Анализ взаимодействия пары направленных по потоку сверхзвуковых вихрей методами визуализации

Scientific visualization has taken a strong place among data analysis tools. Indeed, after all, its methods help not only to visualize the flow, but also to distinguish its main structures, to compare them, etc. The paper present application of visualization methods to analysis and comparison of a streamwise supersonic tip vortex pair interaction at the Mach number of the incoming flow M = 3. Maximum vorticity and the 2 criterion were used for this purpose. A pair of supersonic vortices was generated by two coaxial straight wings with sharp front, side and trailing edges. Two configurations are considered: a pair of counter-rotational vortices and a pair of co rotational vortices. In the first case, the attack angle of the wings was +10, in the second -the attack angle of one wing was +10, of the second -10. Numerical data were obtained in the region of 10 wing chords downstream from the wing axis using a numerical model based on URANS equations with the turbulence model SA. Numerical simulations were carried out on the K-60 hybrid supercomputer system at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences using the developed ARES software package for modeling 3D turbulent flows on high-performance computer systems. The main simulations were performed using 224 processors. Simulations were carried out on unstructured grids with hexagonal cells. The paper also shows an example when commonly used visualization methods application leads to some ambiguousness, because they give false additional vortex zones.

Three-dimensional velocity distributions and corresponding wall stresses are measured concurrently in the inner part of a turbulent boundary layer over a smooth wall using digital holographic microscopy. The measurements are performed in a square duct channel flow atReδ= 50000 andReτ= 1470. A spatial resolution of 3–8 wall units (δυ= μm) in streamwise and spanwise directions and 1 wall unit in the wall-normal direction are sufficient for resolving buffer layer structures and for measuring the instantaneous wall shear stresses from velocity gradients in the viscous sublayer. Mean velocity and Reynolds stress profiles agree well with previous publications. Rudimentary observations classify the buffer layer three-dimensional flow into (i) a pair of counter-rotating inclined vortices, (ii) multiple streamwise vortices, some of them powerful, and (iii) no apparent buffer layer structures. Each appears in about one third of the realizations. Conditional sampling based on local wall shear stress maxima and minima reveals two types of three-dimensional buffer layer structures that generate extreme stress events. The first structure develops as spanwise vorticity lifts from the wall abruptly and within a short distance of about 10 wall units, creating initially a vertical arch. Its only precursors are a slight velocity deficit that does not involve an inflection point and low levels of vertical vorticity. This arch is subsequently stretched vertically and in the streamwise direction, culminating in formation of a pair of inclined, counter-rotating vortices with similar strength and inclination angle exceeding 45°. A wall stress minimum exists under the point of initial lifting. A pair of stress maxima develops 35δυdownstream, on the outer (downflow) sides of the vortex pair and is displaced laterally by 35–40δυfrom the minimum. This flow structure exists not only in the conditionally averaged field but in the instantaneous measurement as well and appears in 16.4% of the realizations. Most of the streamwise velocity deficit generated by this phenomenon develops during this initial lifting, but it persists between the pair of vortices. Distribution of velocity fluctuations shows that spanwise transport of streamwise momentum plays a dominant role and that vertical transport is small under the vortices. In other regions, e.g. during initial lifting, and between the vortices, vertical transport dominates. The characteristics of this structure are compared to early experimental findings, highlighting similarities and differences. Abundance of pairs of streamwise vortices with similar strength is inconsistent with conclusions of several studies based on analysis of direct numerical simulation (DNS) data. The second buffer layer structure generating high wall stresses is a single, predominantly streamwise vortex, with characteristic diameter of 20–40δυand inclination angle of 12°. It generates an elongated, strong stress maximum on one side and a weak minimum on the other and has been observed in 20.4% of the realizations. Except for a limited region of sweep above the high-stress region, this low-lying vortex mostly induces spanwise momentum transport. This structure appears to be similar to those observed in several numerical studies.

