(Open) Adding three stream heat exchanger temperature profiles

3stream.py

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+'''
+Author: Lane Carasik
+Purpose: Three-stream heat exchanger temperature distribution (1-D)
+'''
+
+#----------------------------------------------------------------------------------#
+# import modules
+
+import numpy as np
+from scipy.integrate import solve_bvp
+import matplotlib.pyplot as plt
+import pandas as pd
+from iapws import IAPWS95
+
+#----------------------------------------------------------------------------------#
+# Define functions needed
+
+def Prandtl(c_p,mu,k):
+	# Prandtl number calculation
+	Pr = c_p*mu/k
+
+	return Pr
+
+def Reynolds(rho,vel,D_h,mu):
+	# Reynolds number calculation
+	Re = rho*vel*D_h/mu
+
+	return Re
+
+def f_Blasius(Re):
+    # Friction factor for calculating smooth pipe 
+    # friction factor
+    f = 0.3164*Re**(-0.25)
+
+    return f
+
+def Nu_DB(Re,Pr,horc):
+    # Nusselt number correlation (Dittus Boelter)
+    # for smooth pipe flow
+    # cooling so n = 0.3 or n = 0.4 for heating
+    if horc == 'h':
+    	n = 0.4
+    elif horc == 'c':
+    	n = 0.3
+
+    Nu = 0.023*(Re**0.8)*(Pr**n)
+
+    return Nu   
+
+#----------------------------------------------------------------------------------#
+# Define or import material properties
+
+def thermophys_Na(T):
+    # Where T is in Kelvin
+    Cp = -3.001*(10**6)*T**-2 + 1658 - 0.8479*T + 4.454*(10**-4)*T**2
+    k = 104+0.047*T
+    ln_mu = 556.835/T - 0.3958*np.log(T) - 6.4406
+    mu = np.exp(ln_mu)
+    rho = 1014-0.235*T
+    return rho,Cp,mu,k
+
+def thermophys_FLiBe(T):
+    # Where T is in Kelvin
+    rho = 2413-0.488*(T); #kg/m^3, error +- 2%
+    Cp = 2386
+    k = 1.1
+    mu = (0.116*np.exp(3755/T))*0.001
+    return rho,Cp,mu,k
+
+def thermophys_H20(T):
+    # Where T is in Kelvin
+    # Need to add the ability to change temperature and pressure
+    # Likely need to use the IAPWS to make this easy.
+    rho = 713.8
+    Cp = 5750
+    k = 0.548
+    mu = 0.086e-3
+    return rho,Cp,mu,k
+
+def NaNO2_60wt_KNO2_40wt(T):
+	'''
+	Temp range: 300-600 C (573.16-873.16 K)
+	'''
+	rho = 1000*(2.0772-0.0006*T) # Temp in C - results in kg/m3
+	mu = 0.001*5.103*np.exp(-2.575*(10**3)*(T+273.15)**(-1)+1.305*(10**6)*((T+273.15)**(-2))) # Temp in K - results in Pa-s
+	k = 0.459 + T*0.0003 # Temp in C - results in W/m-K
+	Cp = 1570 # result in J/kg-K
+
+	return rho,mu,k,Cp
+
+def NaNO3_NaNO2_KNO3(T):
+	'''
+	HITEC salt
+
+	Temp range: 174.84-499.84 C (448-773 K)
+
+	Ref: Serrano-Lopez 2013 - Molten salts database for energy applications
+	Density SAM-NREL 2012 (0.07–0.49–0.44)
+	'''
+	rho = 2279.799-0.7324*(T+273.15) # Temp in K - results in kg/m3
+	mu = np.exp(-4.343 - 2.0143*(np.log(T + 273.15-273) - 5.011)) # Temp in K - results in Pa-s
+	k = 0.45 # results in W/m-K
+	Cp = 1560 # result in J/kg-K
+
+	return rho,mu,k,Cp
+
+def thermophys_H20_iapws95(T,P):
+
+    T_inK = T+273.15 # Temperature in Kelvin
+    P_inMPa = P/1e6  # Pressure in MPa
+
+    H20 = IAPWS95(T=T_inK,P=P_inMPa) # Thermophysical (Stream 1)
+    rho = H20.rho
+    cp = H20.cp*1000
