JISC flow features.
Grid dependency of on the symmetry plane in the LES. 16
Nozzle and dimensions of the computational domain (mm).
A priori analysis of scalar flux model alignment: (a) time-averaged scalar value and (b) cos(α) on three planes.
Pdf of cos(α) for the SGDH and GGDH models.
Classification of points based on P − ε > 0 or P − ε < 0 on three planes.
Comparison of Barycentric map from LES and RANS for points where P − ε < 0 and P − ε > 0. (a) Barycentric map coordinates, colored by the displacement angle θ between the RANS and LES maps. (b) Pdfs of the distance D and the angle θ.
(a) Barycentric map of all the points in the LES, indicating the average location and the area that defines the possible perturbations. (b) Pdfs of D and θ for all points in the LES map compared to the average location.
Comparison of turbulent kinetic energy k from RANS and LES, including the difference, on three planes.
Perturbation function for the turbulent kinetic energy. (a) Pdfs of the parameters A 1 to A 4. (b) Perturbation function for k using the peaks of the pdfs for the values of A 1 to A 4. (c) The corrected turbulent kinetic energy on three planes.
(a) Isolines of scalar value and extracted from the isosurfaces at three downstream locations: x/d = 1, x/d = 3, and x/d = 5. (b) Quantity of interest: surface area A encompassed by isoline for at x/d = 5.
Comparison of isolines for and at three downstream transverse planes: LES, SGDH, SGDH with fine grid and GGDH models.
Comparison of isolines for and at three downstream transverse planes: LES and SGDH models with Sc t = 0.9, 0.7, 0.5, 0.3, and 0.1.
Isolines for at three downstream locations: LES, GGDH, and sensitivity of GGDH to (AC1) and k* (K1). Perturbations introduced separately in the Reynolds stress tensor in the momentum equations (RS) and in the scalar flux vector in the scalar transport equation (SF) and combined in both (SF and RS).
Isolines for at three downstream locations: LES, GGDH, and all simulations performed in the optimization procedure.
Illustration of the angles α and β as defined for the analysis of the induced scalar flux vector rotations.
(a) Location of points where sufficient rotation is obtained on the planes y/d = 0.0, z/d = 1.0, and x/d = 5.0. (b) Variation in α and β for Line 1 and Line 2.
Quantity of interest A for LES, GGDH, and SGDH with different Sc t .
Parameters in the different perturbation functions and value for which the maximum of A was found.
Quantity of interest for LES and GGDH, including the bounds found with the optimization procedure.
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