$$$$ PRIM NOTICE CHAT 11/09/12 21:17:44 7124 DATE 11/09/12 Operateur PRIM Voir aussi : a) EVOL2 = PRIM EVOL1 ; b1) RCHPO1 RCHPO2 = 'PRIM' 'PERFMONO' CHPO1 CHPO2 CHPO3 CHPO4 ; b2) RCHPO1 RCHPO2 RCHPO3 RCHPO4 RCHPO5 = 'PRIM' 'PERFMULT' TAB1 CHPO1 CHPO2 CHPO3 CHPO4 ; b3) RCHPO1 RCHPO2 RCHPO3 RCHPO4 (RCHPO5) RCHPO6 = 'PRIM' 'PERFTEMP' TAB1 CHPO1 CHPO2 CHPO3 CHPO4 (CHPO5) (CHPO6) ; ou RCHPO1 RCHPO2 RCHPO3 (RCHPO5) RCHPO6 = 'PRIM' 'PERFTEMP' TAB1 CHPO1 CHPO2 CHPO3 (CHPO5) (CHPO6) ; c) RMAT1 = 'PRIM' 'CONSPRIM' MAIL1 LMOT1 LMOT2 CHPO1 CHPO2 CHPO3 CHPO4 ; d) RCHPO8 RCHPO7 RCHPO6 RCHPO5 RCHPO4 RCHPO3 RCHPO2 RCHPO1 = 'PRIM' 'TWOFLUID' CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 CHPO10 CHPO11; e) RCHD1 RCHD2 RCHV1 RCHV2 RCHP1 RCHP2 RCHT1 RCHT2 = 'PRIM' 'DEM' TABPGAS CHPAL1 CHPAL2 CHPARN1 CHPARN2 CHPAGN1 CHPAGN2 CHPARET1 CHPARET2 CHPTGUE1 CHPTGUE2 EPS ; f) RCHPO0 RCHPO1 (RCHPO2) = 'PRIM' 'GFMP' TAB1 CHPO0 CHPO1 CHPO2 CHPO3 (CHPO4 CHPO5) ; a) The PRIMITIVE operator compute the value of the primitive of an EVOLUTUION object which can represent a function. This function must be defined for increasing abscissa. The value of the primitive of each function for the first abscissa is set to 0. WARNING : the resulting EVOLUTION is given at initial evolution abscissa it may not correctly represent the primitive in between b) Evaluation of the primitive variables (i.e. pressure, speed, temperature...) from the conservative variables (i.e. mass density, momentum, energy, mass density of each species), in the modelling of the Euler Equations or Navier-Stokes Equations. b1 ----------------- | 1st model | ----------------- Thermally perfect gas; specific heats cp and cv do not depend on temperature. RCHPO1 RCHPO2 = 'PRIM' MCLE1 CHPO1 CHPO2 CHPO3 CHPO4 ; Contents : _____________ MCLE1 : MOT object, 'PERFMONO'. CHPO1 : CHPOINT object that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT object that contains the momentum (kg/s/m^2; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). CHPO3 : CHPOINT object that contains the total volumic energy (J/m^3; one component, 'SCAL'). CHPO4 : CHPOINT object that contains the gas gamma (one component, 'SCAL'). RCHPO1 : CHPOINT object that contains the velocity (m/s; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). RCHPO2 : CHPOINT object that contains the pressure (Pa; one component, 'SCAL'). Remarks : ___________ 1) We check that: * the pressure is positive, * 1 < gamma < 3, * the CHPOINTs are defined on the same underlying space. 2) CHPO1, CHPO2, CHPO3 are the conservative variables of the Euler Equation. b2 ----------------- | 2nd model | ----------------- Mixture of thermally perfect gas (cp and cv are temperature independent). RCHPO1 RCHPO2 RCHPO3 RCHPO4 RCHPO5 = 'PRIM' MCLE1 TAB1 CHPO1 CHPO2 CHPO3 CHPO4 ; Contents : __________ MCLE1 : MOT object, 'PERFMULT'. TAB1 : TABLE object that contains: * the names of the species explicitly treated (LISTMOTS object); * the name of the species non-explicitly treated; TAB1 . 'ESPNEULE' (MOT object); * the specific heats of each species: TAB1 . 'CP' (TABLE object) TAB1 . 'CV' (TABLE object). CHPO1 : CHPOINT containing the total mass density (kg/m^3; one component, 'SCAL'). CHPO2 : CHPOINT containing the momentum ( kg/s/m^2; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). CHPO3 : CHPOINT containing the total volumic energy (J/m^3; one component, 'SCAL'). CHPO4 : CHPOINT containing the mass densities of the species explicitly 'splitted' in the Euler Equations (kg/m^3; their names are in TAB1 . 