Comparative analysis of compressible solver schemes for underexpanded jet aerodynamics with Schlieren validation

The accurate prediction of compressible high-speed jet flows remains a critical challenge in computational aerodynamics due to the strong coupling between shock waves, expansion fans, shear-layer turbulence, and mixing processes downstream of nozzles. While density-based (DB) solvers are conventionally used for supersonic and transonic regimes, pressure-based (PB) solvers have recently gained attention for their reduced computational cost; however, their suitability for underexpanded jet modeling remains insufficiently explored. This study provides a systematic evaluation of PB and DB solvers available in ANSYS Fluent for simulating compressible flow discharged from an axisymmetric convergent nozzle over a range of nozzle pressure ratios (PR = 1.92–5). Experimental Schlieren flow visualization was conducted using a custom optical setup to qualitatively assess shock structures and validate near-field flow features. Numerical simulations employed compressible Reynolds Average Navier-Stokes (RANS) formulations with a standard k–ε turbulence model, structured quadrilateral meshes, and consistent boundary conditions for both solvers. Validation against published measurements demonstrated that both solvers accurately predict Mach disk formation and the streamwise location of the first shock cell, with a maximum deviation of 4.5% in peak Mach number. For PR > 1.92, both solvers captured the characteristic diamond shock pattern and the progressive increase in shock cell strength and spacing; the first shock cell occurred at X/De ≈ 1.09, 1.57, and 2 for PR = 3, 4, and 5, respectively. While PB and DB solvers exhibited comparable performance in resolving centerline Mach number and pressure oscillations, the DB solver overpredicted turbulent kinetic energy in the far-field subsonic region due to its known sensitivity at low Mach numbers. Discharge coefficients predicted by both solvers showed close agreement, with differences < 0.2%. Results demonstrate that the PB solver, despite being traditionally associated with incompressible and low-speed flows, can reliably model underexpanded supersonic jets at significantly reduced numerical cost. The findings provide practical guidance for CFD practitioners seeking cost-effective tools for compressible nozzle flow modeling and contribute to broader discussions on solver strategy selection for high-speed aerodynamic simulations.