Experimental and theoretical investigation of boundary layer perturbations on a low-aspect-ratio wing

Laminar-turbulent transition in a boundary layer of low-aspect-ratio wing was investigated. Experiments clarifying the flow structure, its mean and oscillatory characteristics were carried out accompanied by linear stability analysis of the wind tunnel data on the laminar flow velocity profiles. Theoretical results obtained in a parallel flow approximation are in a good agreement with the experimental data on disturbances evolution at the initial stage of transition to turbulence. The study was supported by the Ministry of Education and Science of the Russian Federation (Grant No. RNP 2.1.1.471) and Russian Foundation for Basic Research (Grant No. 03-01-06145)     

Hydrophobic properties of a wavy rough substrate

The wetting/non-wetting properties of a liquid drop in contact with a chemically hydrophobic rough surface (thermodynamic contact angle e>/2) are studied for the case of an extremely idealized rough profile: the liquid drop is considered to lie on a simple sinusoidal profile. Depending on surface geometry and pressure values, it is found that the Cassie and Wenzel states can coexist. But if the amplitude h of the substrate is sufficiently large the only possible stable state is the Cassie one, whereas if h is below a certain critical value hcr a transition to the Wenzel state occurs. Since in many potential applications of such super-hydrophobic surfaces, liquid drops often collide with the substrate (e.g. vehicle windscreens), in the paper the critical drop pressure pW is calculated at which the Cassie state is no longer stable and the liquid jumps into full contact with the substrate (Wenzel state). By analyzing the asymptotic behavior of the systems in the limiting case of a large substrate corrugation, a simple criterion is also proposed to calculate the minimum height asperity h necessary to prevent the Wenzel state from being formed, to preserve the super-hydrophobic properties of the substrate, and, hence, to design a robust super-hydrophobic surface.     

Development of gas-dynamic perturbations propagating from a distributed sliding surface discharge

Results are presented from experimental studies of the plasma layer structure of a distributed sliding surface discharge excited in quiescent air and in a uniform gas flow behind a plane shock wave at gas densities of 0.03–0.30 kg/m³. The dynamics of weak shock waves generated after discharge initiation was studied. According to the experimental and simulation results, 40% of the discharge energy transforms into heat within a surface gas layer in the energy input stage, which lasts up to 200 ns.     

Viscoelastic flow through a wavy curved channel

Time-dependent flow of a viscoelastic material through a wavy curved channel is studied. The flow traversing the wavy curved domain is modelled in the curvilinear coordinates. The viscoelastic fluid is described by the fluid relaxation and retardation times, and their variations are considered in relation to the flow characteristic time scale. The wavy walls of the curved channels are in sinusoidal form, with arbitrary phase difference. Using domain perturbation technique, the analytical solution of the model is obtained, including the velocity and the volumetric flow rate. The analytical solution is explained as a function of the flow domain structure, the viscoelastic fluid properties, and the flow generating force. Flow enhancement due to the flow domain is discussed; we have shown that the flow augmentation depends on the properties of the viscoelastic fluid. Furthermore, comparisons have been made with Newtonian fluid flow, and the prominent variations in the flow behaviours have been reported.     

Supersonic flows with small perturbations in the presence of external effects on the flow. II. Slender wing profile

An analytic theory of a supersonic flow past a slender profile of an arbitrary shape in the presence of local energy release zones and an external force acting on the flow near the surface is developed. Main results are obtained using the linear approximation, which is valid in a wide range of external conditions. Analytic expressions are derived for calculating the spatial distributions of pressure perturbations near the surfaces of a slender profile at a small angle of attack. The results of analytic calculations are compared with the numerical simulation data based on the Euler equations for a wedge at a zero angle of attack. The comparison reveals good agreement between numerical and analytic calculations. The results make it possible to formulate and solve optimization problems for a supersonic aerodynamic flow with the help of external effects on the supersonic flow.     

