Tham khảo tài liệu 'computational fluid dynamics harasek part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 354 Computational Fluid Dynamics Uj t ui u j - uj 0 uj 0 t- ti 1 - s ti 1 2S j - uj uj t e 0 s t eft- s ti 1 -S t e íí 1 - s ti 1 s 43 where i 0 . N -1 j 1 . m Uj 0 is a known value of the initial control at the initial time uj uj1 the spacing s is chosen empirically. In industrial applications the function of the GTN equipment status is often a function of shaft speed variation for all CFSs. It is difficult to calculate the integral of expenses 41 in the constructed optimization model 41-43 analytically. Therefore this integral is calculated numerically. The widely known method of trapezoids is considered quite acceptable as applied to this case . fig .6b r N-1 J u JZ t u t dt Z0 u t0 AtyZ u t0 i -At ZN u tN . 44 0 i 1 Thus for some set of discrete controls u0 u . uN 1 formula 44 allows calculating the quality functional J u0 u1 . uN-1 . Hence the problem of finding an optimal control 41-43 can be replaced with an equivalent problem of nonlinear programming with respect to independent vectors u0 u1 . uN-1 N-1 J u0 u1 . uN-1 u0 y Z ui uN-1 min 45 i 1 subject to the conditions considering 43 i m mavbr 1 - T spedfiol I i i-1 spedfiM I - I u eU u e R max u nconstr Umin _ j. Uj min u Pconsfr Umax _ j. j 1 m 46 i 1 N -1 WW 0 1 N -1 It7t j- k i specified i i 0 1 N-1 u u . u e Q IWi e R 0 . w j u u . u wo . _ _ 47 j 1 l Wj u0 wmafed . j l 1 k i 1 N where us pdiied e Rm and usp fed e Rm are given vectors of the minimum and maximum values null md of control parameters as a rule these vectors are time-independent nconstr e Rm is a given constraint on the maximum step of a single j-th control change in time. The numerous constrains in 47 are attributed to the requirement that variation of GTN operating parameters on transition from one time layer to the next one should be smooth. One should be reminded here that calculations of expenses Zi u for gas transportation through the GTN are enabled by the CFD-simulator. .
