analysis and performance reconstruction of vega

7/21/2019 Analysis and Performance Reconstruction of VEGA

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Analysis and Performance Reconstruction of VEGA

Solid Rocket Motors Qualification Flights

E. Cavallini and B. Favini

Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy

A. Neri

ESA ESRIN, VEGA/IPT Via Galileo Galilei 00044 Frascati (Rome), Italy

VEGA is the launch vehicle developed by the European Space Agency, qualified withits first two maiden flights on February, 13rd 2012 and on May, 7th 2013 and recentlydelivered to the commercial market with the third flight held on April, 30th 2014. Duringthe launcher development, a total of eight static firing tests have been performed for thethree solid stages, which compose the launcher: the first stage P80, the second stage Zefiro23 and the third stage Z9. In this work, the analysis and performance reconstruction ofthe solid rocket motors of the VEGA launch vehicle for the two qualification flights iscarried out with a post-firing reconstruction model, developed for the purpose. The aimis to use the measures acquired during the flights and the experience gained from thestatic firing tests analysis, in order to evaluate the actual behavior of the VEGA solidstages, through the non-ideal parameters: combustion efficiency, thrust efficiency, hump,scale factor and nozzle throat erosion law, which define the actual performance parametersof the solid rocket motors. The purpose of the work is to assess the SRMs performanceparameters from the flight data, comparing the outcomes of the flight data analysis withthe ones provided by the static firing test data analysis. The final aim is to consolidatethe methodology for the analysis and reconstruction of the solid stage flight data, in orderto define/characterize the scattering of the motor performance, reducing the uncertaintiesfor the prediction methodologies in the upcoming and following VEGA flights.

Nomenclature

p non-dimensional average pressurep experimental pressure, bara parameter of the de Saint Robert law, m/sAt nozzle throat area, m

2

aref parameter of the de Saint Robert law, m/sAtf final nozzle throat area, m

2

Ati initial nozzle throat area, m2

c characteristic velocity, m/scF thrust coefficientF thrust, N

h hump parameterhc heat transfer coefficient, W/(m

2 K)kab nozzle throat erosion coefficient, m

3/(W s)Mp propellant mass, kgn parameter of the de Saint Robert lawp pressure, barR universal gas constant, J/(kg K)

rb burning rate, m/sSb burning surface, m

2

SF scale factort time, stb burn-out time, sTf combustion products temperature, KTi propellant grain initial temperature, KTthroat flowfield temperature at throat section, KTwall wall temperature at throat section, Kweb web variable, m

Symbols

c combustion efficiencycF thrust efficiency Vandekerkoven function specific heat ratioM combustion products molecular weight,

kg/kmolp propellant grain density, kg/m

3

Ph.D., Research Fellow, Department of Mechanical and Aerospace Engineering, Email: [email protected] Professor, Department of Mechanical and Aerospace Engineering, Email: [email protected] Senior Principal Engineer - LAU-PVC, Email: [email protected]

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American Institute of Aeronautics and Astronautics
http://[email protected]/http://[email protected]/http://[email protected]/http://[email protected]/http://[email protected]/http://[email protected]/


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I. Introduction

VEGA is the new launcher of the European Space Agency (ESA), qualified with its two first flightsoccurred at the Centre Spatial Guyanais (CSG) in French Guyana on February, 13rd 2012 (VV01) and onMay, 7th 2013 (VV02). Tailored for small payloads and low earth orbit missions, VEGA is a single-bodyfour-staged launcher with three solid propellant rockets and one liquid propulsion upper module. The threeSRMs, the first stage P80 (Europropulsion), the second Zefiro 23 (Avio Group) and the third Zefiro 9 (AvioGroup) share the same finocyl configuration, characteristics and innovative technologies, having different

sizes and performance tailored to the target mission requirements and constraints1,2. In the frame of theVEGA launcher development activities, for the three solid stages, eight static firing tests (SFTs) have beenperformed of VEGA SRMs: two for P80 (P80 DM and P80 QM) at CSG in French Guyane; two for Z23 (Z23DM and Z23 QM) and four for Z9 (Z9 DM, Z9 QM, Z9A QM2, Z9A VT and Z9A VT2) at Salto di Quirra,Sardinia, Italy. The analysis of this amount of data from experimental activities performed in Ref. 3 hasallowed to reach a first knowledge about the solid rocket motor actual behavior and performance assessment.