On the formation of a wavy microrelief on an ion-beam-sputtered semiconductor surface

A mathematical model of regular wavy microrelief formation on a semiconductor surface subjected to an obliquely incident medium-energy ion be am is stated and analyzed. Taking into account the influence of fluctuation forces (the molecular component of the disjoining pressure) and of the ion-beam-transferred electric charge is shown to bring together model predictions and observations.     

Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.     

Effects of stationary phase perturbations on a lock-in mode

Astrofizika Cooperative. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 3, pp. 262–267, March, 1991.     

Acoustic perturbations in a pulsedRF-plasma

The response of a stationary weakly ionized plasma to a density perturbation in the neutral gas component was studied in a neon plasma with the following typical properties: electron density ¯N _e≈8×10¹² cm^?3, electron temperature on the axis of the vesselT _e0≈3.0 eV; neutral gas densityN _n≈1×10¹⁷cm^?3 and neutral gas temperatureT _n0≈600 °K. A neutral density perturbation, generated 50 cm apart from the plasma, produces a fluctuation in the ion density and a sharp spike in the differential voltage of a floating double probe. The experimental observations demonstrate the propagation of an ion sheath and of an electric field perturbation together with the neutral density perturbation. An interpretation of the plasma response to acoustic wave pulses has been proposed by Ingard and Schulz in a theory on acoustic wave modes in a weakly ionized gas. The experimental results are in good agreement with the theoretical expectations.     

Study of leading factors in formation of surface wavy structures on a rubber material

Wavy structures are often observed on the surface of a rubber material (polydimethylsiloxane, PDMS) covered with a thin metallic film. In this study we demonstrate that the orientation, periodicity, location of formation, and range of periodicity of the wavy structures can be regulated by three leading factors including the surface pattern, substrate hardness and the thickness of the metallic film. Results show the orientation of the wavy structures can be adjusted by the location, shape and size of the surface patterns. Enhancement of the substrate hardness can prevent forming random wavy structures. The thickness of surface metallic film significantly influenced the periodicity of the structures. Experimental results revealed an increase of the thickness of surface Au film by 50 nm, the periodicity was increased roughly by 1 μm. A compound structure, combining longitudinally preset patterns and transversely induced wavy structures, and a parallel wavy structure fabricated, respectively, by suitable arrangement of pattern configurations and adjustment of substrate hardness were demonstrated. The relatively simple approaches proposed here show the potential application in fabrication of designated complicate structures.     

Impact of perturbations on watersheds

We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the original and the displaced watershed as well as the probability density to induce, after perturbation, a change at a given distance. Scaling exponents for real and artificial landscapes are determined, where in the latter case the exponents depend linearly on the Hurst exponent of the applied fractional Brownian noise. The obtained power laws are shown to be independent on the strength of perturbation. Theoretical arguments relate our scaling laws for uncorrelated landscapes to properties of invasion percolation.     

Active vibration suppression of a cantilever wing

A method for the active vibration suppression of a cantilever wing is presented. The approach is based on modal control, in which a modal feedback control law relating the motion of the control surfaces to the controlled modes is implemented. Modal displacements and velocities required for feedback are extracted from sensor measurements by means of modal filters. A numerical example is presented.     

Weakly singular perturbations of a discrete spectrum

We consider weakly singular perturbations ¦x¦^–(0<<2) of an even restoring potential. We compute the matrix elements of the perturbation together with the additional point potential associated with the perturbation. It is shown that even for unperturbed wave functions, the matrix elements exist when 0 < < 3/2. The series for the Rayleigh-Schrödinger coefficients converge in all orders for the same interval in , regardless of the form of the restoring potential. For odd states, the matrix elements of the perturbation exist when 0 < < 3, while estimates for the Rayleigh-Schrödinger coefficients give the boundary = 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 14–18, June, 1989.     

Density perturbations in a flat universe

A well-known solution, for a flat model in general relativity obeying the Robertson-Walker metric, a perfect fluid energy-tensor and a perfect gas law of state, with constant deceleration parameter, is now shown to yield growing scalar density perturbations, provided thatq > 0. This study generalizes Weinberg's results for the radiation phase, and shows that any realistic model of this kind contains gravitational instabilities