supersonic diffuser

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Evaluation of the performance of supersonic exhaust diuser usingscaled down models

K. Annamalai a,*, K. Visvanathan a, V. Sriramulu b, K.A. Bhaskaran b

a Vehicle Assembly and static testing complex, Indian space research Organisation, IRT, SHAR Centre, Sriharikota (A.P.), 524 124, Indiab Department of Mechanical Engineering, Indian Institute of Technology, Madras-600 036, India

Received 9 June 1997; received in revised form 5 November 1997; accepted 5 November 1997

Abstract

Experiments were carried out on straight cylindrical supersonic exhaust diusers (SED) using cold nitrogen and hot rocket ex-

haust gases as driving uids, in order to evaluate the eects of the ratios of the SED area to rocket nozzle throat area edaet, SEDarea to rocket nozzle exit area edaee, SED length to its diameter vah and specic heat ratio of the driving gases k on the min-imum starting pressure ratio, oaast, of SED. The rocket nozzle and SED starting transients were also simulated in the models.The study reveals that oaast increases monotonically with increase in edaet and k. One-dimensional normal shock relationswere used in predicting the oaast since the compression in long ducts is basically a normal shock process. Predicted values ofoaast were validated with experimental data. SED eciency factorsgns were arrived at based on one-dimensional normal shockrelations. gns goes down at higher values of edaee. oaast is lower for lower k values for the same edaet. Cylindrical SEDsexhibit no hysteresis. The results of this investigation were utilised in validating the design of high altitude test (HAT) facility

for testing the third stage motor (PS-3) of Polar Satellite Launch Vehicle (PSLV). The simulation of starting transients in the model

revealed that the HAT facility shall not be operated in the unstarted phase, because the rocket nozzle may fail due to violent os-

cillations of the vacuum chamber pressure. These experimental data were also utilised for designing a SED for PS-3 sub-scale motor,

the results of which are covered in this paper. The accuracy of measurements are within a range of 0X4%. Error analysis of the datawere carried out and are presented in Appendix A. 1998 Elsevier Science Inc. All rights reserved.

Keywords: High altitude test (HAT) facility; Supersonic exhaust diuser; Rocket motor testing; Ejectors; Vacuum testing

1. Introduction

Rocket motors, designed for operation in upper at-mosphere, needs a nozzle with large area ratio eeaetfor eective utilisation of the motor pressure o. Whenthey are tested under sea-level conditions, the ow sep-arates in the nozzle. To evaluate the performance ofsuch motors, sucient low pressure environment hasto be simulated in ground testing installations. Variousmethods of simulation of high altitude conditions aregiven in Refs. [1,2]. The development of ejectors to servethe dual purpose of evacuating the test cell and perform-ing as a supersonic exhaust diuser (SED) in propulsionunit test installation, has been in progress worldwide instatic test facilities [1]. Ejector with no induced second-ary ow is referred to as the SED in the context of thisinvestigation. All high altitude test (HAT) facilities use

SEDs either singly or in various combination with othersimulation techniques [2]. The SED is an axisymmetricduct placed adjacent to the exit plane of the rocket noz-zle and attached to the vacuum chamber (see Fig. 1). Byvirtue of this arrangement, the nozzle exit is located in-side the SED, thereby making the exhaust to ow intothe SED. Fig. 1 presents the details of the HAT facility,for testing PS-3 motor under simulated altitude condi-tion. It utilises a SED for the evacuation of the test-celland maintenance of vacuum during the PS-3 motor r-ing. The facility simulates the vacuum ignition and noz-zle full ow altitude conditions, thus allowing thequalication of the motor for vacuum ignition and stea-dy state performance. It is imperative to evaluate theperformance of this facility using scaled down models,before building the actual PS3-HAT facility. Moreover,it is highly expensive and time consuming to build HATfacilities for full size motors. Experiments were conduct-ed on dierent sizes of SEDs and nozzles with cold gasand rocket exhaust gas as driving uids. The results

Experimental Thermal and Fluid Science 17 (1998) 217229

* Corresponding author. Tel.: +91 8623 65117; fax: +91 8623 65067.

0894-1777/98/$19.00 1998 Elsevier Science Inc. All rights reserved.

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indicate that the minimum starting pressure ratiooaast increases with increase in edaet and decreas-es for lower k values for same edaet. For long ductsvah b 4X86, oaast almost remains constant. Forlarge values of edaeeY gns goes down. CylindricalSED exhibits no hysteresis. It would be convenient forthe reader to understand the principle of operation ofthe SED before going in for the details of the study.

