def get_Nu_free(self,T,el,Pr):
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = m.get_rho(el)
g = m.get_g(el)
Pr_atm = self.get_Pr_co2(T_atm)
T_avg = 0.5*(T_atm + T)
rho_avg = p_atm/(Mars_Sphere_Balloon.Rsp_co2*T_avg)
Pr_avg = self.get_Pr_co2(T_avg)
exp_coeff = 1./T_avg
mu = self.get_dynamic_viscocity_co2(T_avg)
Gr = (pow(rho_atm,2)*g*fabs(T-T_atm)*pow(self.d,3))/(T_atm*pow(mu,2))
#print "Gr,", Gr, "Pr," , Pr
try:
Nu = 2 + .45*pow((Gr*Pr),.25)
except:
Nu = 2.45
return Nu
'''
def get_acceleration(self,v,el,T_s,T_i):
"""Solves for the acceleration of the solar balloon after one timestep (dt).
:param T_s: Surface Temperature (K)
:type T_s: float
:param T_i: Internal Temperature (K)
:type T_i: float
:param el: Elevation (m)
:type el: float
:param v: Velocity (m)
:type v: float
:returns: acceleration of balloon (m/s^2)
:rtype: float
"""
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = p_atm/(189.*T_atm)
g = m.get_g(el)
rho_int = p_atm/(self.Rsp_co2*T_i)
F_b = (rho_atm - rho_int)*self.vol*g # Force due to buyoancy
Cd = .8 # Drag Coefficient
F_d = Cd*(0.5*rho_atm*math.fabs(v)*v)*self.cs_area # Force due to Drag
vm = (self.massEnv + self.mp) + rho_atm*self.vol + self.vm_coeff*rho_atm*self.vol
accel = (F_b - F_d - (self.massEnv + self.mp)*g)/vm
return accel
def get_q_int(self, T_s, T_i, el):
"""Calculates sum of Internal Heat Transfer.
.. note::
Currently there are no initial heat sources. So this function returns the negative of *get_q_int()*
:param T_s: Surface Temperature of Envelope (K)
:type T_s: float
:param el: Elevation (m)
:type el: float
:param v: velocity (m/s)
:type v: float
:returns: SUm of Internal Heat Transfer (W)
:rtype: float
"""
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = m.get_rho(el)
g = m.get_g(el)
#print("rho",rho_atm)
Pr = self.get_Pr_co2(T_i)
mu = self.get_dynamic_viscocity_co2(T_i)
k = self.get_k_co2(T_i)
h = 0.13 * k * pow(
(pow(rho_atm, 2) * g * fabs(T_s - T_i) * Pr) / (T_i * pow(mu, 2)),
(1 / 3.)) #THE ERROR WAS HERE. AHHHH
#print("h",h)
#print ("Pr",Pr)
q_int = h * self.surfArea * (T_s - T_i)
#print("q_int",q_int)
return q_int
def get_acceleration(self,v,el,T_s,T_i,mp):
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = p_atm/(189*T_atm) #m.get_rho(el)
g = m.get_g(el)
rho_int = p_atm/(self.Rsp_co2*T_i)
F_b = (rho_atm - rho_int)*self.vol*g
Cd = .8
F_d = Cd*(0.5*rho_atm*math.fabs(v)*v)*self.cs_area
vm = (self.massEnv + mp) + rho_atm*self.vol + self.vm_coeff*rho_atm*self.vol
accel = (F_b - F_d - (self.massEnv + mp)*g)/vm
return accel
def get_q_int(self,T_s, T_i, el):
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = m.get_rho(el)
g = m.get_g(el)
Pr = self.get_Pr_co2(T_i)
mu = self.get_dynamic_viscocity_co2(T_i)
k = self.get_k_co2(T_i)
h = 0.13*k*pow((pow(rho_atm,2)*g*fabs(T_s-T_i)*Pr)/(T_i*pow(mu,2)),(1/3))
q_int = h*self.surfArea*(T_s-T_i)
return q_int
def get_convection_vent(self,T_i,el):
"""Calculates the heat lost to the atmosphere due to venting
:param T_i: Internal Temperature (K)
:type T_i: float
:param el: Elevation (m)
:type el: float
:returns: Convection due to Venting (unit?)
