Page 33 - Computational Fluid Dynamics for Engineers

18 1. Introduction

and the Wilcox k-u model [15,16]. Both can be used with or without wall
functions.
A Challenger aircraft wing/body/nacelle configuration was selected to in-
vestigate the ability of NSU3D to predict flows at high angles of attack up to
and beyond stall. The geometry modelled represents the wind tunnel model
including flap fairings and flow-through nacelles. Even though this is a rela-
tively simple configuration, it presents some meshing difficulties, mainly in the
generation of the prism layers required for Navier-Stokes computations. This is
due to the presence of such features as narrow gaps in the nacelles where prism
layers growing from two facing surfaces can collide if not properly limited. The
modelling of the flap fairings also made the generation of the prism layers more
complex, since the latter have to wrap around the fairings.
The unstructured mesh (Section 9.7) consists of 209,000 tetrahedra in the
field, 6,358,000 prisms around the aircraft surface and 9000 pyramids (to cap
incomplete prism layers). The first prism layer is given a thickness of 6 x 10 - 6
times the wing tip chord to ensure values of y+ of the order of 1 needed for
the application of turbulence models down to the solid surface (Chapter 3).
A growth ratio of 1.3 from one layer to the next is imposed. The number of
layers varies from 26 on the nacelle core cowl to 35 on the wing, fuselage and
wing-body fairing, for a maximum prism layer thickness of 7% of the root chord.
The flow conditions of the wind tunnel data used for comparison are a Mach
6
number of 0.25 and a Reynolds number of 2.2 x 10 , based on the wing mean
aerodynamic chord. The stall pattern on this configuration is typical of transonic
jets with no slats or leading edge flaps. A leading edge flow separation, due to
the bursting of a laminar short bubble, causes a sudden loss of lift at stall.
The relative performance of the Spalart-Allmaras and k-u turbulence mod-
els in predicting the lift variation with incidence was evaluated on this mesh.
Convergence was satisfactory at most angles of incidence: the density residual
was reduced by 4 to 5 orders of magnitude at incidences up to 15°. At higher
angles of incidence, it did not decrease as much, but the convergence of the lift
coefficient was still good. Post-stall isobars and skin-friction lines computed at
a — 14.21° using the k-uo turbulence model are shown in Fig. 1.19a. The pre-
dicted lift variation with incidence for the two turbulence models is compared
with the experimental data in Fig. 1.19b. These results were obtained with the
assumption of fully turbulent flow. At incidences up to 10°, both turbulence
models predict lift fairly well. At higher incidences, however, the predicted lift
is lower than the experimental data before stall, with the one-equation Spalart-
Allmaras model results being worse than those obtained with the two-equation
k-uj model. Both models underpredict the pre-stall lift coefficient, due to an ex-
cessive amount of predicted separated flow on the outboard wing. None of the
numerical results predicts the sudden drop of lift after stall, but the Spalart-
Allmaras predictions show a kink in the lift variation shortly after the experi-