On the base of the static firing tests analysis performed, this work has the aim to analyze the flight data ofthe two first flight of the Vega launch vehicle, in order to provide a complete overview of the internal ballisticsof the VEGA solid stages, comparing the outcome of the static firing tests analysis, with the one of the flightdata. In particular, the purpose is to provide, an assessment of the non-ideal parameters characterizing theactual SRM behavior: the hump curve and the scale factor; the combustion efficiency; the thrust efficiency,allowing a reconstruction of the actual performance of the solid stages. The SFT reconstruction modelconsiders a zero-dimensional quasi-steady modeling of the SRM internal ballistics, already used in Ref. 3for the analysis of the Vega SFTs, which has been tailored for the reconstruction of the SRM flight data,accounting for the different input coming from the flights with respect to the static firing tests. The aimof this activity is to consolidate the methodology used for the solid stage performance reconstruction, inorder to enrich the knowledge of the SRM actual behavior and performance, characterize SRM dispersionand scattering, for the accurate prediction of the forthcoming Vega flights. In the meanwhile, the purposeis to define and individuate possible improvements that are necessary in order to refine model analysis andprediction capabilities.

II. SRM Static Firing Test Reconstruction Model

The SRM firing reconstruction model is able to assess the actual behavior of the SRM during the fir-ing, through the evaluation of the non-ideal parameters of efficiency of the SRM (combustion and thrust

efficiency) and the nozzle throat area evolution in time4

. The non-ideal parameters take into account theSRM actual behavior with respect to: 1) the propellant grain combustion rate, typically coming from smalltests for the propellant characterization (e.g. BARIA tests) and the uncertainties on the propellant grainburning surface evolution, which are taken into account through the product of the hump (accounting forthe propellant rheology during the casting process) and the scale factor (accounting for the small-to-fullscale characterization of propellant combustion); 2) the shift of the grain combustion products composi-tion and combustion chamber conditions with respect to the ideal equilibrium conditions, considered in thecombustion efficiency c ; 3) the thrust efficiency cF to characterize all the thrust losses, i.e. divergence,boundary layer losses and frozen flow effects, in the nozzle flow. These parameters are evaluated exploitingthe experimental measures occurring before, during and after the firing for the SFT and/or the flight, andsome theoretical models, as will be detailed in the following. Since the basic features of the reconstructionmodel have been presented in Ref. 3, in the following they will be recalled with particular attention on theassumptions used in this study and the input available for the analysis of the flight data.

The data measured before and during the flight for each solid stage regarding the SRM internal ballisticsare typically the following: the propellant grain mass loadedMp(from the experimental measures); the initial(At(t= 0) = Ati) nozzle throat area value and nozzle throat expansion ratio (from quality measurements);the propellant densityp (from the experimental measures); the head end pressure p(from the experimentalmeasures); the propellant combustion characterization in terms of a and n of the de Saint Robert-Vieillecombustion law (evaluated by BARIA propellant grain batches analyses). In fact, on the contrary of theSFT where also the final throat are of the SRM is measured post the SFT, in case of a flight, no directmeasure of the nozzle throat erosion is typically provided. In both cases of SFTs or flight, moreover, nodirect measure is provided for the SRM thrust (theoretically it can be possible in case of SFT performed

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on horizontal test beds, that are not the case for the Vega Programme - CSG in French Guyane and Saltodi Quirra, Sardinia, Italy), which has to be reconstructed or from the measure of the bench reaction, eitherfrom the launch vehicle trajectory data.

In the assumption of a simple 0D quasi-steady modeling for the internal ballistics, the SFT reconstructionmodel is based on the following steps. The burning rate model is the classical de Saint Robert-Vieille model,given by the Eq. (1).

rb(t) = a (Ti) p (t)pref

n(1)

The quasi-steady burning represents, in fact, in the majority of the SRMs, the most important termof the overall burning rate, during the quasi-steady state, which represents the most important phase forcharacterizing the SRM actual behavior. In particular, for VEGA SRMs, the quasi-steady burning has beenshown in Refs. 57 to be the only significant term of the burning rate during the internal ballistics. Theerosive is, in fact, completely negligible after the first start-up phase of the SRM, since VEGA SRMs aredesigned to have low flowfield velocities inside the chamber, avoiding significant total pressure drops anderosive burning effects. Moreover, VEGA SRMs propellant grains do not present any effects related todynamic burning during both the ignition transient and the tail-off/burn-out phases.