:rtype: float
"""
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
Q_vent = self.mdot*self.Cv_co2*(T_i-T_atm)
return Q_vent
def get_q_ext(self, T_s, el, v):
"""External Heat Transfer
:param zen: Surface Temperature of Envelope (K)
:type zen: float
:param el: Elevation (m)
:type el: float
:param el: velocity (m/s)
:type el: float
:returns: Power transferred from sphere to surrounding atmosphere due to convection(W)
:rtype: float
"""
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = m.get_rho(el)
g = m.get_g(el)
Pr_atm = self.get_Pr_co2(T_atm)
T_avg = 0.5*(T_atm + T_s)
rho_avg = p_atm/(Mars_Sphere_Balloon.Rsp_co2*T_avg)
Pr_avg = self.get_Pr_co2(T_avg)
exp_coeff = 1./T_avg
kin_visc = self.get_dynamic_viscocity_co2(T_avg)/rho_avg
k = self.get_k_co2(T_avg)
alpha = k/(rho_avg*Mars_Sphere_Balloon.Cp_co2)
Ra = g*exp_coeff*pow(self.d,3)/(kin_visc*alpha)*math.fabs(T_s-T_atm)
# Reynolds number has to be positive, therefore convert negative velocities.
Re = rho_atm*fabs(v)*self.d/self.get_dynamic_viscocity_co2(T_atm)
Nu = self.get_Nu_free(T_s,el,Pr_avg)
k = self.get_k_co2(T_avg)
'''External Free Convection'''
h = (Nu*k)/self.d
'''External Forced Convection'''
h_forced = k/self.d*(2+.41*np.power(Re,0.55))
#Take maximum value between free and forced
h = np.fmax(h,h_forced)
q_conv = h*self.surfArea*(T_s-T_atm)
return q_conv
def solve_states(self, T_s, T_i, el, v, mp, vent, timespace, alt_dz,
vel_dz):
for i in range(0, len(timespace) - 1):
bal = mars_sphere_balloon.Mars_Sphere_Balloon()
rad = mars_radiation.MarsRadiation()
q_rad = rad.get_rad_total(self.lat, self.Ls, el[i], timespace[i],
self.d)
rho_atm = rad.get_rho(el[i])
p_atm = rad.get_P(el[i])
rho_int = p_atm / (self.Rsp_co2 * T_i[i])
tm_air = rho_int * self.vol * self.Cp_co2
dT_sdt = (bal.get_sum_q_surf(q_rad, T_s[i], T_i[i], el[i],
v[i])) / (bal.cf * self.massEnv)
dT_idt = (bal.get_q_int(T_s[i], T_i[i], el[i]) -
self.get_convection_vent(T_i[i], el[i])) / tm_air
T_s.append(T_s[i] + dT_sdt * self.dt)
T_i.append(T_i[i] + dT_idt * self.dt)
dzdotdt = self.get_acceleration(v[i], el[i], T_s[i], T_i[i], mp)
zdot = v[i] + dzdotdt * self.dt
z = el[i] + zdot * self.dt #+dzdotdt*pow(dt,2)#*1000
if z < 0:
v.append(0)
el.append(0)
else:
v.append(zdot)
el.append(z)
if el[i] > alt_dz:
self.mdot = vent
if v[i] < vel_dz:
self.mdot = 0
if i % 3600 == 0:
print "t", timespace[i + 1] / 3600, "el", el[i + 1], "v", v[
i + 1], "accel", dzdotdt, "T_s", T_s[i + 1], "T_i", T_i[i +
1]
return [T_s, T_i, el, v]
def get_Nu_free(self, T, el, Pr):
"""Calculates Free Nusselt Number