+    mu = H20.mu
+    k = H20.k
+
+    return rho, cp, mu, k    
+
+#----------------------------------------------------------------------------------#
+# Options/Inputs
+'''
+This assumes a three stream concentenric heat exchanger 
+Stream 1 - Inner most tube (D_h = D_1in)
+Stream 2 - Intermediate Annulus (D_h = D_2in - D_1out)
+Stream 3 - Outer Annulus (D_h = D_3in - D_2out)
+'''
+
+# Solver Settings
+nodes = 100  # Number of nodes for 1-D calculation
+
+# Input Conditions
+# Geometry of Heat Exchanger
+arrangement = 'P1'
+
+D_1in = 10/100 # m - Inner Diameter (Tube 1)
+D_1out = 11/100 # m - Outer Diamter (Tube 1)
+D_2in = 13/100 # m - Inner Diamter (Tube 2)
+D_2out = 14/100 # m - Outer Diamter (Tube 2)
+D_3in = 16/100 # m - Inner Diameter (Tube 3)
+D_3out = 19/100 # m - Outer Diameter (Tube 3)
+L_HX = 200/100 # m - Length (HX)
+
+# Temperatures
+T_1in = 30 # Inlet Temperature (Stream 1) - C
+T_2in = 80 #50 # Inlet Temperature (Stream 2) - C
+T_3in = 50 #80 # Inlet Temperature (Stream 3) - C
+# Pressures
+P_1in = 101325 # Inlet Pressure (Stream 1) - Pa
+P_2in = 101325 # Inlet Pressure (Stream 2) - Pa
+P_3in = 101325 # Inlet Pressure (Stream 3) - Pa
+# Flow rates
+V_flow_1 = 0.00454609 # Flow rate (Stream 1) - m3/sec
+V_flow_2 = 0.0227304  # Flow rate (Stream 2) - m3/sec
+V_flow_3 = 0.0136383  # Flow rate (Stream 3) - m3/sec
+
+# Call Fluid properties
+'''
+Currently assuming liquids and not gases.
+It currently calls the IAPWS95 database using the IAPWS python module. 
+I created a wrapper function to reduce overhead for the user. 
+It should be portable enough for future users if other fluid properties 
+are needed.
+'''
+[rho_1,cp_1,mu_1,k_1] = thermophys_H20_iapws95(T_1in,P_1in) # Thermophysical (Stream 1)
+[rho_2,cp_2,mu_2,k_2] = thermophys_H20_iapws95(T_2in,P_2in) # Thermophysical (Stream 2)
+[rho_3,cp_3,mu_3,k_3] = thermophys_H20_iapws95(T_3in,P_3in) # Thermophysical (Stream 3)
+
+# Call heat exchanger tube wall properties
+'''
+This just assumes Stainless Steel 316L annealed sheets
+http://www.matweb.com/search/datasheet_print.aspx?matguid=1336be6d0c594b55afb5ca8bf1f3e042.
+Future work would be to make this more general.
+'''
+kw_12 = 15.9 # Thermal conductivity of wall (Stream 1-2) - W/m-K
+kw_23 = 15.9 # Thermal conductivity of wall (Stream 1-2) - W/m-K
+
+#----------------------------------------------------------------------------------#
+# Basic Global Calulations
+
+# Call area calculation
+A_1 = np.pi*(D_1in/2)**2 					   # Flow area of stream 1 - m2
+A_2 = np.pi*(D_2in/2)**2 - np.pi*(D_1out/2)**2 # Flow area of stream 2 - m2
+A_3 = np.pi*(D_3in/2)**2 - np.pi*(D_2out/2)**2 # Flow area of stream 3 - m2
+
+# Call Hydraulic diameter calculation
+Dh_1 = D_1in 			# Hydraulic Diameter (Stream 1) - m
+Dh_2 = D_2in - D_1out	# Hydraulic Diameter (Stream 2) - m
+Dh_3 = D_3in - D_2out	# Hydraulic Diameter (Stream 3) - m
+
+# Call velocity calculation (velocity = flow rate/flow area)
+vel_1 = V_flow_1/A_1 # Velocity (Stream 1) - m/sec
+vel_2 = V_flow_2/A_2 # Velocity (Stream 2) - m/sec
+vel_3 = V_flow_3/A_3 # Velocity (Stream 3) - m/sec
+
