In order to meet the economic and environmental requirements, turbomachine blades and aircraft wings are becoming more light and flexible, and bearing more mechanical and aerodynamic loads. However aerodynamic excitation would bring more variables into the structural vibration, and becoming an aeroelasticity problem. Unlike mechanical resonance vibration, the structure would interact with the aerodynamic excitation, and the aerodynamic excitation frequency would lock into structural natural frequency even the frequency margin is more than 10%. This phenomenon extends the high amplitude response range and should be noticed in safety design in order to deal with the margin in specific resonance conditions. In this paper, the aerodynamic excitation induced forced response is investigated with experimental setup including upstream cylinder and a downstream single NACA airfoil in wind tunnel. The upstream cylinder generates the vortices imposed on the NACA airfoil, brings periodic excitation on the flexible blade. Flow velocity is measured with hot wire anemometer (HWA) at upstream and downstream of the blade synchronously. Numerical simulation is conducted based experimental condition and verified by the measurements. Proper Orthogonal Decomposition (POD) is applied to obtain the major flow structure at one typical flow condition. The structural properties of the airfoil including natural frequency and damping are evaluated through finite element analysis and hammer test. Based on the fluid and structure properties, coupled test and analysis can be conducted. The vibration characteristics of NACA airfoil at 1st and 2nd order modes are explored by altering the freestream velocity and cylinder diameter. The forced vibration of 1st order mode has the lock-in phenomenon, and the maximum amplitude point is not at the resonance point. But 2nd order mode shows typical resonance behavior.
The analytical expression for the quadrupole moment of a charged conducting droplet caused by the presence of the self- and induced charges on the droplet surface is obtained. The droplet is assumed to be motionless in the superposition of gravitational and electrostatic fields. The analytical calculations are carried out in the first order in the dimensionless oscillation amplitude of the droplet. The intensity of electromagnetic radiation of the droplet generated by time variation in its quadrupole moment is estimated in the second order of smallness with respect to the square of the ratio of the characteristic linear droplet size to the length of emitted wave.
The solution of the Buckley-Leverett problem classical for the theory of flow through a porous medium, generalized to the case of two-phase flows in fractured-porous media, is considered. In this case, immiscible displacement of fluid in the porous medium is complicated by the absence of local capillary equilibrium between pore spaces of different scales and in the generic case the solution of problem is not self-similar. The flow through a porous medium is considered in the limiting case of large time scales when capillary equilibrium is established and the flow parameter distributions, as shown in the study, tend to self-similar asymptotics. For the effective ordinary porous medium the average equations of equilibrium flow through the porous medium which describe these asymptotics are obtained
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.
This paper investigates the unsteady aerodynamic characteristics of an oscillating flat plate and the NACA 0012 airfoil around the angle of attack (AoA) close to their static stall angle at a low Reynolds number, 3.2 × 104. The kinematic oscillatory motion is described by a sinusoidal function in which the oscillation frequency and amplitude are variable. Both experimental and numerical methods are applied in the two-dimensional space. The experiment aims at measuring the aerodynamic forces and the moment directly. For numerical simulation, the SST (Shear Stress Transport) gamma theta model is employed to solve the unsteady flow field and to compute the lift coefficients (CLs). Good qualitative agreement between the experimental and numerical results for CL is obtained, which demonstrates the feasibility of the modified RANS model in the flow transition case. In general, NACA 0012 is greatly influenced by the dynamic effect in contrast with the flat plate. For a given reduced frequency, the shape of the hysteresis loop of CL shows some distinguishing features; the process of flow reattachment of NACA 0012 is slower than that of the flat plate in the downstroke phase, so that a smooth transition of CL is observed; there are still vortices shedding from the trailing edge even at small angles of attack, which results in a local instability of CL. By studying the effects of the reduced frequency (K) and the amplitude, it is found that the AoA corresponding to the maximum CL is more sensitive to the former and the reduced pitch rate (a') is the main parameter determining the dynamic stall angle for both flat plate and NACA 0012. In addition, the results for K = 0.07 show that the lift and drag coefficients at a maximum angle of attack are close to their static values for the discussed amplitudes and wing geometries.
The process of laminar-turbulent transition in a boundary layer is studied in terms of vortex evolution, from the growth of weak external disturbances to the formation of intense waves resulting in the development of a turbulent flow having internal scales of the problem. The self-sustained turbulence is obtained and the flow patterns on the plate surface and inside the turbulent boundary layer with fluid plumes propagating from the plate surface in the form of "bursting" are investigated. The basic flow parameters are calculated, such as the frequency and intensity of gas velocity fluctuations in turbulent spots. The validity of a local turbulence similarity law is confirmed. The study is performed on the basis of direct numerical simulation of a flow over a plate with Mach number M = 2 using unsteady Navier-Stokes equations without any closure model of turbulence.
