Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.

Mixing of A Non-Circular Jet into A Counterflow

An elliptic jet and a square jet flowing into a counterflow with different jet-to-current velocity ratios are investigated by using realizable Ice model. Some computed mean velocity and scalar features agree reasonably well with experimental measurements, and more features are obtained by analyzing the computed results. After fluid issues from a nozzle, it entrains ambient fluid, and its velocity and concentration on the centerline decay with the distance downstream from the potential core （10）. The decay ratio increases with the decreasing jet-to-current velocity ratio a. For an elliptic jet, the evolution of the excess velocity half-width b and the concentration half-width be merely remains constant near the jet exit on major-axis plane while they increase linearly on the minor-axis plane. However, the half-widths on the major-axis and minor-axis plane become proportional to the axial distance downstream after equaling each other. For a square jet, b and bc increase linearly with the distance downstream from the jet exit, but the spread ratio is larger on the middle plane than that on the diagonal plane before they equal each other. The radial extent of the dividing streamline r~ or the mixing boundary rs~ increases linearly downstream, and decreases exponentially after reaching a peak at Xb. The ratio on the minor-axis plane is larger than that on the major-axis plane for an elliptic jet. The characteristics are the same for the square jet. b, be, rs, and rsc on two corresponding planes become equal to each other more rapidly for the square jet than for the elliptic jet, because the sharp comer of the square nozzle induces secondary structures that are more intense. The distributions of the excess axial velocity and scalar concentration exhibit self-similarity for either the elliptic jet or square jet in the region of 10 〈 x 〈 xb. On the cross section, four counter-rotating pairs of vortices, which enhance the entrainment between the jet and counterflow, form at the four comers of the square jet or at the two ends of the major-axis plane of the elliptic jet. The recirculation pattern formed by these axial vortices is more complex for the square jet than that for the elliptic jet. The turbulent kinetic energy k have large value in the region near the jet exit and stagnation point. The maximum value ofk for the square jet is larger than that of the elliptic jet near the jet exit. This results in the square jet mixing more strongly than the elliptic jet.

Volumetric, Ultrasonic and Transport Properties of Binary Liquid Mixtures Containing Dimethyl Formamide at 303.15 K

Excess volumes （v^E）, ultrasonic velocities （u）, isentropic compressibility （△Ks） and viscosities （η） for the binary mixtures of dimethyl formamide （DMF） with 1,2-dichlorobenzene, 1,3-dichlorobenzene, 1,2,4-trichlorobenzene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, o-nitrotoluene and m-nitrotoluene at 303.15 K were studied. Excess volume data exhibit an inversion in sign for the mixtures of dimethyl formamide with 1,2- and 1,3-dichlorobenzenes and the property is completely positive over the entire composition range for the mixtures of dimethyl formamide with 1,2,4-trichlorobenzene, o-nitrotoluene and m-nitrotoluene. On the other hand, the quantity is negative for the mixtures of dimethyl formamide with chlorotoluenes. Isentropic compressibility （Ks） has been computed for the same systems from precise sound velocity and density data. Further, deviation of isentropic com- pressibility （△Ks） from ideal behavior was also calculated. AKs values are negative over the entire volume fraction range in all the binary mixtures. The experimental sound velocity data were analysed in terms of Free Length Theory （FLT） and Collision Factor Theory （CFT）. The viscosity data were analysed on the basis of corresponding state approach. The measured data were discussed on the basis of intermolecular interactions between unlike molecules.