Hybrid LES/RANS methods for the simulation of turbulent flows

Effects of large computational time steps on the computed turbulence were investigated using a fully implicit method. In turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined. Turbulence fluctuations could not be sustained if the computational time step was near or larger than the Kolmogorov time scale.

Effects of the computational time step on numerical solutions for turbulent flow

The prediction of the laminar-turbulent transition of boundary layers is critically important to the development of hypersonic vehicles because the transition has a first-order impact on aerodynamic heating, drag, and vehicle operation. The success of transition prediction relies on a fundamental understanding of the relevant physical mechanisms. In the 20 years since the review by Kleiser & Zang (1991) on the direct numerical simulation (DNS) of the boundary-layer transition, significant progress has been made on DNS in the hypersonic flow regime and in the spatial DNS approach. Many high-order shock-capturing and shock-fitting finite-difference methods have been developed and extensively applied to numerical simulations of the hypersonic boundary-layer transition. DNS has become a powerful research tool and has led to discoveries of new transition mechanisms. This article reviews the recent progress of DNS on hypersonic boundary-layer receptivity, instability, and transition. The current status and future directions are also presented.

http://cfdhost.seas.ucla.edu/papers/2012/Zhong-X-2012-annurev-fluid-120710-101208.pdf

Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers

The relationship between the upstream boundary layer and the low-frequency, large-scale unsteadiness of the separated flow in a Mach 2 compression ramp interaction is investigated by performing wide-field particle image velocimetry (PIV) and planar laser scattering (PLS) measurements in streamwise–spanwise planes. Planar laser scattering measurements in the upstream boundary layer indicate the presence of spanwise strips of elongated regions of uniform momentum with lengths greater than 40?. These long coherent structures have been observed in a Mach 2 supersonic boundary layer (Ganapathisubramani, Clemens & Dolling 2006) and they exhibit strong similarities to those that have been found in incompressible boundary layers (Tomkins & Adrian 2003; Ganapathisubramani, Longmire & Marusic 2003). At a wall-normal location of y/?=0.2, the inferred instantaneous separation line of the separation region is found to oscillate between x/?=?3 and ?1 (where x/?=0 is the ramp corner). The instantaneous spanwise separation line is found to respond to the elongated regions of uniform momentum. It is shown that high- and low-momentum regions are correlated with smaller and larger size of the separation region, respectively. Furthermore, the instantaneous separation line exhibits large-scale undulations that conform to the low- and high-speed regions in the upstream boundary layer. The low-frequency unsteadiness of the separation region/shock foot observed in numerous previous studies can be explained by a turbulent mechanism that includes these elongated regions of uniform momentum

Effects of upstream boundary layer on the unsteadiness of shock induced separation

Direct numerical simulations (DNS) were performed to investigate the laminar–turbulent transition in a boundary layer on a sharp cone with an isothermal wall at Mach 6 and at zero angle of attack. The motivation for this research is to make a contribution towards understanding the nonlinear stages of transition and the final breakdown to turbulence in hypersonic boundary layers. In particular, the role of second-mode fundamental resonance, or (K-type) breakdown, is investigated using high-resolution ‘controlled’ transition simulations. The simulations were carried out for the laboratory conditions of the hypersonic transition experiments conducted at Purdue University. First, several low-resolution simulations were carried out to explore the parameter space for fundamental resonance in order to identify the cases that result in strong nonlinear interactions. Subsequently, based on the results from this study, a set of highly resolved simulations that proceed deep into the turbulent breakdown region have been performed. The nonlinear interactions observed during the breakdown process are discussed in detail in this paper. A detailed description of the flow structures that arise due to these nonlinear interactions is provided and an analysis of the skin friction and heat transfer development during the breakdown is presented. The controlled transition simulations clearly demonstrate that fundamental breakdown may indeed be a viable path to complete breakdown to turbulence in hypersonic cone boundary layers at Mach 6.

Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown

Direct numerical simulations were performed to investigate wavepackets in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was forced by a short-duration (localized) pulse. The pulse disturbance developed into a three-dimensional wavepacket, which consisted of a wide range of disturbance frequencies and wavenumbers. First, the linear development of the wavepacket was studied by forcing the flow with a low-amplitude pulse (0.001 % of the free-stream velocity). The dominant waves within the resulting wavepacket were identified as the second-mode axisymmetric disturbance waves. In addition, weaker first-mode oblique disturbance waves were also observed on the lateral sides of the wavepacket. In order to investigate the nonlinear transition regime, large-amplitude pulse disturbances (0.5 % of the free-stream velocity) were introduced. The response of the flow to the large-amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identified at approximately half the frequency of the high-amplitude frequency band, suggesting the possibility of a subharmonic resonance mechanism. However, the spectrum also indicated that the fundamental resonance was much stronger than the subharmonic resonance. A secondary stability investigation using controlled disturbances confirmed that fundamental resonance is indeed a dominant mechanism compared to subharmonic resonance. Furthermore, strong peaks in the disturbance wave spectrum were also observed for low-azimuthal-wavenumber second-mode oblique waves, hinting at a possible oblique breakdown mechanism. Thus, the wavepacket simulations indicate that the second-mode fundamental resonance and oblique breakdown mechanisms are the strongest for the investigated flow. Hence, both mechanisms are likely to be relevant in the natural transition process for a cone boundary layer at Mach 6.

Numerical investigation of the development of three-dimensional wavepackets in a sharp cone boundary layer at Mach 6

Direct Numerical Simulations (DNS) were performed to investigate transition initiated by a localized disturbance in a hypersonic ∞at{plate boundary layer. In order to model a natural transition scenario, the boundary{layer was forced by a short duration (localized) pulse through a hole on the ∞at{plate. The pulse disturbance developed into a threedimensional wave packet which consisted of a wide range of disturbance frequencies and wave numbers. First, the linear development of the wave packet was studied by pulsing the ∞ow with a low amplitude (0:001% of the freestream velocity). The dominant waves within the resulting wave packet were identifled as two-dimensional second mode disturbance waves. Hence the wall{pressure disturbance spectrum exhibited a maximum at the spanwise mode number k = 0. The spectrum broadened in downstream direction and the lower frequency flrst mode oblique waves were also identifled in the spectrum. However, the peak amplitude remained at k = 0 which shifted to lower frequencies in the downstream direction. In order to investigate the nonlinear transition regime, the ∞ow was pulsed with a higher amplitude disturbance (5% of the freestream velocity). The developing wave packet grows linearly at flrst before reaching the nonlinear regime. The wall pressure disturbance spectrum conflrmed that the wave packet developed linearly at flrst. The response of the ∞ow to the high amplitude pulse disturbance indicated the presence of a fundamental resonance mechanism. Lower amplitude secondary peaks were also identifled in the disturbance wave spectrum at approximately half the frequency of the high amplitude frequency band, which would be an indication of a subharmonic resonance mechanism. The disturbance spectrum indicates however, that fundamental resonance is much stronger than subharmonic resonance.

Transition initiated by a localized disturbance in a hypersonic flat-plate boundary layer

Numerical Investigation of Transition in a Flared Cone Boundary Layer at Mach 6

Highly resolved spatial Direct Numerical Simulations (DNS) were performed to investigate the growth and breakdown of a localized disturbance into a turbulent spot in a sharp cone boundary{layer at Mach 6. The ∞ow parameters used in the simulations are based on the experimental conditions of the Boeing/AFOSR Mach 6 quiet{∞ow Ludwieg Tube at Purdue University. 1 In order to model a natural transition scenario, the boundary{layer was pulsed through a hole on the cone surface. The pulse disturbance developed into a three{dimensional wave packet which consisted of a wide range of disturbance frequencies and wave numbers. The dominant waves within the resulting wave packet were identifled as two{dimensional second mode disturbance waves. In addition, weaker oblique waves were observed on the lateral sides of the wave packet. The developing wave packet grows linearly at flrst before reaching the nonlinear regime and eventually leads to localized patches of turbulent ∞ow (turbulent spot). The wall{pressure disturbance spectrum showed strong secondary peaks at the fundamental frequency for larger azimuthal wave numbers. This development indicates that fundamental resonance might be the dominant nonlinear mechanism for a cone boundary{layer at Mach 6. The ∞ow structures within the turbulent spot were studied in detail and general features of the spot were analyzed.

Jayahar Sivasubramanian

Papers

Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown

Numerical investigation of the development of three-dimensional wavepackets in a sharp cone boundary layer at Mach 6

Transition initiated by a localized disturbance in a hypersonic flat-plate boundary layer

Numerical Investigation of Transition in a Flared Cone Boundary Layer at Mach 6

Direct Numerical Simulation of a Turbulent Spot in a Cone Boundary-Layer at Mach 6