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Modern approaches to visualization and automatic identification of separation regions of three-dimensional boundary layers are discussed. The corresponding algorithms are implemented within the framework of the original LOTRAN software package designed to predict the onset of a laminar-turbulent transition in boundary layers over small-curvature surfaces. Their work is demonstrated using two configurations: a swept wing and a prolate spheroid.

The most promising areas of research in the field of plasma aerodynamics are proposed. On the basis of the presented experimental data obtained recently, the possibilities of using the volumetric force effect on the gas flow in aerodynamic applications, which is realized with the help of near-surface electric discharges, are considered. One of these applications is to increase the length of the laminar section of the boundary layer on the swept wing in order to reduce the aerodynamic drag of the aircraft in the cruise flight mode. The second direction is associated with the control of the three-dimensional separation of the boundary layer on the elements of the mechanization of the swept wing in the take-off and landing modes. The third direction is the reduction of surface friction in the turbulent boundary layer, which is realized on most of the surface of modern near- and supersonic aircraft. The proposed studies are not only of applied, but also of fundamental importance due to the physical complexity of the studied phenomena.

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

Abstract—Flow in the three-dimensional boundary layer on a yawed plate of finite length from which a gas is injection along the normal is considered in the case of the regime of strong viscous-inviscid interaction. In order to investigate the upstream disturbance propagation, the flow functions are expanded in four-term series in the neighborhood of the leading edge of plate under the assumption that the base pressure which depends on the transverse coordinate is given on the plate trailing edge. It is shown that these expansions contain an undefined function and its first and second derivatives with respect to the transverse coordinate. The corresponding boundary-value problems are formulated and numerically solved and the eigenvalues are found. It is shown that the possibility of downstream influence becomes significantly higher with increase in both the yawing angle and the intensity of gas injection. The influence of the constitutive parameters on the flow characteristics in the three-dimensional boundary layer is investigated.

Abstract—Wind tunnel experiments on the control of flow in a three-dimensional boundary layer are performed using a multidischarge actuator system. The boundary layer was produced on a swept plate with an induced streamwise negative pressure gradient. The actuator system used a near-surface barrier discharge for producing a unidirectional three-dimensional force action over a lengthy region of the plate surface. The possibility of considerably reducing the cross-flow velocity and mitigating the intensity of stationary vortices that produce the cross-flow instability by means of the action of an actuator system is confirmed.

Suitable slot structure of the compressor blade can generate high-momentum jet flow through pressure difference between the pressure and suction surface, it has been proved that the slot jet flow can reenergize the local low-momentum fluid to effectively suppress the flow separation on the suction surface. In order to explore a slotted method for better comprehensive suppressing effects on the boundary layer separation near blade midspan and the three-dimensional corner separation, a diffusion stator cascade with large camber angle is selected as the research object. Firstly, the Slotted_1 and Slotted_2 whole-span slotted schemes are set up, then the Slotted_3 scheme with whole-span slot and blade-end slots is proposed, finally the performance of original cascade and slotted cascades is computed under a wide range of incidence angles at the Mach number of 0.7. The results show that: in the full range of incidence angles, compared with the whole-span slotted cascades, the development of the endwall secondary flow on the suction surface of Slotted_3 cascade is effectively suppressed, the degree of the mutual interference between the secondary flow and the main flow is reduced. Besides, on the suction surface of Slotted_3 cascade, the boundary layer separation near blade midspan and the corner separation are basically eliminated. As a result, compared with those of original cascade, the total pressure losses of Slotted_3 cascade are reduced in the full range of incidence angles, and its operating range of incidence angles is broadened. Moreover, compared with the whole-span slotted schemes, Slotted_3 scheme has a better adaptability to wide range of incidence angles.

Boundary-layer receptivity is always a hot issue in laminar-turbulent transition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept flat-plate boundary layer is a typical three-dimensional flow. Study of its receptivity is important both in theory and applications. In this paper, a freestream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space discretization. On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer (the infinite back-swept flat-plate boundary layer) by free-stream turbulence is studied numerically. If so, effects of the level and the direction of free-stream turbulence on the three-dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.

Laminar boundary layer flow over an infinite-span, finite-length flat plate is investigated in the regime of strong interaction with a hypersonic gas flow. Under the assumption that an additional condition dependent on the transverse coordinate can be imposed on the trailing edge of the plate the flow functions are expanded in power series in the vicinity of the leading edge. It is shown that these expansions include an indefinite function dependent on the transverse coordinate. The corresponding boundary value problems are formulated and solved and the eigenvalues are determined. It is established that in this case the two-dimensional boundary layer can rearrange itself into a three-dimensional boundary layer.

The flow in the three-dimensional laminar boundary layer on a yawed flat plate of finite length is studied in the regime of strong viscous-inviscid interaction with a hypersonic flow. In the vicinity of the leading edge the flow functions are expanded in series under the assumption that the base pressure dependent on the transverse coordinate is given at the trailing edge of the plate. It is established that the expansions obtained include an indefinite function and its derivative with respect to the transverse coordinate. The corresponding boundary value problems are formulated and numerically solved, the eigenvalues are found, and it is shown that the exponent in the third term of the expansion differs from that in the second term only by one. The plate surface temperature effect on the flow parameters and the initiation of three-dimensional disturbances is investigated.

The three-dimensional stability of two-dimensional natural convection flows in a heated, square enclosure inclined to the horizontal is investigated numerically. First, the computational procedure is validated by comparison of base flow solutions to results reported in literature across a range of inclinations. A bi-global linear stability analysis is then conducted to investigate the stability of these two-dimensional base flows to infinitesimal three-dimensional perturbations, and the effect that buoyancy forces (defined by a buoyancy number $R_N$) and enclosure inclination $\\theta$ have on these stability characteristics. The flow is first observed to become three-dimensionally unstable at buoyancy number $R_N = 213.8$ when $\\theta$ is $180^\\circ$; this increases to $R_N = 2.54 \\times 10^4$ at inclination $\\theta =58^\\circ$. It is found that the two-dimensional base flow is more unstable to three-dimensional perturbations with the critical $R_N$ corresponding to three-dimensional instability being significantly lower than its two-dimensional counterpart across all considered inclinations except $83^\\circ \\leq \\theta \\leq 88^\\circ$, where the most unstable mode is a two-dimensional oscillatory mode that develops in the boundary layers along the conducting walls. Eight different leading three-dimensional instability modes are identified, with inclinations $58^\\circ \\leq \\theta < 88^\\circ$ transitioning through an oscillatory mode, and inclinations $88^\\circ \\leq \\theta \\leq 180^\\circ$ transitioning through a stationary mode. The characteristics of the primary instability modes corresponding to inclinations $88^\\circ \\leq \\theta \\leq 179^\\circ$ indicate the presence of a Taylor–Görtler instability.