2. Supersonic exhaust diuser (SED)-principle of opera-tion

The mechanism of ow of a compressible uid in aconned duct under the inuence of a strong adversepressure gradient has important applications in the de-sign and operation of wind tunnel diusers, inductionsystem in air breathing engines and exhaust diusersof HAT facilities. In the application considered here, it

is a self pumping ejector i.e. it utilises the momentumof the rocket exhaust to lower the nozzle back pressure.The pressure recovery is through a system of shockwaves. The structure of shock wave system in cylindricalducts has been a subject of considerable research. Photo-graphs of shock waves in ducts can be seen in Refs. [36]. The interaction with the boundary layer near the ductentrance causes the normal shock to degenerate into asystem of branched shocks. Near-planar lambda shocksoccur for relatively thin boundary layers and strong ob-lique or X-shaped for very thick boundary layers [2].The SED starting phenomena are discussed in Refs.[1,2] and is illustrated in Fig. 2(a) (taken from Ref.[2]). In region (1) of the performance curve, both nozzleand SED are unstarted. As the oaa increases further,the nozzle ows full, however, the SED is unstarted inregion (2). The unstarted regime consists of two phases.In the rst phase, the ow separates from the nozzlewalls through an oblique shock (Fig. 2(b)), and in thesecond phase, the ow separation is at the nozzle exitlip. In both the cases, the ow coming out of the nozzleadjusts to the prevailing cell pressure. In the secondphase, the ow at the nozzle lip could pass through ei-ther a strong oblique shock (Fig. 2(c)) or a PrandtlMeyer expansion fan (Fig. 2(d)). However, the jet com-ing out of the nozzle breaks down through a complexshock system and the supersonic ow is not prevalent

over the whole cross-sectional area of the SED at anylongitudinal location. Therefore, the ambient pressureinuences the cell pressure. As the oaast is further in-creased, the SED also ows full and the shock system isfully established in the duct. In this regime, the under ex-panded supersonic jet from the nozzle impinges on theSED wall (Fig. 2(e)). At this stage, the SED is said tohave started and corresponding pressure ratio (oaa)is the minimum starting pressure ratio, i.e., point `B'of Fig. 2(a). Any further increase ofo will alter the pat-tern of the shock system and the cell pressure varies lin-early with o in region (3). Due to the adverse pressuregradient of the oblique shock, that results from the turn-ing of the ow, a part of the mass from the shear layer isturned back into the test-cell. The prevailing cell pres-sure aects the expansion of the free jet which, in turn,entrains the mass from the test-cell. The cell pressurecomes to equilibrium when the mass entrained fromthe test cell matches with that owing into it. Such a cell

pressure at point `B' of Fig. 2(a) corresponds to thehighest altitude that can be simulated with the givennozzle-SED combination.

3. Normal shock model

Ref. [2] gives various methods of estimating the(oaa)st of straight cylindrical SED. Out of them, nor-mal shock model is chosen by virtue of its simplicity andconsistency. In order to utilise a straight cylindrical SEDfor rocket motor testing purposes, it is necessary that thedesign (oaa) be greater than the (oaa)st denoted bypoint `B' in Fig. 2. The ability to predict, approximately,the (oaa)st by means of simple theoretical modelwould be of great value. Normal shock model stemsfrom the fact that the overall consequence of the com-pression process in long ducts is closely approximatedby normal shock wave occurring at the inlet Mach num-ber of the duct [4]. (oaa)st is then calculated, takinginto account the static pressure recovery across the nor-mal shock. The starting point is associated with the at-tachment of the jet at the SED inlet. So, oaast iscalculated as if a normal shock wave were situated atthe SED inlet. Then, oaast oa1 1a2.oa1 is isentropic pressure ratio for edaet. 1a2is the static pressure rise across the normal shock with

Fig. 1. PS-3 HAT facility.

218 K. Annamalai et al. / Experimental Thermal and Fluid Science 17 (1998) 217229


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an inlet Mach number of w1 corresponding to edaet.Using the following equations, direct calculation ofoaast is possible.

edaet 1

w1

2

k 11

k 1

2w

21

!k1a2k1Y 1

oaast 1 k1

2w

21

kak12k

k1w21

k1k1

h i X 2After evaluating w1 from Eq. (1) and substituting inEq. (2), oaast can be calculated. The fairly goodagreement (refer Table 1) of calculated and experimen-tal values of oaast is due to the fact that the wallshearing forces in the region of separation are extremelysmall.

4. Description of hat facility

Fig. 1 gives the details of PS-3 HAT facility. The fa-cility has a vacuum chamber of 63.5 m3 volume for ac-commodating the test stand, PS-3 motor and otherthrust measurement links. The vacuum chamber is evac-uated by mechanical vacuum pumps to provide an igni-tion vacuum of 80 Pa corresponding to an altitude of 50km. A cylindrical SED, lined with silica phenolic abla-

tive material for protecting the metal wall from thehot rocket exhaust, is employed for maintaining steadystate altitude condition. The SED end is covered withmembrane assembly (this isolates the facility and atmo-sphere) which has a high tensile steel mesh, for takingcare of atmospheric pressure loading, and the membrane(rubber) to take care of the vacuum sealing. Safety sys-tems like nitrogen and halon purging and water delugeare also provided. Protection of the motor from theback ow during starting and at burnout is achievedby using a collar assembly, that closes the annular gapbetween the nozzle and the SED.

5. Scaling criteria

The main parts of the facility which need to be eval-uated for their performance using scaled down modelsare the SED, the membrane assembly and their interac-tion in dynamic conditions. Since this evaluation is notso easily amenable for theoretical approach, it is essen-tial to carry out model studies. It is required to selecta SED for the given rocket motor, whose o vs. timecharacteristics, kY he and eeaet are known inputs whichare to be simulated as such. Therefore, the parameters inthe control of the designer are edaet and vah only.

