def execute(self):
fs_tube = self.fs_tube = FlowStation()
tube_rad = cu(self.radius_tube, 'cm', 'ft') #convert to ft
inlet_rad = cu(self.radius_inlet, 'cm', 'ft')
#A = pi(r^2)
self._tube_area = pi * (tube_rad**2) #ft**2
self._inlet_area = pi * (inlet_rad**2) #ft**2
self._bypass_area = self._tube_area - self._inlet_area
self._Ts = cu(self.Ts_tube, 'degK', 'degR') #convert to R
self._Ps = cu(self.Ps_tube, 'Pa', 'psi') #convert to psi
area_ratio_target = self._tube_area / self._bypass_area
#iterate over pod speed until the area ratio = A_tube / A_bypass
def f(m_guess):
fs_tube.setStaticTsPsMN(
self._Ts, self._Ps, m_guess
) #set the static conditions iteratively until correct (Ts, Ps are known)
gam = fs_tube.gamt
g_exp = (gam + 1) / (2 * (gam - 1))
ar = ((gam + 1) / 2)**(-1 * g_exp) * (
(1 + (gam - 1) / 2 * m_guess**2)**g_exp) / m_guess
return ar - area_ratio_target
#Solve for Mach where AR = AR_target
self.limit_Mach = secant(
f, .3, x_min=0, x_max=1
) #value not actually needed, fs_tube contains necessary flow information
self.limit_speed = cu(fs_tube.Vflow, 'ft',
'm') #convert to meters/second
#excess mass flow calculation
fs_tube.setStaticTsPsMN(self._Ts, self._Ps, self.Mach_pod)
self.W_tube = cu(fs_tube.rhos * fs_tube.Vflow * self._tube_area, 'lbm',
'kg') #convert to kg/sec
fs_tube.Mach = self.Mach_bypass #Kantrowitz flow is at these total conditions, but with Mach 1
self.W_kant = cu(fs_tube.rhos * fs_tube.Vflow * self._bypass_area,
'lbm', 'kg') #convert to kg/sec
#print "test", fs_tube.rhos, fs_tube.Vflow, self._bypass_area, self.W_kant
self.W_excess = self.W_tube - self.W_kant
def execute(self):
fs_tube = self.fs_tube = FlowStation()
tube_rad = cu(self.radius_tube,'cm','ft') #convert to ft
inlet_rad = cu(self.radius_inlet,'cm','ft')
#A = pi(r^2)
self._tube_area = pi*(tube_rad**2) #ft**2
self._inlet_area = pi*(inlet_rad**2) #ft**2
self._bypass_area = self._tube_area - self._inlet_area
self._Ts = cu(self.Ts_tube,'degK','degR') #convert to R
self._Ps = cu(self.Ps_tube,'Pa','psi') #convert to psi
area_ratio_target = self._tube_area/self._bypass_area
#iterate over pod speed until the area ratio = A_tube / A_bypass
def f(m_guess):
fs_tube.setStaticTsPsMN(self._Ts, self._Ps , m_guess) #set the static conditions iteratively until correct (Ts, Ps are known)
gam = fs_tube.gamt
g_exp = (gam+1)/(2*(gam-1))
ar = ((gam+1)/2)**(-1*g_exp)*((1+ (gam-1)/2*m_guess**2)**g_exp)/m_guess
return ar - area_ratio_target
#Solve for Mach where AR = AR_target
self.limit_Mach = secant(f, .3, x_min=0, x_max=1) #value not actually needed, fs_tube contains necessary flow information
self.limit_speed = cu(fs_tube.Vflow,'ft','m') #convert to meters/second
#excess mass flow calculation
fs_tube.setStaticTsPsMN(self._Ts, self._Ps, self.Mach_pod)
self.W_tube = cu(fs_tube.rhos*fs_tube.Vflow*self._tube_area,'lbm','kg') #convert to kg/sec
fs_tube.Mach = self.Mach_bypass #Kantrowitz flow is at these total conditions, but with Mach 1
self.W_kant = cu(fs_tube.rhos*fs_tube.Vflow*self._bypass_area,'lbm','kg') #convert to kg/sec
#print "test", fs_tube.rhos, fs_tube.Vflow, self._bypass_area, self.W_kant
self.W_excess = self.W_tube - self.W_kant
def execute(self):
"""Calculate Various Paramters"""
bearing_q = cu(self.bearing_air.W,'lbm/s','kg/s') * cu(self.bearing_air.Cp,'Btu/(lbm*degR)','J/(kg*K)') * (cu(self.bearing_air.Tt,'degR','degK') - self.temp_boundary)
