calcolo dello stato di equilibrio -...
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CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Calcolo dello Stato di Equilibrio
Calcolo dello Stato di Equilibrio
In un processo di combustione adiabatico ed isobaro in cui la combustioneraggiunge uno stato di equilibrio chimico valgono le seguenti relazioni:
Vincolo stechiometrico (ponderale): Conservazione delle moli atomiche:
Condizione termodinamica di equilibrio chimico(max entropia == min entalpia libera di Gibbs)
Conservazione dell’energia in termini di entalpia assoluta della miscela
Saturday, July 11, 15
TURBOGETTO SEMPLICE CICLO A PUNTO FISSO CICLO IN VOLO Ese. 5: Turbo-Getto TURBOFAN TURBOF
COMBUSTORE
ANALISI A PUNTO FISSO: COMBUSTORE
EQ. ENERGIA (Ls = 0, M ≪ 1): ∆h0 ≃ ∆h = ∆Q
ηb := Q/(mf Qf ) RENDIMENTO DI COMBUSTIONE
T4: TEMPERATURA ALL’INGRESSO DELLA TURBINA (TIT)
ηpb := p4/p3 RENDIMENTO PNEUMATICO DEL COMBUSTORE
f := mf/ma RAPPORTO COMBUSTIBILE/ARIA, O DI DILUIZIONE
mah3 + mfhf + Q = (ma + mf )h4
f ≪ 1 ⇒ mah3 + Q = mah4 ⇒ macp(T4 − T3) = Q
Q = ηb mf Qf
f =cp (T4 − T3)
ηb Qf=
cpT3
ηb Qf
!
T4
T3− 1
"
p4 = ηpb p3
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Processi chimicamente reversibili: congelati, in equilibrio
Processi chimicamente reversibili: congelati, in equilibrio
Irreversible processes
dS = dSext + dSint
dSext =1
TdU +
p
TdV =
dQext
T= 0 Non adiabatic system
dSint = −1
T
!
j
µjdNj > 0 Chemically reactive system
Internal (chemical) reversible processes
dSint = −1
T
!
j
µjdNj = 0 ⇔ dG =!
i
µidNi = 0
Chemically frozen processes (air intake, compressor, turbine, nozzle)
∀j : dNj = 0 ⇒ Nj = const ⇒ c(v,p)(T, Yi) = const if gas is calorically perfect
Processes in chemical equilibrium (combustion chamber)
dG =!
j
µjdNj = 0 ⇒ Minp,Tgiven
[G (p, T,Nj)] ⇒ Nj = N∗
j (p, T )
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Conservazione delle moli atomiche: stechiometria
Conservazione delle moli atomiche: stechiometria
Supponiamo che la miscela sia formata da 8 specie chimiche:
1 2 3 4 5 6 7 8H2 O2 H O OH H2O HO2 H2O2
La conservazione delle moli atomiche si esprime con 2 equazioni algebriche
NH = 2n1 + n3 + n5 + 2n6 + n7 + 2n8
NO = 2n2 + n4 + n5 + n6 + 2n7 + 2n8
che in forma matriciale si scrive
Adn =
(2 0 1 0 1 2 1 20 2 0 1 1 1 2 2
)
⎧
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
dn1
dn2
dn3
dn4
dn5
dn6
dn7
dn8
⎫
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭
= 0
questo sistema lineare di 2 equazioni in 8 incognite ammette ∞6 = 8 − 2 soluzioni.