Fig. 2. (a) Typical SED characteristic curve taken from Ref. [2]; (b) Unstarted regime, phase-1 nozzle is not owing full- ow separation is with in the

nozzle divergent; (c) Unstarted regime, towards beginning of phase-2-nozzle owing full with oblique shock at nozzle exit; (d) Unstarted regime,

towards end of phase-2-nozzle owing full with the expansion fan at nozzle exit lip; (e) Started regime, supersonic ow with complex shock system

in the SED.

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Once diameter of the SED is xed, edaee is gettingxed, since eeaet is xed by virtue of the motor nozzleto be tested. The SED diameter has to be larger than de,otherwise there will be a nozzle-SED interaction, result-ing in very high starting pressure [7]. Ref. [7] reports thatwhen the nozzle exit was attached to SED so thatde hd, the SED did not start at all. Hence, SED diam-eter shall be so xed, to enable the nozzle to enter intoSED freely (hd b de). Selected (edaet) and vah haveto be simulated as such in the models also. The impor-tance of each parameter is discussed below.

Area ratio edaet: It could be observed from theEqs. (1) and (2), that the oaast is a function of w1

for known (edaet) and k. The higher the ratio of(edaet), the higher the w1 which completely controls(oaa)st for a given value of k. Therefore, it is adequateif (edaet) and k are simulated. This condition tells that,for a given value of k and (edaet), (oaa)st would besame whatever may be the absolute dimensions of thenozzle and SED. The sensitivity of w1 and (oaa)stfor given (edaet) and k are brought out as follows.Fig. 3 gives the variation of w1 and (oaa)st with res-pect to edaet and k. The sensitivity of (oaa)st, for agiven k, is high compared to that of w1 for the samevariation in (edaet). Therefore, (edaet) needs to be sim-ulated, instead of Mach number, for proper estimationof (oaa)st.

Parameter k: From Fig. 3, it is observed that for aparticular (edaet) both w1 and (oaa)st vary with k val-ues. The higher the k, the higher the (oaa)st and w1values. It is fairly easy to conduct experiments usingscaled down models with cold nitrogen gas (k 1X4) asthe driving uid. Since k is equal to 1.2 for rocket ex-haust, the actual (oaa)st is going to be on the lowerside for same (edaet). (oaa)st increases with increasingk values i.e. the actual SED would certainly start at thepressure determined from the cold ow tests. This leadsto the conclusion that cold ow model tests are quite ad-equate to estimate conservatively (oaa)st as long as(edaet) remains constant.

Parameter edaee: At this stage, it is convenient to de-ne SED eciency (gns) which is the ratio of the normalshock pressure recovery to the actual starting pressureratio.

Efficiencygns oaansaoaa actualX

(edaee) gets automatically simulated since (edaet) and(eeaet) are simulated. (edaee) simulates the total pres-sure losses in the PrandtlMeyer expansion region ofthe jet and due to multishock reections. Larger(edaee) results in larger free jet surface and this condi-tion results in higher total pressure loss, resulting inhigher (oaa)st for the same (edaet) and k. Experimentswere conducted by Hale with (eeaet) of 18 and 3.914 inthe same SED of 119 mm in diameter, resulting in(edaee) of 5.486 and 8.965 with corresponding gns of80% and 73% [8]. This indicates that the losses in the freejet is quite considerable. It is also evident from the Ta-ble 1 that the eciency (based on n.s) goes down forhigher values of (edaee).

Fig. 3. Variation of SED starting pressure ratio and SED inlet Mach

Number, M1 with respect to SED cross sectional area to rocket nozzle

throat area ratio for dierent specic heat ratios of the driving gases.

Table 1

Results of cold ow experiment

Sl. no vah edaet edaee oaast actual oaast N.S gns %

1 8.00 11.11 01.23 09.50 08.48 89.2

2 8.00 31.30 01.65 26.8 22.62 84.4

3 8.00 34.60 01.65 29.2 24.80 84.94 9.00 79.20 03.96 65.0 55.63 85.6

5 9.00 82.83 03.98 68.5 58.00 84.7

6 8.66 124.25 06.56 101.8 86.30 84.7

7 8.66 130.60 06.53 108.5 90.70 83.6

8 8.66 136.55 06.56 109.5 94.70 86.5

9 8.90 214.36 11.32 185.0 147.45 79.7

10 8.90 225.30 11.30 202.5 154.80 76.4

11 8.90 235.57 11.30 215.0 161.80 75.3

12 8.00 31.3 1.65 28.0 22.62 80.7

Test no: 12 was with 3 gimballing of the nozzle to the diuser axis.



