Experimental study of the evolution of periodic controlled disturbances in a hypersonic viscous shock layer on a flat plate

Characteristics of the fields of mean density and density fluctuations measured with introduction of periodic disturbances into a hypersonic viscous boundary layer on a flat plate are presented. The experiments are performed for a flow Mach number M_∞ = 21, Reynolds number per meter Re_1∞ = 6·10⁵ m⁻¹, and temperature factor of the surface T _w /T ₀ = 0.26. The disturbances are introduced into the shock layer by an oblique gasdynamic whistle. The work was financially supported by the Russian Foundation for Basic Research (Grants Nos. 04-01-00474 and 05-08-33436).     

Effect of Microbubble Gas Saturation on Near-Wall Turbulence and Drag Reduction

The article presents results of an experimental study of the effect of gravitational orientation of the flow along its lower/upper solid boundaries on reduction of turbulent drag and void fraction profiles with injection of gas through a porous channel wall. The shear stress on the wall was measured in the Reynolds number range Re_x = (0.23–1.1) × 10⁷ by floating element transducers; the void fraction profile was determined using a fiber-optic sensor. The void fraction in the inner (near-wall) region of the boundary layer was shown to be a key parameter for turbulent drag reduction. The size of the inner region depends on the gas flow rate, the fluid velocity, the distance downstream of the gas generator, and the gravitational orientation of the wall.     

An experimental study of the forerunners of boundary-layer localized disturbances at an enhanced turbulence level

Turbulence production processes in boundary layer at a high level of free-stream turbulence have been studied. The tests were carried out in the MT-324 subsonic wind tunnel of ITAM, SB RAS, on models of straight and 45° swept wings at Reynolds numbers Re_c1 = 97000 and Re_c2 = 137000, and also at low (Tu = 0.18 % U _∞) and high (Tu = 0.79 and 2.31 % U _∞) levels of free-stream turbulence. The longitudinal localized disturbances developing in the boundary layer under the action of free-stream turbulence were artificially modeled using local air suction through a slot on the model surface. Wave packets, or forerunners, produced in the boundary layer, in the region preceding the abrupt local change of flow velocity near the localized-disturbance fronts, were examined. The high level of free-stream turbulence was found to accelerate the downstream evolution of the wave packets and their transformation into turbulent spots.     

Large-Time Behaviors of Solutions to an Inflow Problem in the Half Space for a One-Dimensional System¶of Compressible Viscous Gas

The “inflow problem” for a one-dimensional compressible barotropic flow on the half-line R ₊= (0,+∞) is investigated. Not only classical waves but also the new wave, which is called the “boundary layer solution”, arise. Large time behaviors of the solutions to be expected have been classified in terms of the boundary values by [A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, to appear in Proceedings of IMS Conference on Differential Equations from Mechanics, Hong Kong, 1999]. In this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave. Received: 25 April 2000 / Accepted: 20 April 2001     

Effect of CO2 gasification reaction on oxy-combustion of pulverized coal char

For oxy-combustion with flue gas recirculation, as is commonly employed, it is recognized that elevated CO₂ levels affect radiant transport, the heat capacity of the gas, and other gas transport properties. A topic of widespread speculation has concerned the effect of the CO₂ gasification reaction with coal char on the char burning rate. To give clarity to the likely impact of this reaction on the oxy-fuel combustion of pulverized coal char, the Surface Kinetics in Porous Particles (SKIPPY) code was employed for a range of potential CO₂ reaction rates for a high-volatile bituminous coal char particle (130 μm diameter) reacting in several O₂ concentration environments. The effects of boundary layer chemistry are also examined in this analysis. Under oxygen-enriched conditions, boundary layer reactions (converting CO to CO₂, with concomitant heat release) are shown to increase the char particle temperature and burning rate, while decreasing the O₂ concentration at the particle surface. The CO₂ gasification reaction acts to reduce the char particle temperature (because of the reaction endothermicity) and thereby reduces the rate of char oxidation. Interestingly, the presence of the CO₂ gasification reaction increases the char conversion rate for combustion at low O₂ concentrations, but decreases char conversion for combustion at high O₂ concentrations. These calculations give new insight into the complexity of the effects from the CO₂ gasification reaction and should help improve the understanding of experimentally measured oxy-fuel char combustion and burnout trends in the literature.     

