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Assessment of Slag Accumulation in Solid Rocket

Boosters:

Summary of the VKI research

B. Toth,∗ M. R. Lema,† P. Rambaud,‡ J. Anthoine,§

von Karman Institute for Fluid Dynamics, 1640 Rhode-St-Genese, Belgium

J. Steelant¶

ESTEC-ESA, 2200 AG Noordwijk, The Netherlands

In solid propellant rocket motors incorporating a submerged nozzle, the entrapment ofliquid residues of the combustion in the cavity formed in the surrounding of the nozzleintegration part can lead to the accumulation of slag with a considerable mass.

The goal of the present study is to characterize experimentally the driving parametersof the slag accumulation in a stagnant area modelling the nozzle cavity. Furthermore, theexperimental database is used for validating a numerical tool as well.

In the present article a summary of the VKI (von Karman Institute) research carriedout during the last four years is shown. Single-phase and two-phase measurements are per-formed using a cold-gas simplified model. Simultaneously, the experimental configurationis simulated numerically with the help of a commercial solver (CFD-ACE+). The final aimof the article is to point out the driving forces of the droplet entrapment process.

I. Introduction

The first stage of spacecrafts (e.g. Ariane 5, Vega, Shuttle) generally consists of solid propellant rocketmotors (SRM). These are typically operating during the first part of the lift-off providing most of the

thrust to accelerate the vehicle. On one hand, to shorten the overall length, the nozzle is submerged inthe last segment of solid propellant. That means that the convergent, the sonic throat and a part of thedivergent are surrounded by solid propellant. This integration allows orientation of the nozzle to provideadaptation of the rocket trajectory during the launch. During the combustion, the regression of the solidpropellant surrounding the nozzle integration part leads to the formation of a cavity around the nozzle lip.On the other hand, the propellant combustion generates liquefied alumina droplets coming from chemicalreaction of the aluminum composing the propellant grain. The alumina droplets being carried away by thehot burnt gases are flowing towards the nozzle. Meanwhile the droplets interact with the vortices formedby the internal flow and thus may modify their properties. As a consequence, some of the droplets areentrapped in the cavity instead of being exhausted through the throat. The amount of entrapped droplets inthe cavity depends most probably on their interaction with the vortices. The accumulation of the dropletsin the cavity generates an alumina puddle, also called slag. This slag reduces the performances of the solidpropellant motor due to its dead weight absence of impulse generation. In case of the two EAP of Ariane 5the total mass of the accumulated particles can reach up to 4.8 tons by the end of the launch.1

∗Doctoral Candidate, Environmental and Applied Fluid Dynamics Department, Chaussee de Waterloo 72; [email protected];AIAA Student Member.

†Research Engineer, Environmental and Applied Fluid Dynamics Department, Chaussee de Waterloo 72.‡Assistant Professor, Environmental and Applied Fluid Dynamics Department, Chaussee de Waterloo 72.§Associate Professor, Environmental and Applied Fluid Dynamics Department, Chaussee de Waterloo 72; AIAA Member.¶Senior Researcher, Aerothermodynamics section (TEC-MPA), Keplerlaan 1, P.O. Box 299, e-mail:[email protected];

AIAA member.

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American Institute of Aeronautics and Astronautics

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 - 11 July 2007, Cincinnati, OH

AIAA 2007-5760

Copyright © 2007 by The Authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

A. Background

The presence of the slag can lead to control problems and possible vehicle instabilities (e.g. by sloshing ofthe slag or by slag ejection2). As it is pointed out by Dupays et al.,3,4 the slag accumulation process andthe instability of the internal flow-field of the motor are dependent on each-other.

These instabilities occurring in the motor during the launch have been investigated (using analytical,experimental and numerical tools) by several researchers, both in the USA5–9 and in Europe,4,10–18 withinthe frameworks of the ASSM (Aerodynamics of Segmented Solid Motors) and POP (Pressure OscillationProgram for the Ariane 5 solid booster, MPS P230) programs (an overview of these studies can be found inFabignon et al.10) of CNES (Centre National d’Etudes Spatiales).

A global overview is given by Salita19 concerning the slag accumulation studies carried out mainly in theUSA.