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Frictional characteristics of SED: Reynolds numbersimulation is required to simulate the frictional lossesin the duct. The frictional coecient is a function ofReynolds number in the duct. Generally, it is not thateasy to achieve this since (edaet) is xed by the criterionas explained above. The model is geometrically smaller

and utilises cold gas whose dynamic viscosity is lowerthan that of the hot gas. The dierence in the valuesof viscosity and the variations in the diameters of theSED compensates in such a way that their Reynoldsnumbers are almost, of the same order, implying similarfrictional characteristics. Same gns can be assumed forall k values, provided Reynolds numbers of the modeland actual SED are of the same order. Hence, the start-ing pressure can be predicted for hot gas using normalshock model and gns obtained from the cold gas testsfor the same (edaet. It has been found that the predic-tion based on cold ow test agrees well with experimen-tal data from hot gas test. This is dealt clearly in thesubsequent paragraphs on results and discussions.

Parameters: vah nd he: Ref. [2] suggests that thelength of the SED can be 812 times its diameter. How-ever, the study, here in reported, xes the lower limit of

vah as 4.86. Very long SEDs need higher starting pres-sure, resulting from frictional losses. he need to be thesame as that of the main nozzle. Higher he increasesthe angle of impingement, hence higher impact losses,resulting in higher starting pressure. For obtaining thebest results, it is better to simulate vah and he as same.

Simulation of the SED starting transients: PS-3 HATfacility has membrane assembly for the vacuum ignitionsimulation. After vacuum ignition is achieved, the SEDhas to start and maintain a suitable vacuum in the vac-

uum chamber so that the nozzle ows full. The startingtransients need to be studied in geometrically similarmodels using actual rocket exhaust as working uid.Simulation of the starting transients could be broughtunder two categories.

(1) The rst condition is vacuum ignition and subse-quent starting of the SED. The vacuum ignition was tobe achieved in the PS-3 facility by closing the end of theSED by a membrane and then evacuating the vacuumchamber and the SED, using mechanical vacuum pump.Using the hot gas experimental setup, starting transienttests were carried out. The membrane assembly, similarto that of PS-3 facility, suitable for assembly with thehot gas model SED, was designed and used. Fig. 4 givesthe details of the scaled down membrane assembly usedin this performance evaluation programme. Grooveswere provided in the face of the membrane assemblyfor holding the rubber membrane. The face grooveswere evacuated using mechanical vacuum pump. Thevacuum in the face grooves was helpful in holding therubber membrane in position thereby providing vacuumseal against the atmosphere. The principle behind themembrane assembly is thus; the wire mesh to take theatmospheric pressure load and the rubber diaphragmto provide the vacuum seal. Once the vacuum ignitionof the motor took place, hot gas started lling theSED. When the pressure in the duct reached slightly

above the atmospheric pressure, the membrane blewo. Since this was a dynamic system, the inertia of themembrane certainly needed a higher pressure dierentialacross it for blowing itself o. The pressure dierentialacross the membrane was a function of the percentageof the open area of the mesh. The higher the open area,the lesser the pressure dierential required for the mem-brane to blow o.

(2) The second condition occurs when the initial mo-tor pressure is slightly less than the (oaa)st for longtime. A solid motor exhibiting such a pressure vs. timecharacteristics was red in the model SED. Violent uc-tuations of the test cell pressure were observed when the

nozzle was in started condition and the SED was not so.Such uctuations in base pressure (see Fig. 5) got sub-dued once the shock got attached to the SED wall byvirtue of the increase of o above the (o)st. The test cellpressure was analysed for its resonant frequencies andfound to be around 40 Hz. (see Fig. 6). If the natural

Fig. 4. Membrane assembly used in the solid propellant rocket motor

model test.

Fig. 5. Cell or base pressure oscillations in the solid propellant rocket

motor model test.



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frequency of the nozzle coincides with this value, thenozzle may fail due to vibration. This proves that theSED starting shall be instantaneous otherwise someauxiliary pumping system must support the SED so thatthe SED has to start against a lower pressure i.e. less

than the atmospheric pressure. Hence, it is imperativeto design the altitude test facility in such a way thatthe SED starts instantaneously.

6. Experimental investigation

The experimental investigations can be divided intotwo parts: 1. Cold gas model studies, 2. Rocket exhaustgas model studies.

Cold gas model experiments: A sketch of the cold ownitrogen gas model test installation is presented inFig. 7. It consists of a nitrogen gas inlet pipe, primary(simulated rocket) nozzle and the SED. Three congura-

tions were tested. The SED exhausted to atmosphere inconguration no. 1, whereas, it exhausted to a vacuumchamber in the conguration no. 2. Additionally, thenozzle with 20.5 exit half angle was tested with 52.2mm diameter SED with 3 inclination to the SED axisto simulate the gimballed condition. N2 gas was suppliedfrom a high pressure source. o was varied from 0.1 to 4MPa using a pressure regulator. A cylinder of 60 mm di-ameter served as the primary chamber which receivedN2 gas from the pressure regulator. A small cavityaround the nozzle served as the cell (vacuum chamber)or base. Firstly, leak test was carried out. The testingmethodology for the two congurations were dierent.