nozzle_q = cu(self.nozzle_air.W,'lbm/s','kg/s') * cu(self.nozzle_air.Cp,'Btu/(lbm*degR)','J/(kg*K)') * (cu(self.nozzle_air.Tt,'degR','degK') - self.temp_boundary)
#Q = mdot * cp * deltaT
self.heat_rate_pod = nozzle_q +bearing_q
#Total Q = Q * (number of pods)
self.total_heat_rate_pods = self.heat_rate_pod*self.num_pods
#Determine thermal resistance of outside via Natural Convection or forced convection
if(self.temp_outside_ambient < 400):
self.GrDelTL3 = 41780000000000000000*((self.temp_outside_ambient)**(-4.639)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.GrDelTL3 = 4985000000000000000*((self.temp_outside_ambient)**(-4.284)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
#Prandtl Number
#Pr = viscous diffusion rate/ thermal diffusion rate = Cp * dyanamic viscosity / thermal conductivity
#Pr << 1 means thermal diffusivity dominates
#Pr >> 1 means momentum diffusivity dominates
if (self.temp_outside_ambient < 400):
self.Pr = 1.23*(self.temp_outside_ambient**(-0.09685)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.Pr = 0.59*(self.temp_outside_ambient**(0.0239))
#Grashof Number
#Relationship between buoyancy and viscosity
#Laminar = Gr < 10^8
#Turbulent = Gr > 10^9
self.Gr = self.GrDelTL3*(self.temp_boundary-self.temp_outside_ambient)*(self.diameter_outer_tube**3)
#Rayleigh Number
#Buoyancy driven flow (natural convection)
self.Ra = self.Pr * self.Gr
#Nusselt Number
#Nu = convecive heat transfer / conductive heat transfer
if (self.Ra<=10**12): #valid in specific flow regime
self.Nu = (0.6 + 0.387*self.Ra**(1./6.)/(1 + (0.559/self.Pr)**(9./16.))**(8./27.))**2 #3rd Ed. of Introduction to Heat Transfer by Incropera and DeWitt, equations (9.33) and (9.34) on page 465
if(self.temp_outside_ambient < 400):
self.k = 0.0001423*(self.temp_outside_ambient**(0.9138)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.k = 0.0002494*(self.temp_outside_ambient**(0.8152))
#h = k*Nu/Characteristic Length
self.h = (self.k * self.Nu)/ self.diameter_outer_tube
#Convection Area = Surface Area
self.area_convection = pi * self.length_tube * self.diameter_outer_tube
#Determine heat radiated per square meter (Q)
self.q_per_area_nat_conv = self.h*(self.temp_boundary-self.temp_outside_ambient)
#Determine total heat radiated over entire tube (Qtotal)
self.total_q_nat_conv = self.q_per_area_nat_conv * self.area_convection
#Determine heat incoming via Sun radiation (Incidence Flux)
#Sun hits an effective rectangular cross section
self.area_viewing = self.length_tube* self.diameter_outer_tube
self.q_per_area_solar = (1-self.surface_reflectance)* self.nn_incidence_factor * self.solar_insolation
self.q_total_solar = self.q_per_area_solar * self.area_viewing
#Determine heat released via radiation
#Radiative area = surface area
self.area_rad = self.area_convection
#P/A = SB*emmisitivity*(T^4 - To^4)
self.q_rad_per_area = self.sb_constant*self.emissivity_tube*((self.temp_boundary**4) - (self.temp_outside_ambient**4))
#P = A * (P/A)
self.q_rad_tot = self.area_rad * self.q_rad_per_area
#------------
#Sum Up
self.q_total_out = self.q_rad_tot + self.total_q_nat_conv
self.q_total_in = self.q_total_solar + self.total_heat_rate_pods
self.ss_temp_residual = (self.q_total_out - self.q_total_in)/1e6
def configure(self):
tm = self.add('tm', TubeWall())
#tm.bearing_air.setTotalTP()
driver = self.add('driver',BroydenSolver())
driver.add_parameter('tm.temp_boundary',low=0.,high=10000.)