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Conservazione delle moli atomiche: stechiometria
Conservazione delle moli atomiche: stechiometria
Le ∞6 soluzioni si trovano partizionando la matrice A ed il vettore dn:
(2 00 2
){dn1
dn2
}
= −
(1 0 1 2 1 20 1 1 1 2 2
)
⎧
⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
dn3
dn4
dn5
dn6
dn7
dn8
⎫
⎪⎪⎪⎪⎪⎬
⎪⎪⎪⎪⎪⎭
per ogni scelta delle componenti dnj , j = 3, 8 si trovera una ed una sola coppiadnj , j = 1, 2 che soddisfa il sistema di due equazioni
come si possono scegliere le dnj , j = 3, 8 in modo di essere sicuri di averle presetutte ? si utilizza una base di vettori linearmente indipendenti ovvero:
ek ={
eik
}
=
{1 se i = k0 se i = k
}
k = 1,8 - 2 = 6
Con la scelta degli ek effettuata utilizzando vettori linearmente indipendenti
consente di scrivere le ∞6 soluzioni in questo modo:
⎧
⎪⎨
⎪⎩
{dn1
dn2
}
= −
(2 00 2
)−1 (
1 0 1 2 1 20 1 1 1 2 2
)
dn2+k
dn2+k = ekdξk
k = 1, 6
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Conservazione delle moli atomiche: stechiometria
Conservazione delle moli atomiche: stechiometria
Tornando ad una rappresentazione per componenti si ottiene
dn1 = − 12dξ
1
dn2 = 0dn3 = dξ1
⎫
⎬
⎭⇒
1
2H2 = H dξ
1assume valori compresi ≥ 0
che indica che ogni ∞1 soluzioni rappresenta una reazione chimica virtuale
E qundi in una miscela con 8 specie formata da 2 elementi atomici si possono avereal piu 8-2=6 reazioni chimiche linearmente indipendenti
in forma compatta si puo scrivere
dni =∑
k
νki dξ
k
Le 6 direzioni cosı trovate individuano un sottospazio in R8 che in algebra lineare
viene chiamato: spazio nullo della matrice A ( NullSpace[A] in Mathematica ).
Lo spazio nullo e il sottospazio in cui, a partire da una composizione iniziale dellamiscela assegnata, le reazioni chimiche trasformano la miscela in modo che ilnumero di atomi iniziali si conservi
dn1dt = − 1
2dξ1
dt
dn2dt = 0
dn3dt = dξ1
dt
dξ1
dt:= r
1(p, T,Nj) = r1f − r
1b
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Condizione termodinamica di equilibrio chimico
Condizione termodinamica di equilibrio chimico
Reversible (zero entropy) process dG =∑
j
µjdNj = 0
Stoichiometric constraint dNj =∑
k
νkj dξk
⇓
dG =∑
j
µj
∑
k
νkj dξk =∑
k
dξk∑
j
µjνkj = 0
⇓
∀dξk = 0,
⎧
⎨
⎩
∑
j
µjνkj = 0
⎫
⎬
⎭
Nreactions
k=1
⇓
Free Enthalpy (Gibbs) is stationary ⇔ Chemical equilibrium
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Legge di Azione di Massa
Legge di Azione di Massa
Equilibrium Condition∑
j
µj (T, pj) νkj = 0 k = 1,Nreactions
µj(T, pj) := Hj(T ) − T Sj(T, pi) Sj(T, pj) := S0j (T ) − ℜLog(
pj
pref
)
µj(T, pj) := Hj(T ) − T
[
S0j (T ) − ℜLog(
pj
pref
)
]
=(
Hj(T ) − T S0j (T )
)
+ ℜTLog(pj
pref
) = µ0j (T )
∑
j
[
µ0j (T ) + ℜTLog(
pj
pref
)
]
νkj = 0 ⇒
∑
j
[
µ0j (T )
]
νkj = −
∑
j
[
ℜTLog(pj
pref
)
]
νkj
∑
j
[
Hj(T ) − T S0j (T )
]
νkj = −ℜT
∑
j
νkj Log(
pj
pref
) = −ℜT∑
j
Log(pj
pref
)νkj
Exp
⎧
⎨
⎩−
1
ℜT
∑
j
[
Hj(T ) − T S0j (T )
]
νkj
⎫
⎬
⎭
︸ ︷︷ ︸
Kp(T )
= Exp
⎧
⎨
⎩
∑
j
Log(pj
pref
)νkj
⎫
⎬
⎭
Kkp (T ) = Exp
⎧
⎨
⎩Log
∏
j
(pj
pref
)νkj
⎫
⎬
⎭=
∏
j
(pj
pref
)νkj
Law of Mass Action Kkp (T ) =
∏
j
(pj
pref
)νkj
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Calcolo dello Stato di Equilibrio
Calcolo dello Stato di Equilibrio
Ns + 2 incognite : composizione della miscela (N jProducts, j = 1, Ns), Numero
totale di moli (Ntot), e temperatura adiabatica di fiamma (TProducts)
Ns + 2 equazioni:Conservazione delle moli atomiche:
Ni =
Ns!
