ChEn 433 Combustion
Class 11
Premixed flame description
Bunsen flames
Questions?
- Why are they blue?
- Why the inner and outer flame?
- Why the flat cone?
- What’s with the streamlines?
- How thin is the flame?
- What determines the cone angle?
- What makes a flame a flame?
Flame speed
Flame thickness
Fuel comparisons
\(S_L\) Correlation
\[S_L = S_{L,ref}\left(\frac{T_u}{T_{u,ref}}\right)^\gamma\left(\frac{P}{P_{ref}}\right)^\beta(1-2.1Y_{dil})\] \[T_{ref}=298\,\,\text{K},\,\,\,\,\,P_{ref}=1\,\,\text{atm}\] \[S_{L,ref} = B_M + B_2(\Phi - \Phi_M)^2\] \[\gamma = 2.18-0.8(\Phi-1)\] \[\beta = -0.16 + 0.22(\Phi-1)\] \(Y_{dil}\) = mass fraction of diluent in the fuel-air mixture (e.g., for recirculated products).
Turbulent premixed flames
Lean, premixed, H\(_2\) flames (E.R. = 0.31-0.4)
\(\rho\), HR, T;
Ka = 10, 100, 260, 1560
Flame scales
- Damkohler number
- based on large scale mixing rate \[Da = \frac{\tau_{mix}}{\tau_{rxn}} = \frac{\text{rxn rate}}{\text{mixing rate}}\] \[Da = \frac{L_0/u^\prime_{rms}}{\delta/S_L} = \frac{L_0S_L}{\delta u^\prime_{rms}}\]
- Reynolds number
- using Pr=1, \(\alpha = S_L\delta\)
- Looks like a mixed up Da \[Re = \frac{L_0u^\prime_{rms}}{\nu} = \frac{L_0u^\prime_{rms}}{S_L\delta}\]
- Karlovitz number
- like inverse Da using small scale mixing rate \[Ka = \frac{\tau_F}{\tau_\eta} =\frac{\delta^2}{\eta^2} = \frac{v_\eta^2}{S_L^2}\]
Regime diagram
Turbulent flame speeds
Wrinkled flame regime
- Damkohler \[\frac{S_t}{S_L} = 1+\frac{u^\prime_{rms}}{S_L}\]
- Klimov \[\frac{S_t}{S_L} = 1+3.5\left(\frac{u^\prime_{rms}}{S_L}\right)^{0.7}\]
- Clavin, Williams \[\frac{S_t}{S_L} = \left[\frac{1}{2}\left(1+\left(1+8\frac{u^{\prime 2}_{rms}}{S_L^2}\right)^{1/2}\right)\right]^{1/2}\]
Detonation
Difference between detonation and deflagration?
Deflagrations
balance diffusive heat and mass transfer with heat release from reaction
Detonations
balance acoustic compression with heat release from reaction
Detonation velocities