'ESPEULE'). RCHPO1 : CHPOINT containing the speed (m/s; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ', 'UZ '). RCHPO2 : CHPOINT containing the pressure (Pa; one component, 'SCAL'). RCHPO3 : CHPOINT containing the temperature (K; one component, 'SCAL'). RCHPO4 : CHPOINT containing the mass fractions of the different species (the same components of CHPO4). RCHPO5 : CHPOINT containing the "gamma" of the gas (one component, 'SCAL'). Remarks : _________ 1) We check that * pressure is positive * 1 < gamma < 3 * 0 < Y_i < 1 * sum Y_i < 1 * CHPOINTs have the same underlying space. 2) CHPO1, CHPO2, CHPO3, CHPO4 are the conservative variables of the Euler Equations. Example : _________ To show the structure of TAB1, let us consider the following example. PGAZ = 'TABLE' ; * *** GAS: H_2, O_2, H_2O, N_2 * * CP, CV (J/Kg/K @ T = 3000) * * **** Species in the Euler Equations. * PGAZ . 'ESPEULE' = 'MOTS' 'H2 ' 'O2 ' 'H2O ' ; * * Remark: 4 LETTERS |____| |____| |____| * * **** Species not explicitly treated * PGAZ . 'ESPNEULE' = 'N2 '; * 4 LETTERS |____| PGAZ . 'CP' = 'TABLE' ; PGAZ . 'CP' . 'H2 ' = .18729066D+05 ; PGAZ . 'CP' . 'O2 ' = .11886820D+04 ; PGAZ . 'CP' . 'H2O ' = .31209047D+04 ; PGAZ . 'CP' . 'N2 ' = .12993995D+04 ; PGAZ . 'CV' = 'TABLE' ; PGAZ . 'CV' . 'H2 ' = .14571861D+05 ; PGAZ . 'CV' . 'O2 ' = .92885670D+03 ; PGAZ . 'CV' . 'H2O ' = .26589930D+04 ; PGAZ . 'CV' . 'N2 ' = .10024563D+04 ; b3 ----------------- | 3rd model | ----------------- Thermally perfect gas / mixture of thermally perfect gases (are temperature dependent). Multi-component gas: RCHPO1 RCHPO2 RCHPO3 RCHPO4 (RCHPO5) RCHPO6 = 'PRIM' MCLE1 TAB1 CHPO1 CHPO2 CHPO3 CHPO4 (CHPO5) (CHPO6) ; Mono-component gas: RCHPO1 RCHPO2 RCHPO3 (RCHPO5) RCHPO6 = 'PRIM' MCLE1 TAB1 CHPO1 CHPO2 CHPO3 (CHPO5) (CHPO6) ; Contents : __________ MCLE1 : MOT object, 'PERFTEMP'. TAB1 : TABLE object that contains: * the name of the species non-explicitly treated in Euler's Equations in TAB1 . 'ESPNEULE' (MOT object); * the names of the species explicitly treated in TAB1 . 'ESPEULE' (LISTMOTS object); * the degree of the polynomial cv=cv(T), in TAB1 . 'NORD' (ENTIER object, >= 0) * the properties of each gas 'ESPI', in TAB1 . 'ESPI' (TABLE object): - TAB1 . 'ESPI' . 'A' (LISTREEL object) which contains the (TAB1.'NORD')+1 coefficients of cv(T), (A0,A1,...); cv are expressed in J/kg/K; - TAB1 . 'ESPI' . 'R' (FLOTTANT object, J/kg/K) the constant of the gas - TAB1 . 'ESPI' . 'H0K', (J/kg, FLOTTANT object) the enthalpy of formation at 0K (numerical quantity) * TAB1 . 'SCALPASS' = if existing, the names of the transported passive scalars CHPO1 : CHPOINT containing the total mass density (kg/m^3; one component, 'SCAL'). CHPO2 : CHPOINT containing the momentum ( kg/s/m^2; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). CHPO3 : CHPOINT containing the total volumic energy (J/m^3; one component, 'SCAL'). CHPO4 : CHPOINT containing the mass densities of the species explicitly 'splitted' in the Euler Equations (kg/m^3; their names are in TAB1 . 'ESPEULE'). (CHPO5) : CHPOINT containing rho * (passive scalars) (their names are in TAB1 . 'SCALPASS'). (CHPO6) : CHPOINT containing a reference temperature (temperature of first trial for the Newton method, used in order to evaluate the temperature from the total energy) (K; one component, 'SCAL'). RCHPO1 : CHPOINT containing the speed (m/s; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ', 'UZ '). RCHPO2 : CHPOINT containing the pressure (Pa; one component, 'SCAL'). RCHPO3 : CHPOINT containing the temperature (K; one component, 'SCAL'). RCHPO4 : CHPOINT containing the mass fractions of the different species (the same components of CHPO4). (RCHPO5) : CHPOINT containing the splitted passive scalars (their names are in TAB1 . 