Then, the characteristic velocity is defined, as usual, by Eq. ( 2).

c (t) =RTf(t)

M (t) ((t))

(2)

The thrust coefficient is the classical expression given in Eq. (3).

cF(t) = F(t)

p (t) At(t) (3)

The combustion products characterization (in terms of their molecular weight Mand specific heat ratio) and the adiabatic flame temperature Tfare evaluated by means of the chemical equilibrium assumptionfor the propellant grain combustion reactions (evaluated with CEA code8,9).

The nominal evolution of the combustion surface in the web Sb(web), assuming a spatially constant burn-ing rate, in accordance with the 0D model is theoretically evaluated by grain burnback analysis performedwith the GREG model5, 10

For the throat area evolution law, in this work, we have performed the following assumption. For theanalysis of the static firing tests performed in Ref. 3, a constraint to the nozzle throat erosion was givenby the experimental measure of the final value of the nozzle throat (Atf), and the characterization of theerosion rate was assumed as expressed by Eq. (4),11 with the hc coefficient evaluated by semi-empirical laws(i.e. Bartz model12).

Dthroat(t) = kabhc(t) (Tthroat(t) Twall(t)) (4)

For the analysis of the flight, however, no direct measure of the final nozzle throat can be performed,and therefore, we assumed the semi-empirical correlations gained from the SFTs analysis as a functionaldependence of the nozzle throat erosion rate (or mass flow rate per unit area) as a function of the SRMoperating pressure, since in the typical regime of diffusion limited erosion of the throat insert, its is known 1315

that this is the main functional dependence of the nozzle throat erosion. This means that each SFT provides

a nozzle throat erosion correlation for the analysis of the SRM flight data. This assumption represents afirst step in order to exploit as much as possible the SFTs data experience and assess the impact of suchapproach on the results achieved.

The problem, hence, can be expressed in terms of the non-ideal parameters: combustion efficiencyc ,hump and thrust efficiency cF , to be determined as follows.

The combustion efficiency is exploited in order to ensure the overall mass balance during the SFT, asexpressed by equation (5).

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c =

0

tb p (t) At(t)

c (t)

Mp(5)

The product of the hump parameter and the scale factor can be evaluated for each time instant, assumingthe use of a 0D quasi steady state model, through the instantaneous mass balance inside the combustionchamber, as given by Eq. (6).

SF h (web (t)) =

p (t) At(t)

cc (t)

pSb(web (t)) a (Ti)

p (t)

pref

n (6)

For the characterization of the thrust efficiency, we assumed as input the thrust datum as reconstructedfrom the trajectory (provided by ELV), as well as the ambient pressure variation during the firing. Anext step of this activity will considered the evaluation of each solid stage thrust profile starting from thetrajectory rough data and the launch vehicle attitude data.

With the considered assumption the thrust efficiency is simply given by Eq. (7), that accounts also forthe nozzle divergence losses.

cF(t) =

F(t)

cF(t) p (t)At(t) (7)

III. Analysis & Reconstruction of VEGA Qualification Flights

The analysis of the solid stage performance of VEGA will be provided comparing for each SRM the actualSRM behavior assessed from the two qualification flight data (VV01 and VV02) and comparing these datawith the one coming from the static firing test analysis. Note that for the assumption performed with respectto the nozzle throat correlation which considers the scattering of the throat erosion correlations coming fromthe SFTs, a range of possible reconstruction parameters will be obtained from the reconstruction of eachmotor.

Figure 1. VEGA Solid Rocket Motors

A brief resume of the VEGA SRMs data is given in Table 1, in terms of each stage dimensions, propellantweight and performance data, as given in Ref. 2.