driver.add_constraint('tm.ss_temp_residual=0')
driver.workflow.add(['tm'])
test = TubeHeatBalance()
set_as_top(test)
#set input values
test.tm.nozzle_air.setTotalTP(1710, 0.304434211)
test.tm.nozzle_air.W = 1.08
test.tm.bearing_air.W = 0.
test.tm.diameter_outer_tube = 2.22504#, units = 'm', iotype='in', desc='Tube out diameter') #7.3ft
test.tm.length_tube = 482803.#, units = 'm', iotype='in', desc='Length of entire Hyperloop') #300 miles, 1584000ft
test.tm.num_pods = 34.#, units = 'K', iotype='in', desc='Number of Pods in the Tube at a given time') #
test.tm.temp_boundary = 340#, units = 'K', iotype='in', desc='Average Temperature of the tube') #
test.tm.temp_outside_ambient = 305.6#, units = 'K', iotype='in', desc='Average Temperature of the outside air') #
test.run()
print "-----Completed Tube Heat Flux Model Calculations---"
print ""
print "CompressQ-{} SolarQ-{} RadQ-{} ConvecQ-{}".format(test.tm.total_heat_rate_pods, test.tm.q_total_solar, test.tm.q_rad_tot, test.tm.total_q_nat_conv )
print "Equilibrium Wall Temperature: {} K or {} F".format(test.tm.temp_boundary, cu(test.tm.temp_boundary,'degK','degF'))
print "Ambient Temperature: {} K or {} F".format(test.tm.temp_outside_ambient, cu(test.tm.temp_outside_ambient,'degK','degF'))
print "Q Out = {} W ==> Q In = {} W ==> Error: {}%".format(test.tm.q_total_out,test.tm.q_total_in,((test.tm.q_total_out-test.tm.q_total_in)/test.tm.q_total_out)*100)
check('Da_h',test.Da_h, 0.016082)
check('Da_e',test.Da_e, 0.039586)
check('Dw_h',test.Dw_h, test.Di_tube)
check('Dw_e',test.Dw_e, test.Di_tube)
check('Re_a',test.Re_a, 966613)
check('Re_w',test.Re_w, 41650)
check('Pr_a',test.Pr_a, 0.68)
check('Pr_w',test.Pr_w, 2.25)
check('Nu_a',test.Nu_a, 1210.)
check('Nu_w',test.Nu_w, 145.)
check('h_a',test.h_a, 1387.989)
check('h_w',test.h_w, 2570.589)
check('U_o',test.U_o, 879.019)
check('LMTD',test.LMTD, 164.28)
if (test.N < 2): #only check single pass case
check('L',test.L, 14.078)
print "-----Completed Heat Exchanger Sizing---"
print ""
print "Heat Exchanger Length: {} meters, with {} tube pass(es)".format(test.L/2,test.N)
#sqrt(#passes * tube area * packing factor)
#assumes shell magically becomes rectangular but keeps packing factor
packing_factor = (test.A_a/(test.A_a + test.A_w)) + 1
x = cu(((test.N * pi*((test.Do_tube/2)**2)*packing_factor)**0.5),'m','ft')
y = 2*x #height of a double pass
tot_vol = x*y * cu(test.L,'m','ft')
print "Heat Exchanger Dimensions: {}ft (Length) x {}ft (Width) x {}ft (Height)".format(cu(test.L,'m','ft')/2,x,y)
print "Heat Exchanger Volume: {} ft^3".format( tot_vol)
check('Dw_e', test.Dw_e, test.Di_tube)
check('Re_a', test.Re_a, 966613)
check('Re_w', test.Re_w, 41650)
check('Pr_a', test.Pr_a, 0.68)
check('Pr_w', test.Pr_w, 2.25)
check('Nu_a', test.Nu_a, 1210.)
