On the choking mechanism in supersonic ejectors: a one-dimensional analysis of Reynolds-Averaged Navier Stokes simulations

TL;DR

This work addresses choking in supersonic ejectors by developing a unified one-dimensional two-stream framework that can implement both Fabri and compound choking mechanisms and validate them against axisymmetric RANS data processed via cross-sectional averaging. The authors derive the governing 1D conservation equations, introduce closure options (equal static pressure for compound choking or a prescribed dividing streamline for Fabri choking), and incorporate practical mechanisms such as wall/inter-stream friction, pressure equalization, and normal shocks. Calibrated compound choking (Model 1) predicts the secondary mass flow within about 2% on-design and up to ~5% in strongly under-expanded primaries, while Fabri choking (Model 3) achieves <1% error on-design when a CFD-derived dividing streamline is imposed, though it remains highly sensitive to closures and geometry near sonic points. Across test cases, compound choking emerges as the more general flow-blocking mechanism, with Fabri choking offering complementary insights; the framework provides a fast, physically grounded tool for ejector analysis and design, while highlighting opportunities to relax equal-pressure assumptions and extend to nonuniform-pressure conditions.

Abstract

Ejectors are passive devices used in refrigeration, propulsion, and process industries to compress a secondary stream without moving parts. The engineering modeling of choking in these devices remains an open question, with two mechanisms-Fabri and compound choking-proposed in the literature. This work develops a unified one-dimensional framework that implements both mechanisms and compares them with axisymmetric Reynolds-Averaged Navier Stokes (RANS) data processed by cross-sectional averaging. The compound formulation incorporates wall and inter-stream friction and a local pressure-equalization procedure that enables stable integration through the sonic point, together with a normal shock reconstruction. The Fabri formulation is assessed by imposing the dividing streamline extracted from RANS, isolating the sonic condition while avoiding additional modeling assumptions. The calibrated compound model predicts on-design secondary mass flow typically within 2 % with respect to the RANS simulations, rising to 5 % for a strongly under-expanded primary jet due to the equal-pressure constraint. The Fabri analysis attains less than 1 % error in on-design entrainment but exhibits high sensitivity to the dividing streamline and closure, which limits predictive use beyond on-design. Overall, the results show that Fabri and compound mechanisms can coexist within the same device and operating map, each capturing distinct aspects of the physics and offering complementary modeling value. Nevertheless, compound choking emerges as the more general mechanism governing flow rate blockage, as evidenced by choked flows with a subsonic secondary stream.

Figures (15)

• Figure 1: The ejector is modeled with two 1D domains that are coupled in the mixing pipe. The geometry is assumed to be axisymmetric. The boundary conditions consist of the total pressures $p_{t,i}$ and total temperatures $T_{t,i}$ at the inlets and the static back pressure $p_b$. The dividing streamline, indicated by the dotted line, is computed with the Equation \ref{['eq:A_i']} from the compound choking theory or imposed from the RANS simulations. Momentum exchange is accounted for through friction forces (see \ref{['eq:forces_mix']}) or through imposed total pressure gradients from RANS.
• Figure 2: The jump conditions from the inlets to the mixing pipe. The primary cross-sections and hence the flow states are identical on both sides. The secondary stream requires a force balance, where the momentum fluxes and pressure forces are projected on the x-axis with their respective angles. The result is a double flow state at the inlet of the mixing pipe $x=0$, which generally has different static pressures.
• Figure 3: An under- or over-expanded primary stream is brought to a uniform static pressure over a finite distance using Prandtl-Meyer expansion theory or oblique shocks respectively. The procedure results in the angle $\theta$ of the dividing streamline, which suffices to complement the conservation Equations \ref{['eq:p_i']}-\ref{['eq:Tt_i']}.
• Figure 4: Flow chart for computing the choked flow in the primary nozzle. The static pressure at the inlet is found iteratively to satisfy the sonic condition $\hbox{Ma}_p \rightarrow 1, N_p \rightarrow 0$ in Equation \ref{['eq:p_i_denom']}. The approximations in Appendix \ref{['sec:appendix_single_stream']} allow to integrate the governing equations through the sonic point without numerical issues related to division by zero (see also restrepo2022viscousvandenberghe2024extensioncompoundflowtheory).
• Figure 5: The solution procedure iterates on the static pressure at the secondary inlet to find the correct compound- or Fabri-sonic point. A sonic flow in the secondary inlet is not accepted as a valid solution since it is atypical for ejectors. The procedure differs in the compound and Fabri case through the sonic condition and the corresponding approximations of the pressure gradient.