VEGA SRMs share around the same propellant formulation, i.e. HTPB 1912, with 19% Al (aluminum)and 12 AP (ammonium perchlorate). We recall that some small differences are present from SRM-to-SRM and within DM and QM or VV01/VV02 versions of the same stage, in terms of additives and particlesgranulometry, in order to obtain the desired propellant characteristics for the ballistics parameters a and nand combustion. Moreover, VEGA SRMs have the same propellant shape type, 11 points aft-finocyl grains,shown in Fig. 2, with different proportions between the fins and cylindrical part and fins characteristics fromSRM-to-SRM, in order to have the desired pressure and thrust profiles in time and performance. In terms ofcasting, we recall moreover that P80 propellant grain is produced and casted in Kourou, French Guyane byRegulus, whereas its nozzle is made by Safran Herakles with a different kind of nozzle throat insert material

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Characteristics & Performance P80 Z23 Z9A

Overall Length, m 10.5 7.58 3.90

Outer Diameter, m 3 1.925 1.925

Propellant Mass, kg 87730 23820 10570

Inert Mass, kg 7330 1950 940

Firing Time, s 110 77 120

Vacuum Specific Impulse, s 280 287.5 295Max Thrust (vacuum), kN 3015 1120 317

Nozzle Expansion Ratio 16 27 72

MEOP, bar 88 94 75

Nozzle Deflection Angle, 6.5 7 6

Table 1. VEGA SRMs Characteristics and Performance

(Naxeco Pyc Carbon-Carbon) with respect to the one of Zefiro 23 and Zefiro 9A (3D carbon-carbon producedby Safran Herakles). Zefiro 23 and Zefiro 9, instead, are entirely produced by Avio, in Colleferro.

For confidentiality reasons, all the sensible data of the SRMs will be provided in non-dimensional form.

(a) P80 (b) Zefiro 23 (c) Zefiro 9A

Figure 2. VEGA SRMs: Propellant Grain Configurations

A. P80

P80 static firing tests took place in Kourou Solid Booster Test Bench (BEAP) in November 2006, for the DMSRM and in December 2007, for the QM SRM. The two versions of the P80 were nominally identical by apropulsive point of view, in particular, in terms of propellant type and nozzle configuration. Anyhow, becauseof necessary qualification requirements at the system level and slightly different ambient temperatures duringthe SFTs of almost negligible effect, the DM and QM had slightly different burning rates. In particular, thepropellant burning rates have been calibrated in order to have the DM SFT with a slightly lower combustionrate, and hence, lower pressure and higher combustion time, with respect to the QM one (see the ). Theflight units of the P80 SRM for the VV01 and VV02 flight were nominally frozen as configuration with

respect to the QM SFT.Figure3 shows the nozzle throat erosion correlation expressed in terms of the nozzle throat erosion massflow rate per unit area as function of pressure, as extracted by the reconstruction of the SFT DM and QMof the P80 SRM. The scattering among the correlations of the nozzle throat erosion law is small, with anhigher mass flow rate per unit area for the DM with respect to the QM.

Figure4shows the trend of the hump over the non-dimensional web thickness and of the thrust efficiencyover the non-dimensional burning time, comparing each other the outcomes of the SFT analysis (DM andQM) and the flight analysis. The results of the flight reconstruction are performed considering for each flightthe scattering of the nozzle throat erosion law depicted in Fig. 3(e.g. P80 VV01 - DM stands for the results

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Figure 3. P80: Nozzle Throat Erosion Characterization from Static Firing Tests

of the VV01 flight with the use of the DM nozzle throat erosion correlation; whereas, P80 VV01 - QM, theresults of the VV01 flight with the use of the QM one, and so on).

Looking at Fig. 4(a),the hump shape of the P80 SFTs and flights, as related to the propellant rheologicalbehavior during the casting process appear to be very repetitive with a very small scattering among the firings.The presence of a typical peak of the hump shape at approximately 0.3 in non-dimensional thickness, as alsounderlined in Ref. 3, has to be noted.

