Numerical Solver for Dense Gas Flows

Abstract

Introduction D ENSE gas dynamics studies the dynamic behavior of gases in the dense regime, i.e., at temperatures and pressures close to the thermodynamic critical point. In such conditions, complex gasdynamic phenomena can appear in the transonic and supersonic regimes.1 In spite of the additional complexity of the fluid response in the dense regime, the use of dense gases is not only necessary but, in some applications, advantageous. For instance, dense gas effects play a critical role in the performance of turbomachinery and heat-transfer equipment of organic Rankine cycles (ORCs).2 This motivates the interest in developing numerical tools for the analysis and design of advanced ORC turbomachinery components. In the past, several methods for so-called “real gas flows” have been derived. Such methods were in general tailored to deal with hypersonic reacting flows, for which the use of robust upwind numerical solvers was mandatory. Unfortunately, upwind schemes require characteristic decompositions, making their realization for complex multidimensional systems quite involved. On the other hand, for nonreacting flows of gases close to saturation conditions, governed by complex equations of state, and characterized by “exotic” but quite weak waves, the use of sophisticated characteristic decompositions is not essential. For these flows, it could be more convenient to use central schemes, which, in spite of higher numerical diffusivity, have the advantage of conceptional simplicity and low computational cost. In the present work, a centered numerical solver for the computation of inviscid and viscous dense gas flows is developed. A thirdorder-accurate centered method for perfect gas flows3 is extended to the computation of dense gases. The proposed scheme is systematically compared to a well-known second-order flux-difference splitting scheme4 implemented within the same code. The computations are performed using either the van der Waals or the realistic Martin–Hou5 equation of state. The scheme is then extended to the computation of viscous dense gas flows. The fluid viscosity and thermal conductivity are evaluated using thermophysical models appropriate for gases close to saturation conditions. The proposed method is validated for several inviscid and viscous flow problems involving dense gas phenomena.