j=1
aijN
jReac =
Ns!
j=1
aijN
jProducts i = Ne
Condizione termodinamica di equilibrio chimico (Legge di azione di massa)
Kkp (T ) =
"
j
(pj
pref
)νkj k = Ns − Ne pj =
Nj
Ntot
p
Numero totale di moli
Ntot =Ns!
j=1
Nj
Conservazione dell’energia in termini di entalpia assoluta della miscela
H(TReac, NjReac) = H(TProducts, N
jProducts)
Saturday, July 11, 15
CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI COMBUSTIONE:
Risultati del Calcolo dello Stato di Equilibrio
Risultati del Calcolo dello Stato di Equilibrio
MISCELA H2/O2
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
2900
3000
3100
3200
3300
3400
Figure: Variazione Temperatura adiabaticadi equilibrio con rapporto di equivalenza(p=1 e 10 atm); T reagenti = 300K.
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0.001
0.005
0.010
0.050
0.100
0.500
1.000
Figure: Variazione Composizione diequilibrio con rapporto di equivalenza (p=1e 10 atm); T reagenti = 300K.
Saturday, July 11, 15
TURBOGETTO SEMPLICE CICLO A PUNTO FISSO CICLO IN VOLO Ese. 5: Turbo-Getto TURBOFAN TURBOF
FLUSSO ALLA RAYLEIGH
FLUSSO ALLA RAYLEIGH
Variazione di T0 e variazione di Mach in CC
!
T0
T⋆0
"
cal
[M, γ] =2M2
#
1 + δM2$
(γ + 1)#
1 + γM2$2
!
T04
T03
"
cal
[M3,M4, γ] =
%
T0T⋆
0
&
cal[M4, γ]
%
T0T⋆
0
&
cal[M3, γ]
=
#
1 + δM24
$ #
M4 +M23M4γ
$2
#
1 + δM23
$ #
M3 +M3M24γ
$2
Variazione di p0 e variazione di Mach in CC
!
p0p⋆0
"
cal
[M, γ] =2#
1 + δM2$
γγ−1 (γ + 1)
11−γ
1 + γM2
!
p04
p03
"
cal
[M3,M4, γ] =
%
p0p⋆0
&
cal[M4, γ]
%
p0p⋆0
&
cal[M3, γ]
=
!
1 + δM23
1 + δM24
"
γγ−1 1 + γM2
4
1 + γM23
Saturday, July 11, 15
TURBOGETTO SEMPLICE CICLO A PUNTO FISSO CICLO IN VOLO Ese. 5: Turbo-Getto TURBOFAN TURBOF
RENDIMENTO PNEUMATICO
RENDIMENTO PNEUMATICO
Rapporto T04/T03 in funzione della portata di combustibile f
f =cp (T4 − T3)
ηb Qf
≈cpT03
ηb Qf
!
T04
T03− 1
"
⇒T04
T03= 1 +
f ηb Qf
cpT03
Numero di Mach in ingresso M3 della CC per assegnati Mach in uscita M4 erapporto T04/T03
Solve
#
T04
T03==
$
2 +M24 (γ − 1)
% $
M4 +M23M4γ
%2
$
2 +M23(γ − 1)
% $
M3 +M3M24 γ
%2 ,M3
&
Perdite di pressione p0 in funzione della variazione di Mach tra ingresso eduscita della camera
ηpb :=
!
p04p03
"
cal
[M3,M4, γ] =
!