+# Call mass flow rate calculation (mdot = rho*area*vel = rho*vol_flow)
+mdot_1 = rho_1*V_flow_1 # Mass Flow Rate of Stream 1 - kg/sec
+mdot_2 = rho_2*V_flow_2 # Mass Flow Rate of Stream 2 - kg/sec
+mdot_3 = rho_3*V_flow_3 # Mass Flow Rate of Stream 3 - kg/sec
+
+# Call heat capacity rates (C = mdot*cp)
+C_1 = mdot_1*cp_1 # Heat Capacity of Stream 1
+C_2 = mdot_2*cp_2 # Heat Capacity of Stream 2
+C_3 = mdot_3*cp_3 # Heat Capacity of Stream 3
+
+# Call Reynolds number calculation
+Re_1 = Reynolds(rho_1,vel_1,Dh_1,mu_1) # Re Number (Stream 1)
+Re_2 = Reynolds(rho_2,vel_2,Dh_2,mu_2) # Re Number (Stream 2)
+Re_3 = Reynolds(rho_3,vel_3,Dh_3,mu_3) # Re Number (Stream 3)
+
+# Call Prandtl number calcation
+Pr_1 = Prandtl(cp_1,mu_1,k_1) # Prandtl (Stream 1)
+Pr_2 = Prandtl(cp_2,mu_2,k_2) # Prandtl (Stream 2)
+Pr_3 = Prandtl(cp_3,mu_3,k_3) # Prandtl (Stream 3)
+
+# Call Nusselt number calculation
+Nu_1 = Nu_DB(Re_1,Pr_1,horc='h') # Nu Number (Stream 1)
+Nu_2 = Nu_DB(Re_2,Pr_2,horc='h') # Nu Number (Stream 2)
+Nu_3 = Nu_DB(Re_3,Pr_3,horc='c') # Nu Number (Stream 3)
+
+# Call Heat Transfer Coefficient Calculation
+HTC_1 = Nu_1*k_1/Dh_1	# HTC (Stream 1) - W/m2-K
+HTC_2 = Nu_2*k_2/Dh_2	# HTC (Stream 2) - W/m2-K
+HTC_3 = Nu_3*k_3/Dh_3	# HTC (Stream 3) - W/m2-K
+
+# Call Overall Heat Transfer Coefficient Calculation
+# Stream 1 to 2
+UA_12 = 1/(1/(HTC_2*A_2)+1/(2*np.pi*kw_12*L_HX)*np.log(D_1out/D_1in)+1/(HTC_1*A_1))
+# Stream 2 to 3
+UA_32 = 1/(1/(HTC_3*A_3)+1/(2*np.pi*kw_23*L_HX)*np.log(D_2out/D_2in)+1/(HTC_2*A_2))
+
+# Call NTU calculation
+NTU_1 = UA_12/C_1
+print("NTU_1 test is",UA_12/C_1)
+#NTU_1 = 1.25 # Testing purposes only
+
+# Call Heat Capacity Stream Ratio Calculation
+Cs_12 = C_1/C_2 # Heat capacity ratio (1->2)
+Cs_32 = C_3/C_2 # Heat capacity ratio (3->2)
+print(Cs_12+Cs_32)
+#Cs_12 = 0.8 # Testing purposes only
+#Cs_32 = 0.25 # Testing purposes only
+
+# Call Conductance Ratio calculation
+R_star = UA_32/UA_12
+#R_star = 2.0 # Testing purposes only
+
+# Call inlet temperature ratio (Dimensionless)
+theta_3in = (T_3in-T_1in)/(T_2in-T_1in) 
+#theta_3in = 0.75
+#print('theta_3in',theta_3in)
+print('theta_3in',(T_3in-T_1in)/(T_2in-T_1in))
+print('theta_2in',(T_2in-T_3in)/(T_1in-T_3in))
+#theta_2in = (T_2in-T_3in)/(T_1in-T_3in)
+
+
+if arrangement == 'P1':
+	# Parallel, Parallel, Parallel
+	# (i1 = +1, i2 = +1, i3 = +1)
+	i_2 = 1 # Add stream definition
+	i_3 = 1 
+elif arrangement == 'P2':
+	# Parallel, Counter, Parallel
+	# (i1 = +1, i2 = -1, i3 = +1)
+	i_2 = -1 # Add stream definition
+	i_3 = 1 
+elif arrangement == 'P3':
+	# Parallel, Counter, Counter
+	# (i1 = +1, i2 = -1, i3 = -1)
+	i_2 = -1 # Add stream definition
+	i_3 = -1 
+elif arrangement == 'P4':
+	# Parallel, Counter, Counter
+	# (i1 = +1, i2 = +1, i3 = -1)
+	i_2 = 1 # Add stream definition
+	i_3 = -1 
+
+#----------------------------------------------------------------------------------#
+# Boundary Value Problem Calculation
+
+'''
+See notes from Selic three stream heat exchanger design
+Check out Cabezas-Gomez 2007 - Thermal Performance of Multipass Parallel and 
+Counter-Cross-Flow Heat Exchangers.pdf for example problems to debug.