For tests in conguration 1, the pressure regulator wasset to a particular pressure, the gas was allowed to theprimary chamber by opening the globe valve. This wascontinued for about 10 s and the pressure was moni-tored and recorded continuously. This procedure was re-peated for dierent settings of the regulator pressureupto a maximum of 4 MPa. For tests in congurationno. 2, the vacuum chamber was initially evacuated toa pressure of about 300 Pa using mechanical vacuumpumps. The pressure regulator was set to a particularvalue and runs were taken with constant regulator pres-sure, whereas the vacuum chamber i.e. the ambient pres-sure (a) increased continuously.

Hot gas experiments: Fig. 8 gives the experimentalset-up of the hot gas. A solid rocket motor (Agni), hav-ing 40 kg of solid propellant and developing an averagethrust of 17 kN, was the simulated PS-3 motor. It wasattached to a straight cylindrical duct which acted as a

SED. The external surface of the SED was cooled withwater spray. The SED was supported on xed saddles.The motor was resting on the test stand saddles and itwas butting against the thrust wall. A set of two nozzleswith dierent throat diameters were made use of. Boththe nozzles had (eeaet) of 20 and half cone angle of20.5 simulating the PS-3 nozzle (truncated). Three dif-ferent SEDs of (edaet) of 36.7, 35.49 and 34.2 with

vah ratios 10.58, 8.0 and 8.68, respectively, were used.After assembling the igniter and switching on the spraycooling water supply, the motor was red and all mea-surements were recorded in Super-16 computer.

Instrumentation: This was the common instrumenta-tion and data acquisition system for cold gas and hotgas experiments. Pressure measurement locations are in-dicated in the Figs. 7 and 8. The measured pressures are(i) inlet total pressure (o) (ii) cell or base pressure (c)(iii) the ambient pressure (a) and (iv) vacuum pressures(hP) along the length of the SED. The vacuum pressureand the positive pressure transducers were of straingauge type. Positive pressure transducers were mountedon the head end of the Agni motor. Shunt calibrationwas given for measurement channels. The data were am-plied and recorded in Super-16 computer throughADC. The error analysis of these data are presented inAppendix A. The accuracy of the measured thrust andpressure data are within an error band of 0X4%.

Fig. 7. Experimental setup using cold nitrogen gas as working uid-

conguration 1 and 2.

Fig. 6. Spectral distribution of the base pressure oscillations.



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7. Results and discussion

The PS-3 motor has a nozzle whose exit diameter is

895 mm and throat diameter is 195.5 mm.eeaet 20 (It is a truncated version. The actual ightnozzle has eeaet of 50). The diameter of the selectedPS3-SED is 1150 mm, after accounting for the gimball-ing space.

edaet 1150a195X52

34X6Y

edaetaeeaet edaee

34X6a20 1X73

Experiments were carried out for these values ofedaet, eeaet and edaee with cold N2 gas as drivinguid. To make the experimental investigations complete,experiments were conducted for dierent values of

edaet using cold gas. The results of these experimentsare presented in the Table 1. gns values of Table 1 arecalculated as follows from the cold ow test data. Exper-imental oaast for k 1X4 is 29.2 (from Table 1).Normal shock oaast 24X8Y gns 24X8a29X2 0X85or 85%; Fig. 9 gives the SED characteristic curve for

edaet of 34.6. This curve gives the variation of caawith respect to the variation in oaa. It resemblesthe typical curve of Fig. 2. Fig. 10 gives the theoretically

estimated values of oaast for k 1X4 based on onedimensional normal shock relations and the experimen-tally determined oaast are marked on the samegraph. It could be seen that, at lower edaet, the exper-imental values agree closely. The disagreement in thehigher edaet range may be due to large free jet surfacearea which causes more total pressure loss since samenozzle was used while increasing the SED diameter, re-sulting in higher edaee. Fig. 11 gives the experimental-ly determined SED characteristic curves for dierentedaet. The oaast is higher at higher edaet. In-crease in edaet reduces the cell pressure, resulting inhigher altitude being simulated. Fig. 12 brings out thevariation of gns with respect to edaee. For values of

edaee less than 1.5, it exhibits high gns indicating thecompression process is more closer to normal shockpressure recovery. In the middle range of edaee, thegns is almost constant. At higher values of edaee, thegns is less due to more total pressure loss in the larger

Fig. 9. SED characteristic curve for edaet 34X6 and k 1X4 (coldgas).

Fig. 10. Variation of SED starting pressure ratio with respect to the ra-

tio of SED area to rocket nozzle throat area for cold nitrogen gas as

driving uid k 1X4.

Fig. 8. Experimental setup using solid propellant rocket motor exhaust as working uid k 1X2.



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free jet area. Very large edaee is not normally pre-ferred in HAT facilities, unless the eeaet is small andmotor pressure is high enough to start against atmo-spheric pressure. (edaee) shall be kept minimum, so thatmaximum eciency is achieved i.e. the SED could bestarted at a lower (o)st or higher area ratio nozzle could

be tested for the same ost. Ref. [2] suggests that addi-tion of subsonic diuser to SED reduces the oaast.Fig. 13 gives the characteristic curves with and withoutsubsonic diuser.

oaast with subsonic diffuser 26X77Y

oaast without subsonic diffuser 27X75X

The subsonic diuser is supposed to reduce the velocityto zero but it is not so. The total pressure recoveryacross normal shock could be taken for the estimationof the oaast for the SED with subsonic diuser [9].Percentage reduction in oaast 27X75 26X77a27X75 3X53%. There is an improvement of 3.53% in

the performance of the SED or reduction in oaastto the tune of 3.53% due to the presence of the subsonicdiuser. If sucient margin ofoaast is not available,this marginal reduction in oaast could be advanta-geously used by the addition of subsonic diuser at theend of SED duct.

