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- れいな じゅふく
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1 aance course in Reacie Flui Mechanics () Lecure (4/8,5) Flui ynamics of reacing flow Basic Equaions of reacing flow.. Moeling of muli-scale / muli-hysics henomena (Re) (Ma) log (Kn) s. / log
2 Mass: Momenum: Energy: Eq.of gas sae: Chemical sices Chemical reacion ω fu B ex E R Arrhenius law M fu fu ν fu M ox ox ν ox Equaion of sae R W, W C W W C C R CR R W W Ci i mol m -3 Cmol m -3 Wi i W i i i i R
3 Mass ransor ( ) ϖ & ( ) ϖ & ( ) ϖ & ;,, ϖ & ( ) conecion iffusion ( ) ( ) ϖ & Ficks law µ Sc Sc Le Pr Re 5/6 ( ) ( ) ( ) χ f f W W ( ) ( ) ( ),, f f In case of wo sices ( ) ( ) ( ) ( ) ( )( ) isribuion of mole fracion Ficks law Mass ransor
4 Re.5/6 heory. Enhaly eq. emeraure eq. C Energy ransor h s h λ h Φ q λ h c j h j Q Φ Q R Q R Q& reac h h o o ( h c, ) h h, c, o h ϖ& & Q reac. - q λ j C C, k λ C ( C ) k Le λ Ma Energy ransor ξ CH 4 CH 4 O Mixure fracion emeraure ensiy HEP H(SP)(P) SP QSH H S > GHS G(SP)(S) SP G H c H h n c S <
5 Sream lines ouer flame emeraure air air remixe flow air Inner flame fuel isance along sreamline yical burner flame remixe flame (inner flame) iffusion flame (ouer flame) hea & mass ransor Sae Chemical Energy Inu sices Free energy minimizing Mass/energy conseraion Sices mixure fracion Mass ransfer Sae hermal Energy Ouu sices Inu hea Hea ransfer emeraure Ouu hea combusion see ail en fron en of reacie zone xflame roagaion see Proucs (burn gas) reacion finishing sace in x Reacie Reacie zone zone Reacans (unburn gas) reacion saring x sace in
6 Re.5/6 Nussel no. Pranl no. Schmi no. Lewis no. hλ Nu L ν Pr k ν Sc k Le Sc Pr h hea ransfer coefficien λhermal conuciiy kineic iscosiy k em. iffusion conuciiy mass iffusion conuciiy
7 (rimal) amköhler no. τ r ime scale of flow Karlois no. U K η U y urbulen amköhler no. a τ τ c l S u' δ τ r τ c ickness of heaing zone: τ c ime scale of reacion combusion sees λ η c S S urbulen lengh scale u elociy fracuaion: flame hickness. Ex. Ex. Ex. Ex. Ex.
8 . ) ) ) ex. ex. ex. M z x 3 x z?? x y z. F F ε x ( η ) x G ( x), f δf λ δg ()() or f σ /} /}
9 . Problems owars Pea-scale HPC Alicaions LESM 7 LESMflamele 7. iscree role Moel LES (x, u) (x, u) Paricle race M Aroach r r C u u y C r Ckσ C µ y 3 r r F y b y x C b r > () Peer J. O Rourke,e.al., 987 SAE 8789 x
10 .3 Problems owars Pea-scale HPC for Phase inerfaces LESLS () (SGS) (LBMPF) () θ () LES() for Soli inerfaces () -.3 Inerface moel by leel-se hase fiel G-equaion moel for remixe flame roagaion (Williams 985 Kersein 988) G u j G x j S L G Progress ariable moel wih hyerbolic angen Aroximaion (Inage e.al. 989) η 8 S η δ ( η) Γ η S L ( ) ( ) b u u S L c Σhω c (κ/x)
11 .3 L PF couling hin inerface assumion φ r φ s φ η δp P P τ τ δη ( ) φ r δp φ s φ λ δφ ε r ( φ φ ) φ εn ( φ ) δ δp ε r φ φ φ εn φ δφ 4δ ε r r n φ( φ ) εn ( φ ) δ ( )( ) ( ) Lglobal soluion PHlocal soluion λ τ for η φ, φ x η anh δ λε Γ ( τ ) φ( ) :iffusion facor.3 Couling o conseraion lows Couling roceure for mulile hases Leel-se PM Phase fiel AB : ex. : ex.
12 .4 large scale ~ roucion small scale ~ issiaion NS ()
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
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