By S. M. Belotserkovsky, I.K. Lifanov
Approach to Discrete Vortices offers a mathematical substantiation and in-depth description of numerical equipment for fixing singular critical equations with one-dimensional and a number of Cauchy integrals. The publication additionally provides the basics of the idea of singular equations and numerical equipment as utilized to fixing difficulties in such branches of mechanics as aerodynamics, elasticity, and electrodynamics.
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Additional info for Method of discrete vortices
8 Stagnation-point ﬂow regimes for re-entry vehicle distance is small compared to the characteristic dimension of the ﬂowﬁeld, the macroscopic properties can be considered to vary continuously, and the gas can be treated as a continuum. In contrast, a rareﬁed ﬂowﬁeld will have a long relaxation time and hence a longer relaxation distance. 9) where n [number of molecules/m3 ] is the number density of the gas and [m] the effective diameter of gas particles. The mean free path depends only upon the number density of the gas, n, which is a function of the altitude.
As a consequence, Fig. 30 highlights that the entry ﬂight paths slash across major sections of the altitude–velocity map where chemical reactions and vibrational excitation arise. This clariﬁes why high-temperature effects are so important to entry-body ﬂows [2, 3, 7, 9, 10]. 30 suggests also that there will be an increasing number of species occurring in the different domains along with the descent trajectory. Indeed, the ﬂow chemical composition can vary spatially and temporally. Moreover, the continual exchange of energy between the transitional and internal degrees of freedom of the ﬂow molecules results in thermal and/or chemical nonequilibrium in the different domains of altitude–velocity map, as recognized in Fig.
1 Fluid Flow Governing Equations All ﬂuid ﬂowﬁelds are governed by the following three conservation laws: 1. Conservation of mass: continuity equation 2. Conservation of momentum: Newton’s second law of motion 3. Conservation of energy: ﬁrst law of thermodynamics These conservation laws in conjunction with a deﬁnition of the ﬂuid provide the system of equations required to determine the ﬂowﬁeld for a given set of boundary conditions. If the atmosphere around the body is modeled as a continuum, the conservation equations lead to a system of equations based on the bulk properties of air, well known as the Navier–Stokes equations.