'SCALPASS'). RCHPO6 : CHPOINT containing the "gamma" of the gas (one component, 'SCAL'). Remarks : _________ 1) We check that * pressure and temperature are positive * 1 < gamma < 3 * 0 < Y_i < 1 * sum Y_i < 1 * CHPOINTs have the same underlying space. 2) CHPO1, CHPO2, CHPO3, CHPO4 are the conservative variables of the Euler Equations. Example : _________ To show the structure of TAB1, let us consider the following example. PGAZ = 'TABLE' ; * *** GAS: H_2, O_2, H_2O, N_2 * * * **** Species in the Euler Equations. * PGAZ . 'ESPEULE' = 'MOTS' 'H2 ' 'O2 ' 'H2O ' ; * * Warning: 4 LETTERS |____| |____| |____| * * **** Species not explicitly treated * PGAZ . 'ESPNEULE' = 'N2 '; * 4 LETTERS |____| * **** Polynomial degree * PGAZ . 'NORD' = 4 ; * **** Table object which contain gases properties PGAZ . 'H2 ' = 'TABLE' ; PGAZ . 'H2O ' = 'TABLE' ; PGAZ . 'N2 ' = 'TABLE' ; PGAZ . 'O2 ' = 'TABLE' ; * **** R (J/Kg/K) * PGAZ . 'H2 ' . 'R' = 4130.0 ; PGAZ . 'H2O ' . 'R' = 461.4 ; PGAZ . 'N2 ' . 'R' = 296.8 ; PGAZ . 'O2 ' . 'R' = 259.8 ; * **** Polynomials regressions * PGAZ . 'H2 ' . 'A' = 'PROG' 9834.91866 0.54273926 0.000862203836 -2.37281455E-07 1.84701105E-11 ; PGAZ . 'H2O ' . 'A' = 'PROG' 1155.95625 0.768331151 -5.73129958E-05 -1.82753232E-08 2.44485692E-12 ; PGAZ . 'N2 ' . 'A' = 'PROG' 652.940766 0.288239099 -7.80442298E-05 8.78233606E-09 -3.05514485E-13 ; PGAZ . 'O2 ' . 'A' = 'PROG' 575.012333 0.350522002 -0.000128294865 2.33636971E-08 -1.53304905E-12; * **** "Enthalpies" (or energies) of formations a 0K (J/Kg) * PGAZ . 'H2 ' . 'H0K' = -4.195D6 ; PGAZ . 'H2O ' . 'H0K' = -1.395D7 ; PGAZ . 'N2 ' . 'H0K' = -2.953D5 ; PGAZ . 'O2 ' . 'H0K' = -2.634D5 ; c) In the modelling of the Euler Equations or Navier-Stokes Equations, Jacobian of the conservative variables with respect to the primitive variables (single-component calorically perfect gas). RMAT1 = 'KONV' 'VF' 'PERFMONO' 'CONSPRIM' MAIL1 LMOT1 LMOT2 CHPO1 CHPO2 CHPO3 CHPO4 ; LMOT1 : LISTMOTS object Name of conservative variables, respectively mass density, momentum, total energy (per volume unity) LMOT2 : LISTMOTS object Name of primitive variables, respectively mass density, velocity, pressure MAIL1 : geometric support (SPG) of the CHPOINTs CHPO1 : CHPOINT object, mass density (one component, 'SCAL'). CHPO2 : CHPOINT object, velocity (2/3 components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT object, pressure (one component, 'SCAL'). CHPO4 : CHPOINT object, "gamma" (ratio of specific heat capacities) (one component, 'SCAL'). RMAT1 : MATRIK object, Jacobian of conservative variables with respect to the primitive ones. SPG = MAIL1. Primal variables = LMOT2. Dual variables = LMOT1. d) Evaluation of the primitive variables (i.e. void fraction, vapour velocity, liquid velocity, pressure, vapour temperature, liquid temperature) from the conservative variables (i.e. mass density, momentum, energy of each phase), in the modelling of the one-pressure compressible six-equation two-fluid model, only for water and air mixtures. ----------------- Air is suppose a thermally perfect gas and water is characterized by the Stiffened gas equation of state; specific heats cp and cv do not depend on temperature. RCHPO8 RCHPO7 