Gortler Vortices Research Articles

強制波長のゲルトラー渦による二次不安定流れの生成過程

強制波長のゲルトラー渦による二次不安定流れの生成過程

Thermal instability in natural convection flow over a rotating convex surface subject to external magnetic field

This paper presents magnetic effect on the Goertler vortices in natural convection flow over a heated rotating convex surface. The onset position is characterized by the Grashof number, depends on the rotational Reynolds number, the Prandtl number, the Hartmann number, and the wave number. The buoyancy force, the Lorentz force, and the Coriolis force significantly affect the flow structure and heat transfer of the flow. However, centrifugal force has minor stabilizing effect on the flow. Negative rotation and external magnetic field stabilize the convex boundary layer flow. On the contrary, positive destabilizes the flow. The numerical data show agreement with the experimental results in the case of zero rotation.

ゲルトラー渦間に生成する二次不安定流れの可視化(続報)

The forced wavelengths of Gortler vortices are easily given by the leading edge plates with varying the period of a saw-tooth edge, and the variation of the forced wavelengths makes transformation of secondary instability flows. The experiments with concave channel of 1 m radius of the curvature for main airflow velocity of 2.5m/s were performed using the leading edge plates. Variation in secondary instability flows was tested by smoke visualization and hot-wire measurement, and was examined from viewpoints of maximum disturbance amplitude Kmax. It was confirmed that meandering flows whose (Kmax)max varies linearly with the non-dimensional forced wavelength parameter Λ prevail at 100<Λ<200. On the other hand, horseshoe-type vortices with (Kmax)max= {-.7em} aisebox{1.1ex}{.} {.1em} aisebox{-0.2ex}{.} 0.35 are formed at Λ of 250 or greater.

Shock Wave/Transitional Boundary-Layer Interactions in Hypersonic Flow

The experimental and numerical transitional interactions in hypersonic flow are studied. The experiments were performed on a hollow cylinder-flare model in the ONERA R2Ch wind tunnel at a Mach number of 5 and for varying stagnation pressure. Wall pressure and heat-flux measurements, laser Doppler velocimetry, pitot boundary-layer surveys, surface flow visualizations, and schlieren photographs provide a precise and complete description of the flowfield. In all of the cases examined here, grid-converged axisymmetric mathematical solutions of the problem were obtained by use of the two-dimensional numerical simulation, but it was found that these solutions do not fit experiments when the Reynolds number is increased. A purely three-dimensional organization of the flow then appears, characterized by the Gortler vortices. Two families of solutions were thus evidenced, and the precise calculation of the physical one remains a numerical challenge. The prediction of transition by use of stability calculations is only partly possible because the waves used do not have a sufficiently general form to model such a complex physical problem. New information on the true nature of what is commonly called a transition mechanism in this kind of flow is deduced from these results.

Visualizing Görtler vortices

The development of Gortler vortices with pre-set wavelength of 15 mm has been visualized in the boundary-layer on a concave surface of 2.0 m radius of curvature at a free-stream velocity of 3.0 m/s. The wavelength of vortices was pre-set by vertical wires of 0.2 mm diameter located 10 mm upstream of the concave surface leading edge. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different regions can be identified based on different growth rate of the vortices. The occurrence of a secondary instability mode is indicated by the formation of a small horseshoe eddies generated between the two neighboring vortices traveling streamwise, to form mushroom-like structures as a consequence of the non-linear growth of the Gortler vortices.

803 ゲルトラー渦のスパン方向波長に及ぼす境界層厚さの影響について(OS8-1 複雑乱流の計測と制御(境界層),OS8 複雑乱流の計測と制御,オーガナイズドセッション)

803 ゲルトラー渦のスパン方向波長に及ぼす境界層厚さの影響について(OS8-1 複雑乱流の計測と制御(境界層),OS8 複雑乱流の計測と制御,オーガナイズドセッション)

A218 ゲルトラー渦間に生成する二次不安定流れの可視化

Gortler vortices were developed in boundary layers on concave walls, and the high-frequency horseshoe-vortices were generated in the upwash region between pairs of Gortler, vortices downstream. In this experiment, flow visualization by smoke and Hot-wire measurements were conducted for the free air stream velocity of 2.5 m/s using a concave wall of 1 m radius of curvature with different shapes of leading edge plates. The relation between the forced wavelength given by the plate and secondary instability flows of horseshoe vortices mode and sinuous mode are also discussed.

Study of Boundary Layer Flow in Rotating Curvature System (Effects of Wall Curvature and System Rotation on Goertler Type Instability)

The behavior of the boundary layer in rotating channels, such as that in impeller passages of turbomachinery, is dominantly influenced by the centrifugal and Coriolis forces due to the wall curvature and system rotation, respectively. The resultant force may promote or suppress the instability in the boundary layer, depending on its magnitude of the component normal to the wall boundary. The purpose of the present study is to make clear experimentally the effects of Gortler type instability on the laminar boundary layer developing along the concave surface, focusing attention on transition process from laminar to turbulent state in the rotating system with streamline curvature. The longitudinal velocity and turbulent intensity have been measured near the concave surface in the channel whose radii of center line curvature is 2 000 mm. Different types of secondary instability such as varicose and sinuous modes were found to follow the generation of Gortler vortices, depending on the magnitude of the resultant force of centrifugal and Coriolis forces, acting toward the concave wall.

