Before each test, the downstream test-section is purged with a GN 2 §ow by opening MV-4 and MV-2 (see Fig. 1) and unscrewing the measurement module at the test-element end.After this operation, the test section is evacuated by means of a vacuum pump (MV-3 open) to the desired low pressure level.The FOV and MV-2 are then closed and MV-1 is opened to manually prime the upstream pipe.At this point, automatic operations are performed by the controlling software: the tank pressure is set at a given value, the trigger command for data acquisition is given (−500 ms), and FOV opens (time: 0 ms).Data are recorded for 4 s.

Test Matrix
In the case of the 2000-millimeter straight test section, tests with di¨erent pressures in the test-element were performed, while the tank pressure was kept at 20 bar.The pressure in the test-element, or line pressure, for water and ethanol has been set so that the same ratio with respect to their saturation pressure is kept.The vacuum pressure levels are shown in Table 2.Then, the di¨erent geometries are tested at vacuum condition only.The residual gas in the line is GN 2 .Water is pressurized with GN 2 while for ethanol, GHe is used.Tests are repeated three times for each test condition to examine reproducibility.Figure 5 shows an example of the reproducibility achieved.The measured pressure peak di¨erence between the three tests is less than 1.5%.From an experimental point of view, reproducibility of ethanol tests is better than that obtained in water tests.

TEST RESULTS
The target of the experimental campaign is to reproduce the ¦lling process occurring in a spacecraft feedline system and, in particular, to investigate the e¨ect of di¨erent geometries on the water hammer pressure pro¦le.These experiments will also provide a database to validate numerical simulations.In this paper, only the results of tests at vacuum condition (10 mbar for water and 20 mbar for ethanol) are presented and discussed.
The water hammer pressure peak can be estimated with the Joukowsky£s equation * : where ρ is the §uid density; c is the speed of sound in the §uid; and V is the impact velocity at the dead-end.As reported in previous papers [3,11,12], an analytical model based on the rigid liquid column theory can be applied to the priming process of a satellite system to predict the impact velocity of the propellant with satisfactory results (error within 6% with respect to the experimental data).The model considers the liquid as an incompressible slug in unsteady motion.The main issue is to correctly take the friction factor into account, since the results are strongly sensitive to this value [12].Velocity V can be expressed in terms of pressure di¨erence and density according to Bernoulli£s equation: Therefore, at the same pressure conditions, the water hammer pressure peak of two di¨erent §uids can be related as follows: Evaluating Eq. (2) for ethanol (c = 1124 m/s and ρ = 796 kg/m 3 ) and water (c = 1361 m/s and ρ = 1000 kg/m 3 ) gives a theoretical water hammer pressure ratio P eth /P w = 0.74.The speed of sound is calculated taking the elasticity of the pipe material into account according to the Korteweg£s formula: where c f is the uncon¦ned §uid speed of sound; E f is the §uid compressibility modulus; E w is the elasticity modulus of the material; D is the pipe diameter; t is the wall thickness; and µ is the coe©cient depending on the pipe support boundary condition.

Straight pipe
Test results obtained with the 2000-millimeter straight pipe are shown in Fig. 6 for water and ethanol.The maximum pressure peak is 202 and 139 bar, respectively.The pressure ratio ethanol/water is, therefore, 0.69, close to the theoretical value of 0.74.One should also consider that the viscosities of the two §uids are di¨erent and that a¨ects the ¦nal impact velocity.The attenuation of the wave is very similar.With respect to the ¦rst pressure peak, the second pressure peak is, in fact, 58.4% for water and 59% for ethanol (118 and 82 bar).For both §uids, the pressure is more or less damped o¨300 ms after the main pressure peak.
The results of the straight pipe tests will be used to validate the numerical simulations.