1 + δM23
1 + δM24
"
γγ−1 1 + γM2
4
1 + γM23
Saturday, July 11, 15
FP7-SPACE-CALL-1
In Space PropulsionISP-1
Space Propulsion Conference – Bordeaux – May 7-10, 2012
Micro Combustion ChamberM3 Test Bench - DLR
13
M3 chamber characterizes ignition behaviour, with varying injection geometries and flow conditions
Mass flows are determined through Coriolis flow meters
Sonic nozzles set the correct mass flows
Sonic nozzles provide an effective separation between feed lines and injector head, thus minimising low frequency combustion instabilities
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Model Equations for Unsteady CSTR with Energy Deposition
d(ρV )dt
= !mfuel[t,p]+ !moxid[t,p]− !mnozzle[p,T,Y]
d(ρhV )dt
= !mfuel[t,p]hfuel + !moxid[t,p]hoxid − !mnozzle[p,T,Y]h[T,Y]+Vdpdt
+ !q[t]V
dYj
dt=
1ρ[p,T,Y]V
!mfuel[t,p]Yj + !moxid[t,p]Yj − !mnozzle[p,T,Y]Yj( ) + Wj
ρ[p,T,Y]ω j[p,T,Y]−
Yj
ρ[p,T,Y]dρdt[p,T,Y]
p = ρRT →1ρdρdt
=1pdpdt
−1RdRdt
−1TdTdt
R =RUWjj
∑ Yj →dRdt
=RUWjj
∑ dYj
dt
h = hjj∑ Y →
dhdt
= hjj∑ dYj
dt+ Cp
dTdt
→ Cp = Cj , pYjj∑
!q(t)[ ErgCentimeter3Second
] = ε[Joule]4πσ r
3σ t
e−12t− t0σ t210[ Erg
Joule]
!mfuel[t,p] = !mred[p
p0,fuel (t), ηfuel , γ fuel ]
p0,fuel (t)Afuel
RfuelT0,fuel
!moxid[t,p] = !mred[p
p0,oxid (t), ηoxid , γ oxid ]
p0,oxid (t)Aoxid RoxidT0,oxid
!mnozzle[p,T,Y] = !mred[pa
p, ηoxid , γ (T ,Y )] p Aoxid
R(Y)T
!mred[Πp , η, γ ] = 2γγ −1
1Πp
η 1− Πp
γγ −1
⎛
⎝⎜
⎞
⎠⎟
1−η 1− Πp
γγ −1
⎛
⎝⎜
⎞
⎠⎟
with Πp ≥2
γ +1⎛⎝⎜
⎞⎠⎟
γγ −1
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Model Equations for Unsteady CSTR with Energy Deposition
dYj
dt=
R[Y ]TpV
!mfuel[t,p]Yj + !moxid[t,p]Yj − !mnozzleYj( )
+Wjω j[p,T ,Y ]ρ[p,T ,Y ]
−Yj
ρ[p,T ,Y ]dρdt
[p,T ,Y ] j = 1 , Ns
dTdt
=- !mnozzle[p,T ,Y ] + !mfuel[t,p]
hfuel − h[T ,Y ]R[Y ]T
+ 1⎛⎝⎜
⎞⎠⎟
+ !moxid[t,p] hoxid − h[T ,Y ]R[Y ]T
+ 1⎛⎝⎜
⎞⎠⎟
(Cp-R) p V
−hj[T ]
j∑ dYj
dt -T RU
Wj
dYj
dtj∑
(Cp[T ,Y ]-R[Y ])+
!q[t]ρ[p,T ,Y ] (Cp[T ,Y ]-R[Y ])
dpdt
=p γ [T ,Y ]R[Y ]T
- γ [T ,Y ]−1γ [T ,Y ]
hj[T ]j∑ dYj
dt + T RU
Wj
dYj
dtj∑
⎛
⎝⎜⎞
⎠⎟
+ γ [T ,Y ]R[Y ]TV
- !mnozzle[p,T ,Y ] + !mfuel[t,p]hfuel − h[T ,Y ]Cp[T ,Y ] T
+ 1⎛⎝⎜
⎞⎠⎟
+ !moxid[t,p] hoxid − h[T ,Y ]Cp[T ,Y ] T
+ 1⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟
!q[t][ ErgCentimeter3Second
] = ε[Joule]4πσ r
3σ t
e−
12t− t0σ t
210[ Joule
Erg]
R[Y ] = RUWj
Yjj∑
ρ[p,T ,Y ] = pR[Y ]T
h[T ,Y ] = hj[T ]j∑ Yj
dρdt
=1V!mfuel[t, p]+ !moxid[t, p]− !mnozzle[p,T ,Y ]( )
!mfuel[t,p] = !mred[p
p0,fuel (t), ηfuel , γ fuel ]
p0,fuel[t]Afuel
RfuelT0,fuel
!moxid[t,p] = !mred[p
p0,oxid (t), ηoxid , γ oxid ]
p0,oxid[t]Aoxid RoxidT0,oxid
!mnozzle[p,T,Y] = !mred[pa
p, ηoxid , γ (T ,Y )] p Aoxid
R[Y]T
!mred[Πp , η, γ ] = 2γγ −1
1Πp
η 1− Πp
γγ −1
⎛
⎝⎜
⎞
⎠⎟
1−η 1− Πp
γγ −1
⎛
⎝⎜
⎞
⎠⎟
with Πp ≥2
γ +1⎛⎝⎜
⎞⎠⎟
γγ −1
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Data
p0fuel = 2.5 patm; pfuel = p0fuel;Tfuel = 290 Kelvin; T0fuel = Tfuel;ηfuel = 0.8;
p0oxid = 5.0 patm; poxid = p0oxid;Toxid = 290 Kelvin; T0oxid = Toxid;ηoxid = 0.8;
