A quadrature-based LES/transported probability density function approach for modeling supersonic combustion

DQMOM based PDF transport modeling for turbulent lifted nitrogen-diluted hydrogen jet flame with autoignition

“…To avoid numerical singularities, the present approach employs the procedures suggested by Wang and Fox [9] and Koo et al [12].…”

A multivariate quadrature based moment method for LES based modeling of supersonic combustion

“…Consequently, even for small N s , conventional finite-volume or finite-difference methods are intractable. In the past, both stochastic [7,10,[19][20][21][22] and deterministic approaches [5,14,16] have been developed for solving the PDF transport equation. In the stochastic approach, a notional particle ensemble is evolved in time, physical, and composition spaces to indirectly obtain the solution to the PDF transport equation.…”

“…The DQMOM approach was developed by Fox [5,13], and has since been used for solving a variety of problems involving multivariate PDFs [30][31][32]. Recently, this technique has been extended to the composition-enthalpy PDF transport equation [14,16,33]. In this method, transport equations that describe evolution of the quadrature weights and weighted abscissas are solved.…”

“…As a result, apart from the discretization-based errors, estimation of these source terms leads to additional numerical issues when the abscissas are close to each other. Methods to address these issues have been discussed by Akroyd et al [33] and Koo et al [16], and the resulting errors arising from these terms in the DQMOM formulation are independent of the errors discussed here.…”

“…Transport equations for these weights and abscissas are then used to obtain the filtered moments of the composition variables as a function of space and time. While this approach has been used in both subsonic [13][14][15] and supersonic flows [16], numerical errors associated with practical LES implementation introduce a number of issues. It is shown in this study that in the particular application to non-premixed combustion, the DQMOM transport equations may lead to inconsistent evolution of moments resulting in invalid moment sets.…”