Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids

Abstract

Boundary-layer stability analyses of mean flows extracted from unstructured-grid NavierStokes solutions have been performed. A procedure has been developed to extract mean flow profiles from the FUN3D unstructured-grid solutions. Extensive code-to-code validations have been performed by comparing the extracted mean flows as well as the corresponding stability characteristics to the predictions based on structured-grid solutions.Comparisons are made on a range of problems from a simple flat plate to a full aircraft configuration-a modified Gulfstream-III with a natural laminar flow glove. The future aim of the project is to extend the adjoint-based design capability in FUN3D to include natural laminar flow and laminar flow control by integrating it with boundary-layer stability analysis codes, such as LASTRAC.Nomenclature C = wing/airfoil chord length C p = Pressure coefficient f = disturbance frequency (HZ) H = flight altitude (feet) m = meter M a = free stream Mach number N = N factors r1 = geometric stretching rate used in VGRID r2 = the second stretching rate used to tune cell expansion rates in VGRID. Z, z = vertical coordinates δ 99 = boundary layer thickness (distance from surface to 99% of free-stream velocity) δ 01 = distance from wall where U CF reduces to 0.1 |U CF max | ∆ n = normal grid spacing height for the n-th layer ν = kinematic viscosity ν e = boundary layer edge kinematic viscosity σ = growth rate of disturbance α = angle of attack λ = spanwise wavelength (millimeter)

Computational Evaluation and Linear Stability of a Transonic Laminar-Flow Wing Glove

“…Any concerns that may have existed about the suction-side T-S for this simulation due to the increased Reynolds number were relieved by results that showed that T-S was still sufficiently suppressed. All of these results agree reasonably well with follow-on work given by [23,24]. The latter paper included nonlinear PSE and secondary instability analyses that suggest DREs could indeed delay transition to turbulence by suppressing the most unstable crossflow disturbances.…”

Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

“…The resulting glove midspan chord Reynolds number is 24.2 × 10 6 ; however, for convenience, it is identified as 24 × 10 6 elsewhere in the paper. In [29], both structured-grid (OVERFLOW, [31]) and unstructured-grid (FUN3D ¶ ) Navier-Stokes codes were used to compute the aircraft flowfield including the wing glove. Figure 2 shows the upper-surface C p distribution in the glove region.…”

“…It should be noted that the isobars in the glove region have sweep angles smaller than the constant X∕C lines, particularly at larger distances from the leading edge. This unsweeping of the isobars has an important effect on boundary-layer stability, as discussed in [29] and summarized as follows. Figure 3 shows the C p distribution along the Y 234 in: butt line.…”

“…A wing glove was designed by TAMU, with the glove leading-edge sweep of 34.6 deg with a maximum possible chord Reynolds number approaching 30 × 10 6 . The details of the glove design and analyses using computational fluid dynamics and stability-analysis codes have been given in [26][27][28][29][30].…”

Effect of Small Surface Deformations on the Stability of Tollmien–Schlichting Disturbances

“…Thus, the REBL permits a thorough analysis of separated flow systems, which is particularly relevant to the following study because sufficiently deep gaps may form localized pockets of separation. A full description of the extraction procedure is given in the work of Thomas et al [23], whereas similar methods have been developed by Malik [46] and Liao et al [47] for investigating the flow over a flat plate and aircraft configurations.…”