A217 凹曲面境界層内に生成する馬蹄形渦の可視化

Goertler vortices generate in laminar boundary layers on concave walls. The horseshoe vortices generate downstream, and these are broken in laminar-turbulent boundary layers. The experiments were carried out with a concave wall of Im in radius of curvature for 3m/s of main airflow velocity. The behavior of the horseshoe vortices was visualized by smoke and measured with a hot-wire. Additionally, the visualizations and the velocity measurements at four positions were conducted simultaneously. In this paper, the process of the horseshoe vortices breakdown is described.

Study on the formation of Goertler vortices in natural convection flow over a rotating concave surface

This paper presents a numerical study of the formation of Goertler vortices in natural convection flow over a concave surface with rotation. The onset position characterized by the Grashof number Gr δ r , depends on the rotational Reynolds number, the Prandtl number ( Pr = 0.7 for air) and the wave number. The buoyancy force and Coriolis force are found to significantly affect the flow structure and heat transfer. However, centrifugal force has minor stabilizing effect on the flow. Positive rotation stabilizes the boundary layer flow on the concave surface. On the contrary, negative rotation destabilizes the flow. The numerical data show reasonable agreement with the experimental results in the case of zero rotation.

Sediment erosion by Görtler vortices: the scour-hole problem

Experimental results on sediment erosion (scour) by a plane turbulent wall jet, issuing from a sluice gate, are presented which show clearly – it seems for the first time – that the turbulent wall layer is destabilized by the concave curvature of the water/sediment interface. The streamwise Görtler vortices which emerge create sediment streaks or longitudinal sediment ridges. The analysis of the results in terms of Görtler instability of the wall layer indicates that the strength of these curvature-excited streamwise vortices is such that the sediment transport is primarily due to turbulence created by these vortices. Their contribution to the wall shear stress is taken to be of the same form as the normal turbulent wall shear stress. For this reason, the model developed by Hogg et al. (J. Fluid Mech. Vol. 338, 1997, p. 317) remains valid; only the numerical coefficients are affected. The logarithmic dependency of the time evolution of the scour-hole depth predicted by this model is shown to be in good agreement with experiments. New scaling laws for the quasi-steady state depth and the associated time, inspired by the Hogg et al. (1997) model are proposed. Furthermore, it is emphasized that at least two scouring regimes must be distinguished: a short-time regime after which a quasi-steady state is reached, followed by a long-time regime, leading to an asymptotic state of virtually no sediment transport.

Instability of surfactant solution flow in a Taylor cell

The hydrodynamic instability of surfactant solutions between two coaxial cylinders was investigated by using a laser-induced-fluorescence flow visualization technique to clarify the effect of drag-reducing additives on vortex formation in Taylor-Couette flow. The test fluids were Ethoquad O/12 surfactant solutions, which have a gel-like structure called "shear-induced structure" (SIS). Photographs of the formation of Gortler vortices were taken and compared with these of tap water. In the Taylor number range of 1.2 × 10$^5$ l T$_a$ l 7.1×10$^5$, tap water and 10 ppm surfactant solution flows consisted of Taylor vortices and much smaller Gortler vortices at the rotating inner wall. However, for 50 and 100 ppm surfactant solutions, Taylor vortices were not apparent and Gortler vortices were collapsed. Measurements of the wavelength of Gortler vortices lead to the conclusion that surfactant solutions have a stabilizing effect on Gortler instabilities. This effect depends on surfactant concentration and becomes considerable with increasing acceleration of the inner cylinder.

Combination interaction of Taylor–Goertler vortices in a curved shear layer of a supersonic jet

Problems of origination and evolution of streamwise vortex structures in an initial region of the shear layer of a supersonic jet are discussed. Streamwise vortices are generated with the use of artificial microroughnesses on the internal surface of polished nozzles. Results of Pitot pressure distributions measured in a supersonic nonisobaric jet both in the radial and azimuthal directions are presented. Streamline curvature in the initial region of supersonic nonisobaric jets has a significant effect on evolution of streamwise vortex structures. Azimuthal heterogeneity corresponding to streamwise vortices in the shear layer is analyzed with the use of both the Fourier analysis and wavelet analysis.

Seeding of Görtler vortices through a suction and blowing strip

The resulting wavelength of Gortler vortices in boundary layers over concave surfaces is determined by the upstream history of the flow and by wall disturbances such as roughness, heating/cooling strips or suction and blowing. In isotropic disturbance conditions, the predominant wise wavelength corresponds to the strongest growing vortex mode predicted by the linear stability theory. If the disturbance environment is not isotropic, vortices with wavelength different from the one with the highest growth rate may emerge. The present investigation considers the wavelength selection when Gortler vortices are excited by a suction and blowing strip at the wall. The study is based on numerical simulations of the vorticity transport equations derived from the Navier-Stokes equations. They are solved using a compact high-order finite difference technique. The results show that, when the vortices are excited by suction and blowing at the wall, their wise wavelength does not necessarily correspond to the imposed wavelength. Curves of streamwise development of the disturbance energy for different harmonics are presented, showing the evolution of the dominant modes. Isolines of streamwise velocity in the wise plane are also presented, showing how the higher harmonics distort the characteristic mushroom structures.

