Crossflow Instability Research Articles

Multiple instabilities of three-dimensional boundary layers along a concave wall

The initial stage of laminar turbulent transition in boundary layers on a swept wing is governed by two types of instability, namely, the Tollmien-Schlichting instability based on the effect of viscosity and the cross-flow instability associated with the twisted velocity distribution of three-dimensional boundary layers. If the flow is along a locally concave surface, there is another possibility, that of Taylor–Görtler instability induced by centrifugal force. The strength of these instabilities mainly depends upon local Reynolds number, magnitude and direction of the cross-flow, and local curvature of the wall. Thus a model system of linear equations is proposed to describe the initial development of disturbances through the three instabilities, and its eigensolutions are used to evaluate stability limits of the Falkner Skan-Cooke flow to those disturbances. The three types of disturbances can be distinguished from each other by definite differences in the wavenumber and frequency regions. Three subregions in the parameter plane of cross-flow magnitude and wall curvature are determined in correspondence to the three instabilities, each of which gives the lowest value of critical Reynolds numbers in its own Subregion.

115 三次元境界層における乱流遷移の可視化

Turbulent transition problem of three-dimensional (3-D) boundary layers become one of the major research topics in fluid dynamics field, because of further refinement of general fluid machineries. Especially, investigation of the boundary-layer transition over a swept wing is important in order to increase commercial aircraft fuel efficiency. However, turbulent transition process in 3-D boundary layers are not well understood.Purpose of the present investigation is therefore, to clarify the transition process through visualization in the case of rotating axisymmetric bodies in general. Results shows that streamwise vortices appear in advance to T-S wave instability, and appearing instability is influenced by the local flow condition where transition appears, and centrifugal or crossflow instability might appear.

Traveling Disturbances on a Spinning Disk Boundary Layer.

Spinning disk boundary layer provides a flow field convenient for a swept wing boundary layer transition study. In order to examine the randomization process in crossflow dominant three-dimensional (3-D) boundary-layer transition region experimental investigation is performed and two kinds of traveling disturbances with frequencies differing by more than an order of magnitude are detected for the first time. The properties of these disturbances is measured using a rotatable paralle hot wire probe. Results showed that the low frequency disturbance seems to be due to the unsteady crossflow instability (primary instability), while the high frequency one to be inflexional instability (high frequency, secondary instability) and coincides with the structure visualized by smoke visualization technique.

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Experimental investigation of instability wave propagation in a three-dimensional boundary-layer flow

Wave propagation phenomena in three-dimensi onal boundary-layer flows with crossflow instability were investigated experimentally. A 10-element hot-film sensor was flush-mounted on a rotatable insert in a swept flate plate with imposed favorable pressure gradient. By means of cross-spectra l analysis it was possible to obtain direction and magnitude of the phase velocity and the group velocity of the traveling instability waves, thus filling a gap in the knowledge of crossflow instability characteristics. The waves were found to propagate approximately normal to the potential streamline direction, according to linear theory. Phase velocity and the resulting wavelengths also agree satisfactorily, whereas the measured direction and magnitude of the group velocity shows significant differences. Nomenclature c = chord length, 0.5 m cgr = group velocity cph = phase velocity E = voltage F = dimensionless frequency, / • / = dimensional frequency Ga = power spectrum of Xa(t) Gab(f) = cross spectrum of Xa(t) and Xb(t) k - complex wave number vector, k = (kr, &/), IA>l=27r/X

A New Parameter for Predicting Crossflow Instability.

Instability of boundary layers over a concave wall and a rotating disk which were thought to be essentially different in instability sources, are compared in order to investigate whether or not a single crossflow parameter can be defined. Using a newly defined crossflow parameter, prediction was attempted on a yawed cylinder boundary layer transition. By comparing the calculation with the experiment, it was found that this parameter can document fairly well the onset of crossflow instability.

Interaction Between Boundary-Layer Transition and Cavitation Phenomena on a Yawed Cylinder.

In this investigation, the relationship between cavitation phenomena and boundary-layer transition on a 45-degree yawed cylinder is investigated using both wind and water tunnels. The yawed cylinder is an appropriate model for the purpose of such investigations while there appears cross-flow instability, and streamwise vortices will appear in the boundary layer. The transition process in the case of a yawed cylinder is often investigated in relation to a swept = wing boundary-layer transition study. Appearance of the cavitation streaks, which have a regularly aligned fine structure in the streamwise direction, on the cylinder surface show that cavitation selectively appears along each cross-flow vortex where a low-pressure zone exists in the transition region of the boundary layer. The wavelengths of the cross-flow vortices measured in a wind tunnel model and of cavitation streaks measured in a water tunnel model are in good agreement. Since the comparison of other physically measurable flow properties between the 3-D boundary-layer transition and cavitation phenomena came out reasonably well, it can be considered, in general, that the cavitation inception is enhanced by cross-flow vortices appearing in a 3-D boundary layer on a 45 degree yawed cylinder.