radiusoxid = 0.11 Centimeter; Aoxid = Pi radiusoxid^2;innerradiusfuel = 0.24 Centimeter;outerradiusfuel = 0.30 Centimeter; Afuel = Pi (outerradiusfuel^2 - innerradiusfuel^2);
Lchamber = 16 Centimeter;radiuschamber = 3 Centimeter;Volume = Lchamber radiuschamber;
pa = 1 patm; p0a = pa;Ta = 290 Kelvin; T0a = Ta;radiusnozzle = 1 Centimeter;Anozzle = Pi radiusnozzle^2;ηnozzle = 0.8;
T0 = 300. Kelvin; p0 = 1. patm;
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Inputs
0.0 0.5 1.0 1.51¥106
2¥106
3¥106
4¥106
5¥106
0.0 0.5 1.0 1.50
5.0¥108
1.0¥109
1.5¥109
2.0¥109
2.5¥109
3.0¥109
Total Pressures at Fuel & Oxygen Manifold in time
Energy deposition in time
sigr = 1.0*10^-3 Meter;sigt = 2.5*10^-4 Second;eps = minimumEnergy ;c1 = eps/(4 Pi sigr*sigr*sigr*sigt);qdotSI = c1*Exp[-.5*((time - t0)/sigt)^2];SItoCGS = 10;qdot = qdotSI * SItoCGS
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Outputs: Methane/Oxygen SystemSensitivity of peak pressure on energy deposition time
Temperature in time
Peak pressure vs time lag
Pressure in time
• short energy deposition time allow little reactants to fill the chamber -> lower total reactant mass yields a lower pressure peak during ignition
• short/long energy deposition time: ignition develop three/four stages
• first stage[heating]: isobaric T growth due to energy addition• second stage[explosion] (kinetics >> convection): T increases due to fast kinetics, and P follows for inertial confinement
because the kinetics is faster than convection• third stage[relaxation] (kinetics ~ convection): T&P decrease because the higher P produces a larger outflow• fourth stage[near-equilibrium] (kinetics << convection): T&P increase following the arrival of reactants which are instantly
burned
0.10 0.15 0.20 0.25 0.305001000150020002500
0.10 0.15 0.20 0.25 0.301.0¥1061.2¥1061.4¥1061.6¥1061.8¥106
0.5 1.0 1.51.0¥106
1.2¥106
1.4¥106
1.6¥106
1.8¥106
Saturday, July 11, 15
ISP-1 - September 22-23, 2011
Outputs: Methane/Oxygen SystemSensitivity of peak pressure on minimum energy deposition
Temperature in timePeak pressure vs minimum energy deposition
Pressure in time
• too low power levels cannot ignite the mixtures • higher power levels shorten the ignition times• less reactants can fill the chamber• peak pressure exhibits a max at ~50mJ
0.15 0.16 0.17 0.18 0.19 0.20
500
1000
1500
2000
2500
3000
3500
0.15 0.16 0.17 0.18 0.19 0.20
1.1¥106
1.2¥106
1.3¥106
1.4¥106
1.5¥106
1.6¥106
0.02 0.04 0.06 0.08 0.10 0.12 0.141.58¥106
1.59¥106
1.60¥106
1.61¥106
1.62¥106
1.63¥106
Saturday, July 11, 15
FP7-SPACE-CALL-1
In Space PropulsionISP-1
Space Propulsion Conference – Bordeaux – May 7-10, 2012
To check the ability of the physical models and prediction tools to reproduce:
• ignition model • flame propagation
- kernel formation- flame kernel evolution in a turbulent flow
• anchoring process
A dedicated experiment has been carried out at the M3 Test Bench (DLR Lampoldhausen) and has been used as a reference test case to benchmark different numerical approaches
Ignition is triggered using a laser beam to control the ignition point location and energy release, in a well controlled gas/gas injection configuration