The following illustrates how to make use of thesedata from cold ow tests. From the forgoing discussion,the simulation of the frictional characteristics has to beensured. The following are the calculated values of Rey-nolds numbers of the cold ow SED, Agni SED and PS-3 SED.

ReCold gas 9X80 106Y Re Agni 5X56 106Y

RePS-3 11X18 106X

These values of the Reynolds numbers are of the sameorder; particularly the Reynolds numbers of cold gasand PS-3 SED almost coincides. Hence, the frictionallosses would be same and the SED eciency could be ta-ken as the same for all models. Based on this assump-tion, oaast of Agni model was worked out asfollows:

edaet 34X6 for Agni model;

oaast ns 21X5 for k 1X2X

oaast actual 21X5a0X85 25X30

gns 0X85 taken from the cold test for edaet 34X6XFig. 14 gives the experimental result of Agni SED withedaet of 34.2. It could be seen from Fig. 14,oaast was 25. Estimated value of oaast, of25.30 as above, agrees very well with the experimentallydetermined oaast of 25 in Agni model test. From thisfact, it can be concluded that the proposed PS-3 SEDwould also start at 2.5 Mpa (assuming a 0X1 MPa).The initial pressure of the PS-3 motor shall be greaterthan 2.5 MPa. If it is lower, the phenomena explainedin Figs. 5 and 6 are bound to happen. Fig. 5 gives theplot of cell or base pressure oscillations and motor pres-sure vs. time. Violent cell pressure oscillations were ob-

Fig. 13. Performance of the SED with and without subsonic diuser

for cold gas.Fig. 11. SED characteristic curves for dierent ratios of the SED area

to rocket nozzle throat area, for cold nitrogen gas as driving uid

k 1X4.

Fig. 12. SED eciency based on normal shock model vs. the ratio of

SED area to rocket nozzle exit area for k 1X4 (cold gas).



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served till the motor pressure reached ost i.e. 2.5MPa. This pressure was achieved at 4 s and the cell pres-sure becomes stable. After the burnout, around 7.4 s,when the motor pressure falls below 2.5 MPa, the owseparates from the SED wall and consequently, the cellpressure increases. Fig. 6 is the spectral distribution ofthe base pressure oscillations which exhibits a resonantfrequency of around 40 Hz. The amplitudes of the oscil-lations reduce with respect to time since the motor pres-sure is continuously increasing and they die down at 4 s.It has been estimated that the motor nozzle will certainlyfail due to resonance, if its natural frequency is around40 Hz. Such violent uctuations are bound to damage

the nozzle and associated instrumentation. This situa-tion shall be avoided always while designing the SED.Fig. 15 gives the variation of oaast vs. vah. Thegraph indicates that the oaast does not vary abovethe vah ratio of 4.86; Below this value, higher startingpressures are observed. Fig. 16 gives the pressure recov-ery along the length of the SED for k 1X4. Agni modelSEDs were having vah ratios as 8, 8.5 and 10.6 andedaet were varying from 33 to 36.7. All these AgniSEDs started at a pressure between 2.4 and 2.7 MPa.It is adequate if the PS-3 SED is provided with vah ra-tio of 8 or slightly more. The PS-3 SED has a divergentpart at end. This is provided to oset the reduction incross sectional area due to wire mesh blockage. Inciden-

tally, this works as a subsonic diuser also. In additionto the above tests, two tests were conducted simulatingthe vacuum ignition and the starting transients, incorpo-rating the membrane assembly in the model SED. Ta-ble 2 gives the measured o and c with correlatingevents for these two tests.

Table 2 indicates that the SED exit pressure of 0.1485MPa in the rst test at the time of membrane blow owas higher than that of 0.1175 MPa in second test.The motor pressure, at the time of membrane blow oin the rst test, was 2.136 MPa as against 0.576 MPain the second test. Perhaps, the condition of high SEDexit pressure warranted a high motor pressure for blow-

ing o the membrane. Moreover, the time at which themembrane blew o in the rst test was 192 ms comparedto 92 ms in the second test. The test data reveals that theentire duct was above the atmospheric pressure beforethe membrane was blown o and this occurred at a mo-tor pressure well below the starting pressure. The atmo-spheric air could not enter into the duct and cause someproblem since, the duct pressure was above the atmo-spheric pressure. The possible reason for higher SED ex-it pressure in the rst test could be that, the mesh openarea was less in the rst test (69%) compared to secondtest (88%). Therefore, the second test results were morecloser to the expected performance of the PS-3 facility.

Since the blow o pressure was less than the startingpressure, the vacuum ignition condition did not aectthe steady state performance of the facility. The meshopen area for the PS-3 facility can be any value above88%.

