Etude de la combustion de gaz de synthèse issus d'un processus de ...
Etude de la combustion de gaz de synthèse issus d'un processus de ... Etude de la combustion de gaz de synthèse issus d'un processus de ...
Experimental and numerical laminar syngas combustion Pe b δ 35 0 ρ SC q −006 . = = . P (4.19) λ b u u pb Where Pe b is the Peclet number and P the pressure in MPa. This correlation was obtained for stoichiometric methane-air and methanol-air mixtures for pressures 1-40 atm. Recently Boust, (2006) shows that this correlation is also valid for lean (φ=0.7) methane-air mixtures and stoichiometric hydrogen-air mixtures. For these reasons, we shall use correlation (4.19) for syngas-air mixtures. 4.2.1.2 Chemical equilibrium tel-00623090, version 1 - 13 Sep 2011 Gases can have two possible states, burned and unburned. The composition of the burned gases is calculated by the Brinkley method, suggested by Heuzé et al., (1985). This method is based on the determination of the free energy of Gibbs from the Gordon & McBride, (1971) polynomials. The chemical equilibrium is calculated by canceling the chemical affinity in the chemical reactions. It appeals to the thermodynamic properties of the species instead of the equilibrium constants. The combustion products considered are H 2 O, CO 2 , CO, O 2 , N 2 , NO, OH and H 2 . As pressure and temperature conditions change during the compression and cooling phases, is possible to previously recalculate the composition of burned gases. 4.2.1.3 Heat transfer A common approach exploiting a combined convective and radiative heat transfer coefficient has been implemented as representative of heat transfer through the chamber walls, Q w . The formulation couples a convective-equivalent heat transfer coefficient to a radiative term, for taking into account the effects due to high temperature burned gases: Qw = Qc + Qr (4.20) Where Q c and Q r represents the convective and radiative heat transfer, respectively. The unburned gases in contact with the wall are heated by compression under the effect of expansion flame. Due to the higher temperature of the unburned gases in comparison with the chamber wall, which is at room temperature, they yield heat by conduction. This conductive heat transfer is simulated using a convective model (Boust, 2006). 124
Chapter 4 ( ) Q = h T − T (4.21) c g w with T g and T w , respectively, the temperature of the gases and wall and, h, the convective heat transfer coefficient. T w is considered constant as it varies less than 10 K during combustion as reported by Boust, (2006). T g is the local temperature of the gases. The determination of the convective heat transfer coefficient is case sensitive and several models are available in the literature [Annand (1963), Woschni (1967), or Hohenberg (1979)]. In this code the Woschni, (1967) model, which is based on the hypotheses of forced convection is applied and compared with the recent heat transfer model of Rivère, (2005) based on the gases kinetic theory (see appendix C). The Woschni (1967) heat transfer correlation is given as: 02 08 055 08 = 130 − . . − . . hg () t B P() t T() t v() t (4.22) tel-00623090, version 1 - 13 Sep 2011 where B is the bore (m), P and T are the instantaneous cylinder pressure (bar) and gas temperature (K), respectively. The instantaneous characteristic velocity, v is defined as: ⎛ VT ⎞ s r v = ⎜2. 28Sp + 0. 00324 ( P −Pmot) ⎟ (4.23) ⎝ Pr Vr ⎠ Where P mot =P r (V r /V) γ is the motored pressure. S p is mean piston speed (m/s), V s is swept volume (m 3 ), V r , T r and P r are volume, temperature and pressure (m 3 , K, bar) evaluated at any reference condition, such as inlet valve closure, V is instantaneous cylinder volume (m 3 ) and γ is the specific heat ratio. The second term in the velocity expression allows for movement of the gases as they are compressed by the advancing flame. In the model of Rivère, (2005) the heat transfer coefficient is obtained as follows: 3 2 2 ⎛ R ⎞ ⎛ χ λ ⎞ h = ρg. Tg η π ⎜ M ⎟ + − (4.24) ⎝ ⎠ ⎜ T T ⎟ ⎝ ⎠ w w where ρ g , T g and M are, respectively, the density, the temperature and molar mass of the gases. The last parenthesis in the right side of the Eq. (4.26) represents the heat transfer coefficient that depends on the gases temperature that determines the length of the boundary layer. χ and λ are the material constants and η a function of the aerodynamic conditions equal to zero in the advection absence. 125
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Experimental and numerical <strong>la</strong>minar syngas <strong>combustion</strong><br />
Pe<br />
b<br />
δ<br />
35<br />
0<br />
ρ SC<br />
q<br />
−006<br />
.<br />
= = . P<br />
(4.19)<br />
λ<br />
b u u pb<br />
Where Pe b is the Peclet number and P the pressure in MPa. This corre<strong>la</strong>tion was<br />
obtained for stoichiometric methane-air and methanol-air mixtures for pressures 1-40<br />
atm. Recently Boust, (2006) shows that this corre<strong>la</strong>tion is also valid for lean (φ=0.7)<br />
methane-air mixtures and stoichiometric hydrogen-air mixtures. For these reasons, we<br />
shall use corre<strong>la</strong>tion (4.19) for syngas-air mixtures.<br />
4.2.1.2 Chemical equilibrium<br />
tel-00623090, version 1 - 13 Sep 2011<br />
Gases can have two possible states, burned and unburned. The composition of the<br />
burned gases is calcu<strong>la</strong>ted by the Brinkley method, suggested by Heuzé et al., (1985).<br />
This method is based on the <strong>de</strong>termination of the free energy of Gibbs from the Gordon<br />
& McBri<strong>de</strong>, (1971) polynomials. The chemical equilibrium is calcu<strong>la</strong>ted by canceling the<br />
chemical affinity in the chemical reactions. It appeals to the thermodynamic properties<br />
of the species instead of the equilibrium constants.<br />
The <strong>combustion</strong> products consi<strong>de</strong>red are H 2 O, CO 2 , CO, O 2 , N 2 , NO, OH and H 2 . As<br />
pressure and temperature conditions change during the compression and cooling<br />
phases, is possible to previously recalcu<strong>la</strong>te the composition of burned gases.<br />
4.2.1.3 Heat transfer<br />
A common approach exploiting a combined convective and radiative heat transfer<br />
coefficient has been implemented as representative of heat transfer through the<br />
chamber walls, Q w . The formu<strong>la</strong>tion couples a convective-equivalent heat transfer<br />
coefficient to a radiative term, for taking into account the effects due to high<br />
temperature burned gases:<br />
Qw = Qc + Qr<br />
(4.20)<br />
Where Q c and Q r represents the convective and radiative heat transfer, respectively.<br />
The unburned gases in contact with the wall are heated by compression un<strong>de</strong>r the<br />
effect of expansion f<strong>la</strong>me. Due to the higher temperature of the unburned gases in<br />
comparison with the chamber wall, which is at room temperature, they yield heat by<br />
conduction. This conductive heat transfer is simu<strong>la</strong>ted using a convective mo<strong>de</strong>l<br />
(Boust, 2006).<br />
124