On the formulation of the virtual mass term in two fluid models

A review of interaction mechanisms in fluid-solid flows

“…A number of investigators 'perform numerical studies using equation 171 for relative acceleration in their virtual mass terms [Hacox et a3,, 1980;Kazimi and No, 1986;Lahey et al,, 1980;Thorley and Wiggert, 1985] . Lahey et al, [1980] study the effect of adding virtual mt_ss effects _,o their numerical model, They numerically solve a onedimensional two-fluid model for the special case of adiabatic air/w_ter bubbly flows through nozzles and diffusers, The model ,_:lcludes the interaction effects of drag and virtual m_ss, The inclusion of a virtual mass term in their model equation_ did not noticeably ch_nge the final numerical results, though it did enhance th.e numerical ' sta,bility of the system, Hancox et al, [198C1] uses equation 171 in their one-dimensional model for gas-liquid flows and finds that it leads to numerical instability resulting irt imaginary velocities for some 'wdues of _, Kazimi and No [1986] include a virtual mass term using equ_tion 171 as the relative acceleration in their two-fluid model, They 1985] use a similar formulatio7 _¢ ,,_wlut_tepropagation velocities in a m._xture, They conclude that the inclusion of vn,_ual ma_s effects in their model results m a more rLccur_te _md gener_l expression :for the tmou_tic propagation velocity in two-phase media, Drew and L_dmy [1987] also show that the objective form given in equation 171 (with ,_ = 2) reduces to the appropriate expression for the case of a single sphe,re,,1_…”