Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

et al. 2019

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulent statistics and turbulent structures are analyzed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layer subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulent level is promoted by the concave curvature. Due to the increased turbulent generation in the outer layer, secondary bumps are noted in profiles of streamwise and spanwise turbulent intensity. Peak positions in profiles of wall-normal turbulent intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of mean properties and turbulent statistics. The roll cells further give rise to the vortex generation. The large amount of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

Section: Numerical Methods and Inflow Conditionsmentioning

confidence: 99%

The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

Wang

et al. 2019

“…All simulations in this paper solve the three-dimensional unsteady compressible Navier-Stokes equations directly without any modeling, using an in-house DNS code. The code has been previously used for studies of instability, transition and turbulent high-speed flows (Sandham 2016;Sandham et al 2014). Here we provide only a brief recap of the main features of the code.…”

Section: Numerical Simulation and Turbulent Inflow Generationmentioning

confidence: 99%

“…An effective Mach number has also been proposed (Sandham 2016) to evaluate the compressibility effects of a turbulent boundary layer with adverse pressure gradient variation from zero to separation, given by where a means the local sound speed. ∆U + V D refers to the van Driest-transformed velocity increment in the wake region compared to log law using the van Driest profile at y = δ, i.e.…”

Section: Effective Mach Numbermentioning

confidence: 99%

Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature

Sandham

2019

Self Cite

Supersonic turbulent flows at Mach 2.7 over concave surfaces for two different curvature radii were investigated and compared with a flat plate turbulent boundary layer using direct numerical simulations. The streamwise velocity reduces in the outer part of the boundary layer due to the compression while it increases near the wall due to curvature, with a higher shape factor for the concave cases. The near wall spanwise streak spacing reduces compared to the flat plate, with large scale streaks and turbulence amplification also observed. Streamwise velocity iso-surfaces and streamlines show the generation of Görtler-like vortices, consistent with significant centrifugal effects. Abundant small vortices are shown to be associated with large baroclinic production of vorticity that is caused by the density and pressure gradients that are associated with the concave compression. Profiles of turbulent kinetic energy (TKE) and turbulent Mach number exhibit a characteristic two-layer structure in the concave boundary layer cases. In the outer layer, turbulence is greatly amplified, whereas a local balance exists in the inner layer. Turbulent energy budget analysis shows that both production and dissipation increase near the concave wall, whereas in the outer part of the boundary layer, the production is increased and ultimately balanced by convection and turbulent transport.

“…Simulations were run within an in-house code to solve the 3D unsteady compressible Navier-Stokes equations. The code has both direct and large eddy simulation capability and has been applied to many studies of instability, transition and turbulence in supersonic flows (Sandham et al 2014;Sandham 2016) over the years. This paper only includes the main features of the code and explains the flow conditions.…”

Section: Numerical Simulation and Inflow Conditionmentioning

confidence: 99%

“…This paper only includes the main features of the code and explains the flow conditions. The detailed governing equations including the continuity, momentum and total energy equations for 3D flowfield can be found in Sandham et al (2014Sandham et al ( , 2016.…”

Section: Numerical Simulation and Inflow Conditionmentioning

confidence: 99%

Formation of surface trailing counter-rotating vortex pairs downstream of a sonic jet in a supersonic cross-flow

2018

Direct numerical simulations were conducted to uncover physical aspects of a transverse sonic jet injected into a supersonic crossflow at a Mach number of 2.7. Simulations were carried out for two different jet-to-crossflow momentum flux ratios (J ) of 2.3 and 5.5. It is identified that collision shock waves behind the jet induce a herringbone separation bubble in the near-wall jet wake and a reattachment valley is formed and embayed by the herringbone recirculation zone. The recirculating flow in the jet leeward separation bubble forms a primary TCVP (trailing counter-rotating vortex pair) close to the wall surface. Analysis on streamlines passing the separation region shows that the wing of the herringbone separation bubble serves as a micro-ramp vortex generator and streamlines acquire rotating momentum downstream to form a secondary surface TCVP in the reattachment valley. Herringbone separation wings disappear in the farfield due to the cross interaction of lateral supersonic flow and the expansion flow in the reattachment valley, which also leads to the vanishing of the secondary TCVP. A three-dimensional schematic of surface trailing wakes is presented and explains formation mechanism of the surface TCVPs. (a) x/D=3.5 for J =5.5 and x/D=3.5 for J =2.3 (b) x/D=8 for J =5.5 and x/D=5.5 for J =2.3 (c) x/D=12 for J =5.5 and x/D=8 for J =2.3 (d) x/D=18 for J =5.5 and x/D=12 for J =2.3 Figure 11. Contours of the mean flow streamwise velocity and streamlines on cross planes of J =5.5 and J =2.3, isolines of u/U∞=0.0 are superimposed