In Europe, focusing on the slag accumulation, two-phase, quasi-steady, compressible numerical simu-lations were carried out by Cesco et al.17 using an Eulerian-Lagrangian method without simulating thecombustion and the coupling between the phases. The authors found that the alumina droplet size and theturbulence play an important role on the rate of accumulation.

B. Objectives

The goal of the present study is to characterize experimentally the driving parameters of the slag accumu-lation in a stagnant area modelling the nozzle cavity of the MPS P230 of Ariane 5 using a scaled 2D-likecold-gas model. To achieve this objective, the interaction of the droplets (modelling the alumina droplets ofthe SRM) with the vortices of the flow and the droplets entrapment process are investigated.

The experimental approach relies on dedicated non-intrusive optical measurement techniques: the home-made free surface Level Detection and Recording (LeDaR), Particle Image Velocimetry (PIV)20 and ParticleTracking Velocimetry (PTV). The gas-phase is modeled by air while the alumina droplets are modeled bywater droplets.

In complement to the experiments, 3D LES simulations are performed in order to validate existingnumerical tools to model the internal flow-field and the liquid accumulation phenomenon.

In previous Joint Propulsion Conference articles21–23 the main steps of the research are shown in detail.Lately, new data are obtained which allow the present article to refine the earlier observations and describethe links between the different achievements. Thus, a more global understanding concerning the dropletentrapment process is shown.

In the current article the previously published results are briefly reminded and only the newer achieve-ments are detailed.

II. The experimental facility

The geometry of the experimental model (see Fig. 1(a)) is simulating the main characteristic features ofthe SRM of Ariane 5 (MPS P230). It was introduced in Toth et al.21 and further explained in Toth et al.23

In Fig. 1(b) the test section - that is attached to the vertical wind-tunnel - is shown in its real orientation.The test section is designed in a way to allow the use of optical measurement techniques (e.g. PIV) to

characterize the internal flow-field. Therefore, most of the walls are made of planar transparent material.Furthermore, different geometrical parameters (inhibitor height (h) and position (Li), nozzle throat opening(o), cavity width (w)) can be varied.

The square (200 × 200 mm2) test section has a symmetric arrangement. The inhibitor between thesecond and third stages of the MPS P230 is modelled by a pair of inclined obstacles. The presence ofthis inhibitor induces vortex generation, called Obstacle Vortex Shedding (OVS). In order to prevent theinteraction between the OVS downstream the two inhibitors, the test section is separated by a splittingplate. Since the model has a symmetric arrangement and therefore a symmetric flow condition (which hasbeen verified), the measurements are carried out using only one side of the test section.

A model of the submerged nozzle together with the model of the appearing cavity is installed at theoutlet of the test-section. The set-up is designed for subsonic operation. Therefore, the sonic condition ofthe real case at the nozzle is not respected.

The experiments are carried out at room temperature using air to model the gas-phase of the internalfluid of the SRM and using water droplets generated by a spray device to model the alumina droplets. The

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(a) The wind tunnel.

200

h

o

L i

w

U0

5

156

x

yz

Mirror

Cylindricallens

Laser-sheet

Cavity(right)

WaterSpray device in thestagnation chamber

Cavity(left)

Excess waterextraction

Accumulatedliquid

Accumulatedliquid

(b) The test section.

Figure 1. Experimental configuration.

water spray is mounted in the middle of the stagnation chamber of the wind tunnel.

III. The parameters of the slag accumulation

In order to determine the main parameters of the slag accumulation process, altogether 23 differentgeometrical- and flow conditions are defined and investigated by the effective LeDaR technique. The detailsof these experiments and the results can be found in Toth et al.23 Here only the main aspects of theexperimental campaign are given.

The Level Detection and Recording (LeDaR) is a VKI home-made non-intrusive optical measurementtechnique that detects the liquid level in the mid-span plane of the cavity defined by a laser-sheet (seeFig. 1(b)).

From the illuminated plane, images are recorded with a high-speed camera. Later, the captured imagesare analysed by the LeDaR processing algorithm to extract the curve of the gas-liquid interface. Knowingthe time evolution of the interface, the volume increase (the liquid accumulation rate) due to the water sprayis determined.

