sphere_balloon

sphere_balloon solves for the total heat transfer on the solar balloon.

class sphere_balloon.Sphere_Balloon[source]

Initializes atmospheric properties from the earth configuration file

__init__()[source]
get_Nu_ext(Ra, Re, Pr)[source]

Calculates External Nusselt Number.

Determine the external convection due to natural buoyancy

\[\begin{split}Nu_{ext,n}=\begin{cases} 2+0.6Ra^{0.25}, & \text{$Ra<1.5\cdot10^8$}\\ 0.1Ra^{0.34}, & \text{$Ra\geq1.5\cdot10^8$} \end{cases}\end{split}\]

Determine the external forced convection due to the balloon ascending

\[\begin{split}Nu_{ext,f}=\begin{cases} 2+0.47Re^{\frac{1}{2}}Pr^{\frac{1}{3}}, & \text{$Re<5\cdot10^4$}\\ (0.0262Re^{0.34}-615)Pr^{\frac{1}{3}}, & \text{$Re\geq1.5\cdot10^8$} \end{cases}\end{split}\]

To transition between the two correlations:

\[Nu_{ext} = max(Nu_{ext,n},Nu_{ext,f})\]
Parameters:

  • Ra (float) – Raleigh’s number

  • Re (float) – Reynold’s number

  • Pr (float) – Prandtl Number

Returns:

External Nusselt Number

Return type:

float

get_Nu_int(Ra)[source]

Calculates Internal Nusselt Number for internal convection between the balloon envelope and internal gas

\[\begin{split}Nu_{int}=\begin{cases} 2.5(2+0.6Ra^{\frac{1}{4}}), & \text{$Ra<1.35\cdot10^8$}\\ 0.325Ra^{\frac{1}{3}}, & \text{$Ra\geq1.35\cdot10^8$} \end{cases}\end{split}\]
Parameters:

Ra (float) – Raleigh’s number

Returns:

Internal Nusselt Number

Return type:

float

get_Pr(T)[source]

Calculates Prantl Number

\[Pr = \mu_{air} \frac{C_{p,air}}{k}\]
Parameters:

T – Temperature (K)

Returns:

Prantl Number

Return type:

float

get_conduction(T)[source]

Calculates Thermal Diffusivity of Air at Temperature, T using Sutherland’s Law of Thermal Diffusivity

\[k_{air} = 0.0241(\frac{T_{atm}}{271.15})^{0.9}\]
Parameters:

T – Temperature (K)

Returns:

Thermal Diffusivity of Air (W/(m*K)

Return type:

float

get_q_ext(T_s, el, v)[source]

Calculate External Heat Transfer to balloon envelope

Parameters:

  • zen (float) – Surface Temperature of Envelope (K)

  • el (float) – Elevation (m)print fluids.atmosphere.solar_position(datetime.datetime(2018, 4, 15, 6, 43, 5), 51.0486, -114.07)[0]

  • el – velocity (m/s)

Returns:

Power transferred from sphere to surrounding atmosphere due to convection(W)

Return type:

float

get_q_int(T_s, T_i, el)[source]

Calculates Internal Heat Transfer

Parameters:

  • T_s (float) – Surface Temperature of Envelope (K)

  • el (float) – Elevation (m)

  • v (float) – velocity (m/s)

Returns:

Internal Heat Transfer (W)

Return type:

float

get_sum_q_int(T_s, T_i, el)[source]

Calculates sum of Internal Heat Transfer.

Note

Currently there are no initial heat sources. So this function returns the negative of get_q_int()

Parameters:

  • T_s (float) – Surface Temperature of Envelope (K)

  • el (float) – Elevation (m)

  • v (float) – velocity (m/s)

Returns:

SUm of Internal Heat Transfer (W)

Return type:

float

get_sum_q_surf(q_rad, T_s, el, v)[source]

External Heat Transfer

Parameters:

  • q_rad (float) – Power input from external radiation (W)

  • T_s (float) – Surface Temperature of Envelope (K)

  • el (float) – Elevation (m)

  • v (float) – velocity (m/s)

Returns:

The sum of power input to the balloon surface (W)

Return type:

float

get_viscocity(T)[source]

Calculates Kinematic Viscocity of Air at Temperature, T

\[\mu_{air} = 1.458\cdot10^{-6}\frac{T_{atm}^{1.5}}{T_{atm}+110.4}\]
Parameters:

T – Temperature (K)

Returns:

mu, Kinematic Viscocity of Air

Return type:

float