By Hugo A. Jakobsen

ISBN-10: 3319050915

ISBN-13: 9783319050911

ISBN-10: 3319050923

ISBN-13: 9783319050928

Chemical Reactor Modeling closes the space among Chemical response Engineering and Fluid Mechanics. the second one variation includes volumes:

Volume 1: Fundamentals.

Volume 2: Chemical Engineering Applications

In quantity 1 many of the basic thought is gifted. a number of numerical version simulation software examples are given to clarify the hyperlink among concept and purposes. In quantity 2 the chemical reactor apparatus to be modeled are defined. numerous engineering versions are brought and discussed.

A survey of the often used numerical tools, algorithms and schemes is supplied. a number of useful engineering purposes of the modeling instruments are offered and mentioned. The operating rules of numerous experimental innovations hired so that it will get information for version validation are outlined.

The monograph is predicated on lectures usually taught within the fourth and 5th years graduate classes in delivery phenomena and chemical reactor modeling and in a put up graduate direction in sleek reactor modeling on the Norwegian collage of technology and expertise, division of Chemical Engineering, Trondheim, Norway. the target of the e-book is to offer the basics of the single-fluid and multi-fluid versions for the research of unmarried and multiphase reactive flows in chemical reactors with a chemical reactor engineering instead of mathematical bias. geared up into thirteen chapters, it combines theoretical facets and useful purposes and covers the various contemporary learn in numerous components of chemical reactor engineering. This e-book encompasses a survey of the fashionable literature within the box of chemical reactor modeling.

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**Additional info for Chemical Reactor Modeling: Multiphase Reactive Flows**