Although the experiments are performed in a 2D-like facility in cold-gas condition, the dynamic char-acteristics of the droplets of the real booster is attempted to be modelled as much as possible through thecorresponding non-dimensional parameters. Thus, by respecting the volume fraction (αp ≈ 1.6 · 10−4) of theliquid-phase and the Stokes number (St ≈ 9.15), the interaction between the two phases should be similarthan in the real configuration.

From the experiments, one of the main parameters of the accumulation appeared to be the Obstacle tipto nozzle tip distance (OT2NT ). OT2NT (see Fig. 2(b)) is the distance by which a droplet - passing nearthe tip of the inhibitor - has to be deviated by the flow in order to escape through the nozzle and not to betrapped in the cavity.

From the liquid accumulation rate (see Fig. 2(a)) it is seen that by increasing the OT2NT distance, theaccumulation is not affected up to about OT2NT = 15 mm. Beyond this point, increasing OT2NT enhancesgradually the liquid entrapment.

Using the LeDaR technique, one can determine the tendencies of the liquid accumulation rate in function

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XXXXXXXXXXXXXX

OT2NT [mm]

Acc

umul

atio

n[%

]

-20 0 20 40 600

5

10

15

20

25

(a) Accumulation rate (the red ”X” symbols show thenominal configurations).

(b) The definition of the OT2NT distance.

Figure 2. The relative distance between the nozzle tip and the inhibitor tip (OT2NT ).

of various parameters (and analyse the shape of the interface, also shown in Toth et al.23). It provides apowerful database for designing geometrical changes to reduce the slag accumulation. However, from theseexperiments one cannot understand the driving forces of the droplet entrapment phenomenon. Therefore,further investigations are needed.

IV. Analysing the single-phase flow-field

A. Experimental approach

To characterize the internal flow-field, first the whole mid-span plane of the test section (from the inhibitoruntil the nozzle throat, including the cavity) is investigated using the Particle Image Velocimetry (PIV)technique in single-phase flow condition (without operating the water spray). As a reference, the geometryof the nominal condition of the LeDaR investigation is selected (h = 34 mm, Li

∼= 9h, o = 15.4 mm,w = 107 mm, U0 = 10 m/s). In order to have a sufficiently high quality measurement, altogether 12 fields-of-view (camera positions) are used to cover the whole area. In each position 1000 image-pairs are recordedand analysed with the tools of Scarano.24 These fields are combined once the statistical flow properties(mean flow-field and fluctuations) are computed. Some accumulated liquid is modelled using a plexiglasspiece in the cavity. Further details about the experiments and the complete description of the results canbe found in Toth et al.23

Concerning the statistical results, a sample of the mean flow-field is shown in Fig. 3, where a complexrecirculation region is visualized by the streamlines due to the lack of radial flow injection. The contour plotrepresents the RMS of the streamwise velocity component, which visualizes the shear layer attached to thetip of the inhibitor and the probable path of the shed vortices.

B. Numerical approach & CFD tool validation

The goal here is to determine the degree of validation of the numerical tools (i.e. time average, RMS andstructural contents). Therefore, the same domain (starting from X/h = -2.8) is modelled. The 3D numericalstudy is based on a finite volume and unsteady approach. The solution is obtained with a commercial solver(CFD-ACE+) using the Large Eddy Simulation (LES) option to reproduce the physics of turbulence. Thehybrid type grid contains over one million cells. The sub-grid stress tensor is modeled with a dynamicversion of the Smagorinsky model. The numerical methods used to discretize the equations are second orderin time (Crank-Nicolson method) and second order with limiter in space. The linear equations of velocity andpressure correction were solved with the AMG (Algebraic Multi-Grid) numerical solver. The inlet conditionsof the numerical domain are defined using PIV experiments in two perpendicular planes. Concerning thecomputational parameters and the detailed result description, further details can be found in Toth et al.23

and Lema et al.22

From the numerical domain the same type of statistical properties are extracted than the ones obtainedexperimentally in the mid-span plane (only one example is shown in Fig. 4). Comparing the two data sets

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Figure 3. The RMS of the longitudinal velocity component and the streamlines of the single-phase PIVflow-field.

