Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos

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1 Introducton to Toshhsa Ueda School of Scence for Open and Envronmental Systems Keo Unversty, Japan Combuston Mxng and reacton n hgh vscous flud Applcaton of Chaos Keo Unversty 1 Keo Unversty 2 What s reactve flows? The flows wth reactons combuston ar polluton chemcal reactor bo reactor Keo Unversty 3 Keo Unversty 4

2 Most mportant pont of reactve fluds Bass of mult-component flud flud conssts of reactants and products speces concentraton changes locally and temporally wth heat release or absorpton Chemcal reacton mechansm Flud dynamcs Thermodynamcs Transport phenomena Keo Unversty 5 Keo Unversty 6 Concentraton and fracton Understandng reactve flows Concentraton: amount / unt volume mass concentraton m [kg/m 3 ] molar concentraton c [mol/m 3 ] Fracton: rato of concentraton mass fracton Y = m m j molar fracton X = c c j flow moton velocty and pressure u, v, w, p energy transport temperature T speces transport mass fracton of chemcal speces Y Keo Unversty 7 Keo Unversty 8

3 Governng equatons Conservaton equatons of physcal moton Conservaton equatons of physcal moton mass, momentum, energy, chemcal speces Equatons of chemcal varatons Chemcal reacton formula Rate equatons for chemcal reacton concentraton dependence temperature dependence Keo Unversty 9 Mass: Momentum: energy: chemcal speces: ρ ρu ρv ρw = 0 t x y z Du p τxx τyx τzx ρ = Dt x x y z Dh Dp ρ = q + ρ U h + Dt Dt dh = C dt DY ρ = ( ρ U ) + w Dt + Φ ( : for prefect gases) p Keo Unversty 10 Reacton model Reacton model CH 2 H O + CO 4 + O2 2 2 Reacton rate equaton 3 dcch4 a b ω [ m s] = = kc c Concentraton : Temperature : CH 2 4 kmol/ CH 4 O2 dt E = a = n E a k A'exp AT exp R0T R0T Keo Unversty 11 Passve scalar or actve scalar? Passve scalar : scalar varables passve for flow moton Actve scalar : scalar varables actve for flow moton constant propertes Passve scalar varable propertes Actve scalar Keo Unversty 12

4 Passve: constant property Actve: varable property Mass: Momentum: ρ ρu ρv ρw = 0 t x y z Du p τxx τyx τzx ρ = Dt x x y z energy: u, v, w, p Dh Dp ρ = q + ρ U h + + Φ Dt Dt DY chemcal ρ = ( ρ U ) + w Dt speces: Keo Unversty 13 Mass: Momentum: u, v, w, p ρ ρu ρv ρw = 0 t x y z Du p τxx τyx τzx ρ = Dt x x y z energy: Dh Dp ρ = q + ρ U h + + Φ Dt Dt DY chemcal ρ = ( ρ U ) + w Dt speces: (Y, T ), (Y, T ) Keo Unversty 14 Non-dmensonal parameter for reactve flows τ f Damköhler number : Da = τ f :characterstc tme of flud moton (mxng) c :characterstc tme of chemcal reacton c Damköhler number τ >> Da f τ c τ f Da = τ The chemcal reacton s much faster than the flud moton, e.g. engnes, hgh temperature chemcal reactors Flud moton (mxng) determnes the progress n chemcal reacton the chemcal reacton nstantly occurs n reacton surface, as soon as reactants meet c Keo Unversty 15 Reactant A Reactant B Product Reacton surface Keo Unversty 16

5 Damköhler number τ << Da 0 f τ c τ f Da = τ The flud moton s much faster than the chemcal reacton, e.g. low temperature chemcal reactors, boreactors Rate of chemcal reacton determnes the progress n chemcal reacton Reactant A Reactant B Chemcal reacton gradually occurs after Reactants mx well c Product Mxng Mxng due to Molecular dffuson Molecular level mxng necessary for chemcal reacton τ = du µ dy du d ( ρu Newton s s law for momentum transfer τ = µ = ν ) dy dy dt d ρc p Fourer's law for heat conducton q = k = α Fck s law for speces dffuson j = dy dm D dy ( T ) dy Keo Unversty 17 Keo Unversty 18 Mxng Mxng due to advecton Turbulent advecton (Turbulent mxng) mxng by mult-scale vortex moton Chaotc advecton (Chaotc mxng) mxng by stretchng and foldng Mxng When the vscosty s low Mxng due to turbulence s effectve When the vscosty s hgh It s not easy to make the flow turbulent It s necessary to enhance the mxng even n lamnar flow condton Chaotc mxng Keo Unversty 19 Keo Unversty 20

6 Non-steady moton opens new world Perodc moton precse control s possble Turbulent moton transport, such as mxng, s enhanced most reactve systems use turbulent moton engnes furnaces reactors Keo Unversty 21 Non-steady moton opens new world Chaotc advecton enhance lamnar mxng n low Reynolds number area low velocty heat sland ssue low shear bo reactor small area mcro reactor hgh vscous fluds polymer technology non-newtonan fluds artfcal organs Keo Unversty 22 Combuston Combuston plays a key role n many energy devces Combuston Engnes Furnaces Dynamcs of Combuston s a future technology for mprovng combuston Keo Unversty 23 Bunsen flame wth burner rotaton Keo Unversty 24

7 Combuston Combuston over a Clathrate Hydrate Combuston Combuston over a hydrate can be predcted numercally The flame front propagetes upstream drecton Ar Hydrate Keo Unversty 25 Keo Unversty 26 Mxng and reacton n hgh vscous fluds Test secton Mxng and reacton n hgh vscous flud Outer cylnder Inner cylnder Keo Unversty 27 o Reactants Workng flud (glycerne) Sde vew Keo Unversty 28

8 Mxng and reacton n hgh vscous fluds Parameters Workng flud Glycern 1300ml (98wt%) Rato of rad Eccentrcty R R o ε = 0.26 d R o R + [ Fe( CN) ] KFe[ Fe( CN) ] Chemcal reacton Fe 3 + K K Yellow Red Dark blue Mxng and reacton n hgh vscous fluds Flow Feld stretchng chaotc regon Chaotc regon Regular regon foldng regular regon The mxng occurs well The mxng occurs scarcely Keo Unversty 29 Keo Unversty 30 Mxng and reacton n hgh vscous fluds Effect of ntal locatons Both reactants are ntally located n the regular regon Mxng and reacton n hgh vscous fluds Effect of ntal locatons regular-regular regular-chaos chaos-chaos One reactant s n regular, the other n chaotc regon Both reactants are ntally located n the chaotc regon Product Keo Unversty 31 Keo Unversty 32

9 Applcaton of Chaos Applcaton of Chaos Non-element mxer and reactor Non-element mxer and reactor s realzed by usng chaotc advecton (chaotc mxng) Hgh vscosty mxng and reacton n lamnar flow condton Mcro scale and low speed Mcro, mllmeter scale machnes Low shear polymer flud, bo flud Keo Unversty 33 Keo Unversty 34 Applcaton of Chaos Summary ø Stretchng foldng Combuston Mxng and reacton n lamnar flow condton Mcro, mllmeter scale machnes Applcaton of chaos Dffuson normal to the flow drecton s an mportant, nterestng and challengng feld Keo Unversty 35 Keo Unversty 36