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Ex_3_4.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Feb 27 07:52:51 2020
+
+@author: delvigne
+"""
+import math 
+from math import pi
+
+## Basic data : pilot bioreactor
+
+D1 = 1 #m 
+d1 = D1/3 #%m -> standard geometry
+N1 = 180/60 #s-1
+rho = 1000 #Kg/m3
+mu = 0.001 #Pa.s dynamic viscosity
+N_p = 5.4 #Power number
+N_qc = 1.5 #Circulation number
+
+## Computation at pilot scale
+
+Periph_speed_pilot = pi*N1*d1 #m/s
+Q_c_pilot = N_qc*N1*((D1/3)**3) #Circulation flow rate m3/s
+V_pilot = pi*D1**3/4 #m3
+t_c_pilot = V_pilot/Q_c_pilot #circulation time s
+
+## Basic data : industrial bioreactor
+
+V_indus = 50 #m3
+
+## Scaling-up criteria : volumetric power
+
+Re = rho*N1*((D1/3)**2)/mu # if > 10^4 -> turbulent regime
+P = N_p*rho*(N1**3)*((D1/3)**5) # One impeller
+P_V = P/V_pilot # Volumetric power (W/m3)
+
+## Computation at industrial scale
+
+P_indus = P_V*V_indus #W
+D2 = ((4*V_indus)/pi)**(1/3) #m
+d2 = D2/3 #m
+N2 = (P_indus/(rho*N_p*d2**5))**(1/3) #s-1
+
+Periph_speed_indus = pi*N2*d2 #m/s
+Q_c_indus = N_qc*N2*((D2/3)**3) #Circulation flow rate m3/s
+t_c_indus = V_indus/Q_c_indus #circulation time s
+