Figure 4. The RMS of the longitudinal velocity component and the streamlines of the single-phase CFDflow-field.

a good agreement was reported earlier.22

However, in order to verify the numerical simulations on instantaneous basis, the coherent structures ofthe flow in the mid-span plane are identified. To do so, on one hand all the images of the 12 fields-of-view ofthe PIV experiments are reprocessed in order to obtain a uniform spatial resolution (about 0.6 mm vectorspacing). On the other hand, from the 3D domain of the numerical simulations instantaneous fields fromthe mid-span plane are extracted and then interpolated to a rectangular and isotropic grid, which has thesame resolution as the one of the measurements.

Concerning the experimental database, all the 1000 instantaneous fields of all the fields-of-view wereacquired at about 1 Hz, which is a sufficiently low frequency to represent statistically independent flow-fields.On the other hand, the numerical simulations provided 355 instantaneous fields exported at a frequency lowerthan the one associated to the time step. Nevertheless, this frequency of about 1.5 kHz does not allow realindependence from statistical point of view. Despite the fact that this limitation will need to be furtherbroadened (by taking samples from longer time series), the methodology is developed and applied.

In order to identify the vortices of the available instantaneous flow-fields, the VKI wavelet-based vortexdetection algorithm is used (for details concerning the method, please refer to Schram et al.25). The tool isrelying on the λ2 criterion.26 First, it is detecting the structures of high vorticity values by convoluting theenstrophy-field (square of the vorticity) with different scales of a Mexican-hat (Marr) mother wavelet. Later,in order to discriminate between shear- and rotating motions, the value of λ2 is calculated. This coefficientis the second eigenvalue of ∇U = S + Ω, which simplifies to equation 1 in 2D. As it is shown by Jeong andHussain,26 λ2 has always negative values in the core of vortices, therefore the discrimination between shear-and rotation can be made.

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λ2 =(

du

dx

)2

+(

du

dy· dv

dx

)(1)

The thresholds of the detection are set to twice the RMS of the vorticity and negative λ2 values re-spectively. After the analysis, a coarse 40 × 20 rectangular grid is created covering the whole domain andthe number of vortices located in each of the cells of this grid are counted and their properties (e.g. corediameter, Dv) are averaged.

The results are shown in Fig. 5. Due to the non-similar sampling the comparison is difficult, but stillallows highlighting some aspects.

According to the vortex concentration maps (Fig. 5(a) and Fig. 5(c)) similar passage path can be observedexperimentally and numerically. The coherent structures are originating from the shear layer attached tothe inhibitor tip. The region of 0 < X/h < 2 can be considered as the zone where the shear layer is gettinginstable creating vortices. At about 2 < X/h < 4, the zone of high vortex concentration is spreading, whilethe total number of vortices counted crosswise in the region seems to remain constant.

In the zone 4 < X/h < 8 some of the vortices are carried towards the nozzle and the others are descendingcloser to the wall where they travel back towards the inhibitor in the recirculation zone. However, beforereaching it, they probably dissipate, which can be seen from their decreasing number. At this point oneshould add that this recirculation is still clearly visible in the numerical simulation (in Fig. 5(c)), whileexperimentally the vortices appear to dissipate quicker below the limit of detection.

In the area represented by the streamline that closes the cavity entrance between X/h = 8 and the nozzletip (around Y/h = 1.5 in Fig. 3 and Fig. 4) the number of vortices looks to be decreasing, as the free-streamflow accelerates a second time.

Topologically, as it may be seen, in Fig. 3 and in Fig. 4 the streamline reveals the stagnation point createdon the nozzle tip that is blocking the flow downstream (at about X/h = 9.3, Y/h = 1.5). In an averagesense the vortices are convected following the streamlines, but this stagnation point is highly unstable as itmay be seen by the high levels of RMS values of the longitudinal velocity component (please refer to Fig. 3and Fig. 4). Reflecting this observation to the instantaneous point of view, a large amount of vortices flyover the nozzle through the throat, but a large number of vortices enter in the cavity as well. It is worth tonotice that these vortices interact also with the wall vorticity produced at the vicinity of the nozzle lip.

However, following the streamlines of the flow, from the corner between the nozzle lip and the cavitybottom, the vortex production seems to be weaker in the cavity. The existing structures are simply rotatingwith the flow and most of them are disappearing before turning once and reaching again the entrance of thecavity.