The problem of stationary Mach reflection of a Shockwave in a plane channel is considered within the framework of the Euler model. Emphasis is placed on an investigation of the flow parameters at the triple point. In an analytical investigation the local theory for curvilinear shock waves is employed. The conditions on the input data of the problem, at which singularity is realized at the triple point, are derived. Under the singularity conditions the flow parameter gradients and the curvatures of the shock fronts and tangential discontinuity at the triple point increase without bound. In the numerical investigation the second-order Godunov method is used, together with a new technology of contracting the grid toward the triple point in combination with the discontinuity fitting. The calculations confirm the theoretically predicted singularity boundary. Additional numerical experiments show that the singularity boundary is conserved, when artificial source terms are introduced into the energy equation. These results allow one to put forward the hypothesis that the singularity within the same boundaries is also realized for other two-dimensional flows with irregular shock-wave reflection.
At present, the hydraulic fracture technologies are widely used for intensification of oil and gas recovery from reservoirs with hard-to-recover reserves. The simulation of the processes of flow through porous reservoirs with hydraulic fractures is fairly completely developed in the steady-state flow approximation. Unsteady processes of pressure distribution are considered with reference to the theory of hydrodynamic methods of investigations of wells in which asymptotically limited intervals of variations in the coordinates and time, i.e., the distances of the order of the well radius and time much smaller than the characteristic time of the process of flow through the porous medium, are considered. At the same time, in the reservoirs with hard-to-recover reserves (low-permeability reservoirs and high-viscosity oils) the duration of the unsteady processes of pressure redistribution can be of the same order as the characteristic time of flow through the reservoir. In the present study new analytical solutions of the problem of unsteady pressure redistribution in the neighborhood of a well penetrated by a vertical fracture are given. The scientific novelty of the study consists in the fact that, firstly, the fluid compressibility in the fracture and, secondly, the fluid flow not only through the fracture but also through the porous reservoir are taken into account in the model used. The solutions of the problems are constructed using the Laplace transform technique. In particular cases, the expressions well-known in literature follow from the solutions obtained. The analytical solutions obtained which makes it possible to determine the main characteristic features of the processes of flow through a porous medium are analyzed.
The linear stability of combined evaporating liquid—vapor-gas mixture flow is investigated under conditions of inhomogeneous heating within the framework of the conjugate problem. The exact solution of the Navier-Stokes equations in the Boussinesq approximation is used to describe the two-layer flow. The solution takes into account the influence of both nonzero streamwise and transverse temperature gradients and the direct and inverse thermal diffusion effects in the vapor-gas layer and on the phase interface. The influence of the applied external thermal load on the main flow parameters, their structure, the volume vapor content, the mass evaporation rate, and the stability is studied for systems with various liquid-layer thicknesses. The typical forms of characteristic perturbations are distinguished and the critical loads that lead to loss of stability at small transverse temperature drops are determined.
The problem of ice formation in unsaturated soil in the presence of pressure gradient and capillary forces is formulated. The complete system of conditions on the crystallization surface is derived. The one-dimensional problem is investigated in the self-similar formulation. The dependence of the amount of the ice formed on the problem parameters is also investigated. It is found that the ice saturation increases as the pressure on the cooling wall that initiates water inflow to the front decreases and also in the regime of more intense cooling. Increase in the pressure leads to water outflow from the front and decrease in the ice saturation.
The process of laminar-turbulent transition in a boundary layer is studied in terms of vortex evolution, from the growth of weak external disturbances to the formation of intense waves resulting in the development of a turbulent flow having internal scales of the problem. The self-sustained turbulence is obtained and the flow patterns on the plate surface and inside the turbulent boundary layer with fluid plumes propagating from the plate surface in the form of “bursting” are investigated. The basic flow parameters are calculated, such as the frequency and intensity of gas velocity fluctuations in turbulent spots. The validity of a local turbulence similarity law is confirmed. The study is performed on the basis of direct numerical simulation of a flow over a plate with Mach number M = 2 using unsteady Navier-Stokes equations without any closure model of turbulence.
