Experimental Facilities and Modelling for Rarefied Aerodynamics

The present lecture is devoted to experimental and theoretical modelling for rarefied aerodynamics. General features of experimental studies in rarefied flows are discussed. Experimental facilities designed in Saint Petersburg State University for rarefied aerodynamics and plasma flow control are described. Several theoretical models for non-equilibrium reacting flows in the slip regime are presented. 1.0 INTRODUCTION “Aerodynamics of rarefied gases is a branch of mechanics of gases in which their molecular structure must be taken into account in describing their motion. The methods of rarefied aerodynamics are widely applied in the determination of aerodynamic heating during the landing of orbital craft and for low-flying earth satellites, for the calculation of the thermal conditions of instrument transducers of rockets that are exploring the upper layers of the atmosphere, and so on. The exact prediction of the trajectories of lowaltitude planetary satellites that are testing the braking action of rarefied atmosphere is impossible without knowledge of the methods of the aerodynamics of rarefied gases. Using these methods, it is possible to determine the aerodynamic forces and moments that act on an object moving in the gas. The aerodynamics of rarefied gases also investigates the flow of gases in vacuum systems, ultrasonic oscillations in gases, and other problems of molecular physics.” – The Great Soviet Encyclopedia, 3d Edition (1979). Originally, theoretical models for rarefied gas flows were developed in the frame of the molecular kinetic theory. Thus the first self-consistent descriptions of a weakly non-equilibrium gas flow were given by the Hilbert and Chapman-Enskog [1] asymptotic methods and later by the Grad’s moment method [2]. In 1950-60-ies, the interest to the aerodynamics of vehicles at high altitudes became crucial due to the space exploration programs. The prospects of application of molecular approach to the solution of problems of aerodynamics were well understood in the nascent rarefied gas-dynamic community. Theoretical studies carried out at that time are summarized in [3, 4, 5]. Various methods for the solution of the Boltzmann equation were developed, among them linearized and model equations, integral and variational methods, that of discrete velocities and others [5, 6]. The next step in the theoretical rarefied aerodynamics was modelling of strongly non-equilibrium flows with internal degrees of freedom and chemical reactions. Modifications of the Chapman-Enskog method taking into account these effects were proposed in [7-11] and successfully applied for the calculations of different flows. For non-linear problems, the Direct Simulation by the Monte Carlo method (DSMC) was elaborated [12, 13] and, in the present time, it becomes the most popular and efficient tool for the modelling of transition and free molecular flows. Experimental modelling for rarefied flows was rapidly progressing together with theoretical studies. First low density (vacuum) wind tunnels were built in NASA AMES centre, California University, University of Toronto (early 1950-ies), and approximately in the same time in the main Russian scientific centres. The general ideas of experimental facilities and measurement techniques for rarefied gases were formulated in [3] and received further development in the next decades. Great advances in theoretical, experimental and numerical modelling for rarefied flows were achieved RTO-EN-AVT-194 13 1 Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE JAN 2011 2. REPORT TYPE N/A 3. DATES COVERED 4. TITLE AND SUBTITLE Experimental Facilities and Modelling for Rarefied Aerodynamics 5a. CONTRACT NUMBER