Exact solutions of the Navier–Stokes equations describing the interaction of streamwise vortices with a rigid surface are utilized to develop a conceptual model for the surface pressure spectrum associated with the wall region of a turbulent boundary layer. The evolution of single as well as pairs of coherent streamwise vortices, which principally govern the production of turbulence in the wall region, is considered in the presence of local straining flow induced by larger, outer-layer eddies. The surface pressure signatures of the coherent vortex motion and the associated power spectrum of the pressure are examined. Based on the results of the exact solutions, the surface pressure spectrum of an ensemble of independent coherent structures is modeled using the assumption of ergodicity in the manner described by Townsend and Lundgren for homogeneous turbulence. The free parameters in the model are estimated through comparison with available results from experiments and numerical simulations. The model, especially the one involving pairs of streamwise vortices, predicts the high frequency and high spanwise wave number range of the surface pressure spectrum quite well. Further, the probability density function of surface pressure associated with the model compares well with experimental results. Interestingly, the model also suggests that the contribution of the viscous interaction to low wave number spectral elements accounts for the discrepancy between experimental observations at such wave numbers and the prediction of the Kraichnan–Phillips theorem.

A novel method of calculating static derivatives and acceleration derivatives using Computational Fluid Dynamics is presented. This method uses field velocity approach to simulate the unsteady forced-plunging flow field over the aircraft without updating the field grids during each time step. This provides an improvement in computational efficiency over similar precision without loss of generality. Finally, to verify the present method, the Basic Finner missile as the benchmark example was taken to calculate its acceleration derivatives at various Mach number. Results are in fairly good agreement with traditionally method and the tunnel experimental results. Comparisons with the results of time-dependent simulations are also included.

Serrations, which imitate the sawteeth-like structures in the leading edge of owl wing, enable to reduce noises and alter the aerodynamic performance. However, the mechanism is not yet completely understood because the flow fields have three-dimensionality. In this study, in order to investigate three-dimensional mean flow structures on a flat plate with leadingedge serrations, flow fields viewed from the spanwise and vertical directions were measured by two-dimensional time-resolved PIV and stereo PIV at the Reynolds number of 5.0×10. When the angle of attack was 6 degree, the interval of the flow pattern was equal to the width of one sawtooth of the serrations. Whereas the flow over the trough was separated, and the flow over the vertex passed along the surface of the flat plate. This is because pairs of longitudinal vortices induced by the serrations suppress the flow over the vertex on the uppersurface of the flat plate. When the angle of attack was 14 degree, several flows over the vertexes were gathered, and specific flow patterns were formed. The flow over the vertex passed along the surface of the flat plate, so that separation points viewed from the spanwise direction moved to the downstream side. Reverse-flow regions behind the troughs could be divided into two categories, “open” and “closed” ones. Pairs of longitudinal vortices were seen in the closed reverse-flow regions only, and growth of the open reverse-flow regions forces the vortices to move upwards.

Foiling yachts and crafts are both very sensitive to the flying height in terms of stability and performance, raising the scientific issue of the influence of the free-surface when the foil is at low submergence. This work presents numerical simulations of a 2D hydrofoil section NACA0012 at 5° angle of attack in the vicinity of the free surface, for different values of the submergence depth, for a chord-based Froude number of 0.571 and a Reynolds number of 159,000. URANS equations are solved with a mixture model to capture the free surface, and using an automatic grid refinement. Verification of the numerical model and validation with data from the literature are presented. Deformation of the free surface and alteration of the hydrodynamic forces compared to the deep immersion case are observed for a submergence depth-to-chord ratio h/c lower than 2. The foil drag increases up to more than three times the infinite-depth value at h/c ≈ 0.5. The lift force slightly increases until h/c around 1, and then decreases sharply. For h/c < 0.5, the pressure field around the foil is totally modified and the lift is swapped to downward. The study highlights the importance of considering the effect of finite submergence to compute foils’ hydrodynamic forces, for example to be used in Velocity Prediction Programs (VPP) of foiling crafts.

