--- title: "ChEn 433 Combustion" author: David Lignell date: Class 11 lang: en-US slideNumber: false width: 1600 height: 1000 transition: fade css: ../assets/style.css theme: simple title-slide-attributes: data-background-image: "https://d2cbg94ubxgsnp.cloudfront.net/Pictures/2000x1125/3/2/9/130329_gas_flare_shutterstock_548204362_hero.jpg" data-background-opacity: "1.0" verticator: enable: true menu: enable: true chalkboard: enable: false --- # Premixed flames ## Premixed flames ## Premixed flames # Premixed flame description image # Bunsen flames image image image ## Questions? ::: {.cols2} ::: {.col2-v} ::: incremental * 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? ::: ::: ::: {.col2-v} image image ::: ::: ::: notes Density ratio ~ 7 Thickness ~ 1 mm Speed ~ 0.5 m/s ::: ## Flame speed image ## Flame thickness image ## Fuel comparisons image ## $S_L$ 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). image # Turbulent premixed flames image Lean, premixed, H$_2$ flames (E.R. = 0.31-0.4) $\rho$, HR, T; Ka = 10, 100, 260, 1560 ## Flame scales ::: {.cols2} ::: {.col2-l} * 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 $$Ka = \frac{\tau_F}{\tau_\eta} =\frac{\delta^2}{\eta^2} = \frac{v_\eta^2}{S_L^2}$$ ::: ::: {.col2-v} image ::: ::: ## Regime diagram image ## Turbulent flame speeds ::: {.cols2} ::: {.col2-l} ::: {.math} *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 $$\frac{S_t}{S_L} = \left[\frac{1}{2}\left(1+\left(1+8\frac{u^{\prime 2}_{rms}}{S_L^2}\right)^{1/2}\right)\right]^{1/2}$$ ::: ::: ::: {.col2-v} image ::: ::: # Detonation ::: {.cols2} ::: {.col2-l} ***Difference between detonation and deflagration?*** ::: fragment ::: {.byublue} **Deflagrations** balance diffusive heat and mass transfer with heat release from reaction ::: ::: fragment ::: {.red} **Detonations** balance acoustic compression with heat release from reaction ::: ::: ::: ::: ::: {.col2-v} image ::: ::: ## Detonation ::: notes https://www.youtube.com/watch?v=HyBdAT_yCFQ ::: ## Detonation velocities image