(a) Hump (b) Thrust Efficiency

Figure 4. P80 SFTs & Flights: Reconstruction of Hump & Thrust Efficiency

As far as the thrust efficiency comparison among the firing is concerned, slightly higher values of trendover time and the average of the thrust coefficient is obtained from the flights with respect to the firing, buta similar overall trend of the cF among the firing is to be noted. Note that for the P80, the SFT and theflight units nozzle configuration is exactly the same, with the nominal nozzle expansion ratio. The differenceof the nozzle throat operating conditions is mainly related to the atmospheric conditions of the firings:quiescent ambient for the SFT and dynamic atmospheric conditions due to the launch vehicle trajectory forthe flights. A small difference among the flights is present for the thrust efficiency during the first phase of

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the atmospheric flight, which show the VV02 cF in this first phase of the flight near the one shown for theSFTs. For the same flight reconstruction (VV01 or VV02), the nozzle throat erosion law providing a slightlylower nozzle throat erosion, the QM one, implies a slightly higher thrust efficiency, with respect to the DMone. Anyhow, comparing the two flights, the variation of the thrust efficiency trend due to the differentnozzle throat erosion correlation (i.e. DM one or QM one) is very small and well inside the scattering of thisparameter among the flights.

Table2reports the value of the SRM average pressure (non-dimensional) during each firing, the combus-tion efficiency and the scale factor. The first one represents an input for the analysis, as discussed in section

II,provided as reference. The combustion efficiency and the scale factor are instead output of the analysis.Note that for the analysis of the flight, in this table and in the following for Z23 and Z9, a range of the cand SFis provided, as related to the minimum and maximum values obtained from the assumption in thereconstruction of one correlation of the nozzle throat erosion law rather than another one (when a singlevalue is provided, it means that a negligible effect on that parameter is obtained from the analysis).

Quantity Symbol DM QM VV01 VV02

Average Pressure p 0.5647 0.5675 0.5770 0.5699

Combustion Efficiency c 0.9905 0.9886 0.980.9827 0.98130.9840

Scale Factor SF 1.070 1.060 1.064 1.067

Table 2. P80 SFTs & Flights: Average Pressure, Combustion Efficiency & Scale Factor

Since the difference among the DM and QM nozzle throat erosion correlations (Fig. 3) used for the flightdata analysis is small, their effect on the scale factor evaluation is completely negligible (same value for thesame flight reconstruction in case of use of the DM or QM nozzle throat erosion law of Fig. 3). Whereas theeffects of the different nozzle throat law correlation is small but not negligible on the reconstructed combustionefficiency. As expected, the higher combustion efficiency is obtained from the erosion law correlation that ishigher for the same pressure, and therefore for the DM one.

Comparing, the scale factor provided by the flights analysis with respect to the one of the SFTs, thescale factor of the flights is well inside the small scattering experience for this parameter during the twofiring. Concerning the combustion efficiency, the two flights show a slightly lower combustion efficiency withrespect to the SFTs.

B. Zefiro 23

Zefiro 23 SFTs DM and QM occurred at the test bench in Salto di Quirra, Sardinia, Italy, respectively inJune 2006 and March 2008. Unlike P80 DM and QM, Zefiro 23 DM and QM versions of VEGA secondstage were not nominally the same SRM, beyond the different calibration of the propellant burning ratesbetween the DM and QM. In particular, for the Z23 QM, a redesign of the nozzle was considered, using alower nozzle throat area value and keeping constant the expansion ratio, in order to achieve a higher averagepressure during firing (see Tab. 3). For the remaining SRM configuration parameters, the two SRMs werenominally alike and the differences between the propellant grain ballistic parameters, coming from BARIAtesting, have been designed by the system for qualification requirements, as discussed in section Afor theP80.

As for the P80, one correlation for the nozzle throat erosion law is extracted from each SFTs (i.e. a socalled DM one and a QM one), as shown in Fig. 5. In this case, because of the different nozzle throat initialvalues, quite different correlations of the nozzle throat mass flow rate per unit area are obtained, with amass flow per unit area of throat erosion higher for the DM in comparison with the QM one for the same

pressure.Figure 6 shows the hump over the non-dimensional web-thickness and the thrust efficiency over non-

dimensional time. For the same flight, the hump shape (Fig, 6(a)) shows a not-negligible but small variationof the trend for a different correlation of the nozzle throat erosion. Anyhow, the differences among the twoflight reconstructions for the same flight, due to the different nozzle throat erosion laws, is well inside thescattering of the parameter among the firings (SFTs and flights). As for the P80 SRM, a characteristic humpshape for the Z23 has to be noted.