Investigation of separation properties of turbulent boundary layer at its sequential interaction with shocks of different strengths

The results are presented for numerical modelling of two-dimensional flows with large pressure gradients in a wide range of freestream parameters (M = 2−4, Re ₁ = 5−30·10⁶ 1/m) and the intensities of perturbing factors. Computations were performed with the use of averaged unsteady Navier — Stokes equations of a viscous heat-conducting gas. The structure of a turbulent boundary layer at its passage through a single shock and a system of shocks of different strengths, which lie at a fixed distance from one another, was investigated numerically. In the case of the boundary layer passage through a system of shocks, the influence of the first interaction on the structure and separation properties of the boundary layer behind the second shock was investigated. The presence of a preliminary shock was shown to improve the boundary layer capability to withstand separation ahead of the secondary interaction region.     

The influence of surface porosity on the stability and transition of supersonic boundary layer on a flat plate

In the present study, we examined, both experimentally and theoretically, the influence of surface permeability on the stability and laminar-turbulent transition of supersonic boundary layer at free-stream Mach number M_∞ = 2. A satisfactory agreement was obtained between the data calculated by the linear theory of stability and the data obtained in experiments with natural disturbances performed on models with different porous inserts.     

Auto-oscillations in supersonic boundary layer

The production of periodic oscillations in a supersonic boundary layer at the moderate and high Mach numbers (M = 2 and 5.35) is investigated within the framework of the weakly nonlinear stability theory of the second order in nonlinearity. The model includes the effects of self-action, such as the generation of stationary secondary harmonics and the disturbances of double frequencies. It is shown that for two-dimensional vortex disturbances, the character of the excitation of vortex disturbances changes from the mild one to the stiff one with the increasing Mach number, which leads to a reduction of the critical Reynolds number Re_c. For three-dimensional disturbances of low azimuthal wave numbers, a supercritical auto-oscillatory regime sets in. A complex regime realizes for two-dimensional acoustic disturbances at M = 5.35 with a stiff excitation in the region of Re_c.     

Boundary Layer Stability¶in Real Vanishing Viscosity Limit

In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There, the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the form u _t +(F(u)) _x =ν(B(u)u _x ) _x $ (ν≪1) with an “elliptic” matrix B. However, real models, like the Navier–Stokes approximation of the Euler equations for a gas flow, involve incompletely parabolic perturbations: B is not invertible in general. We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for the hyperbolic first order system u _t +(F(u)) _x = 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity. Received: 27 November 2000/ Accepted: 16 March 2001     

Automation of a Mass Flow Controller for Application in Time‐Multiplex SF6+CH4 Plasma Etching of Silicon

In this work is proposed the automation of a gas injection (mass flow) system in order to generate timemultiplex SF₆/CH₄ radiofrequency plasma applied for silicon (Si) etching process. The control of the gas injection system is important in order to better control the process anisotropy, i.e., the high‐aspect‐ratio of mask pattern transfer to substrate surface. In other words, this control allows the attainment of deep Si etching process. Here, the automation of the gas injection system was realized through the interface between a computer and a data acquisition board. The automation software developed allows controlling the gas flow rate switching it on and off during whole process through the use of a square waveform routine, intermittent flow, beyond the conventional condition of a fixed value for gas flow rate, continuous flow. In order to investigate the time‐multiplex SF₆/CH₄ plasma etching of Si, the residual gas analysis was performed. The investigations were made keeping the following process parameters: flow of SF₆: 10 sccm, flow of CH₄: 6 sccm, 100 W rf power, wave period: 20 sec. It were monitored the partial pressure of SF⁺ ₅ (parent neutral specie: SF₆), CH⁺₄ (CH4) and SiF+ ₃ (SiF4) species as a function of time for different gas flow switching and duty cycle. The results showed that with the generation of plasma occurs a drastic change in behavior of partial pressures of SF⁺ ₅ and CH⁺₄ species. Moreover, it is evidenced that the interactions between the SF₆ and CH₄ fragments promotes a high production rate of HF molecule and consequently a decrease of atomic fluorine, mainly when plasma is on. Finally, the behavior of partial pressure of SiF⁺ ₃ specie for alternatively intermittent SF₆ and CH₄ flow operation shows us that both the etching processes and the deposition of a polymer passivation layer are occurring alternatively, a desirable feature for multi‐step etching process (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum properties of two-dimensional electron gas in the inversion layer of Hg1−xCdxTe bicyrstals

