The table below shows the conventions used in this document for Latin equation symbols.
Table 22.1: Latin Symbols
Symbol |
Description |
Chapter |
CGS Units |
---|---|---|---|
|
Pre-exponential factor in sticking coefficient expression |
none | |
|
Activity of the k th bulk-phase species |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models |
none |
|
Standard state specific Helmholtz free energy of the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions |
ergs/g |
|
Coefficients of fits to thermodynamic data |
depends on | |
|
Mean specific Helmholtz free energy of a mixture |
ergs/g | |
|
Total surface area of all materials in the reactor |
cm2 | |
Cross-sectional area of the stream tube encompassing the flame |
cm2 | ||
Cross-sectional area available for flow downstream of the shock wave |
cm2 | ||
Surface Area |
cm2 | ||
|
Mean molar Helmholtz free energy of a mixture |
ergs/mole | |
|
Standard state molar Helmholtz free energy of the k th species |
ergs/mole | |
|
Pre-exponential factor in the rate constant of the i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
depends on reaction |
|
Surface area of the m th material |
cm2 | |
|
Temperature exponent in sticking-coefficient expression |
none | |
|
Concentration of the k th species (gas-phase or bulk-phase) |
mole/cm3 | |
Concentration of the k th species (surface-phase) |
mole/cm2 | ||
|
Activation energy in sticking-coefficient expression. By default, Gas-phase Kinetics and Surface Kinetics use activation energies in thermal calories instead of ergs. |
cal/mole | |
|
Specific heat at constant pressure of gas mixture |
Normal Shock Equations, Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
ergs/(g K) |
|
Specific heat capacity at constant pressure of the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
ergs/(g K) |
|
Internal contribution to the mass specific heat of the k th species |
ergs/(g K) | |
|
Rotational contribution to the mass specific heat of the k th species |
ergs/(g K) | |
|
Specific heat capacity at constant volume of the k th species |
ergs/(g K) | |
|
Mean specific heat capacity at constant pressure |
ergs/(g K) | |
|
Mean specific heat capacity at constant volume |
ergs/(g K) | |
|
Compression ratio for the IC HCCI engine model |
none | |
Ratio defined by shock tube equations. |
none | ||
|
Molar heat capacity at constant pressure of the k th species |
ergs/(mole K) | |
|
Turbulent scalar-to-mechanic time scale ratio |
none | |
|
Standard state molar heat capacity at constant pressure of the species |
Thermodynamic Expressions, Stagnation-Flow and Rotating-Disk CVD |
ergs/(mole K) |
|
Translational contribution to the molar heat capacity of the k th species |
ergs/(mole K) | |
|
Vibrational contribution to the molar heat capacity of the k th species |
ergs/(mole K) | |
|
Rotational contribution to the molar heat capacity of the k th species |
ergs/(mole K) | |
|
Molar heat capacity at constant volume of the k th species |
ergs/(mole K) | |
|
Modeling constant for the IEM model |
none | |
|
Mean molar heat capacity at constant pressure |
Thermodynamic Expressions, Partially Stirred Reactor (PaSR) Model |
ergs/(mole K) |
|
Mean molar heat capacity at constant volume |
ergs/(mole K) | |
|
Chemical creation rate of the k th species |
mole/(cm3sec) | |
|
Cylinder bore diameter for the IC HCCI engine model |
cm | |
|
Hydraulic diameter (4 times the ratio of the cross-sectional area of the tube to the perimeter of the tube) |
cm | |
|
Thermal diffusion coefficient of the k th species |
Surface Chemical Rate Expressions, Gas-phase Species Transport Properties , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Opposed-flow and Stagnation Flames , Stagnation-Flow and Rotating-Disk CVD |
g/(cm sec) |
Ordinary multicomponent diffusion coefficient of the species in species |
Surface Chemical Rate Expressions, Gas-phase Species Transport Properties , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames |
cm2/sec | |
|
Binary diffusion coefficient of species in species |
Gas-phase Species Transport Properties, 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
cm2/sec |
|
Mixture-averaged diffusion coefficient of the k th species |
Gas-phase Species Transport Properties, Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
cm2/sec |
|
Chemical destruction rate of the k th species |
mole/(cm3sec) | |
|
Activation energy in the rate constant of the i th reaction. By default, Gas-phase Kinetics and Surface Kinetics uses activation energies in thermal calories instead of ergs. |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
[cal/mole]* |
1-D Premixed Laminar Flames, Stagnation-Flow and Rotating-Disk CVD |
ergs/mole | ||
|
Energy of a positive ionic species |
[cal/mole]* | |
