are expected to use digital twins, taking another step toward dynamic simulations
which are widely used by the biotech industry and hence pave the way for real-time
simulations 1 day. Once these dynamic simulations are validated, it can be used
together with powerful tools like augmented reality to develop online monitoring
systems once the digital twin of the process is in place.
Acknowledgments This work was partially supported by the German Federal Ministry of Education and Research (BMBF), grant number: FKZ 031B0629.
Abbreviations and Nomenclatures
Abbreviations
CFD
Computational fluid dynamics
DNS
Direct numerical simulation
DO
Dissolved oxygen
EL
Euler-Lagrange
LES
Large eddy simulation
NSE
Navier-Stokes equations
PBM
Population balance model
PFR
Plug flow reactor
RANS
Reynolds-averaged Navier-Stokes
STR
Stirred tank reactor
UDF
User-defined function
Nomenclatures
a
Bubble surface
C glucose
Glucose concentration
C O2
Dissolved oxygen concentration
C
Ã
O2
Equilibrium oxygen concentration
C x
Biomass concentration
d p
Bubble diameter
D
Diffusion coefficient
k
Turbulent kinetic energy
k l
Mass transfer coefficient
K glucose
Saturation constant for glucose
K oxygen
Saturation constant for oxygen
N
Agitation rate
P
Bioreactor power input
q s
Specific substrate uptake rate
q s, max
Maximum specific substrate uptake rate
q O2
Specific oxygen uptake rate
q O2, max
Maximum specific oxygen uptake rate
St
Stokes number
V
Bioreactor volume
Yx
s
Biomass yield
Yo
s
Oxygen yield
ε
Turbulent kinetic energy dissipation rate
μ
Growth rate
μ max
Maximum growth rate
μ liquid
Molecular viscosity
ν
Kinematic viscosity
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
249
which are widely used by the biotech industry and hence pave the way for real-time
simulations 1 day. Once these dynamic simulations are validated, it can be used
together with powerful tools like augmented reality to develop online monitoring
systems once the digital twin of the process is in place.
Acknowledgments This work was partially supported by the German Federal Ministry of Education and Research (BMBF), grant number: FKZ 031B0629.
Abbreviations and Nomenclatures
Abbreviations
CFD
Computational fluid dynamics
DNS
Direct numerical simulation
DO
Dissolved oxygen
EL
Euler-Lagrange
LES
Large eddy simulation
NSE
Navier-Stokes equations
PBM
Population balance model
PFR
Plug flow reactor
RANS
Reynolds-averaged Navier-Stokes
STR
Stirred tank reactor
UDF
User-defined function
Nomenclatures
a
Bubble surface
C glucose
Glucose concentration
C O2
Dissolved oxygen concentration
C
Ã
O2
Equilibrium oxygen concentration
C x
Biomass concentration
d p
Bubble diameter
D
Diffusion coefficient
k
Turbulent kinetic energy
k l
Mass transfer coefficient
K glucose
Saturation constant for glucose
K oxygen
Saturation constant for oxygen
N
Agitation rate
P
Bioreactor power input
q s
Specific substrate uptake rate
q s, max
Maximum specific substrate uptake rate
q O2
Specific oxygen uptake rate
q O2, max
Maximum specific oxygen uptake rate
St
Stokes number
V
Bioreactor volume
Yx
s
Biomass yield
Yo
s
Oxygen yield
ε
Turbulent kinetic energy dissipation rate
μ
Growth rate
μ max
Maximum growth rate
μ liquid
Molecular viscosity
ν
Kinematic viscosity
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
249