RCHPO6 RCHPO5 RCHPO4 RCHPO3 RCHPO2 RCHPO1 = 'PRIM' MCLE1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 CHPO10 CHPO11; Contents : _____________ MCLE1 : MOT object, 'TWOFLUID'. CHPO1 : CHPOINT object that contains the gas total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT object that contains the liquid total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO3 : CHPOINT object that contains the gas momentum (kg/s/m^2; two components in 2D, 'UVX ','UVY ', three components in 3D, 'UVX ','UVY ','UVZ '). CHPO4 : CHPOINT object that contains the liquid momentum (kg/s/m^2; two components in 2D, 'ULX ','ULY ', three components in 3D, 'ULX ','ULY ','ULZ '). CHPO5 : CHPOINT object that contains the gas total volumic energy (J/m^3; one component, 'SCAL'). CHPO6 : CHPOINT object that contains the liquid total volumic energy (J/m^3; one component, 'SCAL'). CHPO7 : CHPOINT object that contains the void fraction evaluated at the previous time step (one component, 'SCAL'). CHPO8 : CHPOINT object that contains the gas temperature evaluated at the previous time step (K; one component, 'SCAL'). CHPO9 : CHPOINT object that contains the liquid temperature evaluated at the previous time step (K; one component, 'SCAL'). CHPO10 : CHPOINT object that contains the pressure correction term for the CATHARE model (one component, 'SCAL'). CHPO11 : CHPOINT object that contains the virtual mass correction term for the CATHARE model (one component, 'SCAL'). RCHPO1 : CHPOINT object that contains the void fraction (one component, 'SCAL'). RCHPO2 : CHPOINT object that contains the gas velocity (m/s; two components in 2D, 'UVX ','UVY ', three components in 3D, 'UVX ','UVY ','UVZ '). RCHPO3 : CHPOINT object that contains the liquid velocity (m/s; two components in 2D, 'ULX ','ULY ', three components in 3D, 'ULX ','ULY ','ULZ '). RCHPO4 : CHPOINT object that contains the pressure (Pa; one component, 'SCAL'). RCHPO5 : CHPOINT object that contains the gas temperature (K; one component, 'SCAL'). RCHPO6 : CHPOINT object that contains the liquid temperature (K; one component, 'SCAL'). RCHPO7 : CHPOINT object that contains the gas density (kg/m^3; one component, 'SCAL'). RCHPO8 : CHPOINT object that contains the liquid density (kg/m^3; one component, 'SCAL'). RCHPO9 : CHPOINT object that contains the pressure correction following CATHARE model (Pa; one component, 'SCAL'). Remarks : ___________ 1) We check that: * the pressure is positive, * the CHPOINTs are defined on the same underlying space. 2) CHPO1, CHPO2, CHPO3, CHPO4, CHPO5, CHPO6 are the conservative variables of the one-pressure compressible six-equation two-fluid model e) Evaluation of the primitive variables (i.e. densities of unburnt and burnt mixture, speed of burnt and unburnt mixture, etc.) from conservative variables related to the Reactive Discrete Equation Method for combustion modelling. Here fresh mixture (upstream of the flame) and burnt mixture (downstream of the flame) are denoted as 1 and 2, correspondingly, and the primitive and conservative variables are assigned to each mixture. The volume fraction \alpha_1 is equal to 1 in the fresh mixture, and 0 - in the burnt mixture, while \alpha_2 is equal to 0 in the fresh mixture, and 1 - in the burnt mixture. RCHD1 RCHD2 RCHV1 RCHV2 RCHP1 RCHP2 RCHT1 RCHT2 = 'PRIM' 'DEM' TABPGAS CHPAL1 CHPAL2 CHPARN1 CHPARN2 CHPAGN1 CHPAGN2 CHPARET1 CHPARET2 CHPTGUE1 CHPTGUE2 EPS ; Arguments: ----------- TABPGAS : TABLE which contains * 'SPECIES' - the species names * 'CHEM_COEF' - chemical coefficients of the considered reaction * 'MASSFRA' initial and final mass fraction of the first appearing in 'SPECIES', final mass fractions of the other (???) species with positive coefficients in 'CHEM_COEF', initial mass fractions for the species with negative coefficients in 'CHEM_COEF' * 'RUNIV' = universal gas constant, * ESPi = table containing the properties of the species ESPi * 'TMAX' maximum temperature for cv expansion; for T>'TMAX', cv(T)=cv('TMAX') * ESPI . 