|
Energy threshold in ion-energy-dependent reactions |
[cal/mole]* | |
|
Energy threshold in reaction yield expression |
[cal/mole]* | |
|
Exponential constant in ion-energy-dependent reactions |
none | |
|
Forward reaction-order specified for the k th species in i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
none |
|
Acceleration of gravity |
cm/sec2 | |
|
Exponential constant in ion-energy-dependent reactions |
none | |
|
Standard state specific Gibb’s free energy for the k th species |
ergs/g | |
|
Mean specific Gibb’s free energy of a mixture |
ergs/g | |
|
Small number (e.g. 1.E-12) |
none | |
|
Linear growth rate for the k th bulk species |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
cm/sec |
|
Standard state molar Gibb’s free energy for the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions |
ergs/mole |
|
Mean molar Gibb’s free energy of a mixture |
ergs/mole | |
|
Specific enthalpy of the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
ergs/g |
Specific enthalpy of the k th species |
ergs/mole | ||
|
Heat transfer coefficient |
ergs/(sec K) | |
|
Specific enthalpy of the electron upon creation of the gas-phase |
ergs/g | |
|
Mean specific enthalpy of a mixture |
ergs/g | |
|
Multiplicative factor in reaction yield expression |
depends on reaction | |
|
Enthalpy of formation |
ergs/mole | |
|
Standard state molar enthalpy of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
ergs/mole |
|
Molar enthalpy of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
ergs/mole |
|
Mean molar enthalpy of a mixture |
ergs/mole | |
|
Total number of reactions |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Homogeneous 0-D Reactor Models , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Flux of gas-phase species into the surface |
mole/(cm2sec) | |
|
Diffusive mass flux of the k th species |
ergs/g | |
|
Jacobian matrix |
none | |
Total number of grid points |
none | ||
|
Boltzmann Constant |
ergs/K | |
|
Forward rate constant of the i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , 1-D Premixed Laminar Flames |
depends on reaction |
|
Reverse rate constant of the i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
depends on reaction |
|
Total number of species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Homogeneous 0-D Reactor Models , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Total number of bulk species |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Total number of bulk species on the m th material. |
none | |
|
Index of the first bulk-phase species in the first bulk phase |
none | |
|
Index of the first bulk species |
none | |
Index of the first bulk-phase species in phase |
none | ||
|
Index of the first bulk-phase species in phase of the m th material |
none | |
|
Index of the last bulk-phase species in the last bulk phase |
none | |
|
Index of the last bulk-phase species in phase |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow |
none |
|
Index of the last bulk-phase species in phase of the m th material. |
none | |
|
Equilibrium constant in concentration units for the i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Stagnation-Flow and Rotating-Disk CVD |
depends on reaction |
|
Total number of gas-phase species |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of the first gas-phase species |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of the last gas-phase species |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Equilibrium constant in pressure units for the i th reaction |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Stagnation-Flow and Rotating-Disk CVD |
depends on reaction |
|
Total number of surface species |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Total number of surface species on the m th material |
none | |
|
Index of the first surface-phase species in the first surface phase |
none | |
|
Index of the first surface species in phase |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow |
none |
|
Index of the first surface species in phase of the m th material |
none | |
|
Index of the last surface-phase species in the last surface phase |
none | |
|
Index of the last surface species in phase |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow |
none |
|
Index of the last surface species in phase of the m th material |
none | |
|
Array containing the number of species in each phase |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Array containing the number of species in each phase for material |
none | |
|
Distance between the shock and the contact surface at infinite distance from the diaphragm |
cm | |
|
Film-thickness length scale |
cm | |
|
Crank-arm length for the IC HCCI engine model |
cm | |
|
