The integration of tabulated chemistry into Lagrangian–Eulerian spray solvers offers substantial computational savings for diesel combustion simulations, yet no integrated and systematically validated solver of this kind is available within the OpenFOAM framework. This work presents flameletSprayFoam, a new spray combustion solver built by extending the gaseous flameletFoam to the two-phase regime. The solver couples Lagrangian droplet tracking with precomputed flamelet libraries parameterized by mean mixture fraction, its variance, and the stoichiometric scalar dissipation rate, and accounts for turbulence–chemistry interaction through a presumed β -PDF approach. Three n-heptane chemical mechanisms, comprising 43, 68, and 188 species, were assessed in the counterflow configuration; only the 43-species mechanism of Liu et al. correctly reproduced ignition delays and the extinction limit at χ _st = 75.30 s^-1 , revealing that targeted reduction quality outweighs mechanism size. The solver was validated against constant-volume chamber measurements from Sandia National Laboratories covering six thermodynamic conditions. Under inert conditions, liquid and vapor penetration lengths and radial mixture fraction profiles agree well with experiments after calibrating the k– ε constants to c_1ε = 1.55 and σ _ε = 1.4 . Under reactive conditions, the model reproduces the measured ignition delay and flame lift-off length with mean absolute deviations of about 13 T_a ≥ 1000 K; at T_a ≤ 900 K the deviations grow to 43–61
This work investigates the involutive, adjoint, and spectral structures arising in the extended Alpha Group. Starting from the four-dimensional Alpha Group transformation matrix, whose angular depen- dence is governed by coupled tan θ and cot θ modes, an iterative commutator procedure generates a sixteen-dimensional real Lie algebra. Within this algebra, the operators B5 and B6 are identified as structurally distinguished elements and analyzed through their adjoint actions. The operator B6 is veri- fied to be involutive and induces an 8 + 8 decomposition of the Lie algebra, while the adjoint action of B5 defines an eight-dimensional invariant mixed sector through a polynomial kernel. The restricted adjoint operators preserve this sector, and their coupled action generates an idempotent operator Q, satisfying Q2 = Q, revealing an invariant projective structure. The spectral analysis further identifies characteristic- polynomial factorizations associated with B5 , B6 , and their compositions, including golden-ratio relations among distinct generators of the extended algebra. These results establish structural connections between the original modal representation, Lie-algebraic involution, adjoint dynamics, projective organization, and the spectral structure of the extended Alpha Group.
A high-order shock-fitting method is developed within the discontinuous flux reconstruction framework to compute shock waves accurately. The method is realized using a dynamic mesh solution approach and a robust shock detection algorithm. A strategy analogous to the method of characteristics is employed to determine the velocity of the identified shock front. The shock velocity is, then, used to move the mesh in a physically consistent manner. A one-sided operator is used to compute the common flux at the shock front, automatically satisfying the Rankine-Hugoniot condition. To accommodate the motion of the shock front, a computationally efficient mesh deformation algorithm is introduced, including a methodology that enables the shock nodes to move along the domain boundaries. In the present study, linear (Q1) and quadratic (Q2) triangular meshes are used, the latter allowing curved shocks to be represented by piecewise quadratic curves, thus achieving high-order accuracy. Several benchmark problems are used to evaluate the method’s performance and accuracy for steady applications, leading to excellent agreement with analytical solutions or data available in the literature.
Transitional Reynolds-averaged Navier–Stokes (RANS) models have become relevant in the computational fluid dynamics (CFD) community as a practical approach to predict the transition to turbulence over the surface of aerospace configurations. These models capture the transition caused by the amplification of Tollmien-Schlichting waves, the bypass transition, and the stationary crossflow vortices. A fundamental aspect of transitional RANS models that still deserve continued attention is their numerical behavior. The source terms that are part of their formulation are commonly based on highly nonlinear functions, rendering more challenges in their convergence when compared to the underlying fully turbulent RANS models. The present work investigates the effects of smoothing these highly nonlinear, discontinuous functions that are embedded in the source terms of the Langtry-Menter transition model and its companion turbulence closure. There is particular interests in identifying improvements in the lift and drag coefficient convergence behavior. We consider the flat plate, the NACA 0012 and NLF(1)-0416 airfoils, and the 6:1 prolate spheroid configuration as test cases for transition caused by the amplification of Tollmien-Schlichting (TS) waves. We also consider flow conditions for which transition over the inclined 6:1 prolate spheroid is triggered by the amplification of stationary crossflow vortices. Our results show that the smooth functions lead to a faster convergence of the aerodynamic coefficients, which represents a reduced computational cost when compared to the original model.