:param T: Temperature (K)
:type T: float
:param el: Elevation (m)
:type el: float
:param Pr: Prandtl Number
:type Pr: float
:returns: Free Nusselt Number
:rtype: float
"""
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
p_atm = m.get_P(el)
rho_atm = m.get_rho(el)
g = m.get_g(el)
Pr_atm = self.get_Pr_co2(T_atm)
T_avg = 0.5 * (T_atm + T)
rho_avg = p_atm / (Mars_Sphere_Balloon.Rsp_co2 * T_avg)
Pr_avg = self.get_Pr_co2(T_avg)
exp_coeff = 1. / T_avg
mu = self.get_dynamic_viscocity_co2(T_avg)
Gr = (pow(rho_atm, 2) * g * fabs(T - T_atm) *
pow(self.d, 3)) / (T_atm * pow(mu, 2))
try:
Nu = 2 + .45 * pow((Gr * Pr), .25)
except:
Nu = 2.45
return Nu
def get_convection_vent(self, T_i, el):
m = mars_radiation.MarsRadiation()
T_atm = m.get_T(el)
Q_vent = self.mdot * self.Cv_co2 * (T_i - T_atm)
return Q_vent
def model(T_s,t):
m = mars_radiation.MarsRadiation()
Q_sun = m.get_rad_total(lat,Ls,el,t,d)
dTdt = (Q_sun-Q_loss(T_s))/(cf*M)
return dTdt
def solve_states(self,T_s,T_i,el,v,timespace,alt_sp,vel_sp):
"""This function numerically integrates and solves for the change in Surface Temperature, Internal Temperature, and accelleration
after a timestep, dt.
:param T_s: Surface Temperature (K)
:type T_s: float
:param T_i: Internal Temperature (K)
:type T_i: float
:param el: Elevation (m)
:type el: float
:param v: Velocity (m)
:type v: float
:param alt_sp: Altitude Setpoint (m)
:type alt_sp: float
:param v_sp: Velocity Setpoint (m/s)
:type v_sp: float
:returns: Updated parameters after dt (seconds)
:rtype: float [T_s,T_i,el,v]
"""
for i in range(0,len(timespace)-1):
bal = mars_sphere_balloon.Mars_Sphere_Balloon()
rad = mars_radiation.MarsRadiation()
q_rad = rad.get_rad_total(self.lat,self.Ls,el[i],timespace[i],self.d)
rho_atm = rad.get_rho(el[i])
p_atm = rad.get_P(el[i])
rho_int = p_atm/(self.Rsp_co2*T_i[i])
tm_air = rho_int*self.vol*self.Cp_co2
dT_sdt = (bal.get_sum_q_surf(q_rad, T_s[i], T_i[i], el[i], v[i]))/(bal.cf*self.massEnv)
dT_idt = (bal.get_q_int(T_s[i], T_i[i], el[i])-self.get_convection_vent(T_i[i],el[i]))/tm_air
T_s.append(T_s[i]+dT_sdt*self.dt)
T_i.append(T_i[i]+dT_idt*self.dt)
dzdotdt = self.get_acceleration(v[i],el[i],T_s[i],T_i[i])
zdot = v[i] + dzdotdt*self.dt
z = el[i]+zdot*self.dt
#if zdot < -800: #terminal velocity?
# zdot = -800.0
if z<0:
v.append(0)
el.append(0)
else:
v.append(zdot)
el.append(z)
if el[i] > alt_sp:
self.mdot = self.vent
else:
self.mdot = 0
if i % 360 == 0 :
print("t", timespace[i+1]/(3600), "el", el[i+1], "v", v[i+1], "accel", dzdotdt, "T_s", T_s[i+1], "T_i", T_i[i+1])
return [T_s,T_i,el,v]
