jpc 2011 pres ferretti

15/01/10Sapienza Activity in ISP-1 Program Pagina 1

Pressure oscillations simulationin P80 SRM first stage VEGA launcherV. Ferretti?, B. Favini?, E. Cavallini?, F. Serraglia∗ and M. Di Giacinto?

?Dipartimento di Ingegneria Meccanica e Aerospaziale (DIMA), Sapienza University of Rome∗

VEGA IPT ESA/ESRIN, Frascati (Rome), Italy

47th AIAA/ASME/SAE/ASEE Joint Propulsion ConferenceSan Diego (California), 31 July - 2 August 2011

Vortex sound quasi-one dimensional model

• Quasi-one dimensional model for the simulation of the internal ballistic inSRMs.

• Only the acoustic pressure oscillations are considered (combustion oscillationsare neglected).

Pressure oscillations simulation in P80 SRM31 July - 2 August 2011

Viviana Ferretti2 / 23

Introduction

• Large SRM (e.g: US Space Shuttle SRM, P80 SRM, Ariane 5 P230 SRM, TitanSRM, ETM-3) can exhibit sustained pressure oscillations during their operativelife.

• Their frequency is close to the first acoustic mode or one of its multiple.• The pressure oscillations result from the complex feedback mechanism fed by

vortex shedding and acoustic waves.

• The P80 SRM is the first stage of the new European Vega launcher. The twostatic firing tests, P80 DM and P80 QM, present the same configuration exceptfor the pressurizing gas (nitrogen for P80 QM, helium for P80 DM).

• The P80 QM exhibits three pressure oscillating phase, the P80 DM four.



Aeroacoustic coupling

Aeroacoustic coupling feedback loop• vortical structure generation by hydrodynamic instability of the shear flow• vortex shedding (parietal, obstacle and corner vortex shedding) and

convection by the flow• interaction with an obstacle and acoustic field excitement• acoustical triggering of the shear flow instability

Vortex shedding: stand-off distance li,frequency fvs

Acoustics: combustion chamber lengthL, acoustic frequency fa

Resonant coupling: the vortexshedding frequency is synchronizedwith the chamber acoustic modes(fvs = fa)



Vortex sound quasi-one dimensional model

• Two phase flow effects are neglected.• A mixture of non reacting perfect gases, with thermophysical properties

variable in space and time, is considered.• The grain combustion reactions occur in a thin layer on the grain surface; the

propellant mass is added without any axial momentum.• Combustion unsteady models are not considered.



Q-1D vorticity equation I

Vorticity equation for a newtonian fluid without viscous terms

∂(ρω)∂t

+∇ · (ρωu) = ρω · ∇u− ρω∇ · u (1)

ω · ∇u: stretching or tilting termω∇ · u: compressibility effect

1. Expression in cylindrical coordinates

2. Axysimmetric flow (uθ = 0, ∂∂θ

= 0)⇒ scalar equation in conservative form3. Integration on the port area (mean value Ap) on a cell of thickness ∆x

Quasi-one dimensional vorticity equation

∂(ρωθAp)∂t

+∂(ρωθuxAp)

∂x= −

∫Ap

∂(ρωθur)∂r

dAp −∫

Ap

ρωθur

rdAp (2)

−∫

Ap

ρωθ∂ur

∂rdAp −

∫Ap

ρωθ∂ux

∂xdAp =

Sω1 + Sω2 + Sω3 + Sω4



Q-1D vorticity equation II

• Sω1: radial addition• Sω2: deformation contribution; Sω3, Sω4: compressibility effect• The deformation and the compressibility effects are not considered; Sω2, Sω3

and Sω4 are neglected.• The only radial addition term Sω1 remains to be modeled.• Ω variable:

Ω = ρωAp (3)


∂ Ω∂t

+∂ (Ω u)∂x

= Sω1 (4)



Q-1D quasi-one dimensional governing equations


∂(ρiAp)