The electronic and magnetotransport properties of conduction electrons in the grain boundary interface of p-type Hg_1−xCd_xTe bicrystals are investigated. The results clearly demonstrate the existence of a two-dimensional degenerate n-type inversion layer in the vicinity of the grain boundary. Hydrostatic pressure up to 10³ MPa is used to characterize the properties of the two-dimensional electron gas in the inversion layer. At atmospheric pressure three series of quantum oscillations are revealled, indicating that tthree electric subbands are occupied. From quantum oscilations of the magnetoresistivity the characteristics parameters of the electric subbands (subband populations n_si, subband energies E_F−E_i, effective electron masses m^*_ci) and their pressure dependences are established. A strong decrease of the carrier concentration in the inversion layer and of the corresponding subband population is observed when pressure is applied A simple theoretical model based on the triangular-well approximation and taking into account the pressure dependence of the energy band structure of Hg_1−xCd_xTe is use to calculate the energy band diagram of the quantum well and the pressure dependence of the subband parameters.     

Impedance analysis of Bi<Subscript>3.25</Subscript>La<Subscript>0.75</Subscript>Ti<Subscript>3</Subscript>O<Subscript>12</Subscript> ferroelectric ceramic

AC impedance spectroscopy technique has been used to study electrical properties of Bi_3.25La_0.75Ti₃O₁₂ (BLT) ceramic. Complex impedance plots were fitted with three depressed semicircles, which are attributed to crystalline layer, plate boundary and grain boundary and all three were found to comprise of universal capacitance nature [C = C0w ⁿ⁻¹]. Grain boundary resistance and capacitance evaluated from complex impedance plots have larger values than that of plate boundary and crystalline layer. The activation energies (E _a) for DC-conductance in grain boundary, plate boundary and crystalline layer are 0.68 eV, 0.89 eV and 0.89 eV, respectively. Relaxation activation energies calculated from impedance plots showed similar values, 0.81 eV and 0.80 eV for crystalline layer and plate boundary, respectively. These activation energy values are found to be consistent with the E _a value of oxygen vacancies in perovskite materials. A mechanism is offered to explain the generation of oxygen vacancies in BLT ceramic and its role in temperature dependence of DC-conductance study.      

Measurement and simulation of edge plasma flow in the Tore Supra tokamak

A simple fluid model is used to interpret two edge flow phenomena that are observed in the scrape-off layer of the Tore Supra tokamak. (1) The Mach number of the parallel flow midway between the two sides of the toroidal limiter is always a significant fraction of the ion sound speed, typicallyM _?=?0.3÷?0.6. directed towards the high field side. In Tore Supra theE×B drift is relatively unimportant, so the esixtence of alarge parallel flow implies a significant poloidal aysmmetry of the SOL source. (2) Massive injection of neutral gas leads to a recycling source that is poloidally localized near the nozzle. The parallel Mach number changes during injection. The sign of the change is positive for injection on the high field side, and negative for injection on the low field side. The ionization source that is needed to produce the change is about 5÷10% of the total amount of injected gas, consistent with atomic physics calculations.     

Distribution of mean velocity in turbulent boundary layer over permeable surface with air blowing

In the present article, we investigate the possibility of using simple physical models for predicting properties of incompressible turbulent boundary layer on permeable wall at various values of air-microblowing mass flow rate. It is shown that the velocity scaling U _??*/?? ₉₉ can be successfully used to approximate the distribution of mean velocity in the outer region of the boundary layer. The use of this scaling makes the velocity profiles invariant with respect to Reynolds-number variation; this circumstance largely facilitates the analysis of experimental data, making it independent of upstream flow conditions. The distribution of mean velocity in the logarithmic flow region of the boundary layer over permeable surface can be described with a modified law of the wall involving a constant C ₀ equal to the same constant for canonical boundary layer, and a quantity K being a weak function of blowing ratio.     