check('Nu_w', test.Nu_w, 145.)
check('h_a', test.h_a, 1387.989)
check('h_w', test.h_w, 2570.589)
check('U_o', test.U_o, 879.019)
check('LMTD', test.LMTD, 164.28)
if (test.N < 2): #only check single pass case
check('L', test.L, 14.078)
print "-----Completed Heat Exchanger Sizing---"
print ""
print "Heat Exchanger Length: {} meters, with {} tube pass(es)".format(
test.L / 2, test.N)
#sqrt(#passes * tube area * packing factor)
#assumes shell magically becomes rectangular but keeps packing factor
packing_factor = (test.A_a / (test.A_a + test.A_w)) + 1
x = cu(((test.N * pi * ((test.Do_tube / 2)**2) * packing_factor)**0.5),
'm', 'ft')
y = 2 * x #height of a double pass
tot_vol = x * y * cu(test.L, 'm', 'ft')
print "Heat Exchanger Dimensions: {}ft (Length) x {}ft (Width) x {}ft (Height)".format(
cu(test.L, 'm', 'ft') / 2, x, y)
print "Heat Exchanger Volume: {} ft^3".format(tot_vol)
def execute(self):
"""Calculate Various Paramters"""
bearing_q = cu(self.bearing_air.W,'lbm/s','kg/s') * cu(self.bearing_air.Cp,'Btu/(lbm*degR)','J/(kg*K)') * (cu(self.bearing_air.Tt,'degR','degK') - self.temp_boundary)
nozzle_q = cu(self.nozzle_air.W,'lbm/s','kg/s') * cu(self.nozzle_air.Cp,'Btu/(lbm*degR)','J/(kg*K)') * (cu(self.nozzle_air.Tt,'degR','degK') - self.temp_boundary)
#Q = mdot * cp * deltaT
self.heat_rate_pod = nozzle_q +bearing_q
#Total Q = Q * (number of pods)
self.total_heat_rate_pods = self.heat_rate_pod*self.num_pods
#Determine thermal resistance of outside via Natural Convection or forced convection
if(self.temp_outside_ambient < 400):
self.GrDelTL3 = 41780000000000000000*((self.temp_outside_ambient)**(-4.639)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.GrDelTL3 = 4985000000000000000*((self.temp_outside_ambient)**(-4.284)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
#Prandtl Number
#Pr = viscous diffusion rate/ thermal diffusion rate = Cp * dyanamic viscosity / thermal conductivity
#Pr << 1 means thermal diffusivity dominates
#Pr >> 1 means momentum diffusivity dominates
if (self.temp_outside_ambient < 400):
self.Pr = 1.23*(self.temp_outside_ambient**(-0.09685)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.Pr = 0.59*(self.temp_outside_ambient**(0.0239))
#Grashof Number
#Relationship between buoyancy and viscosity
#Laminar = Gr < 10^8
#Turbulent = Gr > 10^9
self.Gr = self.GrDelTL3*(self.temp_boundary-self.temp_outside_ambient)*(self.diameter_outer_tube**3)
#Rayleigh Number
#Buoyancy driven flow (natural convection)
self.Ra = self.Pr * self.Gr
#Nusselt Number
#Nu = convecive heat transfer / conductive heat transfer
if (self.Ra<=10**12): #valid in specific flow regime
self.Nu = (0.6 + 0.387*self.Ra**(1./6.)/(1 + (0.559/self.Pr)**(9./16.))**(8./27.))**2 #3rd Ed. of Introduction to Heat Transfer by Incropera and DeWitt, equations (9.33) and (9.34) on page 465
if(self.temp_outside_ambient < 400):
self.k = 0.0001423*(self.temp_outside_ambient**(0.9138)) #SI units (https://mdao.grc.nasa.gov/publications/Berton-Thesis.pdf pg51)
else:
