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Register a new userLinear stability analysis of hypersonic boundary layers computed by a kinetic approach: A semi-infinite flat plate at Mach 4.5 and 9
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Linear stability analysis is performed using a combination of two-dimensional Direct Simulation Monte Carlo (DSMC) method for the computation of the basic state and solution of the pertinent eigenvalue problem, as applied to the canonical boundary layer on a semi-infinite flat plate. Three different gases are monitored, namely nitrogen, argon and air, the latter as a mixture of 79% Nitrogen and 21% Oxygen at a range of free-stream Mach numbers corresponding to flight at an altitude of 55km. A neural network has been utilised to predict and smooth the raw DSMC data; the steady laminar profiles obtained are in very good agreement with those computed by (self-similar) boundary layer theory, under isothermal or adiabatic wall conditions, subject to the appropriate slip corrections computed in the DSMC method. The leading eigenmode results pertaining to the unsmoothed DSMC profiles are compared against those of the classic boundary layer theory. Small quantitative, but no significant qualitative differences between the results of the two classes of steady base flows have been found at all parameters examined. The frequencies of the leading eigenmodes at all conditions examined are practically identical, while perturbations corresponding to the DSMC profiles are found to be systematically more damped than their counterparts arising in the boundary layer at the conditions examined, when the correct velocity slip and temperature jump boundary conditions are imposed in the base flow profiles; by contrast, when the classic no-slip boundary conditions are used, less damped/more unstable profiles are obtained, which would lead the flow to earlier transition. On the other hand, the DSMC profiles smoothed by the neural network are marginally more stable than their unsmoothed counterparts.
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Wall cooling has substantial effects on the development of instabilities and transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional DNSs is used to analyze Mach~6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability radiates energy. Fluid-thermodynamic analysis shows that this radiation comprises both acoustic as well as vortical waves. 2D simulations show that the conventional trapped nature of second-mode instability is ruptured. Although the energy efflux of both acoustic and vortical components increases with wall-cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled-wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket displays different behavior; moderately-cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly-cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. In moderately cooled-walls, the spatially-localized wall loading is due to coherent structures in the leading turbulent head region. In highly-cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.
This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_tau approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would require a camera and laser that moves with the flow, effectively `chasing eddies as they advect downstream.
The turbulent boundary layer over a flat plate is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations as a test bed for a synthetic turbulence generator (STG) inflow boundary condition. The inlet momentum thickness Reynolds number is approximately 1,000. The study provides validation of the ability of the STG to develop accurate turbulence in 5 to 7 boundary layer thicknesses downstream of the boundary condition. Also tested was the effect of changes in the stabilization scheme on the development of the boundary layer. Moreover, the grid resolution required for both the development region and the downstream flow is investigated when using a stabilized finite element method.
In this work, the static stability of plates with fixed trailing edges in axial airflow is studied using the framework of Possio integral equation. First, we introduce a new derivation of a Possio integral equation that relates the pressure jump along thin plates to their downwash based on the linearization of the governing equations of an ideal compressible fluid. The steady state solution to the Possio equation is used to account for the aerodynamic forces in the steady state plate governing equation resulting in a singular differential-integral equation which is transformed to an integral equation. Next, we verify the solvability of the integral equation based on the Fredholm alternative for compact operators in Banach spaces and the contraction mapping theorem. Then, we derive explicit formulas for the characteristic equations of free-clamped and free-pinned plates. The minimum solutions to the characteristic equations are the divergence speeds which indicate when static instabilities start to occur. We show analytically that free-pinned plates are statically unstable. After that, we move to derive analytically flow speed intervals that correspond to static stability regions for free-clamped plates. We also resort to numerical computations to obtain an explicit formula for the divergence speed of free-clamped plates. Finally, we apply the obtained results on piezoelectric plates and we show that free-clamped piezoelectric plates are statically more stable than conventional free-clamped plates due to the piezoelectric coupling.
The kinematics of a gliding flat-plate with spanwise oscillation has been optimized to enhance the power efficiency by using Bayesian optimization method, in which the portfolio allocation framework consists of a Gaussian process probabilistic surrogate and a hybrid acquisition strategy. We tune three types of acquisition function in the optimization framework and assign three different balance parameters to each acquisition function. The design variables are set as the dimensionless oscillating amplitude and reduced frequency of the spanwise oscillation. The object function is to maximize the power factor to support a unit weight. The optimization results in a maximal power factor of 1.65 when the dimensionless oscillating amplitude and reduced frequency vary from 0 to 1. The features of the probabilistic response surface are also examined. There exists an optimal reduced frequency for the power efficiency at the oscillating amplitudes above 0.40. In addition, the higher power efficiency may be obtained by increasing the amplitude beyond 1.00.
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