Tees and elbow geometries
The pressure history at the dead-end for di¨erent tested geometries is shown in Fig. 7. Table 3 summarizes the pressure peaks obtained in the di¨erent geometries.As expected, the pressure peaks for T and L con¦gurations are smaller than the straight pipe case due to the momentum loss introduced by the connector.The attenuation of the pressure wave is more pronounced in the case of the T con¦guration for both water and ethanol.
In the case of water and L con¦guration, the ¦rst pressure peak shows a double spike, with the ¦rst spike at 165 ms and the second spike at 172 ms.This is not present in the case of ethanol.In an attempt to better understand the origin of it, an additional test-campaign has been run using GHe instead of GN 2 as the pressurizing gas for water.Preliminary results indicate that this double spike is due to a combined e¨ect of the dissolved gas GN 2 in water and the concentrated pressure loss at the L-piece.With GHe tests, this phenomenon does not occur as GHe is much less dissolvable in water than GN 2 .The authors hypothesize that the L-piece enhances the gas desorption from the liquid and causes the separation of a liquid slug that precede the main §ow and hit the  dead-end (¦rst spike), followed a few milliseconds later by the main §ow.When injected in vacuum, the liquid undergoes §ash boiling and, in addition, starts desorbing the dissolved gas.Additional tests are in progress to validate this hypothesis.
Figure 8 Pressure pro¦les at the dead-ends for the T2 geometry: 1 ¡ PD-6L is the pressure sensor at the longer branch dead-end; 2 ¡ PD-6R is the sensor at the shorter branch dead-end; and 3 ¡ PD-6B is the pressure sensor at the T-connector In the case of the T geometry, the pressure peaks in the two branches deadends are identical (< 1 bar di¨erence) and their impact time is practically the same: the maximum time delay between the peaks in the two branches is 0.2 ms.The e¨ect of the pressure wave re §ection is visible in the case of asymmetrical branches (T2).Figure 8 depicts the pressure evolution at both dead-ends and at the tee junction for the T2 geometry.The pro¦le of the pressure peak at both ends is the result of multiple re §ections of the pressure wave traveling from one end to the other.First, the ¦lling of the branch generates the ¦rst pressure peak, occurring sooner for the shorter branch.The higher pressure peak (225 bar, PD-6L) takes place in the longer branch because it is the last cavity to be ¦lled with the liquid.This causes a compression wave that propagates to the shorter branch inducing a second spike (210 bar, PD-6R) which, in turn, causes a spike on the longer branch.
The time delay between the two peaks is 1.3 ms.Considering the distance between the two sensors (1500 mm), this gives a speed of sound of 1154 m/s.This value is 15% smaller than the theoretical value of 1361 m/s for water: this is due to the amount of residual gas in the line that reduces the speed of sound.
The main wave moves subsequently upstream towards the tank and the pressure in the test-element ends drops to about 5 bar.When the main pressure wave moves again downstream, the mutual interference of the re §ections is still present in the second pressure peak (at about 240 ms).Now, the shorter branch has a slightly higher pressure of 86 bar compared to 82 bar of the longer branch.From the forth peak on t > 290 ms, the e¨ect of the acoustic re §ections is no longer detectable in the pressure pro¦le.
In future, the experiments will be run with di¨erent branch lengths and also with a di¨erent arrangement of the T-piece, e. g., bottom/side instead of left/right.

NUMERICAL SIMULATIONS
A numerical model of the test-bench is built by using EcosimPro R in conjunction with the ESPSS library, an ESA-developed tool capable of one-dimensional, twophase §ow transient simulations.The model schematics used for the simulation is shown in Fig. 9.
For the simulation, the straight 2000-millimeter test-element is modeled and results with water are used.As described in the present authors£ previous work [12], the friction factor is to be increased in order not to overpredict the pressure peak.The increase of the friction factor is physically motivated by the unsteady conditions of the §ow.Changes occurring in the velocity pro¦le during acceleration of the §ow produce varying shear stress at the wall.Due to this Figure 9 EcosimPro/ESPSS model of the test-bench used for the simulation varying shear stress, the viscous boundary layer is not established and a higher velocity gradient is found at the wall than would be expected for steady §ow.Because of the higher velocity gradient at the wall, a greater friction coe©cient should be used.Empirically, a multiplier value of 3 for the friction factor is set in order to better agree with the experimental data.
First, a grid sensitivity study is carried out.The test-element is modeled with an increasing number of nodes, respectively, 50, 100, and 200 nodes.While the ¦rst pressure peak is identical in each case (Fig. 10), the frequency and the attenuation of the wave strongly depend on the number of nodes.The arrival time of the ¦rst peak is ∼ 11 ms faster than the experimental value (note that in Fig. 10, the experimental curve has been shifted to match the pressure peaks Figure 10 Comparison between numerical results (1 ¡ 50 nodes; 2 ¡ 100; and 3 ¡ to allow a better comparison).The predicted value of the ¦rst pressure peak matches the experimental one: it would suggest that the impact velocity at the dead-end is also the same, with respect to the Joukowsky£s equation (see Eq. ( 1)).Nevertheless, the friction factor has been adjusted to arti¦cially match the pressure peak but that also a¨ects the acceleration history of the §ow.Two di¨erent acceleration pro¦les can lead to the same ¦nal velocity yet with di¨erent impact time.That could be easily seen by considering the ¦nal velocity as the de¦nite integral of the acceleration.
Increasing the number of nodes leads to a decrease in the frequency and to a less damped wave.The experimental frequency calculated after the 4th peak (to avoid the e¨ect of the column separation at the dead-end) is 51 Hz, while the numerical one is 60 Hz in the case of 200 nodes.The reason behind this disagreement is the di©culty of calculating the speed of sound in a two-phase §ow.The presence of gas decreases the speed of sound in a nonlinear way.Since the real §uid, when injected in vacuum, desorbs the dissolved pressurizing gas, an extra amount of gas is added to the residual one in the line (10 mbar of GN 2 ).This additional amount further decreases the speed of sound c and, thus, the frequency f , as f = c/(4L).In the numerical model, the desorption of gas from the liquid is not taken into account and, therefore, the numerical frequency is higher than the experimental one.
The wave attenuation is also underestimated: the experimental pressure signal is more damped than the numerical prediction.This is due to three main e¨ects: (1) the aforementioned additional released gas which further attenuates the pressure wave; (2) the friction factor which, as already explained, is modeled in ESPSS only for steady §ow conditions; and (3) the structural vibrations absorbing some energy.
The implementation of an unsteady friction model will be addressed in future work as well as a more detailed experimental investigation on the §uidstructure interactions.