'A' CV_i = \sum_{j=0,k} A_{i,j} T^j * ESPI . 'W' (Kg/mole) * ESPI . 'H0K' e_{0,i} = h_{0,i} = h_{T_0,i} - {R_i * T_0 + {\sum_{j=0,k} A_{i,j} / (j+1) T_0^(j+1)}}; CHPAL1 : CHPOINT which contains the volume fraction alpha_1 of 1 (one component, 'SCAL'). CHPAL2 : CHPOINT which contains the volume fraction alpha_2 of 2 (one component, 'SCAL'). CHPARN1 : CHPOINT which contains the alpha_1 * density of 1 (one component, 'SCAL'). CHPARN2 : CHPOINT which contains the alpha_2 * density of 2 (one component, 'SCAL'). CHPAGN1 : CHPOINT which contains the alpha_1 * momentum of 1 (two components, 'UX', 'UY'). CHPAGN2 : CHPOINT which contains the alpha_2 * momentum of 2 (two components, 'UX', 'UY'). CHPARET1: CHPOINT which contains the alpha_1 * total energy of 1 (one component, 'SCAL'). CHPARET2: CHPOINT which contains the alpha_2 * total energy of 2 (one component, 'SCAL'). CHPTGUE1: CHPOINT which contains the guess value for the temperature of 1 (one component, 'SCAL'). CHPTGUE2: CHPOINT which contains the guess value for the temperature of 2 (one component, 'SCAL'). EPS : FLOTTANT such that if ALPHA_i < EPS, we can say that species i does not exists Results: --------- RCHD1 : CHPOINT which contains the density of 1 RCHD2 : CHPOINT which contains the density of 2 RCHV1 : CHPOINT which contains the speed of 1 RCHV2 : CHPOINT which contains the speed of 2 RCHP1 : CHPOINT which contains the pressure of 1 RCHP2 : CHPOINT which contains the pressure of 2 RCHT1 : CHPOINT which contains the temperature of 1 RCHT2 : CHPOINT which contains the temperature of 2 f) Evaluation of the primitives variables (i.e. density, velocity, mass fractions) from the conservative variables in the case of the modelling of interface propagation in a two phase medium, via the Ghost Fluid method for the poor (GFMP, Stiffened gas). RCHPO0 RCHPO1 (RCHPO2) = 'PRIM' 'GFMP' TAB1 CHPO0 CHPO1 CHPO2 CHPO3 (CHPO4 CHPO5) ; TAB1 : TABLE which contains : * the species names explicitly involved in the Euler equations in TAB1 . 'ESPEULE' (LISTMOTS) ; * the name of the species which is not involved (TAB1 . 'ESPNEULE' (MOT)) ; * gamma and pinf in the region phi < 0 TAB1 . 'MGAM' (LISTREEL) ; TAB1 . 'MPIN' (LISTREEL) ; * gamma and pinf in the region phi > 0 TAB1 . 'PGAM' (LISTREEL) ; TAB1 . 'PPIN' (LISTREEL) ; NB The first value in LISTEEL TAB1 . 'MGAM', ... is the one of the species TAB1 . 'ESPNEULE'; the others are the ones in TAB1 . 'ESPEULE'. CHPO0 : CHPOINT, phi (one component, 'SCAL'). CHPO1 : CHPOINT, density (one component, 'SCAL'). CHPO2 : CHPOINT, momentum (2 components in 2D, 'UX ','UY '); CHPO3 : CHPOINT, total energy per unit volume (one component, 'SCAL'). CHPO4 : CHPOINT, densities of the single species (components = TAB1. 'ESPEULE'). CHPO5 : CHPOINT, volume fractions (components = TAB1. 'ESPEULE'). RCHPO0 : CHPOINT, speed; (2 components in 2D, 'UX ','UY '); RCHPO1 : CHPOINT, pressure; RCHPO2 : CHPOINT, mass fraction (components = TAB1. 'ESPEULE').
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