This way a clean experimental configuration is obtained, allowing to check the ability of the numerical tools to reproduce flame propagation and anchoring
Two test campaigns have been carried out:
• ambient pressure• low pressure
Objectives of ISP-1 WP 2.5
20
Saturday, July 11, 15
FP7-SPACE-CALL-1
In Space PropulsionISP-1
Space Propulsion Conference – Bordeaux – May 7-10, 2012 21
Test case computed : 21.07.2011-7 (ambient, attached)
Ignition Sequence
- 117 -57 0 ignition Time line ms
The ignition overpressure (if all the quantity of propellant in the chamber prior to ignition is burnt instantaneously) can be found from:
pmaxpc
=!miτ i!mτ r
Decreasing the ignition delay decreases the overpressure during ignition.
τ r :=
M!me
These findings helped the selection of an ignition sequence of the test campaign able to minimize the overpressure.
An accurate selection of the ignition sequence is essential to avoid undesired peaks in the chamber pressure.
τ i is the ignition delay
τ r is the mean residence time in the chamber
!me is the massflow rate of gases exhausted though the nozzle
M is the mass of gas inside the chamber
!miτ i is the mass of reactants in the chamber over the time τ i
!mτ r is the mass of propellants in the chamber at any time
Accumulated unburnt masses prior to ignition determine the pressure rise during ignition and its overpressure.
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Gaseous Oxygen, before ignition
Coaxial Methane, before ignition, with Oxygen
Schlieren images of laser pulse (150 mJ); Expanding blast wave; Sequence sampled from multiple laser shots therefore only an estimate for the timing can be given; Time step ~ 50 µs
Schlieren image sequence of laser ignition of CH4/O2 gas/gas
COLD FLOW
HOT FLOWLASER-PULSE ON QUISCENT NITROGEN
Micro Combustion ChamberM3 Experiment - DLR
22
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Main experimental findings from DLR
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Flame lift-off length inversely proportional to chamber pressure
Excitation caused by heat release results in spontaneous emission of OH radicals at ca. 305-309 nm
Spontaneous emission in the UV-range is recorded by an intensified high-speed CCD video camera
Complete chamber is visualised with a resolution of 512 x 256 pixels
A band-pass filter (310 nm ± 5 nm) selects only OH-radical emission
Ambient pressure ignition
CC pressure rising due to heating
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Blast Wave
Motivations for CFD Analyses
Recirculation
Fuel Blockage
Quantitative analysis of ignition can be done by a "Well-Stirred Reactor" (WSR) or "Continuously Stirred Tank Reactor" (CSTR) models
Both models assume infinitely fast and efficient mixing in the chamber
These models allow to readily carry out all the relevant sensitivity analyses
Why then making the costly and tedious CFD analyses ?
Because of the critical role of multi-dimensional phenomena !!