CONCLUDING REMARKS
At DLR Lampoldshausen, a new test facility to investigate the ¦lling process occurring in spacecraft and satellite feedlines has been built.Priming tests in evacuated pipelines have been performed with water and ethanol, the latter being the best replacement §uid for the toxic hydrazine.The theoretical correlation based on the §uid properties to relate the water hammer pressure peak between two §uids proves to give a satisfactory result when compared against the test data.
Di¨erent geometries have been tested, namely, straight pipe, elbow, and tees.The use of junctions such as elbow and tees causes not only a reduction of the pressure peak with respect to the straight pipe, but also a di¨erent shape in the pressure history.In the case of the elbow test-section, the authors hypothesize that the desorption of the dissolved gas has a strong in §uence on the pressure peak causing a double-spike pro¦le.Preliminary results con¦rmed the in §uence of the pressurizing gas: when helium is used instead of nitrogen, the pressure pro¦le is di¨erent.Further tests are in progress to investigate this aspect.
The tee setup with asymmetrical branches shows the e¨ect of the mutual interference of the acoustic re §ection resulting from the two dead-ends.The pressure peak at one dead-one causes a wave re §ection that a¨ects the pressure pro¦le at the opposite end and this can lead to higher pressure peaks.
Numerical simulations have been performed by means of EcosimPro in conjunction with library ESPSS.A grid sensitivity study showed that the frequency and the wave attenuation are dependent on the number of nodes, while the ¦rst pressure peak is not a¨ected.The calculated frequency is higher than the experimental one due to the di©culty in calculating the speed of sound for a two-phase §ow.The lack of a model for the desorption of gas from the liquid leads to underestimation of the amount of gas and, therefore, induces a higher speed of sound and, consequently, higher wave frequencies.For the same reason, the attenuation of the pressure wave is also not well predicted, where the experimental pressure signal is more damped than the predicted one.The inadequacy of the steady friction model when applied to unsteady §ow contributes also to the mismatching.In unsteady conditions, the friction factor is higher than in steady §ow which results in a more damped pressure wave.Future simulations will include the implementation of an unsteady friction model, while future experimental work will focus on §uidstructure interactions.

Figure 1
Figure 1 Fast opening valve pneumatically actuated (a) and its opening pro¦le (b)

2. 1 . 1
Geometries for priming tests Schematic of the test facility is shown in Fig. 2. The geometry of the test-element is a 2000-millimeter straight stainless steel pipe (1.4541, AISI 321) with a relative large outer diameter (3/4 in or 19.05 mm) in order to examine high mass §ow rate that is typical of spacecraft feedlines like the European Space Agency (ESA) Automatic Transfer Vehicle (ATV).

Figure 2
Figure 2 Schematics of M3.5 §uid transient test facility at DLR Lampoldshausen.The 2000-millimeter straight test section is depicted

Figure 3
Figure 3 Con¦guration of the T/T2 (a) and L (b) geometries used

Figure 4
Figure 4 Details of the T and L connectors with the insert hole for the pressure sensor (a); and the dead-end measurement piece with the pressure sensor (1) and an accelerometer (2) (b)

Table 1
Dimensions of the test-bench

Table 2
Test-matrix: Line pressure for water and ethanol for the di¨erent tested geometries (P tank =20 bar) Figure 5 Example of reproducibility; pressure signal at dead-end with straight pipe, §uid is water: 1 ¡ test #01; 2 ¡ test #02; and 3 ¡ test #03

Table 3
Pressure peaks for di¨erent tested geometries (P tank = 20 bar)