Concerning the mean size of the vortices, first of all one should notice that the range of the core size inthe experimental case (see Fig. 5(b)) considerably differs from the numerical data (shown in Fig. 5(d)). Thismight be the result of the considerably lower numerical spatial resolution. While the PIV measurementshave a constant high resolution (about 0.6 mm), the numerical grid is refined close to the walls, but rathercoarse unstructured cells (typically of the order of 2 mm, but cells larger than 4 mm also exist) are appliedfarther away from the boundaries. Although the numerical data is interpolated to a rectangular grid thathas the same resolution as the experimental grid, the unresolved details of the flow can not be retrieved.As a result, experimentally a large quantity of small vortices are identified and the range of the mean sizedistribution shifts towards smaller diameters. However, as one can see in the figures, the pattern of the sizedistribution of the two cases are comparable.

In both of the plots, starting from the tip of the inhibitor the growth of the vortices is clear. However,from about X/h = 2 the test section could be divided into two parts: on one hand, the structures transportedat higher Y/h locations (typically Y/h > 1.4) are able to maintain their larger diameter due to the energytransfer from the free-stream flow. On the other hand, the vortices, which enter in the recirculation zone(at lower Y/h locations) are breaking up resulting smaller core diameters. Longitudinally, this divided zoneextends until about X/h = 8, where the shear layer (which closes the cavity) begins. Downstream from here,the core size of the larger vortices decreases as well roughly to the level of the vortices of the recirculationregion.

At the impingement on the nozzle head, the destruction of the vortices deviating towards the throat canbe seen once again. On the cavity side of the nozzle, the mean vortex core diameter appears to be increasingespecially in the very low velocity central region of the cavity. One has to add that in Fig. 5(d) the large

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(a) Vortex concentration (PIV experiment). (b) Mean vortex core diameter (PIV experiment).

(c) Vortex concentration (single-phase LES). (d) Mean vortex core diameter (single-phase LES).

(e) Vortex concentration (poly-disperse spray in LES). (f) Mean vortex core diameter (poly-disperse spray in LES).

Figure 5. Statistical properties of the identified coherent structures.

spot of minimum vortex core diameter happens to be simply the result of no detected vortical structures inthe corresponding cells (please see Fig. 5(c) as well).

As a summary, concerning the instantaneous structures of the flow, the comparison at the present statusis not fair because of the different resolution of the experimental and numerical data. For this last technique,if the main PIV vortices are smaller than the LES grid size then they relay on the sub-grid model, which isessentially dissipating all the small events. As the pattern of areas seeded with vortices matches, accordingto the opinion of the authors, by performing the simulations on a finer mesh, a better matching could beobserved by comparing similar classes of vortices.

V. Two-phase flow numerical approach

After the overall satisfactory single-phase flow validation, the second phase is injected in the numericaldomain. The Lagrangian water-droplets may act on the air-phase through a two-way coupling source term.In practice, two simulations were performed. One with droplets of constant diameter (dp = 100 µm) andone using the same (poly-disperse) droplet-size distribution than during the LeDaR experiments. The waterflow-rate was always the same as during the experiments.

At the walls of the numerical domain vanishing droplet condition is applied, but through a user subroutinethe mass of the droplets hitting the walls of the cavity are counted in each time-step and therefore the liquidaccumulation is measured as well. These achievements together with the statistical air-phase properties werediscussed previously by Lema et al.22

Since then, similarly to the single-phase flow case, in the poly-disperse configuration the vortices of theair-phase in the mid-span plane of the domain are also identified using the same wavelet-based algorithm.

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355 fields are considered, which are also sampled at an average of 1.5 kHz.

Figure 6. The RMS of the longitudinal velocity component and the streamlines of the two-phase CFD flow-fieldin the presence of poly-disperse droplets.

Looking at the resulting vortex concentration map (see Fig. 5(e)), although the pattern resembles thesingle-phase simulations (Fig. 5(c)), one can notice some differences.

First of all, the shear layer attached to the inhibitor tip seems to contain more vortical structures, whichcould be attributed to the destabilizing effect of the droplets, which are present in high concentration. Asthe bigger droplets have a considerable relaxation time, they may drag the air-phase locally that may leadto the generation of a larger number of vortices.