**Sample text**

F ›k;1 'ðf Þ 'viscous ' Nomenclature Sub-grid kinematic viscosity in LES (m2/s) Net source term denoting the loss of the property ˆ caused by inelastic collisions Calculation domain Continuous size domain › ¼ ½0; $max in sectional methods Imaginary arbitrary volume in phase space, used in classical mechanics Rotational speed, › ¼ jXj (s-1) Angle between the velocity C and the normal vector n in collision cylinder analysis Angular velocity (rad/s) Interpolation formula parameter Rotational speed of the shaft (rad/s) Species mixture mass fraction ðÀÞ The angular frequency of the applied current in ECT (radians/s) Eddy-bubble collision probability density (s m31 ½m) Eddy-bubble collision probability density, differential because it is eddy-bubble interaction specific (s m31 ½m) Weight of the delta function centered at the characteristic particle size $ﬁ Shaft angular velocity (rad/s) Macroscopic breakage rate (s m1 3 ) Total breakage rate for particles of size di ðs m1 3 Þ Macroscopic coalescence rate (s-1 m-3) Bubble–bubble collision density ðm13 sÞ Buoyancy collision density ðs m1 3 Þ Collision density caused by turbulent motion and expressed in the framework of a discrete numerical scheme ðs m1 3 Þ Collision density due to laminar shear ðs m1 3 Þ Collision integral for viscosity in kinetic theory ðÀÞ Eddy-bubble collision rate (s m1 3 ) 1 Modified particle collision density (m3 s ½m ½m) Collision integral for self-diffusion in kinetic theory ðÀÞ Collision integral for diffusion in kinetic theory ðÀÞ 1 Modified particle collision density (m3 s ½m ½m) 1 Single particle collision density (s ½m ) Collision integral for thermal conductivity in kinetic theory ðÀÞ Presumed PDF ðÀÞ Viscous dissipation function (sÀ2 Þ) Basis (or trial) functions in truncated series expansion Nomenclature ' ' ' / / / / / / / / / /ðrÞ 'eff 'I ð–yv Þ /i 'o ðy–Þ /r /s 'v ð–yv Þ /1;2 'total /I;c P"g Pgp pi;j Pkg ˆ ˆ ˆ ˆ ˆ ˆðr; c; tÞ lvii Perturbation function in Enskog expansion Potential energy per unit mass (m2/s2) The phase field or order parameter used in the phase field method Blade attachment angle (°) or (rad) Coefficient in the Zehner and Schlünder model for the convective heat transfer ðÀÞ Local instantaneous source term of the generalized quantity ˆ Model parameter Polar angle Polar coordinate Potential function in time-splitting method The electrical potential distribution or voltage (V) Unknown variable in TDMA outline Limiter function in TVD schemes Effective global energy dissipation function (s-2) Non-dimensional function characteristic for the inner log-law or inertial sub-layer ðÀÞ Fugacity coefficient for species i Non-dimensional function characteristic for the outer layer ðÀÞ The off-axis angle in the PDA optical arrangement ( ) Sphericity of solid particles ðÀÞ Non-dimensional function characteristic for the viscous sublayer ðÀÞ The normalized cross-correlation function in F-OPT theory ðÀÞ Entropy production rate (kJ/m3 s K) Rate of production of the quantity ˆk per unit mass at each point on AI Interaction term in "g model equation for gas phase (kg/m s4) Interaction term in kgp transport equation (kg/m s3) Weighted breakage function Interaction term in kg model equation for gas phase (kg/m s3) Generalized conserved quantity Microscopic molecular property of dilute gas (referred to a single molecule) in elementary kinetic theory Polar angle The elevation angle in the PDA optical arrangement (°) Variable in simplified PD algorithm solution in SQMOM A generalized physical function that denotes a property of the molecules located at time t near r with a velocity near c lviii ˆðr; c; tÞ q q q q qL ðsÞ qp ¾k ¾ ¾ ¾ ¾0AT ¾1 ¾A ðXÞ ¾I ¾i ¾2i ¾s ðdÞ ¾t ðdÞ ¾ ¾AT ¾A ¾2A ¾sr ¾sr ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ cp ¿ tg ¿ tgp Nomenclature Generalized particle property function located near r, with a velocity near c at time t A parameter used in LD theory ðÀÞ Instantaneous field mass density (kg/m3) Spectral reflectivity, q ¼ Gref =G ðÀÞ The electric charge density measured in coulombs per cubic metre (C/m3) Autocorrelation coefficient ðÀÞ Mass density of particle (kg) kminus; turbulence model parameter ðÀÞ Stefan–Boltzmann constant, ¼ 5:67 Â 10À8 (W/m2 K4) The electrical conductivity given in siemens per metre (S/m) Variable in simplified PD algorithm solution in SQMOM Alternative total (scattering) collision cross section (m2) Collision diameter used in kinetic theory (m) Differential scattering cross section (m2) Surface tension (N/m) Standard deviation or rms velocity measured by LDA (m/s) Unbiased variance of "vi measured by LDA (m2/s2) Surface restoring pressure of a bubble of size d (Pa) Average deformation stress for bubbles of size d (Pa) k- turbulence model parameter ðÀÞ Total scattering cross section (m2) Standard deviation, the squared root of the variance ðÀÞ Variance, a statistical measure of the dispersion of data about the mean ðÀÞ Characteristic Lennard-Jones diameter (Å) Characteristic Lennard-Jones energy (J) Kolmogorov micro time scale (s) A geometric parameter used in LD theory ðÀÞ Average residence time of the elements in surface renewal theory (s) The cross-correlation time delay between two signals in F-OPT theory (s) Time domain Time variable in history force expression (s) Tortuosity of porous medium ðÀÞ Transmissivity, ¿ ¼ Gtrans =G ðÀÞ Characteristic particle–particle collision time (s) Time scale of large turbulent eddies in gas phase (s) Interaction time between particle motion and gas fluctuation or eddy life time seen by a particle (s) Nomenclature ¿1 ¿!

P ^ pk;I ai fipure J J(f) k ‘ ~ esK D ~ esr D ~ sk D e ij C e L ij e ij R e S ij M ^ YðCÞ Dsr A xliii Symmetric multi-component Fickian diffusivity for the s and r pair of gases [26]: Chap. 2, Curtiss (1968), [27]: Chap. 187) Boltzmann constant (J/K) Lagrange polynomial Effective Knudsen diffusivity of species s in porous medium (m2/s) Effective bulk diffusivity of binary pair s – r in porous medium (m2/s) Maxwell–Stefan diffusivities (m2/s) Residual stress tensor in LES (Pa) Leonard stress tensor in LES (Pa) Residual stress tensor in LES (Pa) The large scale strain-rate tensor in LES (m2/s) Mass (kg) Space for the norms measuring the residual in C Symmetric multi-component Fickian diffusivity for the s and r pair of gases [9]: Chap.

ICAI h. iXk qk h. iA h. ie h. iM h. iV h. iAI hˆk iXT k hˆk iXVk hˆk iTk hˆk iVk B L j. j rÁ r rI rc ðÞ rr ðÞ f h.

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