Length of the connecting rod for the IC HCCI engine model |
cm | |
|
Reduced molecular mass for the collision |
g | |
|
Molecular mass of the k th species |
Surface Chemical Rate Expressions, Gas-phase Species Transport Properties |
g |
|
Mass flow rate at inlet |
g/sec | |
|
Mass loss rate at the lower boundary |
g/(cm(1-α)sec) | |
|
Mass flow rate at outlet |
g/sec | |
|
Mass loss rate at the upper boundary |
g/(cm(1-α)sec) | |
|
Mass flux at the channel inlet |
g/(cm(1-α)sec) | |
|
Mass flux |
g/(cm(1-α)sec) | |
Mass flow rate |
g/sec | ||
|
Number of materials in the surface reaction mechanism |
none | |
Reactor mass |
g | ||
|
Molecular weight of the k th species, replaces . |
g/mole | |
|
Mean molecular weight of a mixture, replace . |
g/mole | |
|
Total molar concentration of a mixture |
mole/cm3 | |
|
Interior unit normal vector. Surface-normal unit vector; points from the gas into the bulk layer |
cm | |
|
Number of coefficients in polynomial fits to |
Thermodynamic Expressions, Surface Chemical Rate Expressions , Stagnation-Flow and Rotating-Disk CVD |
none |
Total number of event (statistical) particles |
none | ||
Total number of phases |
none | ||
|
Total number of phases for the m th material |
none | |
|
Avogadro’s number |
none | |
|
Total number of bulk phases |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Number of event (statistical) particles to be effected by convection |
none | |
|
Total number of bulk phases for the m th material |
none | |
|
Index of the first bulk phase |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of the first bulk phase for the m th material |
none | |
|
Index of the last bulk phase |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of the last bulk phase for the m th material |
none | |
|
Number of gas phases (always equal to 1) |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models |
none |
|
Number of event (statistical) particles to be effected by molecular mixing |
none | |
|
Total number of surface site types (phases) |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Total number of surface site types (phases) |
none | |
|
Index of first surface phase |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of first surface phase |
none | |
|
Index of last surface phase |
Surface Chemical Rate Expressions, Stagnation-Flow and Rotating-Disk CVD |
none |
|
Index of last surface phase |
none | |
|
Nusselt number for heat transfer for the IC HCCI engine model |
none | |
|
Scaled circumferential velocity () at the inlet |
1/sec | |
|
Pressure |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
dynes/cm2 |
|
Spatially-varying component of pressure in radial momentum equation. |
dynes/cm2 | |
|
Pressure of one standard atmosphere |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Homogeneous 0-D Reactor Models |
dynes/cm2 |
|
Probability density function of scalar |
none | |
|
Energy source term for heating of surface |
ergs/(cm2sec) | |
|
Prandtl number for the IC HCCI engine model |
none | |
|
Net heat transfer from reactor to ambient |
ergs/sec | |
|
Total energy deposited into the gas from a heat source |
ergs/(cm2sec) | |
Heat flux |
ergs/(cm2sec) | ||
|
Rate of progress of the i th gas-phase reaction. |
mole/(cm3sec) | |
Rate of progress of the i th reaction. |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
mole/(cm2sec) | |
|
Heat loss to the walls for the IC HCCI engine model |
ergs/sec | |
|
Radial coordinate |
cm | |
|
Universal gas constant |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
ergs/(mole K) |
|
Universal gas constant, in units consistent with activation energy |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
[cal/(mole K)]* |
|
Reverse reaction-order specified for the k th species in the i th reaction. |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
none |
|
Ratio of over for the IC HCCI engine model |
none | |
|
Reynolds number for the IC HCCI engine model |
none | |
|
Standard state specific entropy of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
ergs/(g K) |
|
Mean specific entropy of a mixture |
ergs/(g K) | |
|
Production rate of the k th species from surface reactions |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , Stagnation-Flow and Rotating-Disk CVD |
mole/(cm2sec) |
|
Standard state molar entropy of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions |
ergs/(mole K) |
|
Molar entropy of the k th species |
ergs/(mole K) | |
|
Spatially distributed thermal energy source |
ergs/(cm3sec) | |
|
Mean molar entropy of a mixture |
ergs/(mole K) | |
|
Average piston speed for the IC HCCI engine model |
cm/sec | |
|
Time |
Surface Chemical Rate Expressions, Normal Shock Equations , Homogeneous 0-D Reactor Models , Partially Stirred Reactor (PaSR) Model , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