Effect of boundary layer thickness before the flow separation on aerodynamic characteristics and heat transfer behind an abrupt expansion in a round tube

Results of numerical investigation of the boundary layer thickness on turbulent separation and heat transfer in a tube with an abrupt expansion are shown. The Menter turbulence model of shear stress transfer implemented in Fluent package was used for calculations. The range of Reynolds numbers was from 5·10³ to 105. The air was used as the working fluid. A degree of tube expansion was (D ₂/D ₁)² = 1.78. A significant effect of thickness of the separated boundary layer both on dynamic and thermal characteristics of the flow is shown. In particular, it was found that with an increase in the boundary layer thickness the recirculation zone increases, and the maximum heat transfer coefficient decreases. The work was financially supported by the Russian Foundation for Basic Research (project codes 07-08-00025 and 06-08-00300).     

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Re_th(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Re_th(p) → ∞, only at p = p _k = k, p = p _1/k = 1/k, and \(p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2\) , where k = 1, 2, 3, …. The minimum Reynolds number Re_th(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Re_th = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.     

Numerical Simulation of the Receptivity of a Supersonic Boundary Layer to Acoustic Disturbances in Compression and Rarefaction Flows

Doklady Physics - The receptivity of a boundary layer on a flat plate to acoustic disturbances in an incoming supersonic gas flow is studied numerically. Angles of attack are considered, at which...     

Recycling inflow method for simulations of spatially evolving turbulent boundary layers over rough surfaces

The technique by Lund et al. to generate turbulent inflow for simulations of developing boundary layers over smooth flat plates is extended to the case of surfaces with roughness elements. In the Lund et al. method, turbulent velocities on a sampling plane are rescaled and recycled back to the inlet as inflow boundary condition. To rescale mean and fluctuating velocities, appropriate length scales need be identified and for smooth surfaces, the viscous scale l_ν = ν/u_τ (where ν is the kinematic viscosity and u_τ is the friction velocity) is employed for the inner layer. Different from smooth surfaces, in rough wall boundary layers the length scale of the inner layer, i.e. the roughness sub-layer scale l_d, must be determined by the geometric details of the surface roughness elements and the flow around them. In the proposed approach, it is determined by diagnosing dispersive stresses that quantify the spatial inhomogeneity caused by the roughness elements in the flow. The scale l_d is used for rescaling in the inner layer, and the boundary layer thickness δ is used in the outer region. Both parts are then combined for recycling using a blending function. Unlike the blending function proposed by Lund et al. which transitions from the inner layer to the outer layer at approximately 0.2δ, here the location of blending is shifted upwards to enable simulations of very rough surfaces in which the roughness length may exceed the height of 0.2δ assumed in the traditional method. The extended rescaling–recycling method is tested in large eddy simulation of flow over surfaces with various types of roughness element shapes.     

Control of boundary layer on a flat plate by means of cavity flow

This paper describes the control of boundary layer on a flat plate by means of cavity flow. In this study, classifying the shapes of cavities into circular arc, rectangle and triangle makes the discussion, and the depths of the cavities are changed systematically. It is made clear, by numerical calculations and experiments, what states of flow are shown in the internal parts of cavities and what kinds of influence are exerted to the boundary layers in the upstream and downstream flows. As a result, the following facts are made clear. By taking up properly the depth ratios (k/c) of cavities complying with the individual cavity shapes, the boundary layer thickness in the flow upstream and downstream of the cavities can be controlled. Meanwhile with any of the cavities, the existence of the minimum boundary layer thickness (δ/δ _m ) _min min is seen at a depth ratio.     

Self-Similar Gas Motion Near The Evaporating Electrode of An Electric Arc

Simple solutions of 1Dt gas-dynamical equations based on similarity analysis are possible for the gas surrounding a point source of mass and energy such as an electrode (cathode) arc spot. To obtain nontrivial (non-zero temperature) solutions throughout, two-scale formulation is used that permits an additional boundary condition near the source. Three generalised gas flow variables, R, Z and V, related to gas density, temperature and velocity are calculated and presented as functions of a single similarity parameter, λ, related to position and time. The computational results are compared with data from two gas discharge experiments: on gas disturbances due to an electric arc of micrometer length in atmospheric air and on expansion of a metal-vapour plasma cloud generated by a low-pressure cold-cathode arc.