Effects of uniform suction on the stability of flow on a rotating disc

The effects of uniform distributed suction on the cross-flow instability of the boundary layer on a rotating disc are considered. A vorticity-velocity formulation is used to obtain exact linear equations governing the development of infinitesimal disturbances to the steady flow on a rotating disc. A parallel flow approximation is made as a first step in determining the effect of suction on the instability. It is shown that suction has a stabilizing effect on the flow, whereas blowing is destabilizing. Small values of the suction parameter are found to increase significantly the critical Reynolds number associated with stationary modes of disturbance. The wave angle of the spiral vortices that precede turbulent flow is estimated from critical conditions and is shown to decrease with increase in suction rate. This is shown to be consistent with prediction based on an in viscid analysis. The corresponding estimate of the expected number of vortices is shown to increase with suction. Suction appears to make the second minimum on the neutral curve more pronounced, suggesting a possible increase in the relative importance of the associated low wavenumber mode of disturbance.

Complex demodulation applied to the transition to turbulence of the flow over a rotating disk

A complex demodulation technique based on the Hilbert transform is applied to hot-film velocity measurements of the flow over a rotating disk. As the cross-flow instability of the boundary layer of the disk sets in, finite bandwidth packets of Fourier modes appear and grow along the radius. These wave packets, giving strong amplitude and frequency modulations, allow the calculation of the envelope and instantaneous frequency of the signals. This decomposition in amplitude and frequency is used to determine different behaviors of the flow as the Reynolds number increases. Three concentric regions are accurately detected: a first one consisting of a linear growth of disturbances, a second zone where the flow becomes more organized, and finally a turbulent region. The transition to turbulence is also precisely determined and allows an interpretation in terms of defects (amplitude holes) occurring in the flow pattern.

The Linear Stability of a Flat Plate Boundary-Layer Approaching a Cylindrical Obstacle

The linear stability of the low-speed three-dimensional flow over a flat plate with an attached cylinder is studied. The region of interest is upstream of the initial separation point and includes the effects of both adverse and favorable pressure gradients, as well as crossflow. The resulting boundary-layer is subject to both the Tollmien-Schlichting (TS) and crossflow instabilities. Linear stability calculations, using N-factor correlations, indicate that the transition process would be dominated by TS instabilities, although for low frequencies crossflow-type disturbances are important.

Laminar-Turbulent Transition on a Swept Wing.

Three-dimensional boundary-layer transition experiments are currently being conducted on a 45° swept wing in the Arizona State University Unsteady Wind Tunnel. Crossflow-dominated transition is produced via a model with contoured end liners to simulate infinite swept-wing flow. Fixed-wavelength, stationary and traveling crossflow vortices are observed. The frequencies of the most amplified traveling waves are in agreement with linear-stability theory; however, traveling waves at frequencies an order of magnitude higher than predicted are also observed near transition. Boundary-layer profiles measured at several spanwise locations show streamwise disturbance profiles characteristic of the crossflow instability. Near the transition location, severe distortions of the steady boundary-layer profiles are observed in the form of multiple inflection points. This distorted boundary layer is due to the stationary crossflow vortex and is subject to a Rayleigh-type instability in the stream direction. As a result, a high-frequency secondary instability is detected in the transition region, and spatial relations of the process are well documented by the coupled use of flow visualization and hot-wire measuremests. In all cases, we observe a transition due to this high-frequency Rayleigh instability induced by the stationary crossflow vortex.

TIME-DEPENDENT INVISCID VORTICES IN THREE-DIMENSIONAL BOUNDARY LAYERS

We address the inviscid stability problem for time-dependent Görtler vortices within a three-dimensional boundary layer. As the crossflow component is increased the Görtler vortex is found to suffer a change in structure to either that of a crossflow instability or to a vortex which is trapped in a thin zone within the boundary layer. These results are natural counterparts to those found by Bassom and Hall (19) who were concerned with stationary inviscid and viscous Görtler vortices. We investigate the two forms into which the vortex may evolve with increasing crossflow and in particular we obtain an asymptotic description of the high wavenumber inviscid modes. Significantly, we demonstrate how the properties of these latter modes may be matched to the time-dependent viscous vortices of Bassom and Hall (19) and how the frequency of the disturbance crucially affects its characteristics.

