In the present study, we perform direct numerical simulations to investigate the spatial development and basic flow statistics in the supersonic turbulent boundary layers at the free-stream Mach number of 2.0 over smooth and disturbed walls, the latter of which enforces extra Reynolds shear stress in the streamwise direction to emulate the drag increment and mean streamline curvature effects of rough walls. Such disturbances escalate the growth rate of turbulent boundary layer thickness and the shape factor. It is found that under the rescaled global coordinate, the mean velocity, Reynolds stresses and pressure fluctuation variances manifest outer-layer similarity, whereas the average and fluctuation variances of temperature and density do not share such a property. Compressibility effects are enhanced by the wall disturbances, yet not sufficiently strong to directly impact the turbulent kinetic energy transport under the presently considered flow parameters. The generalized Reynolds analogy that relates the mean velocity and temperature can be satisfied by incorporating the refinement in modifying the generalized recovery coefficient, and that associates the fluctuating velocity and temperature works reasonably well, indicating the passive transport of temperature fluctuations. The dispersive motions are dominant and decay exponentially below the equivalent sand grain roughness height $k_s$, above which the wall disturbances are distorted to form unsteady motions responsible for the intensified density and pressure fluctuations in the free-stream travelling isentropically as the acoustic radiations.

Effects of wall disturbances on the statistics of supersonic turbulent boundary layers

Hydro-viscous drive (HVD) plays a significant role in smoothly transferring torque and flexibly regulating the velocity of the disks. By hydro-viscous drive, we mean that the viscous shear stress of the thin oil film between a multi-layer assembly of rotating parallel disks is generated to transmit torque and power. The laminar-to-turbulent transition is an extremely complicated issue due to the combined effects of squeeze and shear on the oil film within the microscale friction pair system. Hence, a comprehensive and thorough analysis of flow instability in fluid-thermal-solid interaction of tribodynamic behavior is highly desirable. Following a brief introduction of fundamentals of HVD, this paper provides an overall review on the instability mechanisms for three types of canonical flow dynamic models, i.e., plane squeeze flow, plane shear flow, and rotating-disk flow. The effects of various aspects of wall conditions and working media, such as surface microstructure, and temperature-dependent viscosity, on flow instability are then summarized, which can serve as a reference and guidance for optimizing the design of friction pair systems. Based on the review of the former progress, this paper not only explores the in-depth mechanisms regarding the laminar-to-turbulent transition in microchannel flow, but also provides the possibility of bridging the gap between flow instability and tribodynamic behavior.

A review on flow instability in hydro-viscous drive

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR’s efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations.

A Novel Cell-Based Adaptive Cartesian Grid Approach for Complex Flow Simulations

Wall functions are extensively applied in engineering simulations with turbulence. They facilitate a significant increase in the scale of the grids next to the wall, which in turn reduces the total number of grids needed. This optimization enhances computational efficiency, making the simulation process more effective and streamlined. However, the current commonly used wall functions, such as the Spalding wall function, are an implicit expression that needs to be solved iteratively, which affects the computational efficiency, and the multilayer segmented wall function is not smoothly articulated, which affects the fidelity. In this study, based on flat plate direct numerical simulation (DNS) data, combined with structural ensemble dynamics theory, the de-thresholding Douglas–Peucker algorithm is introduced to construct an explicit wall function expression in the form of multilevel power exponential concatenated multiplication. The comparison of the new wall function against DNS data reveals that it demonstrates superior fitting accuracy in contrast to the traditional ones, and eliminates the need for manual calibration, reduces subjective influence, and enhances reliability. The numerical simulation outcomes for the flat plate boundary layer and a series of airfoils showcase the new wall function's exceptional accuracy, which not only meets but also surpasses the demanding standards of engineering practice. 

An explicit multilevel power turbulent wall function based on the de-thresholding Douglas–Peucker algorithm

In this paper, we investigate the effect of uniform vertical crossflow on the plane Poiseuille channel flow. The derivation and linearization of the Navier–Stokes equations are performed to enable numerical solution through the fourth-order Orr–Sommerfeld equation. The Chebyshev collocation method is employed for this purpose. A dual approach is employed to examine the basic velocity profile, involving both reference velocity analysis (z = 0) and maximum streamwise velocity analysis (z = zmax). The two approaches provide distinct perspectives on the flow and may yield different stability predictions, depending on the values of the parameters used. Modal analysis is conducted to comprehend the asymptotic behavior of the system, achieved through the plotting of eigenspectrum, neutral stability curves, and growth rate curves for disturbances. Accurate values of critical triplets are obtained, aligning with the existing literature. The non-modal analysis is performed to understand the short-term behavior of the system, aided by pseudospectra, evolutionary patterns of energy amplification of the disturbances G(t) over time, and delineation of regions, indicating stability, potential instability, and instability. The collective results from both analyses reveal that the crossflow serves as a dual agent, contributing to both the stabilization and destabilization of the system. 