Figure 6(b) shows the evolution in time of the thrust efficiency, comparing the ones coming from theanalysis of the static firing tests of the ones reconstructed by the flight analysis. As for the P80, fairly higher

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Figure 5. Z23: Nozzle Throat Erosion Characterization from Static Firing Tests

thrust efficiency are obtained from the flights with respect to the SFTs, with a small scattering from theVV01 to the VV02 (higher) and for the same flight, the lower nozzle throat erosion law correlation (the QMone) provides the slightly higher thrust efficiency. Anyhow, this difference is of the order inside the scatteringobtained comparing the VV01 flight results with the VV02 ones. The difference among the thrust efficiencyassessed at the SFT conditions (lower values ofcF) with respect to flights (higher values ofcF) is directlyrelated to the fact that the SFTs are held in ambient conditions, rather than in the vacuum operative ones,so that, the SFT versions of the Z23 and Z9A had cut versions of the nozzles with respect to the flightunits, with expansion ratios dictated more by technological and production reasons, rather than to the needto have near adapted conditions for the nozzles itself, at the SFT conditions. From a global point of view,similar trend of the thrust efficiency among the firing is to be noted, except from the last part of it, fornon-dimensional time greater that 0.6.


Figure 6. Z23 SFTs & Flights: Reconstruction of Hump & Thrust Efficiency

Table3 reports the non-dimensional average pressure, the combustion efficiency and the scale factor forthe Z23 firings. It is worth noting that for a different nozzle throat erosion correlation (DM or QM one)

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has almost a negligible effect on the scale factor of the propellant. Comparing the scale factor value for thedifferent Z23 firings, the ones of the flights are near the one of the DM one (that had a lower average operatingpressure), whereas the scale factor of the QM one, that worked at around the same average operating pressureof the VV01 and VV02, is lower.

Symbol Symbol DM QM VV01 VV02

Average Pressure p 0.6059 0.6708 0.6799 0.6572

Combustion Efficiency c 0.9671 0.9550 0.95650.9704 0.95430.9681

Scale Factor SF 1.043 1.018 1.039 1.040 1.041 1.042

Table 3. Z23 SFTs & Flights: Average Pressure, Combustion Efficiency & Scale Factor

Looking at the values of the combustion efficiencies of the firings, it has to be noted that this value isstrongly dependent, as expected, on the nozzle throat erosion correlation used for the flight reconstruction,with a variation that is of the order of 1.5 % among the DM one and the QM one. In particular, as for theP80, the lower is the throat erosion rate correlation, the lower is the evaluated SRM combustion efficiency.Therefore, by using the throat erosion correlation coming from the DM SFT, for the two flights, a combustionefficiency near the DM one is obtained and conversely for the QM, with a high dispersion of this parameterfrom the firings.

C. Zefiro 9

Zefiro 9 (Z9) is the third stage of VEGA launcher in its improved and overloaded configuration, redesignedafter the failure of the first qualification firing test (QM) of Zefiro 9, in March 2007, due to some weaknessesin the design of the nozzle and in manufacturing quality on some of its components.

In fact, taking advantage of the schedule shift because of the redesign of the Z9 nozzle, the project decidedto increase the Z9 performance with an overloading of propellant (560 Kg), allowing to improve the launcherpayload capability of more than 60 Kg. The new configuration of the Zefiro 9 is, therefore, characterized bya very high web fraction and, as a consequence, the motor chamber volume is quite reduced with respect theprevious one2, 16,17. Because of these significant changes in the third stage configuration, two firing tests wereplanned to demonstrate the qualification. The first one, the QM2 was successfully performed in October2008, and the second one, the VT, in April 2009, at the test bench in Salto di Quirra, Sardinia, Italy.

Figure 7. Z9: Nozzle Throat Erosion Characterization from Static Firing Tests

During both the Z9A QM2 and VT static firing tests, an unforeseen negative reaction peak was detectedon the bench axial load cells, around few milliseconds after the SRM start-up16,17. An igniter re-design was,hence, carried out in order to decrease the negative peak force during the pre-ignition phase. The re-designwas then tested during the VT2 SFT, in May 2010, at Salto di Quirra test bench, with successful results.

