Page 688 - Bird R.B. Transport phenomena

668 Chapter 21 Concentration Distributions in Turbulent Flow

PROBLEMS 21A.1. Determination of eddy diffusivity (Figs. 18C.1 and 21A.1). In Problem 18C.1 we gave the
formula for the concentration profiles in diffusion from a point source in a moving stream. In
isotropic highly turbulent flow, Eq. 18C.1-2 may be modified by replacing ЯЬ АВ by the eddy
diffusivity 4b%. This equation has been found to be useful for determining the eddy
diffusivity.
(a) Show that if one plots sc A versus s - z the slope is —v /24b %.
A
Q
(b) Use the data on the diffusion of CO from a point source in a turbulent air stream shown
2
in Fig. 21 A.I to get ЯЬ% for these conditions: pipe diameter, 15.24 cm; v 0 = 1512 cm/s.
(c) Compare the value of %b% with the molecular diffusivity %b AB for the system CO -air.
2
(d) List all assumptions made in the calculations.
2
Answer: (b) <&% = 19 cm /s
21A.2. Heat and mass transfer analogy. Write the mass transfer analog of Eq. 13.4-19. What are the
limitations of the resulting equation?
21B.1. Wall mass flux for turbulent flow with no chemical reactions. Use the diffusional analog of
Eq. 13.3-7 for turbulent flow in circular tubes, and the Blasius formula for the friction factor,
to obtain the following expression for the Sherwood number,

7/8
Sh = 0.0160 Re Sc 1/3 (21B.1-1)
valid for large Schmidt numbers. 1
21В.2. Alternate expressions for the turbulent mass flux. Seek an asymptotic expression for the
turbulent mass flux for long circular tubes with a boundary condition of constant wall mass
flux. Assume that the net mass transfer across the wall is small.
(a) Parallel the approach to laminar flow heat transfer in §10.8 to write

Cd + 11,(0 + C (21B.2-1)
2
in which f = r/D,^ = (z/D)/ReSc, а> is the inlet mass fraction of A, and j is the interfacial
л]
A 0
mass flux of A into the fluid.

1.2

О
1.0
о
0.8 о
4- + с
с + +
0.6 + + Fig. 21A.1. Concentration traverse data for
I °+ + о CO injected into a turbulent air stream with
2
"o 0.4 + Re = 119,000 in a tube of diameter 15.24 cm.
о +о
+ The circles are concentrations at a distance
+ z = 112.5 cm downstream from the injection
0.2
о point, and the crosses are concentrations at
z = 152.7 cm. [Experimental data are taken
0
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 from W. L. Towle and T. K. Sherwood, Ind.
r/R — Eng. Chem., 31,457-462 (1939).]

O. T. Hanna, О. С Sandall, and C. L. Wilson, Ind. Eng. Chem. Res., 28, 2286-2290 (1987).
1