Thermodynamic refinement and numerical validation of the Schnerr-Sauer cavitation model with MRG-Aleksandrov thermal coupling for cryogenic applications

Evaporative cooling destroys the local vapor pressure and changes cavity dynamics making it simple to see how isothermal cavitation models are fundamentally inadequate for cryogenic fluids. In this work, we develop an Extended Schnerr-Sauer (ESS) cavitation model using a coupling of the Mikic-Rohsenow-Griffith (MRG) inertial growth formulation and Aleksandrov convective thermal growth rate via effective thermal coefficient, f thermal . This coupling allows for continuous transitions from inertia-dominated to thermally-governed bubble growth regimes. It also includes a Clausius-Clapeyron vapor-pressure adjustment and one for turbulent kinetic energy. Using the realizable k - ε turbulence model, validation simulations for LN 2 and LH 2 cavitating flows are conducted over 0.5-caliber hydrofoil ( Re = 2.2–5.6 × 10 7 , σ = 1.50–1.75). Overall compared to previous efforts, the ESS model reduces the mean absolute temperature error by 77.1% (Mean Absolute Error (MAE) = 0.090 K), with case specific improvements of 55–85% vs LN 2 and 71% vs LH 2 to Hord’s benchmark data. Leading-edge pressure predictions show a 74.8% improvement, confirming that the thermodynamic fidelity in the cavity formation zone is improved. Monotonic relations between peak temperature gradients (Δ T max = 0.6–1.5 K) and the thermodynamic parameter Σ for nitrogen are well reproduced by the model, which also reproduces the observed short, foamy cavities. Relying on quantitative vorticity budget analyses whose results are common to all eight test cases in both fluids, we show that thermodynamic coupling drives a systematic differential redistribution of vorticity production: the peak baroclinic torque is suppressed by 47–82% and 49–69% in LN 2 and LH 2 , respectively, while the peak vortex dilatation is enhanced up to 125–179% and 104–144%, respectively, increasing the dilatation-to-baroclinic dominance ratio by approximately an order of magnitude. This mirror-image structure is consistent in direction across both cryogenic fluids tested and across all experimental operating conditions studied, providing independent evidence of the physical fidelity of the model; A three-dimensional calculation for Hord case 295D confirmed that this conclusion does not depend on dimensionality. The previously absent vortex-stretching term remains secondary to dilatation in both models, with | T stretch |/| T dilat | = 0.182 versus 0.253 at the source maxima and 0.152 versus 0.107 for the volume averages, in the extended and standard models respectively. Baroclinic torque is likewise subordinate, though thermodynamic coupling cuts its peak magnitude by 89.8% while raising its volume-averaged value by 52.4%. Dilatation therefore remains the leading production mechanism even in three dimensions. However, where liquid hydrogen is concerned, the narrow thermocouple temperature sensitivity at about 20 K systematically over-estimates temperature gradients, suggesting better property representations are required for fluids of high thermosensitivity. The ESS model with MRG-Aleksandrov coupling thus constitutes a physically-motivated, numerically-accurate thermodynamic framework for cryogenic cavitation predictions, although our LH 2 results reveal the need for more accurate treatments at extreme cryogenic conditions.