Further downstream, in the recirculation zone a longitudinal shift can be seen in terms of the zonescontaining larger number of vortices. The coherent structures of the recirculation zone using the poly-disperse spray appear to shift upstream with respect to the single-phase flow configuration. It suggeststhat the coherent structures are descending earlier closer to the wall and starting their journey towards theinhibitor. It indicates that the liquid droplets might push the vortices closer to the bottom wall.

In the cavity although some differences are apparent, conclusion should not be drawn as the statisticalconvergence is questionable.

Concerning the mean vortex core diameters (shown in Fig. 5(f)), a very similar pattern is visible than inthe single-phase flow configuration (see Fig. 5(d)).

Furthermore, by processing the droplets distribution in the CFD domain, it is observed that the liquidentrapment appears to be governed by the vortical structures entering in the cavity. These vortices arecarrying a considerable amount of small droplets, which are the main contributors to the accumulationprocess. Fig. 7 is showing the mean spray mass loading. However, as one can see most of the liquid mass isremaining in the free-stream of the flow and escapes through the nozzle throat.

Figure 7. Average spray mass loading in the symmetry plane (based on 1 flow-through).

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VI. The driving forces of the droplets entrapment

While travelling with the flow, the water droplets appear to encircle the larger vortical structures thatare located at the border of the free-stream (the droplets are shown in Fig. 8(a)). Only a few of them areentering in the core of the coherent structures (generally represented by high local vorticity values). Thisbehavior is confirmed experimentally as well using two-phase PIV measurements downstream the inhibitor(see Fig. 8(b)).

(a) Monodisperse droplets (dp = 100 µm) in the numerical domain. (b) Two-phase PIV visualisation (the vectors representthe instantaneous air-phase velocity).

Figure 8. Instantaneous droplet distribution.

Furthermore, various transverse slices of instantaneous vorticity plots are extracted from the poly-dispersesimulation (see Fig. 9, where the X axis points towards the reader). A 5 mm thick elementary volume isdefined upstream and downstream from this plane and the droplets present in these volumes are indicatedby sphere symbols, which have a diameter proportional to the droplet sizes (the smaller droplets are almostinvisible). The velocity vectors of the droplets help understand their migration (and visualizes the smallerdroplets). Furthermore, the light yellow droplets are located in the volume downstream the vorticity sheet(in front of it), while the transparent-looking darker droplets are located in the volume upstream the vorticityplane.

In these figures (Fig. 9) it can be seen that the flow (and thus the vortices) does not have a considerableeffect on the large droplets (typically dp > 100 µm) as they stay primarily in the free-stream. On the otherhand, the small droplets (dp < 100 µm) tend to respond quicker to the fluctuations of the continuous phaseand therefore they could be transported by the coherent structures.

As it was explained with Fig. 5(a), the vortices are impinging on the nozzle tip, then some are deviatedtowards the throat, the others are entering the cavity. All of them are carrying smaller droplets, which thusmay enter in the cavity with the latter structures. Most of these droplets are hitting one of the walls of thecavity, and contribute to the accumulation. This is the droplet entrapment process.

It has to be mentioned that despite the size differences between large vortices extracted from LES andsmall vortices extracted from PIV, it has been observed that the latter are more energetic. The presentauthors believe that the coarse resolution adopted with the LES does not prevent finding a correct localenergy density of these vortices and therefore it is believed that the interaction between the vortices and thedroplets is well represented in the CFD.

Thus, concerning the effect of the flow, one should examine the path of the vortices and look at thedroplet sizes to get an indication about the motion of the droplets. By computing the rate of entrapmentin the numerical simulation (counting the mass of the droplets hitting the cavity walls using poly-dispersedroplet-size distribution), it results to be approximately 0.7% of the injected mass. However, in the samecondition experimentally about 8% accumulation was observed with LeDaR. Thus, a deviation of an orderof magnitude is present.

In order to explain this deviation, the attention is turned to the inhibitor itself. During the LeDaR imagerecording it was seen that large droplets of water are dripping from the downstream face of the inhibitor(see Fig. 10). The dripping happens despite the fact that the inhibitor was oriented against the gravity anda liquid extraction system was installed to reduce this effect by evacuating a major quantity of depositing

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(a) X/h = 7.4. (b) X/h = 9.2.

