Abstract
Experimental temperature profiles and biological kill data from dead-ended tubes of various diameters and lengths commonly used in biotechnology applications were compared to those predicted by a finite element model for steam-in-place (SIP) sterilization at 122°C. Diameter was shown experimentally and numerically to have a significant effect with larger diameter tubes exhibiting greater buoyant driven convective flow and more rapid sterilization. The overall Grashof number was shown to be the significant parameter relating magnitude of convective flow to tube diameter and varied as the diameter cubed. Analysis of air/steam mixture flow patterns showed air displacement from 0.4 cm diameter tubes to be due primarily to molecular diffusion, whereas 1.0 and 1.7 cm tubes showed a two-stage convective flow pattern. There exists a critical diameter of 0.4 cm below which SIP sterilization due to buoyancy driven flow does not occur and steam bleeders should be used.
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Abbreviations
- Ar:
-
geometric aspect ratio, L/D
- C p :
-
mixture specific heat at constant pressure, J/kg — °C
- C 1 :
-
mass fraction of air
- D :
-
inside tube diameter, m
- D 121C :
-
time to reduce population one log when exposed to saturated steam at 121°C, s
- g :
-
gravitational vector, m/s2
- Gr c :
-
solutal Grashof number, gβ c (C 1H −C 1C )ρ 2 D 3/μ 2
- Gr T :
-
thermal Grashof number, gβ T (T H −T C )ρ 2 D 3/μ 2
- Gr 0v :
-
overall Grashof number, Grc+GrT
- h :
-
convective heat transfer coefficient, W/m2 — °C
- k :
-
mixture thermal conductivity, W/m — °C
- L :
-
tube length, m
- N :
-
buoyancy parameter, Gr cl /Gr T
- P :
-
mixture total absolute pressure, Pa
- Pr :
-
Prandtl number, μc p/k
- P sat :
-
saturated water vapor absolute pressure, Pa
- q :
-
heat flux, W/m2
- R 0 :
-
reference vector in equation (9)
- R :
-
air gas constant, 287.0 J/kg — K
- R(u i ):
-
residual vector in equation (9)
- Sc :
-
Schmidt number, μρα 1
- t :
-
time, s
- T :
-
mixture temperature, °C
- T amb :
-
ambient temperature, °C
- T sat :
-
saturated steam temperature, °C
- u :
-
velocity vector, m/s
- u i :
-
calculated parameter at ith iteration
- u x :
-
x — component of velocity, m/sec
- Z :
-
temperature difference resulting in one log change rate of biological kill, °C
- μ :
-
mixture dynamic viscosity, Pa-s
- ρ :
-
mixture density, kg/m3
- ρ 0 :
-
mixture density at reference temperature and concentration, kg/m3
- ρ sat :
-
saturated water vapor density, kg/m3
- α :
-
binary mass diffusivity, m2/s
- β c :
-
mixture coefficient of concentration expansion
- β T :
-
mixture coefficient of thermal expansion
- ε u :
-
calculated parameter convergence parameter
- ε f :
-
residual tolerance parameter
- H :
-
maximum fluid property
- C :
-
minimum fluid property
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Young, J.H., Lasher, W.C. & Gaber, R.P. Transport processes during sterilization of vertical and 5 degree horizontal dead-legs. Bioprocess Engineering 12, 293–304 (1995). https://doi.org/10.1007/BF00369506
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DOI: https://doi.org/10.1007/BF00369506