∂t+∂(ρiuAp

)∂x

= rbPbρp +msAp

V+

migAp

V+ mvs for i = 1, . . . , 6

∂(ρuAp

)∂t

+∂[(ρu2 + p

)Ap]

∂x− p

∂Ap

∂x=

migApvinj

V+

12ρu2cf + qvs

∂(ρeAp

)∂t

+∂[(ρe + p) uAp

]∂x

= rbPbρpHf +migApHig

V+

msApHs

V+ evs

∂ Ω∂t

+∂ (Ω u)∂x

= Sω1

(5)

• mvs, ˙qvs, ˙evs: excitation of the acoustic field by vortex shedding phenomenon



Vortex growth, detachment and acoustic field excitation I

• Sω1 is here related to the radial contribution due to the presence of a corner(obstacle and parietal vortex shedding are not taken into described). It existsonly at the corner where the vortex generation occurs and it is expressed as:

Sω1 = ρΓ (6)

• Vortex shedding excitement by acoustic field: vortex properties as a functionof time varying flow conditions.

• Rate of variation of the circulation (kΓ is a calibration parameter):

Γ = kΓ u2(t) (7)

• The vortex separation is imposed at each descendent node of the pvs(t)(positive velocity antinode):

d2pvs

dt2= 0 (8)

dpvs

dt⇒ local minimum (9)



Vortex growth, detachment and acoustic field excitation II

• mvs, qvs and evs are the Euler equations source terms for the sound generationdue to vortex impingement

• From a phenomenological description combined with a dimensional analysis):

mvs,i = 0 (10)

qvs = Ωu

Ap

(dAp

dx

)2

(11)

evs = ρuqvs =ρΩAp

(u

dAp

dx

)2

(12)

• The expression introduced to model the source terms and to close the model,derives from a heuristic process.

• A calibration process is then necessary to obtain a good estimation of theoscillation amplitude.



Internal Ballistic quasi-one dimensional model AGAR

• AGAR quasi-one dimensional model for the simulation of the internal ballisticin SRMs.

• AGAR model is composed by the following submodels:

• SPINBALL(Solid Propellant rocket motor INternalBALListics)gasdynamic model, for the analysis of solid rocket motor internalballistics; it is completed by a cavity model, a heat transfer model, ...(Ref: E. Cavallini, Modeling and numerical simulation of solid rocket motor internalballistic, Ph.D. Thesis, Dipartimento di Ingegneria Aerospaziale e Astronautica, Sapienza,Università di Roma 2010 )

• GREG(Grain REGression) 3D grain burnback model (burning surfaceevolution with time); it provides the required geometrical parameters(Ref: E. Cavallini, Modeling and numerical simulation of solid rocket motor internalballistic, Ph.D. Thesis, Dipartimento di Ingegneria Aerospaziale e Astronautica, Sapienza,Università di Roma 2010 )

• the quasi-one dimensional aeroacoustic model here presented



P80 DM solid rocket motor

• P80 SRM is the first stage of the European Vega launcher.• Finocyl grain; helium as pressurizing gas.• 3 (+1) blows can be noted along the combustion time.• A correct reconstruction of the motor ballistics has been obtained; non ideal

parameters (hump, scal factor and combustion efficiency) evaluated fromstatic firing test data by a 0D model have been used.



P80 DM solid rocket motor and ballistic reconstruction

• The simulation of the P80 DM aeroacoustic coupling is provided.



P80 DM pressure and vorticity (Ω) distribution

• Second blow.• Two pressure nodes (velocity antinode): cell 240 and cell 310.• The vorticity is gradually damped with the convection towards the nozzle.• Ω regular envelopment characterizes a resonant configuration.• Each Ω local maximum corresponds to a vortex =⇒ 4 vortices.• The number of vortices increases with the combustion time (grain regression,

core flow velocity decrease, higher number of slower vortices) from 4 to 5.



Detachment criterion

• The red lines correspond to a vortex shedding.• Separation related to a relative minimum of the first derivative and to a zero

second derivative.• Detachment at each pressure descending node, corresponding to a negative

velocity antinode.



