ME 525: Combustion Lecture 10: Binary and Multi-component Diffusion

1. ME 525: CombustionLecture 10: Binary and Multi-component Diffusion • Species conservation for reacting flows • Effective binary diffusivity formulation for • multi-component diffusion • Non-dimensional species conservation equation • Reynolds, Prandtl, Schmidt, Lewis, and Damkohler • numbers Question: What is the third subscript “f” of the fourth term in the following equations?

2. Example Problem: One Dimensional Advection-Diffusion Consider a one dimensional steady flow of a fuel air mixture from a burner into a quiescent oxidizer that diffuses into the fuel in a one dimensional manner. The fuel mixes with the oxidizer but does not react. Write the species conservation equations for the fuel and oxidizer and seek solutions with appropriate assumptions and with the boundary conditions: YF=YFoand YO=YOo, x=0 and YF=0 and YO2=YO2L, x=L. Steady State No reaction Large velocity, small K Small velocity, large K

3. Example problem for effective diffusion coefficient calculations • Example Problem Multi-component Diffusion • Lecture 9: ME 525 SP2013 Courtesy: Prof. Lucht •  The table below lists flame properties calculated using the CHEMKIN PREMIX code for a burner-stabilized H2-air flame. The flame temperature (K) and the mole fractions of H2, O2, H2O, and N2 are listed as a function of distance z (in cm) from the burner surface. The mole fractions of all other species in the flame gases total less than 1% and can be neglected in calculating MWmix. The pressure of 1 atm is uniform throughout the flowfield. Assume that the multi-component diffusion coefficient Di,mix for a species i in the mixture is approximately equal to the binary diffusion coefficient for species i and N2, Di,N2. Use the Chapman-Enskog formula and the Lennard-Jones parameters, both given in the equation sheets, to calculate the binary diffusion coefficients. The atomic hydrogen (H) mole fraction profile and the polynomial fit to the data are shown in the plot on the next page. •  (a) Calculate the diffusive velocity, the total species velocity, the diffusive mass flux, and the total species mass flux for atomic hydrogen (H) at the axial flame position z = 0.0094 cm. Assume that the molecular weight of the mixture is approximately constant as a function of axial position at z = 0.0094 cm.

4. Complexities of multi-component Diffusion

5. Calculations involved in multi-component Diffusion For atomic hydrogen at Calculation of diffusion coefficient of hydrogen atom See Turns Appendix D, equation D4 and Table D.2 page 709

6. Orders of Magnitude in Combustion: Molecular Scales meet Combustor Scales

7. Similar calculations needed for then finally

8. Multi-Component Diffusion Considering concentration and thermal diffusion only:

9. Simplified Approach to Multi-component Diffusion Review of Example 7.2: Mixture of H2, O2, N2

10. Species Conservation for Reacting Flows with Spatial Gradients Net Velocity & components Convection/Advection Velocity & components Diffusion Velocity & components Divide by the small volume and take limits as the small volume tends to 0

11. Species Conservation Equation: Characteristic Lengths and Times