Abstract: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 … Show more
“…Thus, the domain is wide enough for the principle turbulence mechanisms to be unaffected. Additionally, consistency with previous studies 40–43 regarding the minimum value of R C uu = −0.2 is apparent, and this z position denotes half the distance between the streamwise high- and low-speed streaks. Figure 6.Spatial two-point correlation function in spanwise direction at x = 9.0 for Case 1.…”
Section: Effects Of Spanwise Domain and Grid Scales On Turbulent Resultssupporting
Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.
“…Thus, the domain is wide enough for the principle turbulence mechanisms to be unaffected. Additionally, consistency with previous studies 40–43 regarding the minimum value of R C uu = −0.2 is apparent, and this z position denotes half the distance between the streamwise high- and low-speed streaks. Figure 6.Spatial two-point correlation function in spanwise direction at x = 9.0 for Case 1.…”
Section: Effects Of Spanwise Domain and Grid Scales On Turbulent Resultssupporting
Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.
“…boundary-layer transition on a concave or convex wall (e.g. Wang et al 2016Wang et al , 2019. The image-based model could be extended to predict other important flow properties such as the heat transfer and turbulent noise, which are related to the coherent structures, after appropriate adaption or modification.…”
Section: Discussionmentioning
confidence: 99%
“…2011 b ; Wang, Wang & Zhao 2016; Wang et al. 2019). Similar to the passive scalar used in the experimental imaging, the Lagrangian scalar field, as an ideal passive tracer field with vanishing diffusivity, is applied to study structural evolution in isotropic turbulence (Yang, Pullin & Bermejo-Moreno 2010), Taylor–Green and Kida–Pelz flows (Yang & Pullin 2010), the K-type transition in channel flows (Zhao, Yang & Chen 2016), fully developed channel flows (Yang & Pullin 2011) and the transition in a weakly compressible boundary layer (Zheng, Yang & Chen 2016).…”
Section: Introductionmentioning
confidence: 99%
“…The structures can be visualized by experimental imaging methods employing dye (Falco 1977;Head & Bandyopadhyay 1981), hydrogen bubbles (Kline et al 1967;Lee & Wu 2008) and small droplets (Smith & Smits 1995). Furthermore, the recently developed nanoparticle-based planar laser scattering (NPLS) can visualize clear coherent structures in supersonic boundary-layer transition (He et al 2011b;Wang, Wang & Zhao 2016;Wang et al 2019). Similar to the passive scalar used in the experimental imaging, the Lagrangian scalar field, as an ideal passive tracer field with vanishing diffusivity, is applied to study structural evolution in isotropic turbulence (Yang, Pullin & Bermejo-Moreno 2010), Taylor-Green and Kida-Pelz flows , the K-type transition in channel flows (Zhao, Yang & Chen 2016), fully developed channel flows (Yang & Pullin 2011) and the transition in a weakly compressible boundary layer (Zheng, Yang & Chen 2016).…”
We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition. The images are extracted from a passive scalar field by a sliding window filter on the streamwise and wall-normal plane. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angle of spatially evolving filtered component fields at different scales ranging from a boundary-layer thickness to several viscous length scales. In general, the averaged inclination angles increase along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. Inspired by the coincidence of the increasing averaged inclination angle and the rise of the skin-friction coefficient, we propose a simple image-based model of the skin-friction coefficient. The model blends empirical formulae of the skin-friction coefficient in laminar and fully developed turbulent regions using the normalized averaged inclination angle of scalar structures at intermediate and small scales. The model prediction calculated from scalar images is validated by the results from the direct numerical simulation at two Mach numbers, 2.25 and 6, and the relative error can be less than 15 %.
“…Wang studied the behavior and characteristics of boundary layer. [28][29][30][31] Approximate modeling of unsteady aerodynamics based on effective shapes for hypersonic aero-elasticity also attracts a wide range of interests. McNamara et al 32 examined two different viscous approximations based on effective shape and combined approximate computational approach, respectively.…”
When the panel is under limit cycle oscillation, the location of maximum vibration amplitude always locates at 0.75 of panel length under different dynamic pressure. However, this conclusion is drawn from engineer practice without further investigations on its theoretical basis. Thus, the current study focuses on the theoretical and mathematical basis of this problem. The pattern of the location of maximum amplitude is verified at first by using three numerical methods. Then, based on the law of energy conservation, the displacement function of linear panel oscillation is derived for theoretical investigation. The linear panel consists of two structural modes. Theoretical analysis shows that, under critical dynamic pressure, the generalized displacement responses of two structural modes have opposite phase, the same vibration amplitude and the same vibration frequency. As a result, the superposition of displacement function of two structural modes, which is the displacement function of panel, leads to the occurrence of maximum vibration amplitude at 0.7 of panel length. With more structural modes considered, the location of maximum moves to 0.75 of panel length.
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