ME 525: Combustion Lecture 9: Mass and Species Conservation

1. ME 525: CombustionLecture 9: Mass and Species Conservation • Rudiments of Mass Transfer • Some Applications of Mass Transfer • Mass Conservation for Reacting Flows • Species Conservation for Reacting Flows

2. Molecular Basis for Diffusion Fuel and oxygen must diffuse into each other before they can react. Products must diffuse away from flame before reaction can proceed. Reactive species/radicals must diffuse into mixture

3. Mass Transfer Rate Laws YB B A Note that the magnitude of gradient adjusts to balance the magnitude of diffusivity. YA Yi x

4. Some Applications of Mass Transfer Mass Transfer occurs in many applications in Chemical, Pharmaceutical and Biological engineering. Large applications of Mass Transfer in Mechanical Engineering involve: humidifiers, dryers, carburetors, fuel sprays, fire extinguishing sprinkler sprays, agricultural sprays, etc. A vaporizing drop in a spray or a carburetor which contains a liquid at whose surface the fuel vaporizes and mixes with air flowing in a direction parallel to the liquid surface Consider a Carburetor Gas B Gas B + Vapor A x=L x=0 Liquid A

5. Mass Conservation for Reacting Flows with Spatial Gradients Divide by the small volume and take limits as the small volume tends to 0 Similar derivations can be performed in the cylindrical and spherical coordinate systems

6. 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

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

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

9. 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

10. 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.