PackedSpheres
The function
PackedSpheres(Fluid$, m_dot, d, A_fr, L, T, P: f, h, NTU, DP)
returns the friction factor (f), heat transfer coefficient (h) and the number of transfer units for a well packed matrix of spheres.
Inputs:
Fluid$ - string variable indicating a specific fluid in EES database or in the Solid-Liquid_Props fluids list
m_dot - mass flow rate of fluid [kg/s] or [lbm/min]
d - diameter of the spheres [m] or [ft]
A_fr - the frontal area of the matrix exposed to fluid flow [m^2] or [ft^2]
L - length/depth of stacked screens [m] or [ft]
T - inlet temperature of the fluid [C], [K], [F], [R]
P - pressure of the fluid at the inlet [Pa], [kPa], [bar], [MPa], [atm], or [psia]
Ouputs:
f - friction factor [-]
h - heat transfer coefficient [W/m^2-K] or [Btu/hr-ft^2-R]
NTU - number of transfer units on the flow side [-]
DP - pressure drop [Pa], [kPa], [bar], [MPa], [atm], or [psia]
Notes: This function determines the fluid properties at the stated pressure and temperature, and the Reynolds number from the sphere diameter. The hydraulic diameter upon which the Reynold's number is based is calculated using correlations suggested in Ackermann (1997). With the Reynold's number found, the non-dimensional function PackedSpheres_ND is called to determine the values for the Colburn j and friction factor. The Colburn j factor is interpreted by PackedSpheres and returned as a heat transfer coefficient. The porosity of the matrix is assumed to be 0.35. The porosity for a theoretically perfect spherical matrix, i.e., all the spheres are exactly the same diameter and are packed as close as possible, is 0.30 but porosity usually ranges from 0.32 to 0.37. The pressure drop is determined based on frictional considerations. Pressure drop due to fluid acceleration is not included.
Example:
$unitSystem SI K Pa J
Fluid$='air'
m_dot=34.2 [kg/s] "flow rate"
d=0.001 [m] "diameter of spheres"
A_fr=3.5 [m^2] "frontal area"
L=0.03 [m] "length in the flow direction"
T=650 [K] "inlet temperature"
P=101300 [Pa] "inlet pressure"
call PackedSpheres(Fluid$,m_dot, d, A_fr, L, T, P: f, h, NTU, DP)
{Solution:
f=0.6907
h=1551 [W/m^2-K]
NTU=17.47
DP=165735 [Pa]
}