Pressure oscillations HHT analysis

• The Hilbert-Huang transform (HHT) is the result of the empirical mode decomposition(EMD) and the Hilbert spectral analysis (HSA).

• The signal is decomposed into so-called intrinsic mode functions (IMF) and theinstantaneous frequency and amplitude are obtained.



Pressure oscillations HHT analysis

blow ttc

ffac,IIblow

AAmax,IIblow

II 0.23 - 0.472 0.94 0.75III 0.65 - 0.752 0.86 0.525IV 0.866 - 0.944 0.989 0.53



P80 DM experimental data comparison

ttc

ffac,IIblow

AAmax,IIblow

II 0.23 - 0.472 0.94 0.75III 0.65 - 0.752 0.86 0.525IV 0.866 - 0.944 0.989 0.53

Numerical simulation

ttc

ffac,IIblow

AAmax,IIblow

II 0.252 - 0.488 1 1III 0.69 - 0.79 1.044 0.535IV 0.88 - 0.97 1.064 0.44

Experimental data

• The fluctuating head pressurecomponent is filtered between0.774-1.5474 of thenon-dimensional frequency.

• The numerical results show a goodagreement with both the blowtime and amplitude.

• The model correctly describes thesystem resonant windows.



P80 DM FFT analysis comparison

• Numerical simulation: two frequency peaks around ∼ 0.856-1 of thenon-dimensional frequency (acoustics), while the second in around ∼1.297-1.42 (pressure first node-throat antinode characteristic length).

• Experimental data: a frequency peaks between∼0.1-1.064 (acoustics), a secondpeak can be noted between ∼1.48-1.55 (pressure first node-throat antinodecharacteristic length).

• The existence of the two frequency components (∼1 and ∼1.5) is in agreementwith the spectra obtained for the numerical simulation.

Numerical simulation Experimental data



P80 DM Rossiter’s analysis

m Tvs =li

kR u+

li(a − u)

+ ∆t (13)

• Rossiter’s analysis provides an estimate of the number of vortices thatcorresponds to a resonant configuration (it does not take into account both twophase flow effects and combustion instability).

• kR = 0.58, in accordance with literature.• The number of vortices increases with the combustion time, moving from 7 to

11.• Because of this too high values, Rossiter’s model does not identify any

possible resonance solution for this motor.

I II III IVli 2.6 2.85 2.9 2.9k 0.58 0.58 0.58 0.58u 40 30 30 28m 7 10 10 11



Concluding remarks I

• The model has been applied to the simulation of the aeroacoustic coupling ofP80 DM solid rocket motor.

• Two frequency components can be noted, the first related to the acoustics andthe second to the node-throat antinode characteristic length.

• None spatial pressure node is located at the step position.• The simulation of the last three blows is in good agreement with the

experimental data (blow timing and the oscillation amplitude). The frequencycharacterization is also coherent, notwithstanding the obtained values areslightly lower than the experimental.



Concluding remarks II

• AGAR quasi-one dimensional model for the simulation of the flow timeevolution in SRMs is presented.

• The model provides a good phenomenological description of the aeroacousticcoupling mechanism, of the system adjustment to resonance condition and ofthe following coming out.

• The heuristic process followed to close the model makes it necessary anamplitude calibration. A model improvement can arise from a deepening andre-discussion of the adopted closure.

• Other improvements: parietal and obstacle vortex shedding, two phase-floweffects and combustion instability.

• Analysis of other solid rocket motors in order to complete the modelunderstanding and description⇒ Ariane 5 SRM



Acknowledgements

The present activities were partially financed by ESA/ESRIN.

The authors would like to thank Avio, Europropulsion, CNES, ELV and ESA.

The development and production of Vega SRMs are mainly due to AVIO GroupS.p.A. (Colleferro Factory). Avio is prime contractor for the P80 SRM with adelegation to Europropulsion, France. The Program is managed by CNES/ESA.



jpc 2011 pres ferretti

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