一般化された流体運動の基本方程式を使用して流れに平行に置かれた矩形板周りの運動とその摩擦抵抗係数の研究
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Most equations of mathematical physics are simplified by various assumptions in order to obtain their solutions easily. Therefore, solutions of such equations show qualitative results but occationally quantitative discrepancies with experimental data and the facts observed by experiments can't be explained. Considering the progress of the method of measurement and the appearance of supersonic airplane, the author recognises the need of reexamination for fundamental equations of the fluid motion. The solutions of N-S equations which are considered to govern the fluid motion show the disagreements with experimental facts as followings : 1. Along the boundary of boundary layer N-S equations do not hold unless all derivaties of the x-component of velocity vanish. Consequently it is assumed that N-S equations can be utilized only within 60% of the thickness of boundary layer. 2. Solutions of N-S equations can't give the scale effect. 3. The effects of Mach's number are almost not explained. 4. The coefficients of frictional resistance in the turbulent flow differ widely from them obtained by experiments. 5. In the discussion of turbulent motion are adopted periodic functions instead of irregular non-periodic functions representing the fluctuations in the turbulent motion. 6. The fact that the profile of velocity distribution varies with the velocity does not be accounted. 7. If y_1 represents the thickness of foundary layer at its end, which has nearly the order of 10^<-2>, the fluid can be regarded as a continuous medium within such range as terms of the order y_1^<11/2> or y_1^<13/2> can be neglected. In order to avoid these defects, the author takes the equation of continuity, the equations of motion and the equation of energy in the most general form and transforms them into the forms of zero dimension so that Reynolds' number, Mach's number, the variation of the density, etc. can appear explicitly. If the velocity components, the pressure, etc. as power series of y_1, are given and substituted into fundamental equations and equating of the coefficients of same power of y_1, a group of differential equations will be obtained for Mach's number in a standard condition M_0 = y_1^5, y_1^<9/2>, y_1^4, y_1^<7/2>, y_1^3, y_1^<5/2>, y_1^2, y_1^<3/2>, y_1, y_1^<1/2>, 1, y_1^<-1/2>, y_1^<-1>, y_1^<-3/2>, y_1^<-2>, y_1^<-5/2>, y_1^<-3>, y_1^<-7/2>, y_1^<-4>, y_1^<-9/2>, y_1^<-5> respectively, when the x-component of velocity is given properly, the other components of velocity, the pressure, the stress, the temperature and the variation of density can be obtained from above differential equations. When the temperature varies, the nessesary corrections must be inserted in the starting equations and calculation must be continued similarly as before. By repeating the same process, the required solutions can be obtained. As results of this calculations, the author obtained the effect of aspect ratio on the coefficient of frictional resistance of a plate placed parallel to the flow, the mechanism of turbulent flow and the fact that the turbulent motion is originated by the effect of compressibility.
- 明治大学の論文
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