The proper planning of a space mission of a satellite and/or of a space platform relies also on a correct evaluation of the aerodynamic drag and moments acting on it. The aerodynamic drag is responsible for the orbit decay and therefore for the operative life of the space vehicle, the moments are responsible for the attitude changing and therefore for its working. A correct evaluation of the drag and moments provides: 1) information for a proper design of the propulsion system for the station keeping, 2) when the vehicle is a platform for micro-gravity experiments, the knowledge of the induced acceleration. Even though the problem of the satellite aerodynamics (or of the Free Molecule Flow: FMF) has been already widely studied, however the just started program of the International Space Station (ISS) proposes again this problem. For the ISS the above mentioned problems are far more stressed compared with the ones of the satellites. In fact, the ISS is characterized by a much more complex geometry, for which the interference effects of the surfaces are more prominent and the orbit altitude is pretty low. As well known, the orbit of the ISS is circular and is at an altitude of about 380 km. Because of the aerodynamic drag this orbit could decay even down to 280 km, where the atmospheric density is high enough to produce noticeable aerodynamic effects. For this reason, the ISS needs to be re-boosted periodically (about every three months) to its operating height by the Space Shuttle. Fig. 1 shows the front views of the ISS with the solar panels normal (a) and parallel (b) to the velocity. The total front areas are 3717 and 858 m2, respectively. In FMF the aerodynamic interactions are usually evaluated by means of equations from the maxwellian theory. As well known, these equations, computing the normal and the tangential stresses and heat flux were obtained from the general Boltzmann equation through simplifying and restrictive hypotheses: 1. the gas is spatially homogeneous and dilute. It is made of mono-atomic, non-reacting molecules and is free of external forces, as well as of gradient of any thermo-fluid-dynamic quantity; in a word the gas is in equilibrium. 2. The molecules, striking the body surface and then reflected back into the flow, do not collide with the free stream ones. This hypothesis makes possible computing the normal and tangential stresses and the heat flux as the sum of the contributions of the incident and reflected molecules. Furthermore the surface of the body can be divided in small elements, each one working independently of the other ones. The surface pressure and shear stress are then integrated over the complete body for computing the overall aerodynamic force. The aim of the present paper is to evaluate the accuracy of the maxwellian theory when the above hypotheses could be not longer rigorously verified. This check will be made by the comparison of the aerodynamic coefficients from the maxwellian theory with the ones from a Direct Simulation Monte Carlo (DSMC) code, and by the analysis of thermo-fluid-dynamic quantities, as per local rarefaction level of the flow field, computed from DSMC data, in order to evaluate the departure from the hypotheses on which the maxwellian theory relies. The computation of the drag will be approximated considering two circular disks (diameters 69 and 33 m) of area equivalent, respectively, to the front sections (a) and (b) of the ISS (Fig.1), normal to the free steam. Runs will be made in the altitude range of interest of the ISS (280-380 km) and with the maxwellian, “classical” models of surface reflection: diffuse fully accommodate, specular and partially diffusive. (a) (b) Fig. 1 - Front views of the ISS with solar panels normal (a) and parallel (b) to the velocity

ACCURACY OF THE MAXWELL'S THEORY IN SPACE APPLICATION / Zuppardi, Gennaro. - (2003), pp. 1-13. (Intervento presentato al convegno XVII Congresso Nazionale dell'Associazione Italiana di Aeronautica ed Astronautica tenutosi a Roma (Italia) nel 15-19 Settembre 2003).

### ACCURACY OF THE MAXWELL'S THEORY IN SPACE APPLICATION

#####
*ZUPPARDI, GENNARO*

##### 2003

#### Abstract

The proper planning of a space mission of a satellite and/or of a space platform relies also on a correct evaluation of the aerodynamic drag and moments acting on it. The aerodynamic drag is responsible for the orbit decay and therefore for the operative life of the space vehicle, the moments are responsible for the attitude changing and therefore for its working. A correct evaluation of the drag and moments provides: 1) information for a proper design of the propulsion system for the station keeping, 2) when the vehicle is a platform for micro-gravity experiments, the knowledge of the induced acceleration. Even though the problem of the satellite aerodynamics (or of the Free Molecule Flow: FMF) has been already widely studied, however the just started program of the International Space Station (ISS) proposes again this problem. For the ISS the above mentioned problems are far more stressed compared with the ones of the satellites. In fact, the ISS is characterized by a much more complex geometry, for which the interference effects of the surfaces are more prominent and the orbit altitude is pretty low. As well known, the orbit of the ISS is circular and is at an altitude of about 380 km. Because of the aerodynamic drag this orbit could decay even down to 280 km, where the atmospheric density is high enough to produce noticeable aerodynamic effects. For this reason, the ISS needs to be re-boosted periodically (about every three months) to its operating height by the Space Shuttle. Fig. 1 shows the front views of the ISS with the solar panels normal (a) and parallel (b) to the velocity. The total front areas are 3717 and 858 m2, respectively. In FMF the aerodynamic interactions are usually evaluated by means of equations from the maxwellian theory. As well known, these equations, computing the normal and the tangential stresses and heat flux were obtained from the general Boltzmann equation through simplifying and restrictive hypotheses: 1. the gas is spatially homogeneous and dilute. It is made of mono-atomic, non-reacting molecules and is free of external forces, as well as of gradient of any thermo-fluid-dynamic quantity; in a word the gas is in equilibrium. 2. The molecules, striking the body surface and then reflected back into the flow, do not collide with the free stream ones. This hypothesis makes possible computing the normal and tangential stresses and the heat flux as the sum of the contributions of the incident and reflected molecules. Furthermore the surface of the body can be divided in small elements, each one working independently of the other ones. The surface pressure and shear stress are then integrated over the complete body for computing the overall aerodynamic force. The aim of the present paper is to evaluate the accuracy of the maxwellian theory when the above hypotheses could be not longer rigorously verified. This check will be made by the comparison of the aerodynamic coefficients from the maxwellian theory with the ones from a Direct Simulation Monte Carlo (DSMC) code, and by the analysis of thermo-fluid-dynamic quantities, as per local rarefaction level of the flow field, computed from DSMC data, in order to evaluate the departure from the hypotheses on which the maxwellian theory relies. The computation of the drag will be approximated considering two circular disks (diameters 69 and 33 m) of area equivalent, respectively, to the front sections (a) and (b) of the ISS (Fig.1), normal to the free steam. Runs will be made in the altitude range of interest of the ISS (280-380 km) and with the maxwellian, “classical” models of surface reflection: diffuse fully accommodate, specular and partially diffusive. (a) (b) Fig. 1 - Front views of the ISS with solar panels normal (a) and parallel (b) to the velocityI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.