스테레오 PIV를 이용한 워터젯 흡입덕트 내부의 난류유동측정

Stereoscopic PIV measurements were made in the wind tunnel with the actual size waterjet model. The main wind tunnel provides the vehicle velocity while the secondary wind tunnel adjusts the jet issuing velocity. Experiments were performed at the range of jet to vehicle velocity ratio (JVR), 3.75 to 8.0 and the Reynolds number of 220,000 based on the jet velocity and the hydraulic diameter of the waterjet intake duct. Wall pressure distributions were measured for various JVRs. Three dimensional velocity fields were obtained at the inlet and outlet of the intake duct. It is found that severe acceleration is occurred at the lip region while deceleration is noticeable at the ramp side. The detailed three dimensional velocity fields can be used as the accurate velocity input for the CFO simulation. It is interesting to note that there are many different types of vortices in the instantaneous velocity field. It can be considered that those vortices are generated by the comer of rectangular section of the intake and Gortler vortices due to the curved wall. However, typical secondary flow with a pair of counter rotating vortex pair is clearly seen in the ensemble averaged velocity field.br/

Instability-wave propagation in boundary-layer flows at subsonic through hypersonic Mach numbers

Direct numerical simulations (DNS) form an important ingredient to physics-based prediction of laminar-turbulent transition in boundary-layer flows, particularly in applications where it is desirable or even essential to model the various stages of transition process in an integrated manner. This paper addresses two building-block issues towards such capability: application to instability-wave propagation in boundary layers over curvilinear surfaces and robust outflow boundary conditions across the speed regime. In particular, detailed comparisons of linear and nonlinear development of instability waves in a range of boundary-layer flows are used to cross-validate a high-order direct numerical simulation algorithm against the approximate but computationally more efficient technique of parabolized stability equations (PSE). Three separate flow configurations are investigated in this study: (i) development of a Tollmien-Schlichting (TS) instability wave over a two-dimensional (2D), symmetric, low-speed airfoil, (ii) both first and second-mode development in a self-similar, flat plate boundary layer at Mach 4.5, and (iii) amplification of first and second modes of Rayleigh instability and a stationary Gortler vortex in the hypersonic, axisymmetric boundary layer over a flared cone. The satisfactory agreement between the DNS and PSE predictions for both amplitudes and mode shapes of the instability waves confirms the overall efficacy of the DNS algorithm, while underscoring the accuracy of predictions based on the PSE approximation.

Transition on Concave Surfaces

Boundary layer measurements have been made on the concave surfaces of two constant curvature blades using hot wire anemometry. All the current experiments were performed with negligible streamwise pressure gradient. Grids were used to produce a range of freestream turbulence levels between 1% and 4%. The freestream velocity increases with distance from a concave wall according to the free vortex condition making the determination of the boundary layer edge difficult. A flat plate equivalent boundary layer procedure was adopted, therefore, to overcome this problem. The Taylor–Goertler (TG) vortices resulting from the concave curvature were found to make the laminar and turbulent boundary layer profiles fuller and to increase the skin friction coeffiicent by up to 40% compared with flat plate values. This leads to a more rapid growth in boundary layer thickness. The evolution in the intermittency through transition is very similar to that for a flat plate, however, the shape factors are depressed slightly throughout the flow due to the fuller velocity profiles. For all the current experiments, curvature promoted transition. This was very marked at low freestream turbulence level but remained significant even at the highest levels. It appears that the velocity fluctuations associated with the TG vortices enhance the freestream turbulence resulting in a higher effective turbulence level. A new empirical correlation for start of transition based on this premise is presented. The ratio of end to start of transition momentum thickness Reynolds numbers was found to be approximately constant.

A232 三次元縮流筒壁に沿うゲルトラー渦の可視化

A232 三次元縮流筒壁に沿うゲルトラー渦の可視化

Optimal Disturbances in Compressible Boundary Layers

The problem of transient growth in compressible boundary layers is considered within the scope of partial differential equations including the nonparallel flow effects. As follows from previous investigations, the optimal disturbances correspond to steady counter-rotating streamwise vortices. The corresponding scaling of the perturbations leads to the governing equations for a Gortler-type of instability, with the Gortler number equal to zero. The iteration procedure employs back and forth marching solutions of the adjoint and original systems of equations

Optimal Disturbances in Compressible Boundary Layers

The problem of transient growth in compressible boundary layers is considered within the scope of partial differential equations including the nonparallel flow effects. As follows from previous investigations, the optimal disturbances correspond to steady counter-rotating streamwise vortices. The corresponding scaling of the perturbations leads to the governing equations for a Gortler-type of instability, with the Gortler number equal to zero. The iteration procedure employs back and forth marching solutions of the adjoint and original systems of equations