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URANS MODELLING OPTIONS (CFD++ METACOMP Tech)• Flow geometry 2D Axi-symmetric • real gas, compressible equations• Ideal gas equation of state• multi-species with frozen/active detailed chemical kinetics• viscous flow• transient integration (time accurate, point implicit)• second order space discretization• turbulent modelling on: RANS two-eqns k-epsilon • Ignition by « hot spot »
ICs: • quiescent Nitrogen fills the chamber at T=290 K, and p=101325 Pa
BCs:• Walls are assumed isothermal, post tip and nozzle are considered
adiabatic• Inflow: constant total pressure and temperature for both fuel and
oxygen• Outflow: subsonic flow with prescribed ambient pressure
MESH: ~ 230K cells; block-structured
CHEMICAL KINETIC MECHANISM FOR CH4/O2+INERT NITROGEN: • GRI3.0 (53 species) with Nitrogen kinetics removed involves 36
species• Mechanism simplification (in-house tools) trimmed the mechanism to
15 species
URANS & LES Modelling Options
25
LES MODELLING OPTIONS (CEDRE ONERA)• Flow geometry 3D • real gas, compressible equations• Ideal gas equation of state• multi-species with a frozen/active global reaction mechanism• viscous flow• transient integration (time accurate)• second order space discretization• Smagorinski model for LES subgrid closure• Ignition by « hot spot »
ICs: • quiescent Nitrogen fills the chamber at T=290 K, and p=101325 Pa
BCs:• Walls are assumed adiabatic• Inflow: ramped total pressure and temperature for both fuel and
oxygen• Outflow: subsonic flow with prescribed ambient pressure
MESH: ~ 10M cells; unstructured
CHEMICAL KINETIC MECHANISM FOR CH4/O2+INERT NITROGEN: • Global kinetics (Jones and Lindstedt, adapted by Kim)
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Test case computed : 21.07.2011-7 (ambient, attached)• Step 1 : O2 cold flow– Not the whole injector is meshed : to account for pressure losses in Ox tube, boundary condition pressure is Pi=9 bars– To account for pressure increase vs time, relaxation is activated on the boundary condition– From t=-117ms to -57ms
• Step 2 : CH4 cold flow– Along with stabilized O2 cold flow– From t=-57ms to t=0ms
CFD AnalysesInflow BCs for LES
The filling process of the chamber by the cold reactants needs to be accurately replicated because the total mass of reactants at time T0 sets the total level of energy available for combustion during the ignition start-up
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How we trim the kinetics
Detailed (NS36) vs Simplified (NS15)
27
GRI-Mech 3.0 (53 spcs and 325 reversible rcns) is used as reference mechanism
All N-containing species are removed, except N2, together with all N-related reactions, to yield a detailed mechanism with 36 spcs and 219 reversible rcns
Mechanism simplification done by in-house tools
A spatially homogeneous, iso-choric, adiabatic, forced ignition with gaussian energy deposition drives the simplification procedure
The selected simplified mechanism involves 15 species and 57 reactions
The fastest time scale of the simplified mechanism is two orders of magnitude larger than the one of the detailed (stiffnes reduction)
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O⇣
1pdpdt
⌘⇡ O
�1T
dTdt
�+O
�1R
dRdt
�+O
⇣mF
⇢V + mOx
⇢V � mOut
⇢V
⌘
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Test Case#07 Ambient Pressure
Chamber pressure time evolution
URANS & LES return similar chamber pressure histories
Both feature a larger-than-experiment chamber pressure peak value and growth rate
Chamber pressure peak exceeds fuel manifold pressure -> fuel blockage
Late pressure evolution exhibits oscillations tuned with chamber acoustics
NB: Chamber pressure growth rate proceeds as:
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Test Case ValuesMethane = 0.60 g/sOxygen = 2.26 g/s
Test Case#07 Ambient Pressure
Massflows
Methane and oxygen inflows not fixed at their choked values when the pressure drop falls below the critical value
Hot products outflow eventually fixed by sonic condition at nozzle
Nearly constant massflows at late times suggest a nearly steady condition
URANS & LES fluxes are quite in agreement one to another (despite the slight different treatment of the inflow BCs)
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Test Case#07 Ambient Pressure
Propellants Mach Number
Oxygen stream choked during cold flow injection (M>1)Oxygen stream subsonic when chamber pressure peaks (M<1)Methane stream never choked (M<1); tends to zero near chamber pressure peak
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• A blast wave propagates spherically outward, reflects at the injector plate and at the wall, head-on collides at the symmetry axis, propagates downstream towards the nozzle only to be reflected backward towards the injector plate
