An efficient reduced-order model for low Mach number reacting flows using auxiliary variables

In the nonisothermal gaseous flows through open vessels with chemical reaction and combustion processes, the flow can be approximated with compressible Navier–Stokes equation where density depends on temperature but is independent of velocity and pressure fields, which is called the low mach number approximation. To implement advanced estimation and control schemes such as Kalman filtering and optimal feedback control to low Mach number flows, it is necessary to find an accurate and reliable reduced-order model. One of the best methods available for this purpose is the Karhunen–Loeve Galerkin (KLG) procedure. The application of the KLG procedure to low Mach number flows, however, is never straightforward because some variables depend on temperature nonlinearly or exponentially and the velocity field is not solenoidal which prohibits the elimination of pressure in the Galerkin procedure. In the present investigation, we have overcome these difficulties by introducing appropriate auxiliary variables and have successfully derived a reduced-order model for low Mach number flows with radiative heat transfer and chemical reactions. The resulting reduced-order model is found to yield accurate results efficiently. The present work sets up the first stage for the real-time estimation and control of various gaseous nonisothermal reactors and combustors.