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**DSMC Program DS2V (ver. 3) for 2D Plane and Axially Symmetric Flows **

Integrated Demonstration/Tutorial Examples Program feature In example # Axially symmetric flow 1,2,3,4,7 Two-dimensional flow 5,6,8 Eventually steady flow 1,2,3,4,5,8 Continuing unsteady (time accurate) flow 6,7 Multiple reference gas streams with initial property discontinuity 3 Gas models with specified hardness and Schmidt number 1,2,3,4,5,6,7,8 Gas mixtures ,2,7,8 Rotational and vibrational energy with specified relaxation rates 1,2,7,8 Gas phase chemical reactions 2 Stream boundaries ,2,6,7,8 Stream entry surfaces 2,7 Specified inflow boundaries 1 Periodic boundaries 5 Constant pressure boundaries 3 Planes of symmetry ,6,8 Moving surface boundary 6 Solid surfaces with a choice gas-surface interaction models 1,2,3,4,5,6,7,8 Adsorbing and/or outgassing surfaces 4 Surface reactions Insulated or perfectly (thermally) conducting surfaces with radiation 8 Gas or surface motion normal to the flow plane, or rotating surface 8 The data menus for the examples may be reviewed and the programs may be run without a password. All flow illustrations are direct reproductions of the “single pushbutton” generated output bitmaps. All computational parameters other than the initial number of megabytes are set automatically. This means that the setup time for new applications is measured in minutes rather than hours or days.

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**Tutorial / Demonstration Example # 1**

Steady flow of air at a Mach number of 5 past a sphere with an upstream facing jet of nitrogen. The Knudsen number based on the diameter of the sphere is about The initial density of the jet is 3.5 times the stream density and the initial Mach number of the jet is 2.8. The sphere in inserted into a uniform stream at zero time and the unsteady development of the eventual steady flow may be followed on the interactive display. The initial number of simulated molecules is about 480,000 and there is only a slight increase. It is a relatively undemanding computation. The program employs separate cell systems for collisions and for the sampling of flow properties. The former are smaller and “push button” cell adaptions to a specified number of simulated molecules per cell may be made at any time.

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**Tutorial / Demonstration Example # 2**

70o Blunt Cone Re-entry Body at 7,500 m/s in Air at 200 K and a Number Density of 1020 / m3. An initial 800,000 molecules increases to more than 2 million when steady flow is finally established. It is a five species real air calculation with 23 chemical reactions, and the surface is 2% catalytic to the recombination of atomic oxygen. The front surface is at 1,000 K and the gas density at the surface is about 50 times the freestream density. There is a continued slow build up after the apparent establishment of steady flow when the molecule number first levels off. This is a demanding calculation that requires several days on a 3.2 MHz Pentium.

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**Tutorial / Demonstration Example # 3**

A typical MEMS flow through a circular tube with specified pressures at the ends. Because the entry speeds are unknown, constant pressure boundaries are employed. To keep the velocities low and to allow for non-uniform conditions at the entry and exit planes, conical “reservoirs’ have been added at the ends. There is initially a dividing plane at the center of the tube that separates the upstream and downstream reference gases. The entering and exiting mass fluxes are made equal to the mass flux that develops across the separation plane. The vortex indicates that a different shape for the dowstream reservoir would be desirable.

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**Tutorial / Demonstration Example # 4**

An axially symmetric free jet in a cryogenically pumped vacuum chamber. The free jet expands to a Mach number of about five before passing through the shock wave that forms ahead of the target surface. The cryogenic panel is the 98% adsorbing section of surface where the number flux of reflected molecules is near zero. A regular vacuum pump could be simulated by setting a surface interval as a “specified flow boundary” with a very low density or a vacuum as the specified “flow”. Note the use of the alternative color maps and of the white background option.

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**Tutorial / Demonstration Example # 5**

Thermal creep driven vacuum pump at a Knudsen number (based on channel semi-height) of 0.5. An eventually steady flow that, because of the very low speeds, requires a very long run to build up the required sample size. The top is a surface, the lower boundary is a plane of symmetry and the ends are periodic boundaries. This flow was devised by Sone to illustrate a practical application of thermal creep that vanishes in both the collisionless and continuum regimes. It is driven by the imposed temperature gradients and the flow is from cold to hot, i.e. the opposite to better known thermal diffusion effect.

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**Tutorial / Demonstration Example # 6**

Diffraction of Mach 2.5 shock wave in argon by a vertical flat plate with a height of 250 m.f.paths. An unsteady flow calculation with 4 million simulated molecules that requires 10 hours computation on a 3.2 MHz Pentium. The vertical white line at the left of the pictures is the instantaneous location of the specularly reflecting moving piston that generates the wave. There were 1.8x109 collisions and 1.7x1010 molecular moves in the computation. The closed path-line indicates the instantaneous location of the vortex that is a feature of this flow. ASCII output files AFnnnn.DAT and ASnnnn.DAT are automatically generated at the end of each output interval.

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Numbered bitmap files may be generated automatically at the end of each output interval and these are readily made into a movie by the well-known freeware program Animator-9.

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**Tutorial / Demonstration Example # 7**

Unstable oscillatory airflow past a blunt cone with a towed toroidal ballute at a Mach number of 5.8. The upper picture shows the flow at the minimum number of two million simulated molecules. Those on the right are for the maximum 2.5 million. The period of the oscillation is almost exactly twice the transit time of the stream from the front of the blunt cone to the rear of the torus. The stagnation point on the torus oscillates from -13o to +26o. The drag on the blunt cone is positive near the minimum, but negative near the maximum. There are significant phase lags the oscillations of the various flow features. Note the similarity to the “intake buzz” phenomenon.

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**This movie shows a typical cycle of the periodic oscillation.**

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**Tutorial / Demonstration Example # 8**

Steady flow of air past a 45o swept cylinder with an insulated surface at M= 10 and Kn= The calculation is made in the x-y plane normal to the axis of the cylinder and and the stream has a z direction velocity component equal to that in the x-y plane. An identical calculation in a different frame of reference could be made by giving the surface a normal-to-plane velocity component. The “adiabatic surface” option for an insulated surface automatically sets the temperature distribution for zero local heat transfer. The emissivity is set to 0.8 and 20% of the incident energy is radiated. A perfectly (thermally) conducting surface is an alternative “adiabatic” option.

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TYPICAL SCREEN IMAGE

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