self.k = 0.0002494*(self.temp_outside_ambient**(0.8152))
#h = k*Nu/Characteristic Length
self.h = (self.k * self.Nu)/ self.diameter_outer_tube
#Convection Area = Surface Area
self.area_convection = pi * self.length_tube * self.diameter_outer_tube
#Determine heat radiated per square meter (Q)
self.q_per_area_nat_conv = self.h*(self.temp_boundary-self.temp_outside_ambient)
#Determine total heat radiated over entire tube (Qtotal)
self.total_q_nat_conv = self.q_per_area_nat_conv * self.area_convection
#Determine heat incoming via Sun radiation (Incidence Flux)
#Sun hits an effective rectangular cross section
self.area_viewing = self.length_tube* self.diameter_outer_tube
self.q_per_area_solar = (1-self.surface_reflectance)* self.nn_incidence_factor * self.solar_insolation
self.q_total_solar = self.q_per_area_solar * self.area_viewing
#Determine heat released via radiation
#Radiative area = surface area
self.area_rad = self.area_convection
#P/A = SB*emmisitivity*(T^4 - To^4)
self.q_rad_per_area = self.sb_constant*self.emissivity_tube*((self.temp_boundary**4) - (self.temp_outside_ambient**4))
#P = A * (P/A)
self.q_rad_tot = self.area_rad * self.q_rad_per_area
#------------
#Sum Up
self.q_total_out = self.q_rad_tot + self.total_q_nat_conv
self.q_total_in = self.q_total_solar + self.total_heat_rate_pods
self.ss_temp_residual = (self.q_total_out - self.q_total_in)/1e6
def configure(self):
tm = self.add('tm', TubeWallTemp())
#tm.bearing_air.setTotalTP()
driver = self.add('driver',BroydenSolver())
driver.add_parameter('tm.temp_boundary',low=0.,high=10000.)
driver.add_constraint('tm.ss_temp_residual=0')
driver.workflow.add(['tm'])
test = TubeHeatBalance()
set_as_top(test)
#set input values
test.tm.nozzle_air.setTotalTP(1710, 0.304434211)
test.tm.nozzle_air.W = 1.08
test.tm.bearing_air.W = 0.
test.tm.diameter_outer_tube = 2.22504#, units = 'm', iotype='in', desc='Tube out diameter') #7.3ft
test.tm.length_tube = 482803.#, units = 'm', iotype='in', desc='Length of entire Hyperloop') #300 miles, 1584000ft
test.tm.num_pods = 34.#, units = 'K', iotype='in', desc='Number of Pods in the Tube at a given time') #
test.tm.temp_boundary = 340#, units = 'K', iotype='in', desc='Average Temperature of the tube') #
test.tm.temp_outside_ambient = 305.6#, units = 'K', iotype='in', desc='Average Temperature of the outside air') #
test.run()
print "-----Completed Tube Heat Flux Model Calculations---"
print ""
print "CompressQ-{} SolarQ-{} RadQ-{} ConvecQ-{}".format(test.tm.total_heat_rate_pods, test.tm.q_total_solar, test.tm.q_rad_tot, test.tm.total_q_nat_conv )
print "Equilibrium Wall Temperature: {} K or {} F".format(test.tm.temp_boundary, cu(test.tm.temp_boundary,'degK','degF'))
print "Ambient Temperature: {} K or {} F".format(test.tm.temp_outside_ambient, cu(test.tm.temp_outside_ambient,'degK','degF'))
print "Q Out = {} W ==> Q In = {} W ==> Error: {}%".format(test.tm.q_total_out,test.tm.q_total_in,((test.tm.q_total_out-test.tm.q_total_in)/test.tm.q_total_out)*100)