Detailed three-dimensional measurements of the first vortex pairing of a large plane mixing layer reveal excitation of several three-dimensional instability modes. Time evolution in three-dimensional space (x, y, z, t) shows how the two-dimensional rollers become three-dimensional as they approach each other and that the linear growth of at least two instability waves leads to a spanwise periodic pairing. The results are based on phase-locked measurements made in three-dimensional spatial grids, with a mesh spacing of 8.5% of the fundamental instability wavelength. Spanwise-uniform, periodic acoustic excitation stabilizes the most probable two-dimensional natural features – roll-up and first pairing. The second subharmonic is added to study the effect of alternate streamwise pairing locations on the three-dimensional characteristics of vortex pairing. Velocities are measured using hot-wire anemometry, and the coherent structures are reconstructed from the ensemble-averaged vorticity field.Vortex pairing is shown to initiate through local ‘bridging’ at the maxima of periodic spanwise undulations. The undulations result from linear amplification of various instability modes on pairing rollers having different strengths. Bridging results from the change of the relative phase between the spanwise undulations of the pairing rollers from in-phase (due to the initial translative mode) to out-of-phase (due to the amplification of bulging-like and non-axisymmetric modes). It is found that when pairing occurs sufficiently far upstream, only axisymmetric waves are amplified and the evolution results in axisymmetric merging. In contrast, when pairing occurs sufficiently far downstream, both axisymmetric and non-axisymmetric waves are amplified and the evolution results in non-axisymmetric merging.The results indicate that vortex pairing is accompanied by the counter-rotating pairs of secondary structures (‘streamwise vortices’ or ‘ribs’) located in the mixing-layer braids and residing in the valleys of the spanwise-roller waves. Time evolution of these secondary structures shows that they move in the transverse direction, following the rollers.

Experiments were conducted with a counter-rotating, streamwise vortex pair embedded in flat plate boundary layers, in a low-turbulence wind tunnel, to understand the role of local separation on transition. Steady, streamwise vortices were generated downstream of gaps in spanwise-uniform, smooth hills (of height h) affixed to the plate, 175 mm from its leading edge. The flow between is directed away from the plate. At the four tunnel speeds 1.8–3.5 m/s considered, the Reynolds numbers based on displacement thickness at this location varied from 248 to 346. Small, medium and large gaps of 2, 4 and 8 mm, respectively, were set up; they were about a third to twice the boundary layer thickness (\(2/3< b/h < 8/3\)). With the closest vortex pairs, transition was observed at all freestream speeds considered. With larger spacing, transition occurred at the highest speed only. The vortex pair caused the flow to separate in all but the largest-gap cases. Separation was steady and re-attachment unsteady in all cases. Velocity fluctuations grew slightly upstream of re-attachment in transitional cases. No evidence was found for separation or re-attachment as a direct cause for transition; transition occurred even without separation. Instead, whenever transition was observed, its origin could be traced to instability of a streak of sufficient amplitude that had been created by the vortex pair. Streak instability appeared as fluctuations growing along its sides and spreading. Anomalous behaviour was also observed with moderate spacing, where transition did not occur in spite of flow separation and streak amplitudes in excess of known thresholds for streak instability.

Extensive hot-wire measurements have been made to determine the structure of the large eddy in a synthejc turbulent boundary layer on a flat-plate model. The experiments were carried out in a wind tunnel at a nominal free-stream velocity of 12 m/s. The synthetic turbulent boundary layer had a hexagonal pattern of eddies and a ratio of streamwise scale to spanwise scale of 3.2:1. The measured celerity of the large eddy was 84.2 percent of the free-stream velocity. There was some loss of coherence, but very little distortion, as the eddies moved downstream. Several mean properties of the synthetic boundary layer were found to agree quite well with the mean properties of a natural turbulent boundary layer at the same Reynolds number. The large eddy is composed of a pair of primary counter-rotating vortices about five δ long in the streamwise direction and about one δ apart in the spanwise direction, where δ is the mean boundary-layer thickness. The sense of the primary pair is such as to pump fluid away from the wall in the region between the vortices. A secondary pair of counter-rotating streamwise vortices, having a sense opposite to that of the primary pair, is observed outside of and slightly downstream from the primary vortices. Both pairs of vortices extend across the full thickness of the boundary layer and are inclined at a shallow angle to the surface of the flat plate. The data show that the mean vorticity vectors are not tangential to the large-eddy vortices. In fact, the streamwise and normal vorticity components that signal the presence of the eddy are of the same order of magnitude. Definite signatures are obtained in terms of the mean skin-friction coefficient and the mean wake parameter averaged at constant phase. Velocities induced by the vortices are partly responsible for entrainment of irrotational fluid, for transport of momentum, for generation of Reynolds stresses, and for maintenance of streamwise and normal vorticity in the outer flow. A stretching mechanism is important in matching spanwise vorticity close to the wall to variations in turbulent shearing stress. Regions where the stretching term is large coincide with regions of large wall shearing stress and large turbulence production.