• The under-expanded oxygen jet gradually fades away when the flow becomes subsonic• Note the formation of transient traveling pressure peaks at the symmetry axis
Test Case#07 Ambient Pressure
Blust Wave following Laser Pulse
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HCO
Temperature
Test Case#07 Ambient Pressure
Kernel initiation and flame propagation
• The flame kernel propagates downstream near the symmetry axis as convected by the fast central jet
• The flame kernel propagates across the recirculation region away from the axis
• When methane is not entering the chamber anymore, the cold oxygen jet is not consumed and leaves the chamber unburned-> the temperature field at the axis becomes very cold
• A significant amount of hot products is still present in the chamber ready to reignite the propellants when the chamber pressure is lowered by the mass loss through the choked nozzle
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• Methane blockage is clearly monitored by this movie• Note the role of the cavity as an accumulator of the blocked methane• The blockage process exhibits fluctuations coupled with the chamber acoustics
Methane
Oxygen
Test Case#07 Ambient Pressure
Fuel blockage
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LESTemperature iso-contour at T=2000K
Overall LES dynamics consistent with URANS predictions
LES captures the non symmetric flow evolution triggered by the off-axis laser pulse location
LES captures 3-D jet instabilities
LES captures a “breathing” evolution of the flame front as also noticed in experiments
LES captures the development of cold unreacted pockets
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URANS OH vs Experimental OH*
The comparison shows that the computed OH field is qualitatively exhibiting a similar shape and shape evolution, moves downstream at about the right speed, and posses a brighter core region surrounded by a darker halo, where locally the light intensity is proportional to the amount of OH
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LES Temperature vs Experimental OH*
The shape and position of the OH∗ emission field is quite similar to the one of the temperature and reactive zones in the LES computation
OH* emission field accounts for the integral contribution along the chamber cross-section, whereas both LES and URANS results refer to cut-planes passing through the chamber axis
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Flame Index at “stationary” conditions
FI = ∇yFuel ⋅∇yOxidFI > 0 ⇒ fuel and oxidizer fluxes aim at same direction (pre-mixed nature) FI < 0 ⇒ fuel and oxidizer fluxes aim at opposite directions (non pre-mixed)
(nearly) stationary flame is: lifted, and pre-mixedCo-axial Jet Mixing layer
Pre-heat, pre-mixed flame region(Solid lines are HCO mass fraction lines)
Fuel and oxidizer from both jet and recirculation region mix here
Negative T IndexNon-premixed mixture
Positive T IndexPremixed mixture
llift−off ∼ vjetτ ignvjet ∼ p0 − pCCllift−off ∼ p0 − pCCτ ign
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Main problem found• Larger-than-experiment chamber pressure peak value and growth rate
Possible causes (given that the pressure peak is mostly linked to the mass of CH4 and O2 in the chamber at T0)
• neglecting nitrogen filling the propellant manifold at T0 (volume of pipe(s) between the probe and the boundary conditions) realizes "too much" reactants in the chamber
• supersonic oxygen jet spreads too quickly by numerical dissipation and causes an excess of oxidant in the chamber at T0
Conclusions
Lesson learned
• URANS axi-symmetric calculations can be effectively able to provide a rather detailed picture of the ignition events, albeit there remains a number of issues for the quantitative accuracy of the URANS predictions
• 2D axi-symmetric URANS and 3-D LES provide predictions in satisfactory agreement, even when rather different kinetic mechanisms have been adopted
• CFD analyses offered interesting contributions in the understanding of a number of critical ignition phenomena, which are difficult to appreciate on the basis of experimental diagnostics alone
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This work has been carried out with the support of:
FP7 EU Grant no.218849, titled "In-Space Propulsion-1" (ISP-1)
M.Valorani acknowledges the support of:
CASPUR Competitive HPC Grant 2009
The URANS flow solver is: CFD++ by Metacomp Technologies, Inc.
The LES flow solver is: CEDRE, an ONERA in-house software package
Acknowledgements
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