Merge pull request #13964 from rmcdermo/master

FDS User Guide: fix typos

Author: rmcdermo

Manuals/FDS_User_Guide/FDS_User_Guide.tex

@@ -3394,9 +3394,9 @@ \section{Pyrolysis and Energy Conservation}
 H_{\rm x} \left(T_{\rm ref} \right) + H_{\rm x,adj} + H_{\rm x,r} \left(T_{\rm ref} \right) = \sum_{i=1}^{\rm N_residues} \nu_{\rm i} \left( H_{\rm i} \left(T_{\rm ref} \right) + H_{\rm i,adj}  \right) +
 \sum_{j=1}^{\rm N_species} \nu_{\rm j}  H_{\rm j} \left(T_{\rm ref} \right)
 \ee
-where $H(T)$ is the enthalpy of a material or gas, $H_{\rm r}$ is the \ct{HEAT_OF_REACTION}, $T_{\rm ref}$ is the temperature at which the \ct{HEAT_OF_REACTION} was specified for, $\nu$ is a yield, and $H_{\rm adj}$ is a constant that forces the correct entahlpy to balance the reactions. During initialization, $H(T)$ for a material is initialized using the defined \ct{SPECIFIC_HEAT} or ramp. $H(T)$ for a gas is defined per the discussion in Sec.~\ref{gas_species_props}. No adjustment parameter is included for gases since typically pryolysis is either producing a predefined species such as carbon dioxide or water vapor or it is producing a fuel species use on \ct{REAC}. For a predefined species, the enthalpy is known. When a non-predefined species is used on \ct{REAC}, FDS adjusts the species enthalpy so that the correct \ct{HEAT_OF_COMBUSTION} is obtained. This means it cannot be adjusted again to balance a material reaction.
+where $H(T)$ is the enthalpy of a material or gas, $H_{\rm r}$ is the \ct{HEAT_OF_REACTION}, $T_{\rm ref}$ is the temperature at which the \ct{HEAT_OF_REACTION} was specified for, $\nu$ is a yield, and $H_{\rm adj}$ is a constant that forces the correct enthalpy to balance the reactions. During initialization, $H(T)$ for a material is initialized using the defined \ct{SPECIFIC_HEAT} or ramp. $H(T)$ for a gas is defined per the discussion in Sec.~\ref{gas_species_props}. No adjustment parameter is included for gases since typically pyrolysis is either producing a predefined species such as carbon dioxide or water vapor or it is producing a fuel species use on \ct{REAC}. For a predefined species, the enthalpy is known. When a non-predefined species is used on \ct{REAC}, FDS adjusts the species enthalpy so that the correct \ct{HEAT_OF_COMBUSTION} is obtained. This means it cannot be adjusted again to balance a material reaction.
 
-The result is a system of linear equations where the $H_{\rm adj}$ values are the unknowns. This results in a matrix whose row count is the total number of reactions over all materials, and whose column count is the total number of materials that are either a reactant or a residue. The number of rows and columns may not be equal to one another. If they are equal, provided the matrix is not singular, then a standard matrix solution can be done. If there are more equations than materials, then the system is overdetermined, and there may not be a solution that conserves energy. In this case, a least-squares solution of the system is performed to find the best possible values for the $H_{\rm adj}$ values. A warning message will be written in this case. If there are more materials than reactios, then the system is underdetertmined, and there will be an infinite number of solutions. In this case, the matrix is solved to yield a minimal solution for $H_{\rm adj}$ values. That is it attempts to find values for $H_{\rm adj}$ where the vector of values has the smallest magnitude.
+The result is a system of linear equations where the $H_{\rm adj}$ values are the unknowns. This results in a matrix whose row count is the total number of reactions over all materials, and whose column count is the total number of materials that are either a reactant or a residue. The number of rows and columns may not be equal to one another. If they are equal, provided the matrix is not singular, then a standard matrix solution can be done. If there are more equations than materials, then the system is over-determined, and there may not be a solution that conserves energy. In this case, a least-squares solution of the system is performed to find the best possible values for the $H_{\rm adj}$ values. A warning message will be written in this case. If there are more materials than reactions, then the system is under-determined, and there will be an infinite number of solutions. In this case, the matrix is solved to yield a minimal solution for $H_{\rm adj}$ values. That is it attempts to find values for $H_{\rm adj}$ where the vector of values has the smallest magnitude.
 
 In the case of a singular matrix, a warning is written that no adjustment is done. A singular matrix happens when a row in the matrix is a linear combination of one or more other rows. If this happens, there is likely an error in one of the \ct{MATL} definitions.