Resarch on the Key Techniques of CFD in the calculation of rowing blade

The wing rock induced by a hemisphere–cylinder forebody was investigated experimentally using an isolated delta wing and wing body. For the delta wing with sweep angle of 30 deg, no apparent limit-cycle wing rock occurs at angles of attack of 0–90 deg. The mean roll angles exhibit nonzero values at angles of attack of less than 15 deg and become zero at angles of attack of more than 15 deg. For the wing body with a hemisphere–cylinder forebody, apparent wing rock exists at angles of attack of 0–90 deg; the wing rock is induced by the forebody. The phase diagrams showed that the wing rock motion is a typical limit-cycle oscillation at lower and moderate angles of attack. With increasing angles of attack, however, stochastic components in wing rock motion are increased gradually, and the motion types start to deviate from a limit-cycle oscillation. The phase-locked particle-image-velocimetry measurements for the wing body revealed that the vortex pair over the forebody exhibits apparent dynamic hysteresis in position and strength during wing rock, and the dynamic hysteresis of forebody vortices further influence flowfields over the wing, resulting in asymmetric distributions of wing flow, which provides the driving moments sustaining the wing rock.

A Scheme for Generating Unstructured Grids on Spheres with Application to Parallel Computation

The three-dimensional behavior of flow transition in circular and 6-chevron jets at Re = 5000 is investigated with experiments conducted on a free water jet by time-resolved tomographic particle image velocimetry. The emphasis is on the unsteady organization of coherent flow structures, which play a role in the generation of acoustic noise. Shedding and pairing of vortices are the most pronounced phenomena observed in the near field of the circular jet. The first and second pairing amplify the axial pulsatile motion in the jet column and lead to the growth of azimuthal waves culminating in the breakup of the vortex ring. Streamwise vortices of axial and radial vorticity are observed in the outer region and move inward and outward under the effect of the vortex rings. In the jet with chevrons, the axisymmetric ring-like coherence of the circular jet is not encountered. Instead, streamwise flow structures of azimuthal vorticity emanate from the chevron apices, and counter-rotating streamwise vortices of axial and radial vorticity develop from the chevron notches. The decay of streamwise vortices is accompanied by the formation of C-shaped structures. The three-dimensional analysis allows quantifying the vortex stretching and tilting activity, which, for the circular jet exit, is related to the azimuthal instabilities and the streamwise vortices connecting the vortex rings. In the chevron jet, stretching and tilting peak during the formation of C-structures. Following Powell’s aeroacoustic analogy, the spatial distribution of the source term is mapped, evaluating the temporal derivative of the Lamb vector. The spatio-temporal evolution of such source term is visualized revealing that the events of highest activity are associated with the processes of vortex-ring pairing and vortex-ring disruption for the circular jet, and with the decay of streamwise instabilities and the formation of C-shaped structures for the chevron case.

Undesirable effects such as a decrease in lift and an increase in drag can be the result of the occurrence of cavitation on hydrofoils. The goal of this research is to investigate the effect of water injection on the lift and drag coefficient of a 2-D hydrofoil. An unsteady uniform flow of water over a NACA hydrofoil (2D) is numerically simulated. For the numerical simulation of a cavitating flow, a bubble dynamics cavitation model is used to describe the generation and evaporation of the vapor phase. The RNG k-ε turbulence model is used as a turbulence model. To simulate the cloud cavitation, a modification to the turbulent viscosity which is necessary, is implemented. This simulation is done for various angles of attack and different injection velocities. Comparison between experimental data and the numerical simulation obtained here is done to validate the numerical results. The results presented here show that, as the mass flow of the water injection increases, the lift coefficient decreases for all angles of attack but the rate of this decrease decreases for higher angles of attack. As the mass flow rate increases, the drag coefficient increases more for small angles of attack and decrease for larger angles of attack.

РАВНОВЕСНЫЕ ФОРМЫ ЖИДКОСТИ НА ВНУТРЕННЕЙ ПОВЕРХНОСТИ ВРАЩАЮЩЕГОСЯ ЦИЛИНДРА И ИХ УСТОЙЧИВОСТЬО.А