Figure 9. Instantaneous vorticity slices in the transverse direction combined with droplets contained in a±5 mm thick elementary volume around the slice (poly-disperse droplet-size distribution).

liquid from the upstream corner of the inhibitor. From high-speed camera investigation of the nominalconfiguration (h = 34 mm) the diameter of these droplets turned out to be very large, around dp = 8 mmand in average, about 6.8 droplets are observed each second falling down along the whole width of theinhibitor (200 mm). Furthermore, these drops are not necessarily generated at the tip of the inhibitor, butthey tend to grow at around 2/3h from the base of the obstacle (see Fig. 10(b)).

(a) Front view. (b) The bottom of the inhibitor.

Figure 10. Sample frames of the high-speed camera visualization of the dripping phenomenon (using h = 17 mm).

Between the continuous-phase and these very large droplets no coupling is assumed. These droplets areway too large to be noticeably influenced by the lower-velocity flow of the recirculation region. On the otherhand, the droplet frequency is sufficiently low, which ensures that this liquid does not modify the air-phase.

However, due to gravity, these droplets are all falling in the cavity and directly contributing to the liquidaccumulation. Using the previously-mentioned quantities, the contribution of the dripping is about 6.1% ofthe total injected liquid in the nominal condition.

Therefore, by subtracting the amount of dripping liquid from the total accumulation, the order of magni-tude of the rate of entrapment (around 2%) can be obtained in the experimental case, which fairly resembles

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the numerical result.

Figure 11. Mean airflow-field around the inhibitor using the poly-disperse droplets.

In order to quantify, what could be the amount of dripping in the numerical domain, the average flow-field around the inhibitor is investigated. Fig. 11 shows the streamlines of the mean flow in the presence ofthe poly-disperse droplets. It is assumed that the droplets are falling on the upstream face of the inhibitoruniformly. Furthermore, all the liquid that falls between the obstacle base and the stagnation point ofthe impinging airflow (at about y/h = 0.34 from the tip in Fig. 11) is assumed to be evacuated by thesuction system in the experiments. On the other hand, the droplets falling between the stagnation pointand the inhibitor tip are assumed to form a liquid film and flow over the tip to the downstream face, whereit accumulates in form of semi-spheres. When the mass of these semi-spheres reaches a critical value, thedroplet finally falls directly into the cavity.

Therefore, the total mass of the droplets hitting the upstream face of the inhibitor is counted, whichresults to be about 19%. Then, this value is repartitioned according to the location of the stagnation pointon the upstream face of the obstacle. Thus, the amount to be evacuated would be 19 · 0.66 = 12.54% andthe rate of dripping should be 19 · 0.34 = 6.46%, which appears to be close to the one observed during thehigh-speed camera experiments.

VII. Conclusions

Within the present study of liquid accumulation inside a large SRM both experimental and numericalinvestigation were conducted. The experiments involve optical measurement campaigns using a 2D-like cold-gas facility. The same experimental conditions were modelled numerically through time-resolved, two-phase,3D LES simulations. The time average quantities of the numerical simulations are validated first by theexperimental data. In the present article a validation attempt of the instantaneous content is describedthrough the characterization of the coherent structures of the flow. These results look promising consid-ering the relatively coarse resolution used in the LES. It is believed that a finer grid will lead to a closerdescription of the vortex contents. By introducing the droplet-phase in the numerical domain, the mass ofthe accumulated liquid is calculated in the cavity. In terms of the accumulation rate a large difference isobserved with respect to the experiments, because the simulations are not taking into account the drippingphenomenon. However, a preliminary estimation of its magnitude was already possible. Therefore, furtherstudy may be performed using VOF (Volume of Liquid) in order to capture this process as well.

The liquid accumulation in the present configuration appears to be governed on one hand by the dropletentrapment due to the vortices of the airflow and on the other hand by the dripping phenomenon. Currently,the dripping phenomenon appears to be the primary source, which is influenced first of all by the inhibitorheight.

However, extrapolation to a real SRM is still delicate concerning the dripping. At present time there isno guaranty that this process is the primary source of liquid accumulation in the Ariane 5 configuration.Therefore, further research is mandatory in this domain.

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Acknowledgments

This study is supported by the European Space Agency through the GSTP activity number C51.MPA-818.

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