Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lecture 6. Laminar Non-premixed Flames part 2 Content • Structures of laminar non-premixed flames • Mixture fraction • Burke-Schumann flame-sheet model • Jet diffusion flames • Laminar diffusion flame at high mixing rate X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? Mixing length ! Zst A F Burnable mixture Diffusion velocity: Fick’s Law Yi Vi = Di !Yi , X.S. Bai Vi = Di / Yi !Yi " Di / ! Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Zst A Post flame zone Preheat zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? O2 F F O2 Oxidizer-rich mixing zone Zst A Reaction zone Fuel-rich mixing zone F Burnable mixture X.S. Bai Laminar Non-premixed Flames Where is the reaction zone? T Tst Tcr T1 T2 0 Zst Fuel-lean Z 1 Fuel-rich Zst A F Burnable mixture X.S. Bai Laminar Non-premixed Flames Burke-Schumann flame-sheet structure Soot problem Yi 1 A P P F Zst Fuel-rich Fuel-lean Reaction zone X.S. Bai Z Reactions occur in a zero thickness sheet at Z=Zst Laminar Non-premixed Flames Burke-Schumann flame-sheet structure T NOx problem Tst T1 T2 Z 0 Zst Fuel-rich Fuel-lean Reaction zone X.S. Bai 1 Reactions occur in a zero thickness sheet at Z=Zst Laminar Non-premixed Flames Content • Structures of laminar non-premixed flames • Mixture fraction • Burke-Schumann flame-sheet model • Jet diffusion flames • Laminar diffusion flame at high mixing rate X.S. Bai Laminar Non-premixed Flames Laminar jet diffusion flames Zst Mixing layer Air Fuel A non-reactive fuel jet Zst Burnable mixture X.S. Bai Laminar Non-premixed Flames Laminar jet diffusion flames soot NOx F Reaction zone A+P Air rich Air P O2 c-d F+P Fuel rich c-d Air a-b F O2 Fuel A jet diffusion flame a-b YF = Z − Z st 1− Z , YA = 0, YP = 1 − Z st 1 − Z st YF = 0, YA = 1 − X.S. Bai Z Z , YP = Z st Z st Fuel rich zone Fuel lean zone Laminar Non-premixed Flames Jet diffusion flame: mathematical description Zst Mixing layer Air D F = D P = D, Fuel A non-reactive fuel jet Z = YF + ! F + ! P Zst = 0 ! !! Z + " # ( ! vZ) = " # ( ! D"Z) !t 1 YP = YF + YP Z st 1+ γ A Z = YF X.S. Bai ! !! Yi + " # ! Yi v = " # ! Di "Yi + " i !t ! !! YF + " # ! YF v = " # ! D F "YF + " F !t ! !! YP + " # ! YP v = " # ! D P "YP + " P !t Combustion No combustion (pure mixing) Laminar Non-premixed Flames Height of laminar jet flame Mixing layer analysis 0 x ! !! Z + " # ( ! vZ) = " # ( ! D"Z) !t R A+P Lf F+P !D / R 2 air !v F / Lf vf The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. R X.S. Bai vFR 2 Lf ! D Laminar Non-premixed Flames Height of laminar jet flame Mixing layer analysis X = v F t, x 1 Y = R ! VO2 t = R ! DO2 t ! R A+P X = Lf = v F t f , Lf F+P air 1 Y = 0 = R ! DO2 t f ! vf The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. R Yi Vi = Di !Yi , X.S. Bai v F R" v F R 2 Lf ! ! D D Vi = Di / Yi !Yi " Di / ! Laminar Non-premixed Flames Jet diffusion flame: experimental obervation vFR 2 ! vFR $ Lf ! =# & R = Pe ' R D " D % O x U F O Pe 50 X.S. Bai Pe 50 Pe 200 Pe 1 Laminar Non-premixed Flames Propagation of laminar diffusion flame ! !! + " # !v = 0 !t ! !! Yi + " # ! Yi v = " # ! Di "Yi + " i !t ! !! !! v + "! vv = " # pI + ! !t ( N+5 PDE equations ) N $ $ ' Dh Dp 1 ' ! + # : "v" ! ! = " # && !""h ! !" *&&1! )) h i "Yi )) + Q r Dt Dt Le % ( % ( i=1 i X.S. Bai Laminar Non-premixed Flames Burke-Schumann flame-sheet model ! !! + " # !v = 0 !t 6 PDE equations ! !! Z + " # ( ! vZ) = " # ( !""Z) !t ! !! !! v + "! vv = " # pI + ! !t ( ) N $ $ ' Dh Dp 1 ' ! + # : "v" ! ! = " # && !""h ! !" *&&1! )) h i "Yi )) + Q r Dt Dt Le % ( % ( i=1 i Yi = a + bZ T = c + dZ X.S. Bai Burke-Schumann flame sheet relation Laminar Non-premixed Flames Content • Structures of laminar non-premixed flames • Mixture fraction • Burke-Schumann flame-sheet model • Jet diffusion flames • Laminar diffusion flame at high mixing rate X.S. Bai Laminar Non-premixed Flames Finite-rate chemistry effect • Burke-Schumann flame-sheet model is not always true; it is true only when the chemical reactions are much faster than the mixing of fuel and the oxidizer • If the mixing is very fast, what is going to happen? Zst Burnable mixture X.S. Bai Laminar Non-premixed Flames Flamelet equation Flamelet assumption: Yi (x, y,z, t) = Yi (Z(x, y,z, t)), !(x, y,z, t) = !(Z(x, y,z, t)), T(x, y,z, t) = T(Z(x, y,z, t)) ! !! Yi + " # ! Yi v = " # ! Di "Yi + " i !t ! !! Z + " # ( ! vZ) = " # ( ! D"Z) !t X.S. Bai Species transport Mixture fraction Laminar Non-premixed Flames Flamelet equation 2 d Yi 1 ! !" = #i 2 2 dZ d 2 Yi 2! i =! 2 "# dZ ! = 2D(!Z " !Z) Scalar dissipation rate: mixing rate Damköhler number Da = (mixing time)/(chemical reaction time) X.S. Bai Da ! 2!i "# Laminar Non-premixed Flames Z st Finite rate chemistry effect Yi Yi d 2Yi →∞ 2 dZ d 2Yi = finite 2 dZ F F O2 O2 Z st Damköhler number infinity X.S. Bai Z Z st Z Damköhler not very high Laminar Non-premixed Flames χ↑ Effect of mixing rate Yi Yi O2 χ↑ F χ↑ Z Z st Z Z st Increase of scalar dissipation rate leads to • the leakage of fuel to the oxygen rich side increases • the leakage of oxygen to the fuel rich side increases • the flame temperature decreases, as a result of insufficient oxidation of the fuel X.S. Bai Laminar Non-premixed Flames Flame quenching at high scalar dissipation rate Quenched Flamelet TP Flame sheet With preheating Adiabatic flame Tq With radiation heat loss χ P −1 [ s ] χ q −1 X.S. Bai Laminar Non-premixed Flames Laminar jet diffusion flame Diffusion flame F+P A+P Lean premixed flame Rich premixed flame Lift-off hight Fuel inlet Air c Zst Burnable mixture X.S. Bai Laminar Non-premixed Flames Effect of mixng rate • For very small scalar dissipation rate the flame temperature is high; changing the scalar dissipation a little would not affect the flame temperature. This regime can be described by the simple Burke-Schumann flame sheet model. • For intermediate scalar dissipation rate, the flame temperature is lower than the Burke-Schumann flame temperature. Increasing the scalar dissipation rate leads to a decrease of the flame temperature until to a critical condition, at which the flame temperature changes rapidly. This regime may be called flamelet • For scalar dissipation rate higher than the quenching scalar dissipation rate, no flame exists. The flame is quenched. X.S. Bai Laminar Non-premixed Flames