sec |
|
Laboratory time |
sec | |
|
Gas-particle time |
sec | |
|
Temperature |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Partially Stirred Reactor (PaSR) Model , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
K |
|
Reduced temperature for the collision |
none | |
|
Reduced temperature of the k th species |
none | |
|
Ambient temperature |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Stagnation-Flow and Rotating-Disk CVD |
K |
|
Electron temperature |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models |
K |
|
Temperature of the ions. |
K | |
|
Surface temperature |
Homogeneous 0-D Reactor Models, Stagnation-Flow and Rotating-Disk CVD |
K |
|
Chamber wall temperature for the IC HCCI engine model |
K | |
Temperature to which the surface radiates |
K | ||
|
Axial velocity of fluid mixture ( direction) |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
cm/sec |
Gas velocity in shock-fixed coordinates |
cm/sec | ||
|
Exponential constant in reaction yield expression |
none | |
|
Specific internal energy of the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions |
ergs/g |
|
Mean specific internal energy of a mixture |
ergs/g | |
|
Gas velocity in laboratory-fixed coordinates |
cm/sec | |
|
Molar internal energy of the k th species |
ergs/mole | |
|
Reflected shock velocity |
cm/sec | |
|
Incident shock velocity |
cm/sec | |
|
Standard state internal energy of the k th species |
ergs/mole | |
|
Mean molar internal energy of a mixture |
ergs/mole | |
|
Fluid velocity in direction |
cm/sec | |
|
Gas velocity (vector) |
Gas-phase Species Transport Properties, Normal Shock Equations |
cm/sec |
|
Volume |
Surface Chemical Rate Expressions, Homogeneous 0-D Reactor Models , Partially Stirred Reactor (PaSR) Model , Stagnation-Flow and Rotating-Disk CVD |
cm3 |
Scaled radial velocity |
1/sec | ||
|
Clearance volume in an engine cylinder for the engine model |
cm3 | |
Correction velocity |
1-D Premixed Laminar Flames, Stagnation-Flow and Rotating-Disk CVD |
cm/sec | |
|
Diffusion velocity of the k th species |
Surface Chemical Rate Expressions, Gas-phase Species Transport Properties , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
cm/sec |
|
Diffusion velocity of the k th species in the division |
cm/sec | |
|
Ordinary diffusion velocity of the k th species |
Gas-phase Species Transport Properties, 1-D Premixed Laminar Flames |
cm/sec |
|
Ratio used shock tube equations |
none | |
Scaled circumferential velocity |
1/sec | ||
|
Half-width of the distribution of energy source term |
cm | |
|
Mean molecular weight of a mixture |
Thermodynamic Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames |
g/mole |
|
Molecular weight of the k th species |
Thermodynamic Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Partially Stirred Reactor (PaSR) Model , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
g/mole |
|
Thermal diffusion velocity of the k th species |
Gas-phase Species Transport Properties, 1-D Premixed Laminar Flames |
cm/sec |
|
Molecular weight of the positive ionic species in a Bohm-type reaction |
g/mole | |
|
Spatial coordinate along principal flow direction |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
cm |
|
Position of the center of the energy source term |
cm | |
|
Array of surface species mole fractions |
none | |
|
Mole fraction of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Determining Chemical Equilibria , Normal Shock Equations , Homogeneous 0-D Reactor Models , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Molar concentration of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Stagnation-Flow and Rotating-Disk CVD |
mole/cm3 |
|
Cross-stream coordinate |
cm | |
|
Maximum channel dimension |
cm | |
|
Mass fraction of the k th species |
Gas-phase Chemical Rate Expressions, Surface Chemical Rate Expressions , Gas-phase Species Transport Properties , Normal Shock Equations , Homogeneous 0-D Reactor Models , Partially Stirred Reactor (PaSR) Model , Boundary-layer Channel Flow , 1-D Premixed Laminar Flames , Stagnation-Flow and Rotating-Disk CVD |
none |
|
Distance |
cm | |
|
Array of surface species site fractions |
none | |
Ratio used in Shock Reactor. |
none | ||
|
Site fraction of the k th species at a site |
none | |
|
Site fraction of the k th species on surface phase |
Surface Chemical Rate Expressions, Boundary-layer Channel Flow |
none |
|
Site fraction of the k th species on site of the m th material |
none |
Note: The energy CGS units that are noted by an asterisk (*) depend upon user input at the REACTIONS
line or in the UNITS
auxiliary keyword for chemistry input files. The default unit is thermal calories.