Stability of three-dimensional supersonic boundary layers

A rotating cone that is located in a supersonic free stream at zero angle of attack is used as a model to investigate the stability of three-dimensional supersonic boundary layers. The boundary-layer profiles on the surface are calculated using the Cebeci–Keller box scheme. The stability equations are solved to determine the eigenvalues using a two-point fourth-order finite-difference scheme [Malik et al., Z. Angew. Math. Phys. 33, 189 (1982)]. The results show that the amplification rate of the first mode is increased by a factor of 2 to 4 due to the cross-flow, compared with a two-dimensional flow with the same streamwise profile. This increase decreases with increasing Mach number. The instability with cross-flow covers a wide range of unstable frequencies (including zero) and wave numbers. The results also show that the second mode in a three-dimensional boundary layer is oblique whereas the second mode in a two-dimensional boundary layer is two dimensional. The maximum amplification rate of the second mode decreases more slowly with increasing wave angle in a three-dimensional boundary layer than in a two-dimensional boundary layer. It is concluded that the cross-flow instability becomes important for cross-flow Reynolds number on the order of 50 for low Mach numbers and 100 for high Mach numbers, this Reynolds number range corresponds to a maximum cross-flow velocity of about 4%.

Forward sweep - A favorable concept for a laminar flow wing

The application of laminar flow on swept wings is authoritatively limited at high Reynolds numbers by a sweep angle where crossflow instability and attachment line transition lead to fully turbulent boundary layers on the wing. For a laminar flow wing, the reduction in sweep in the case of a forward swept wing leads to a more stable laminar boundary layer concerning transition because of crossflow instability and attachment line transition. Thus, with this concept, a laminar forward swept wing can be realized more easily than a comparable swept back wing

Keel Design for Low Viscous Drag

Foil and planform parameters which govern the level of viscous drag produced by the keel of a sailing yacht are discussed. It is shown that the application of laminar boundary-layer flow offers great potential for increased boat speed resulting from the reduction in viscous drag. Three foil shapes have been designed and it is shown that their hydrodynamic characteristics are very much dependent on location and mode of boundary-layer transition. The planform parameter which strongly affects the capabilities of the keel to achieve laminar flow is leading-edge sweep angle. The two significant phenomena related to keel sweep angle which can cause premature transition of the laminar boundary layer are crossflow instability and turbulent contamination of the leading-edge attachment line. These flow phenomena and methods to control them are discussed in detail. The remaining factors that affect the maintainability of laminar flow include surface roughness, surface waviness, and freestream turbulence. Recommended limits for these factors are given to insure achievability of laminar flow on the keel. In addition, the application of a simple trailing-edge flap to improve the hydrodynamic characteristics of a foil at moderate-to-high leeway angles is studied.

Stability of Three-Dimensional Boundary Layers

The computational modeling of the transition process characteristic of flows over swept wings is discussed. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that regular stability theory is insufficient to explain the discrepancies between experiments and between theory and experiment. The leading edge region of a swept wing will be considered in a three-dimensional spatial simulation with random disturbances as the initial conditions.

Investigations on high Reynolds number laminar flow airfoils

For further operating-cost reduction on transport aircraft, drag reduction by extended laminar flow on wings and empennages is mandatory. With carefully designed airfoils, laminar flow can be achieved even at high Mach and Reynolds numbers and moderate sweep angles. With laminar airfoils the fuel consumption decreases on the order of 30%. Twoand three-dimensional stability theory seems to be a good tool for determining laminar-turbulent boudary-layer transition caused by Tollmien-Schlichting and crossflow instabilities, but it must be checked by extensive flight tests.

Transition effects on slender cone pitch damping

A previously developed analytic theory for the effects of boundary-layer transition on slender cone pitch damping is amended to account for the fact that when the vehicle is perturbed from zero angle of attack, transition no longer occurs through Tollmien-Schlichting instability of the axial flow but through crossflow (inflexional) instability. This greatly improves the agreement between predicted and measured dynamic transition effects.

Wave interactions in swept-wing flows

The leading-edge region of swept wings is dominated by the crossflow instability, resulting in vortices that all rotate in the same sense. The effect of these vortices on the behavior of other disturbances is examined and an interaction between these and disturbances of half the dominating crossflow wavelength is predicted. According to theory, the interaction is of crossflow–crossflow type. The effect explains the anomalies found in the experimental observations of Saric and Yeates [Laminar-Turbulent Transition (Springer, Berlin, 1985), p. 429]. Visually Saric and Yeates observe vortices at the wavelength predicted by linear theory; however, in their hot-wire measurements they find that the second harmonic dominates disturbance growth, with eventually three times the amplitude of the primary wave. In this case, the usual transition–prediction methods would fail, clearly indicating the importance of studying interactions of this sort.

Some expectation on the mechanism of cross-flow instability in a swept wing flow

Three-dimensional boundary layer transition on axisymmetric rotating bodies is the subject of a comprehensive experimental study. Based on this study, hypotheses are made on the mechanism of cross-flow instability for swept wing flow. These new results are combined with past explanations to provide a rough sketch for the entire flow field over the swept wing. From this new viewpoint there appears the mechanism of traveling waves, being induced by a stationary disturbance. Some uncertainties appearing in recent papers concerning this flow field are discussed. Among these uncertainties for which an explanation is provided, is the discrepancy of frequencies between the hot wire signal and the visualized flow pattern.