+'''
+
+
+# Call Function to Solve
+def fun(x,y):
+	return np.vstack((NTU_1*(y[1]-y[0]),
+		i_2*NTU_1*Cs_12*(y[0]-y[1])+i_2*NTU_1*R_star*Cs_12*(y[2]-y[1]),
+		i_3*(Cs_12/Cs_32)*R_star*NTU_1*(y[1]-y[2])
+	))
+
+#Call Boundary Conditions to use
+def bc(ya,yb):
+	res_1 = ya[0]
+	if i_2 == 1:
+		res_2 = ya[1]-1
+	elif i_2 == -1:
+		res_2 = yb[1]-1
+	if i_3 == 1:
+		res_3 = ya[2]-theta_3in
+	elif i_3 == -1:
+		res_3 = yb[2]-theta_3in
+
+	return np.array([res_1,res_2,res_3])
+
+# def bc(ya,yb):
+# 	res_1 = ya[0] - 1
+# 	if i_2 == 1:
+# 		res_2 = ya[1]-theta_2in
+# 	elif i_2 == -1:
+# 		res_2 = yb[1]-theta_2in
+# 	if i_3 == 1:
+# 		res_3 = ya[2]
+# 	elif i_3 == -1:
+# 		res_3 = yb[2]
+
+# 	return np.array([res_1,res_2,res_3])
+
+# Solve and make sure it can handle different directions of the 
+# parallel/counter flow heat exchanger
+x = np.linspace(0,1,nodes)
+y = np.zeros((3,x.size))
+
+#Call bvp solver
+sol = solve_bvp(fun,bc,x,y,max_nodes = 1e6,verbose=2)
+
+Theta_1 = sol.sol(x)[0] # Stream 1
+Theta_2 = sol.sol(x)[1] # Stream 2
+Theta_3 = sol.sol(x)[2] # Stream 3
+
+T_1 = Theta_1*(T_2in-T_1in) + T_1in
+T_2 = Theta_2*(T_2in-T_1in) + T_1in
+T_3 = Theta_3*(T_2in-T_1in) + T_1in
+
+#----------------------------------------------------------------------------------#
+# Output Formatted Text
+
+print(Pr_1)
+print(Pr_2)
+print(Pr_3)
+print(Re_1)
+print(Re_2)
+print(Re_3)
+print(Nu_1)
+print(Nu_2)
+print(Nu_3)
+print(HTC_1)
+print(HTC_2)
+print(HTC_3)
+
+#----------------------------------------------------------------------------------#
+# Output relevant plots
+
+h = 10
+w = 8
+
+lw = 2.5
+fs = 14
+
+k = 1
+plt.figure(k, figsize=(h,w))
+plt.plot(x*L_HX,Theta_1,'r--',linewidth = lw,label=r'$\theta_{1}$')
+plt.plot(x*L_HX,Theta_2,'k--',linewidth = lw,label=r'$\theta_{2}$')
+plt.plot(x*L_HX,Theta_3,'b--',linewidth = lw,label=r'$\theta_{3}$')
+#plt.axhline(y=Tboil, xmin = 0, xmax = 1, color = 'r',linewidth = lw, label='Coolant Boiling Temp')
+#plt.axhline(y=TmeltCoolant, xmin = 0, xmax = 1, color = 'b',linewidth = lw, label='Coolant Melting Temp')
+plt.legend(loc='center left')
+plt.xlabel('Length - m',fontsize = fs)
+plt.ylabel('Theta - ',fontsize = fs)
+plt.grid()
+# fig = TCinput.Reactor_Title + '_Axial_Temperatures'
+# if print_logic == 0:
+#     plt.savefig(fig + '.png', dpi = 300, format = "png",bbox_inches="tight")
+#     plt.savefig(fig + '.eps', dpi = 300, format = "eps",bbox_inches="tight")
+#     plt.savefig(fig + '.svg', dpi = 300, format = "svg",bbox_inches="tight")
+k = k + 1
+
+plt.figure(k, figsize=(h,w))
+plt.plot(x*L_HX,T_1,'r--',linewidth = lw,label=r'$T_{1}$')
+plt.plot(x*L_HX,T_2,'k--',linewidth = lw,label=r'$T_{2}$')
+plt.plot(x*L_HX,T_3,'b--',linewidth = lw,label=r'$T_{3}$')
+#plt.axhline(y=Tboil, xmin = 0, xmax = 1, color = 'r',linewidth = lw, label='Coolant Boiling Temp')
+#plt.axhline(y=TmeltCoolant, xmin = 0, xmax = 1, color = 'b',linewidth = lw, label='Coolant Melting Temp')
+plt.legend(loc='center left')
+plt.xlabel('Length - m',fontsize = fs)
+plt.ylabel('Theta - ',fontsize = fs)
+plt.grid()
+# fig = TCinput.Reactor_Title + '_Axial_Temperatures'
+# if print_logic == 0:
+#     plt.savefig(fig + '.png', dpi = 300, format = "png",bbox_inches="tight")
+#     plt.savefig(fig + '.eps', dpi = 300, format = "eps",bbox_inches="tight")
+#     plt.savefig(fig + '.svg', dpi = 300, format = "svg",bbox_inches="tight")
+k = k + 1
+
+plt.show()