Some Problems of the Dynamics of a Space Vehicle with Tanks Partially Filled with Liquid

Abstract

During a space flight conditions on board the space vehicle approach zero-g conditions. As a result, many physical processes, in which mass forces are of considerable importance, differ from those in the Earth. In particular, surface tension forces become especially effective on the liquid free surface. The liquid partially filling the space vehicle tanks, tends to assume the position corresponding to the energy minimum of the gas-liquid-solid system. Equilibrium forms of the liquid free surface affected by gravity and surface tension forces may be determined by [1]:

$$ 2H - {B^{*}}z - \lambda = 0 $$

((1))

where $H = \frac{1}{2}\;\left( {R_1^{{ - 1}} + R_2^{{ - 1}}} \right)\;$ = surface mean curvature; R ₁, R ₂ = the principal radii of curvature at any point; B*=ngϱl ²/σ = Bond number which is the ratio of gravity forces to surface tension forces (a dimensionless parameter); z = dimensionless free surface ordinate (z-axis is parallel to gravity forces); λ = a constant.