Experiments were conducted on overexpanded equilateral triangular supersonic jets (Mach 1.8) at Reynolds numbers 6.71 × 105 and 4.81 × 105 to study their decay and spread characteristics by means of measuring the jet centreline and lateral total pressure distributions. Schlieren images of the jets were also taken to study the shock patterns in the jet structure. The above Reynolds numbers correspond to the nozzle inlet total pressures of 550 kPa (6.71 × 105) and 360 kPa (4.81 × 105). For comparison purposes the above experiments were repeated on a circular nozzle with the same exit area and area ratio (1.44) and total pressures. The observations from the experiments reveal that the triangular jet exhibits a shorter supersonic core compared with the circular jet, i.e., reduction of 34.25% at 360 kPa and 31.11% at 550 kPa. The total pressure decay is more abrupt and a greater loss of the total pressure occurs closer to the nozzle exit plane in the case of the triangular jet compared to the circular jet. The lateral total pressure distribution reveals that the jet spreading rate is greater on the flat than on the corner side of the triangular jet.
The technique of experimental investigation of the effect of an accelerated shear flow on the development of the Rayleigh—Taylor (RT) instability at the interface of two fluids at a small Atwood number is developed. Using a counterpart of the laser sheet method (laser induced fluorescence) the data on the structure of the RT mixing zone are obtained and the instability stabilization under the action of an accelerated shear flow is confirmed.
An open cavity flow exhibits intense self-sustained oscillations. This transient behavior stimulates violent pressure fluctuations because of multiple-order cavity tones. Detached eddy simulation was conducted to simulate the cavity flow at the freestream Mach number of 1.19. In order to improve the understanding of the shear layer convection processes and frequency characteristics the velocity of the flow field at cavity mid-span was studied using the dynamic mode decomposition (DMD) algorithm. The first three modes of the supersonic cavity flow were extracted to describe the flow configuration at the dominant frequencies. The two-vortices, three-vortices, and four-vortices are the corresponding first three DMD modes. The simplified mode structures are proposed to explain the flow dynamics in a supersonic cavity. When a feedback compression wave encounters the extrusion wave at a special location, an “analogous sonic boom” phenomenon appears causing violent noise in the cavity.
Features of the processes of sound generation in turbulent jet flows are analyzed. Two possible processes are considered, namely, noise of dissipating turbulence and noise generated by largescale turbulent-flow perturbations which accompany propagation of turbulent jets. The data of the theoretical and experimental investigations of statistical turbulence theory are used to estimate the first of the above-mentioned effects. The data of computational experiments are used to analyze the process of sound generation by large-scale perturbations. In these numerical experiments time-dependent subsonic turbulent jet flows were directly calculated using the LES technology and the experimental data. It is shown that the noise of large-scale perturbations can be satisfactorily reproduced by the numerical simulation and its properties correspond to the experiments on studying sound generation in jets; the contribution of noise of dissipating turbulence to the total jet noise seems to be insignificant.
After publication of the paper, the authors realized that the affiliation of the fourth author (Tiberiu Esanu) was given incorrectly. Its correct version appears above. Moreover, a second funding grant was missed in the acknowledgements. We give their complete correct version below.
The results of experiments on the motion of a plate rigidly fastened to a dynamometric trolley performed in the water channel of Moscow State University are presented. The wave wake behind the body and the flow ahead of it in a finite-depth fluid were investigated at near-critical velocities of the motion and small planing angles. The observations show that a steady periodic wave wake occurs together with a nose wave of fixed shape, while in the case of detached rear waves the waves are excited ahead of the planing plate. The well-known Russell formula for the solitary wave amplitude is experimentally confirmed. It is shown that, accurate to small parameters, it coincides with Lavrent’ev’s results. The experimental conditions are numerically simulated using the XFlow™ software package. The results of the experiments performed in the water channel are in agreement with the numerical results.
The present numerical work is devoted to the effect of an external magnetic field on a pulsating flow through an open cavity in a horizontal channel. The cavity is heated uniformly from the bottom wall. The finite volume method is used to solve the energy and NavierStokes equations. At the inlet of the channel flow pulsations are produced by adding a sinusoidal component to the velocity. The investigation is conducted for different Strouhal (0 St 1), Richardson (0.25 Ri 1), and Hartmann numbers (0 Ha 50) and for various aspect ratios of the cavity (L/H = 1, 1.5, and 2) at a pulsation amplitude A = 0.1. Various characteristics of the flow, such as isotherms, streamlines, and average and normalized Nusselt numbers are presented. The results indicate that the influence of the external magnetic field on the temperature distribution, flow field, heat transfer mode, and heat transfer enhancement rate vary with the Hartmann number. The effect of pulsations on the heat transfer enhancement is well correlated with the magnetic field intensity, Richardson number, and aspect ratio of the cavity.