HyperCODA for Two-Phase Flows: Two-Phase Water Ejector Analysis

Kurzfassung

The decarbonization of industrial thermal processes necessitates a transition away from fossil fuels toward sustainable alternatives, among which High Temperature Heat Pumps (HTHPs) represent a particularly promising class of technology. Water is a highly attractive working fluid for such systems, owing to its zero Global Warming Potential (GWP) and non-toxicity.

The integration of two-phase water ejectors, in the thermodynamic circuit of these devices, can serve as a secondary steam compression mechanism. Highly pressurized water can be mixed with hot steam from the compressor, achieving simultaneous cooling and pressure increase. This integration offers the potential to reduce both the power and the number of stages required to obtain the specified compression. Accurate numerical simulation of two-phase ejectors presents considerable challenges, as compressed liquid, two-phase mixture, and superheated vapor regions coexist within a single computational domain. Conventional solvers designed for high-speed compressible flows generally lack the thermodynamic closures required to operate beyond the ideal-gas assumption.

CODA (CFD for ONERA, DLR and Airbus) is the CFD software developed as part of a collaboration between the French Aerospace Lab ONERA, the German Aerospace Center (DLR), and Airbus. HyperCODA, an extension of the CODA solver into the hypersonic regime, is capable of simulating non-ideal gas thermodynamics by providing tabulated thermodynamic data. Thermodynamic properties are pre-computed and stored in NetCDF format, and the solver uses these files to close the fluid equations. To support multiphase flow modeling, the flow is treated as single-phase, which means neglecting surface tension, assume mechanical and thermal equilibrium, but allowing largely varying fluid properties. This is a valid assumption since the liquid travels in contact with vapor at high velocity and high temperature-corresponding to a high Weber number, where inertial forces dominate over surface tension effects. This model therefore requires a robust thermodynamic equation of state capable of capturing the largely varying fluid properties across the vapor, liquid and two-phase regimes. The Helmholtz Equation of State, accessed via the CoolProp library, provides multiparameter correlations for pressure, temperature, and the speed of sound. Within the two-phase dome, mixture quantities are determined through qualityweighted averaging, and the mixture speed of sound is evaluated using the Wood formula, ensuring correct recovery of single-phase limits.

The primary lookup table is indexed by the conserved scalars-density and specific internal energy — that are evolved by the compressible density-based Euler solver. Auxiliary tables, indexed by alternative thermodynamic variables such as enthalpy, pressure or entropy, are generated via a Newton–bisection hybrid method to support boundary condition enforcement.

Achieving adequate resolution of sharp thermodynamic gradients near the saturation boundary with a uniform discretization grid demands a prohibitively large number of table nodes. A saturation-curve refinement strategy mitigates this cost by explicitly inserting anchor points along the saturation curve into the table axes, sweeping reference temperatures across the operating range. Since the table constitutes a tensor product structure, querying the saturated liquid and vapor states introduces complete rows and columns of nodes aligned precisely with the saturation curve, thereby concentrating resolution where gradients are steepest and reducing the total number of nodes required to adequately capture thermodynamic transitions across the phase boundary. As a consequence of the resulting non-uniform axis spacing, the original constanttime cell-index lookup kernel in HyperCODA was replaced by a binary search algorithm with logarithmic computational complexity.

The simulation methodology was validated against exact Riemann solutions across five benchmark configurations. An ideal-gas Sod shock tube problem verified table parsing and interpolation functionality. A liquid–liquid dodecane shock tube provided validation for liquid states, which have low compressibility, and also demonstrated the capability of successfully simulating different fluids, like hydrocarbons. A two-phase water shock tube assessed vapour fraction tracking and wave propagation across mixture states, which lie within the saturation dome. A compressed liquid to low pressure vapor shock tube successfully reproduced a complex four-wave structure-comprising a rarefaction fan, an evaporation front, a contact discontinuity, and a compression shock-across coexisting liquid, vapor, and mixture states. The saturation refinement strategy is evaluated in this test-case, comparing uniform against refined thermodynamic tables. A symmetric double rarefaction expansion tube modelled evaporation and served as the basis for a thermodynamic grid sensitivity study.

A convergent–divergent nozzle is investigated using the newly implemented computational methodology, including a systematic mesh convergence study to assess numerical robustness. In addition, the predicted static pressure distributions and vapor volume fraction fields are compared against both experimental measurements and simulations performed with ANSYS Fluent. The validated HyperCODA simulation methodology is applied to a simplified two-dimensional two-phase water ejector geometry developed in collaboration with GEA Wiegand GmbH. Vapor volume fraction, static pressure and Mach number profiles along the ejector’s longitudinal axis are evaluated.

The non-commercial nature of HyperCODA affords greater control over the physical modelling and avoids commercial license constraints, making it a viable tool for parametric studies of operating conditions and initial-estimate analyses of two-phase flows. Nevertheless, further investigation is required to establish simulation best practices for this complex test case, in order to reduce simulation time. Future work should focus on implementing thermal nonequilibrium models and extending the current framework to the full NavierStokes equations to enable boundary layer interaction analysis. This extension will facilitate a direct comparison with the current model. Furthermore, experimental data and ANSYS Fluent simulations—which are currently unavailable for this ejector configuration-are of the utmost importance to measure its true deviation from reality.