The Free-Jet Expansion of Supercritical CO2 from a Capillary Source

Abstract

In this paper we present computational and experimental results for the expansions of supercritical CO 2 from capillary sources, and compare them with similar expansions from orifices of the same diameters, with source pressures up to 100 bar and temperatures up to 70 o C. The expansions impact a vertical flat plate near ten diameters along the centerline. The subsonic flow from stagnation source conditions to the capillary exit is calculated as a quasi-onedimensional viscous flow to exit Mach number = 1 conditions, and then a time marching, two-step predictor corrector Lax-Wendroff axisymmetric method is used to calculate the two-dimensional supersonic expansion, shock structure, and subsonic flow against the flat plate. Experimentally we have made shadowgraph measurements of the shock structure, and temperature and pressure measurements at the flat plate. We find very good agreement between our calculations and experiments for both the capillary and orifice sources for flow rate and shock structure, quantitatively characterized by the Mach disk location as a function of source conditions and flat plate location. The differences between the two types of sources and the non-ideal fluid effects are significant, and well reproduced by the calculations. While we have good agreement for the flat plate pressure profiles for expansions from the orifice source, the agreement is not as good for the expansions from the capillary sources. The experiments show that the pressure profiles at the flat plate are significantly different for the two sources, even when scaled to the same mass flow rate or to the same source exit sonic pressure.

The structure of supercritical fluid free‐jet expansions

“…We have shown elsewhere that the Peng-Robinson equation gives very similar results. 7 We have also verified that this ideal gas result from our time-dependent method agrees very well, to within 3%, with the exact method of characteristics for the ideal gas in the isentropic region upstream of the shock.…”

“…7,18 Although the temperature-dependent parameters make the Peng-Robinson and 27-parameter equations of state more rigorous, especially at higher pressures, the axisymmetric results presented here primarily use the simple Redlich-Kwong cubic equation of state…”

“…We have shown previously that our computed flow rates are in good agreement with the measured flow rates. 7,18 We have assumed no streamline curvature at the inlet to the free-jet, which is an approximation best achieved by a short converging nozzle. 22 The two-step Lax-Wendroff approach we have used is taken from Sinha et al 15 as modified by Forney.…”

“…The details are given elsewhere. 7 Referring to Figure 2, the inflow sonic boundary conditions are applied at grid points that correspond to the orifice diameter. The boundary conditions on all grid points above the orifice are based on ambient conditions, with zero velocity in both axial and radial directions.…”

Fracture Initiation of an Inhomogeneous Shale Rock under a Pressurized Supercritical CO2 Jet

“…The total pressure on the perforation wall was loaded in two-step solutions. According to fluid mechanics, the total pressure is defined according to Equation (6).…”