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As far as the other SRM design parameter are concerned, the three SFTs of Z9A, QM2, VT and VT2had nominally the same propellant, beyond the dispersion in the ballistic parameters, as measured with theBARIA tests of the batches, but different nozzle configurations. In particular, the Z9A QM2 and VT2 hadthe same nozzle, whereas for the VT a different (higher throat area) nozzle design was tested.

The nozzle throat erosion law correlation for the three SFTs is shown in Fig. 7. From the SFTsreconstruction, the throat higher erosion rate for a given pressure is obtained from the VT one, whichoperated at lower pressure; whereas the VT2 has the lower throat erosion rate. The QM2 SFT provides anozzle throat erosion law that is a roughly in the middle of the other two, slightly shifted towards the VT2.

As for the previous VEGA stages, Figure8(a)depicts the hump shape over non-dimensional web-thicknessand Figure8(b),the evolution in time of the thrust efficiency for all the Z9 firings.


Figure 8. Z9 SFTs & Flights: Reconstruction of Hump & Thrust Efficiency

Comparing each other the firings, the hump curves shows that similar trend are present for the QM2,VV01 and VV01, that are slightly difference with respect to the ones experienced for the VT and VT2, which

are similar each other. This deviation is significantly present after non-dimensional web-thickness 0.65,whereas before, some small scattering is presence between all the firings. A possible cause for such behaviorwas discussed in Ref. 3,where the analysis of the VEGA solid rocket motors static firing tests was presented,as a preceding work of this paper. As for the P80 and the Z23 SRM, in the flight data reconstruction, theuse of different nozzle throat erosion laws (as extracted by the SFT data analysis) provides small variationof the trend of the hump, well inside the scattering among the two flights.

Concerning the thrust efficiency (Fig. 8(b)), it is recalled that as for the Z23, the SFT units of Z9 werefired with a nozzle expansion ratio far from the flight unit one (as reported in Tab. 1), since the SFT wasperformed in air, and that the nozzle truncation was dictated mainly by by technological and productionreasons, rather than to the need to have near adapted conditions for the nozzle during the SFT. Therefore,from the reconstruction of both the flights (VV01 and VV02), which operated in vacuum conditions at thenominal expansion ration reported in Tab. 1, significant higher values of the thrust efficiencies are expected,as shown in Fig. 8(b). Anyhow, considering all the firing, a similar trend over time of the

cF

is to be notedfor Z9. As for the previous cases, the influence of the imposed nozzle throat erosion law entails small effectson the evaluation of this parameter, that are well inside the scattering among the VV01 and VV02 flight.Moreover, the effect of the throat erosion law on the cF , for the same flight, is similar to the one discussedfor P80 and Z23: the lower nozzle throat correlation provides the higher thrust efficiency.

Table4reports the comparison of the average operating pressure, the scale factor and the combustionefficiency for the Z9 firings. It is worth underlining that as for the hump shape, the scale factor of the twoflights are similar each other and with a small scattering (slightly lower) with respect to the QM2 SFT.Whereas, the scale factors for the VT and VT2 SFT are slightly higher and similar each other. The effectof the nozzle throat erosion correlation chosen for the flight reconstruction on the scale factor parameter is

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For these reasons, in order to reduce the uncertainties related to the reconstruction of the solid rocketactual behavior from the flight data, it is necessary to try to improve the capability of the prediction modelfor the nozzle throat erosion evaluation, through the introduction of more complex correlations of the nozzlethroat erosion phenomena, well rooted on the base of full models of the thermo-chemical phenomena of thenozzle throat and experimental data. A further improvement of the reconstruction model will also considerthe evaluation of the thrust of the solid stages directly from the trajectory data of the launch vehicle.

AcknowledgmentsThis work is supported and funded by the ESA-ESRIN/Contract No. 4000101871/10/I/JD. All the

required motor data have been kindly granted by ESA ESRIN VEGA Integrated Project Team.VEGA launch vehicle has been developed within an European Program promoted by the European Space

Agency (ESA), as a cooperative project with Member States within the ESA framework. VEGA Programmehas been managed by an Integrated Project Team that, under the responsibility of the European SpaceAgency, involves also staff from the Italian (ASI) and French (CNES) Space Agencies.

References

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analysis and performance reconstruction of vega

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