Fig. 15. Variation of starting pressure ratio with respect to vah ratioof SED for k 1X4 (cold gas).

Fig. 16. Pressure recovery characteristics along the length of the SED

for cold nitrogen gas as driving uid (k 1X4).

Fig. 14. SED characteristic curve for the ratio of the SED area to rock-

et nozzle throat area, for hot rocket exhaust gas k 1X2.



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8. Application and usefulness of this investigation

These investigations were useful in designing theHAT facility for evaluating the performance of a scaleddown version of PS-3 nozzle with eeaet of 50. The mo-tor was of 550 mm in diameter and 1000 mm long withcase bonded HTPB based propellant system. It was t-ted with a nozzle having an area ratio of 50 and a con-tour identical to that of PS-3 ight nozzle. The HATfacility consisted of a vacuum chamber of 50 m3 volumefor housing the load links, the test motor and a self-starting SED with subsonic diuser whose external sur-face was cooled by water. Fig. 17 gives layout of HATfacility for testing PS-3 sub-scale motor under simulatedaltitude conditions. The objective of this programmewas (1) determination of the vacuum specic impulseof PS-3 (2) Evaluation of solid particle impingement, ifany, in the nozzle divergent region.

Nozzle throat diameter 80 mmY

Nozzle exit diameter 566 mmY

eeaet 50Y k 1X2YSelected SED diameter 640 mmY

edaet 640a802

64Y

From normal shock tables for k 1X2 the total pressureratio across the normal shock 02a01 0X0281;

01 1a0X0281

3X5587 MPaY taking gns as 857Y

ost actual 35X587a0X85 4X186 MPaY

(It is better to take total to total pressure ratio across the

normal shock as per Ref. [9] for SED having subsonicdiuser). This SED had a straight cylindrical length of5.9 m and subsonic diuser of length 2.9 m with totallength of 8.8 m. The subsonic diuser had an exit to inletarea ratio as 4 with 5.5 as half cone angle. Fig. 18 givesthe results of this test. It is a plot of oaa vs. time andcaa vs. time. The vacuum chamber was pre evacuat-ed to 2700 Pa using mechanical vacuum pumps. The ig-nition vacuum was 2700 Pa. On motor ignition, the massfrom motor charged the vacuum chamber i.e. c startedraising in consonance with o till the ost reached 4.2MPa. Further increase in o brought down the c, tothe corresponding equilibrium base pressure. The vacu-um chamber pressure was quite stable without oscilla-tions, indicating that the SED was in startedcondition. Fig. 19 gives the cross plot of caa andoaa. caa increased till oaa reached around42. Beyond this, the SED started pumping out the gases

Fig. 17. HAT facility for testing PS-3 sub-scale motor under simulated altitude conditions.

Table 2

Test results of the simulation of starting transient

Sl. no. Events 1st Test 2nd Test

1. Starting pressure (MPa) 2.682 2.472

2. Time of occurrence of membrane blow o (ms) 192 92.00

3. Cell pressure at the time of membrane blow o (MPa) 0.1010 0.10374. SED exit pressure at the time of membrane blow o (MPa) 0.1485 0.1175

5. Motor pressure at the time of membrane blow o (MPa) 2.136 0.576

6. Mesh opening area as percentage of SED exit area 69% 88%



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from the vacuum chamber. There was a lag, since it hadto pump out a large vacuum chamber. Finally, the curveattained the equilibrium base pressure. In such a state,cao was constant. It is, generally, dicult to estab-lish accurately oaast in a pre-evacuated vacuumchamber. It is more convenient to take the starting pres-sure from the burnout pressure trace, since cylindricalSEDs do not exhibit hysteresis [2]. From digital data,the ost was found as 4.142 MPa. Fig. 20 gives the plotof various vacuum pressures measured along the lengthof the SED. The DP 7 which was measured at the exitplane of the subsonic diuser read a constant value of0.1 MPa indicating that the pressure recovery was com-plete. This test has shown a vacuum specic impulse of293 s for the actual PS-3 motor [10]. This value was ta-ken for planning the 3rd launch of PSLV. The measuredspecic impulse from the mission was 294 s [11]. This re-veals that the specic impulse measured in the simula-tion test was accurate.

9. Conclusions

(1) The model tests indicate that the PS-3 SED willstart at a nominal motor pressure of 2.5 MPa. (2) The

vah 10 (including the divergent part) of the PS-3SED is quite adequate for the complete pressure recov-ery. (3) The vacuum ignition is possible without impair-ing the starting condition of the SED by use ofmembrane assembly. (4) The scaled down model testsprove that the proposed HAT facility would meet thetest requirements of vacuum ignition and evaluation ofsteady state ballistic performance of PS-3 motor. (5)The starting pressure ratio is primarily a function of

e

dae

tand k only. It is essentially independent of the

primary nozzle type or area ratio. (6) Geometric simula-tion of edaet is adequate to get the starting pressure.(7) The fair agreement of the starting pressure ratioswith normal shock pressure ratios substantiates the con-cept that the compression is basically a normal shockprocess. (8) Large values of edaee reduces gns due tothe total pressure losses in the PrandtlMeyer expansionregion and due to multi-shock reections. (9) Theoaast is slightly higher at 28 in the gimballed condi-tion 3 as against 26.8 in the ungimballed conditiondue to the fact that the impact losses are more at im-pingement point and the ow is not axisymmetric. How-ever, the SED performance is same as in the

ungimballed condition in the started phase. (10) Samegns can be taken for a particular edaee for calculationof the starting pressure using normal shock model forother k values, provided duct Reynolds numbers are ofthe same order.

