What we measure on shock waves and how we interpret the results

 

 

 

                What we measure on shock waves and how we interpret

                                               the results.

 

       In order to reasonably use the shock waves in the technique projects where they are the "technological tools" for achievement of the desirable results,  is necessary in a first turn to know theirs true properties in the different real conditions. This properties are defined by the significations of theirs defining parameters:  normal strain (the pressure)  p, specific volume  V, specific inner energy  e, mass velocity  U (or, in an arbitrary count system,  v)  and the velocity of wave relatively of in front matter  D. On the base of three conservation laws - the mass, the impulse and the energy -  it are determined three equations binding that five parameters; for to define all them, two from them must be measured experimentally, then others can be calculated from that equations. On the practice as a rule experimentally measured are the velocities  D and  U , especially for the condensed materials; the other parameters are calculated from system of equation of the conservation laws.

       In a contemporary generally accepted theory of shock waves as the system of equation of the conservation laws always is used the Rankine - Hugoniot (R. - H.) system, in which as the energy equation (in any materials, with any amplitudes, and so on) appears equation of Hugoniot. But the shock waves on which Hugoniot equation is fulfilled - that is the conservation law reality had the form of it - inevitable are the elastic waves. The reason is obvious: this equation is based on the hypothesis about of adiabatic shock deforming of the matter in wave. In any adiabatic processes

                                       (delta) e = (delta) w            (1)

so that the work of the deformations w find oneself as the function of state (dw is the full differential): such conditions are possible only if deforming of the material is elastic .

       In the nature and technics mostly meet the non adiabatic shock waves in which deformations of the matter are non elastic; just such "technological tools" in most cases are needful for the major contemporary technique projects. The radical theirs difference from the elastic waves consist in that the process of deforming of the matter in them is non adiabatic one: it is accompanied by the shock heat transference (SHT)  (or "shock heat exchange")  of the deformed on shock rupture material with its environment. The discovery of this phenomenon had been fixated in the article

 "Л.Г.Филиппенко. Следствия из уравнения Гюгонио. Сб. «Гидромеханика», вып. 36, Киев, «Наукова думка», 1977г." / The English text: L.G.Philippenko. The consequences from the Hugoniot equation. See at URL:  http://www.leonid-philippenko.narod.ru/index.html

 , in which strict proves of the  inevitability of existence the SHT  and the properties of Hugoniot  equation (where the SHT is absent) are detailed analysed ; the equation of the law of energy conservation have on the non adiabatic waves the form:

                 (delta) e =  Q + (delta) w         (2)                                                             

where Q is the specific measure of SHT.

      Naturally, the correlations among defining parameters in non adiabatic shock waves are essentially different from that in the adiabatic waves. None the less in contemporary scientific practice calculations of p, V and e on the essentially non adiabatic shock waves, corresponding to measured D and U, as yet execute by the R. - H. system. It leads to arise the "theoretic" errors additional to experimental ones; until the amplitude of the wave is enough little, these errors can also be little, but on the strong non adiabatic shock waves such "theoretic" errors can essentially exceed experimentally errors. The situation is analogical to that if the big plastic deformations were calculated by the formulae  of elastic deforming.

      Still more false is generally accepted method of the measurement of the velocities D and U on the stationary shock waves. At the first turn, the non elastic, strong shock waves, which mostly meet - and have the most importance - in nature and technics, are as a rule the non stationary waves. The practical importance of science researches is defined by the practical importance of theirs  results; here it means that for the practice the most interest have researches of the characteristics of not stationary shock waves. But on some systematic considerations in the contemporary scientific practice it is decided to restrict oneself by the stationary shock waves.

      The realization of stationary waves is a complicated problem. For to remain the stationary character the shock waves demand  supporting of the strict outer conditions: it is enough any (already a little) accidental decreasing of the amplitude in order to the non adiabatic shock wave instantly had left of its shock character and had turned into continuous wave. The conditions in which are absent already the little accident fluctuations of the parameters, in a reality endure rarely (and in experiment scarcely are accessible). From the analysis of contemporary experimentally equipment used in this researches and by the second principle of thermodynamics it is clear: the significations of the velocities  D and  U which were measured out of the limits of elastic diapason, apparently, as a matter of fact, were measured on the strong (and enough steep ) non adiabatic continuous compressing waves. By theirs  profiles such waves are similar to the shock waves; moreover, the velocities D and U with non adiabatic continuous waves also depend from theirs amplitude; this circumstance promote to confuse them with the true shock waves. But there exist the essentially differentiation among them: on continuous wave the velocity of its front is the (non adiabatic) sound velocity: D = c , (here  c  depends from the amplitude because of warming of the in front matter), while on the shock wave D > c. The experimentally discovered linear dependence among D and U is peculiar, most probably, for binding in continuous but not shock waves.

      But assume that the experimental equipments were so perfect that any accidental fluctuations in the wave parameters were excluded and the stationary shock waves could be realized. Behind the front of stationary shock wave the flow can be only the constant flow: p = Const., V = Const., and so on. From the second principle of thermodynamics from it leads: on the front of stationary shock wave the viscosity effects (as and other dissipative processes) does not display himself, and deforming of the matter is the inner local reversible one: the irreversible character of such wave results only from the irreversibility of SHT. Such waves are the exclusive phenomenon in nature and technique applications and hardly have the big interest for the practice.

      The all said above in strict detailed account is contained in article

"L.G.Philippenko. What we measure and how we interpret it" which is placed on author's site "Shock Heat Transference" at URL:    http://www.leonid-philippenko.narod.ru/index.html

  

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