K.1.2 Sources

K.1.2.1. Outgassing

For a material that outgassses at a constant rate, independently of the quantity present, such as e.g. during evaporation or sublimation from a bulk, the process is described as a zero order reaction.

(K-1)

where

is the outgassing rate (g cm^-2s^-1);

k is the reaction constant.

The weightloss through evaporation, at a temperature T is given by [RD.93]

(K-2)

where

is the weight loss per unit area in g cm^-2s^-1;

P_s is the vapour pressure in hPa;

M is the molecular mass;

T is the temperature in K.

The outgassing is often described as a first order reaction [RD.93], i.e. the material outgasses at a rate that is proportional to the mass available, and using Arrhenius law temperature dependency. Important parameters for the outgassing rate are temperature, exposed surface area (or the surface available for evaporation), surface morphology, dimensions of the material (characteristic dimension, thickness).

(K-3)

The factor k can be seen as a measure for the temperature dependent time constant (τ) of the outgassing phenomenon.

(K-4)

Integration of

(K-5)

gives

(K-6)

Assuming the Arrhenius relation to be valid

(K-7)

it is possible to determine the outgassing as function of temperature.

The mass loss can be expressed as

(K-8)

K.1.2.2. Plumes

Evaluation of plumes of thrusters or vents is often described by specific application related models. Parametric descriptions of plumes constitute an interesting alternative to spacecraft designers.

The mass flux Φ of a plume can be expressed in the most generic form

(K-9)

where

Φ(r, Θ) is the flux at a given position from the vent;

r is the radial distance from the vent;

Θ is the angle from the centerline of the vent;

is the mass flow from the vent;

where, moreover, the function f depends on the plume type. However this formula can in general be reduced in a good approximation to the product

(K-10)

where

A is a normalization coefficient.

For a thruster, the function f₁ is peaked around Θ = 0 and can be expressed as a sum of decreasing exponentials [RD.94] or as a (high) power law of cos(Θ) or both [RD.95]. It is in some extent specific of each thruster.

Plumes from vents are more standard and the f₁ function can consequently be fixed: the mass flux is approximated by the following engineering model:

(K-11)

where 1 ≤ n ≤ 2 is used for space station design.

Their divergence is larger than that of thrusters.