Fig. 19. SED characteristic curve from PS-3 sub-scale motor test.

Fig. 20. Plot of vacuum pressures measured along the length of SED at

dierent locations in PS-3 sub-scale motor test.Fig. 18. (oaa) vs. Time and (caa) vs. time graphs obtained in thetest of PS-3 sub-scale motor.

Nomenclature

ed cross sectional area of SED in m2.

ee cross sectional area of the nozzle exit in m2.

et cross sectional area of the throat in m2.

h SED diameter.de exit diameter of the nozzle.



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Appendix A. Error analysis of the thrust and pressuremeasurement system

The details of the thrust and pressure data measure-ment chain is presented in Fig. 21. The chain includes allthe subsystems from pressure transducer to recorder.The physical calibration of pressure transducers wascarried out using a dead weight calibrator. The load cellswere calibrated using MFL calibration unit. The electri-cal calibration of the thrust and pressure measurementchain were carried out using shunt calibration box.

The overall accuracy of the thrust and pressure measure-ment chain is 0X4%. The details of this calculation areas follows [12,13].

Total error RSS in thrust

0X042

0X272

0X122

0X0012

30X052

1a2

0X37Y

Total error RSS in ve pressure 0X15

2 0X27

2 0X12

2 0X001

2 30X05

2

1a2

0X357X

Vacuum pressure transducers are calibrated in situ withcapsule gauges as reference.

Total error RSS in vacuum

0X202

0X272

0X122

0X0012

0X052

1a2

0X3677

The total error (RSS) in thrust, positive and vacuumpressure is less than 0.4% in each.

Measurement chain sub-system Error in sub-system

BLH load cell 0.04%Positive pressure transducer 0.15%Vacuum pressure transducer 0.20%

Error for 95% reliability (1.96r) 0.27%Ravika dead weight calibrator 0.12%Vacuum pressure calibrator 0.10%Digital volt meter 0.001%Transducer power supply 0.05%Amplier 0.05%Super-16 computer 0.05%MFL load cell calibration machine 0.06%

Fig. 21. Thrust and pressure measurement scheme.

hP vacuum pressure in SED in Pascals.k specic heat ratio.

v SED length.w1 SED inlet Mach number.a ambient pressure in MPa.c cell pressure in Pascals.e nozzle exit static pressure in Pascals.o motor pressure in MPa.

ost minimum starting pressure in MPa.oaast minimum starting pressure ratio.

1 static pressure upstream of the normal shockin Pascals.

2 static pressure downstream of the normalshock in Pascals.

01 total pressure upstream of the normal shockin MPa.

02 total pressure downstream of the normalshock in MPa.

RSS root sum square.he nozzle angle at the exit lip in degrees.gns SED eciency based on normal shock

recovery.



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References

[1] B.H. Goethert, High altitude and space simulation testing, ARS

Journal (1962) 872882.

[2] E.J. Roschke, P.F. Massier, H.L. Geer, Experimental investigat-

ion of diusers for Rocket Engines, JPL Report TR 32-210, 1962.

[3] H.W. Emmons, Fundamentals of Gas Dynamics, vol II of Series,High Speed Aerodynamics and Jet Propulsion, Princeton Uni-

versity Press, Princeton, NJ, 1958.

[4] A.H. Shapiro, The Dynamics and Thermodynamics of Com-

pressible uid ow, vol. I, Ronald Press, New York, 1953.

[5] J. Fabri, J. Paulon, Theory and Experiments on Supersonic Air to

Air Ejectors, NACA TM 1410, 1958.

[6] P.J. Waltrup, F.S. Billig, Structure of shock waves in cylindrical

ducts, AIAA Journal 11 (10) (1973) 14041408.

[7] N.S. Joseph, C.L. Meyer, D.J. Peters, Experimental evaluation of

rocket exhaust diusers for altitude simulation, NASA TN D-

298.

[8] J.W. Halle, Inuence of pertinent parameters on ejector-diuser

performance with and without ejected mass, AEDC-TDR-64-134,

1964.

[9] D. Taylor, Ejector Design for a variety of applications, AGAR-

DO graph no. 163.

[10] Evaluation of vacuum impulse of PS3 ight motor from subscale

test, Propulsion Group, VSSC, 1995.

[11] PSLV-D3 mission-Post-ight analysis-report, 1995.

[12] IDAP, VAST, Instrumentation system for S139 motor static test,

ISRO, SHAR Centre, 1997.

[13] R.J. Moat, Describing the uncertainties in experimental results,

Experimental Thermal and Fluid Science, vol. I, (1988) pp 317.


supersonic diffuser

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