Simulation Of Hypersonic Boundary Layer Transition Research Articles

Simulations of Hypersonic Boundary-Layer Transition over a Flat Plate with the Spalart-Allmaras One-Equation BCM Transitional Model

Transitional flow has a significant impact on vehicles operating at supersonic and hypersonic speeds. An economic way to simulate this problem is to use computational fluid dynamics (CFD) codes. However, not all CFD codes can solve transitional flows. This paper examines the ability of the Spalart–Allmaras one-equation BCM (SA-BCM) transitional model to solve hypersonic transitional flow, implemented in the open-source CFD code Eilmer. Its performance is validated via existing wind tunnel data. Eight different hypersonic flow conditions are applied. A flat plate model is built for the numerical tests. The results indicate that the existing SA-BCM model is sensitive to the freestream turbulence intensity and the grid size. It is not accurate in all the test cases, though the transitional length can be matched by tuning the freestream intensity. This is likely due to the intermittency term of the SA-BCM model not being appropriately calibrated for high-velocity flow, though if the model can be recalibrated it may be able to solve the general high-velocity flows. Although the current SA-BCM model is only accurate under certain flow conditions after one calibration process, it remains attractive to CFD applications. As a one-equation model, the SA-BCM model runs much faster than multiple-equation flow models.

Direct numerical simulations of hypersonic boundary-layer transition for a flared cone: fundamental breakdown

Direct numerical simulations (DNS) were carried out to investigate the laminar–turbulent transition for a flared cone at Mach 6 at zero angle of attack. The cone geometry of the flared cone experiments in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was used for the simulations. In the linear regime, the largest integrated spatial growth rates ($N$-factors) for the primary instability were obtained for a frequency of approximately $f=300~\text{kHz}$. Low grid-resolution simulations were carried out in order to identify the azimuthal wavenumber that led to the strongest growth rates with respect to the secondary instability for a fundamental and subharmonic resonance scenario. It was found that for the BAM6QT conditions the fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently, for the case which led to the strongest fundamental resonance onset, detailed investigations were carried out using high-resolution DNS. The simulation results exhibit streamwise streaks of very high skin friction and of high heat transfer at the cone surface. Streamwise ‘hot’ streaks on the flared cone surface were also observed in the experiments carried out at the BAM6QT facility using temperature sensitive paint. The presented findings provide strong evidence that the fundamental breakdown is a dominant and viable path to transition for the BAM6QT conditions.

Direct numerical simulations of hypersonic boundary-layer transition with finite-rate chemistry

AbstractThe paper describes a numerical investigation of linear and nonlinear instability in high-speed boundary layers. Both a frozen gas and a finite-rate chemically reacting gas are considered. The weakly nonlinear instability in the presence of a large-amplitude two-dimensional wave is investigated for the case of fundamental resonance. Depending on the amplitude of this two-dimensional primary wave, strong growth of oblique secondary perturbations occurs for favourable relative phase differences between the two. For essentially the same primary amplitude, secondary amplification is almost identical for a reacting and a frozen gas. Therefore, chemical reactions do not directly affect the growth of secondary perturbations, but only indirectly through the change of linear instability and hence amplitude of the primary wave. When the secondary disturbances reach a sufficiently large amplitude, strongly nonlinear effects stabilize both primary and secondary perturbations.

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.