Dual analysis of stability in plane Poiseuille channel flow with uniform vertical crossflow

Microchannels are important components of microelectromechanical systems (MEMSs) that encounter rarefaction effects due to their small-scale characteristics. The influence of rarefaction effects on the flow stability of microchannels should be investigated to improve MEMS performance. Based on kinetic theory, a linear stability analysis approach for low-speed rarefied flows was developed by using the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation with an external force term. This approach was applied to study the linear temporal stability of microchannel flows. A slip flow model was introduced for comparison. The corresponding eigenvalue problem was solved with a Chebyshev collocation method. This novel approach yielded a critical Reynolds number of 5778. Analysis of the validity and accuracy of the slip flow model shows that although this model cannot capture the Knudsen layer structure, this approach effectively improves the prediction accuracy of the growth rate of the least stable mode. However, the prediction accuracy gradually decreases with increasing Knudsen number. Compared with the stability results obtained from the BGK equation, the Navier–Stokes equations-based stability analysis method always underestimates the disturbance growth rate, regardless of whether a slip flow model is used. The stability analysis results show that rarefaction effects stabilize the flow. The degree of rarefaction does not affect the trends of growth rate and phase velocity with wavenumber, nor does it affect the shape of the velocity eigenfunctions. For a rarefied case, increasing the Mach number has a destabilizing effect on low-speed microchannel flows.

A new linear stability analysis approach for microchannel flow based on the Boltzmann Bhatnagar–Gross–Krook equation

Abstract The reentry vehicle will encounter thermal ablation, especially at the stagnation point regime. A theoretical work has been done to analyze the thermal effect of gas blowing due to thermal ablation of surface material on the head of a general hypersonic vehicle. By deriving the formulation, research takes into account the effect of gas blowing on the thermal dynamics balance, and then solves them by numerical discretization. It is found that gas blowing will increase the temperature and heat flux at the surface of stagnation point regime. 

/pdf/effect-of-gas-blowing-on-the-head-of-thermal-ablation-29z9n6zs.pdf

Effect of gas blowing on the head of thermal ablation vehicle

Compared to traditional body-fitted moving grids and overset grids, adaptive Cartesian grids offer significant advantages, including no need for grid deformation, highly automated generation process, natural adaptability to complex geometries, and ease of implementing solution-based adaptive mesh refinement. However, in high Reynolds number simulations involving large motions, these grids face the issue of “grid catastrophe” due to the extreme grid resolution required for turbulent boundary layer simulation. To address this, we employ the immersed boundary-dynamic wall function model combined with an implicit dual-time-stepping method, effectively resolving near-wall flow structures without significantly increasing grid count. To handle the assignment of newly emerged Eulerian cells during motion, a three-point interpolation method is used for flow field initialization. This computational framework has been validated through a series of steady-state benchmark cases. Through simulations of typical dive processes and typical pitching airfoil benchmarks, we demonstrate the high efficiency and fidelity of our method in solving turbulent flow fields under dynamic boundary conditions at subsonic and critical sonic speeds. This method provides efficient and reliable numerical simulation support for the aerodynamic design and optimization of various new aircraft.

An efficient immersed boundary–dynamic wall function model based on adaptive cartesian grids

A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of both the eigenfunctions and eigenvalues, the first- and second-order cell functions, the microscale features of this heterogeneous materials are defined successively. Then, the homogenized quadratic eigenvalue problems are derived and the second-order expansions of the eigenfunctions are formed. The eigenvalues are also broadened to the second-order terms by introducing proper auxiliary elastic functions defined in the composite structure, and the nonlinear expressions of the correctors of the eigenvalues are derived. The finite element procedures are established, linearized methods are discussed for solving the quadratic eigenvalue problems and the second-order asymptotic computations are performed. Effectiveness of the asymptotic model is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions, and the converging behavior of the eigenfunctions are numerically verified. It is also indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells.

https://www.mdpi.com/2073-8994/15/7/1299/pdf?version=1687452447

Multiscale Asymptotic Computations for the Elastic Quadratic Eigenvalue Problem in Periodically Composite Structure

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