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Numerical Simulations of Rarefied Gas Flow with ''Direct Simulation Monte Carlo'' Method
Language: English This thesis is written in English
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Matteo Cimini, Università degli Studi di Roma La Sapienza, 2016-17
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The target of this work is the characterization of rarefied gas flows using the Direct Simulation Monte Carlo (DSMC) computational method. The study of rarefied gas flows is frequent in many applications in aerospace at high altitudes, such as re-entry vehicles in upper atmosphere or entry into other planets of the solar system, satellites and spacecrafts on LEO and in deep space, nozzles and jets in space environment, dynamics of upper planetary atmospheres, global atmospheric evolution and atmospheres of small bodies.
After a more in-depth introduction for the problem and a brief presentation of the work, at first it has been analyzed the simple dilute gas, the binary elastic collision and the various molecular models used in the DSMC method. In order to characterize the gas at the molecular level, the kinetic theory of gases was briefly introduced, focusing on the velocity distribution function, the Boltzmann equation and the Chapman-Enskog theory. The latter allows us to find an explicit relationship between viscosity and temperature.
Subsequently, the DSMC method was studied in detail, describing its relationship with the Boltzmann equation and describing each procedural step within the code. The DSMC method is a direct particle simulation method based on kinetic theory. The method is explicit and time-marching and provides a probabilistic physical simulation of a gas flow by simultaneously following the motion of representative model molecules in physical space. The particles’ motion and interactions are then used to modify their positions, velocities, or chemical reactions. Particle motions are modeled deterministically, while the collisions are treated statistically. The core of the DSMC algorithm consists of four primary processes: move the particles, index and cross-reference the particles, simulate collisions, and sample the flow field. These procedures are uncoupled during each time-step.
In this work a series of one-dimensional and two-dimensional applications were studied in order to understand rarefied gas flow and to test, validate and analyze the DSMC code. The one-dimensional flows that have been analyzed are the Couette flow and the normal steady shockwave for an Argon gas flow. The Couette flow was studied from a quasi-continuous regime up to the Collisionless one, while the normal shockwave was studied by varying the upstream velocity and density, focusing on the temperature, density and thickness profiles. The two-dimensional flow that has been analyzed is an Argon flow around a circular cylinder. The DSMC solutions has been compared to a continuous solutions achieved using a numerical solver of the Navier-Stokes equations. Compared solutions are characterized by different values of the freestream velocity and density.
The last case analyzed is an axisymmetric air flow for the ESA Vega launcher. This launcher has been studied in its third stage configuration at an altitude of 130 km, paying particular attention to the scaling law of the geometric configuration, the variation of the wall temperature and the molecular air model.