Curved Shear Layer Research Articles

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers via Nonlinear Boundary Region Equations

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number M∞, the shear layer thickness δ, the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer ΔV on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing ΔV and A decreases with increasing delta. It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure’s amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration.

Experimental and numerical study of coherent structures in a roughness induced transition boundary layer at Mach 5

A wind tunnel experiment and large eddy simulation are carried out for the investigations of a Mach 5 boundary layer transition flow induced by distributed ramp shaped roughness elements. The wind tunnel experiment is carried out using the nano-tracer planar laser scattering technique to capture the coherent structures, whereas implicit large eddy simulation is carried out in the same flow conditions. Dominant unstable modes are analyzed. Comparisons show that the major frequencies obtained from the experiment and the computation generally agree with each other, although transition occurs much earlier in the wind tunnel. Coherent structures play a significant role in the transition process. Their formation and development are analyzed. The roughness generates a pair of counter-rotating streamwise vortices in its wake. Two high vorticity regions, i.e., the detached curved shear layer formed by streamwise counter-rotating vortices and the near-wall boundary layer, contribute to a majority of the transition process. In the early transition stage, hairpin-like vortices are generated as a consequence of the Kelvin-Helmholtz instability of the curved shear layer. Meanwhile, vertical convection is formed, which enhances the disturbance growth in the near wall boundary layer and finally accelerates the transition.

Rapid Analysis of Scramjet and Linear Plug Nozzles

interaction between operating condition and plume shape complicates the analysis of such nozzles compared to traditional bell nozzles. A method that is based on Riemann interactions is proposed for the analysis of two such nozzle geometries. The method assumes two-dimensional geometries and supersonic flow. Unlike the method of characteristics, this method accounts explicitly for the presence of oblique shocks and curved shear layers. Comparisons to both experiment and computational fluid dynamics are shown. The solution method requires no grid generation and typically runs in less than a minute on a single desktop computer, which is ideal for conceptual design, control design, or control evaluation studies. It includes high-temperature gas modeling and finite-rate chemistry. Nomenclature A = area c = specific heat Ex = momentum conservation error H = height or length scale M = Mach number nexp = number of discrete waves in expansion nsp = number of species p = pressure r = length of characteristic R = normalized gas constant T = temperature u = magnitude of flow velocity W = molecular weight x, y = spatial coordinates Y = mass fraction = angle between wave and upstream flow = ratio of specific heats = deflection angle across a wave = angle of deflection caused by boundary layer = flowpath angle = momentum thickness = ratio of static pressures = Mach angle = Prandtl-Meyer angle = streamwise coordinate = density = angle between wave and x-axis ˙ ! = molar rate of production

302 曲がりせん断層での渦の合体における渦度の消失(流体工学I)

302 曲がりせん断層での渦の合体における渦度の消失(流体工学I)

The mean and turbulent flow structure of a weak hydraulic jump

The turbulent air–water interface and flow structure of a weak, turbulent hydraulic jump are analyzed in detail using particle image velocimetry measurements. The study is motivated by the need to understand the detailed dynamics of turbulence generated in steady spilling breakers and the relative importance of the reverse-flow and breaker shear layer regions with attention to their topology, mean flow, and turbulence structure. The intermittency factor derived from turbulent fluctuations of the air–water interface in the breaker region is found to fit theoretical distributions of turbulent interfaces well. A conditional averaging technique is used to calculate ensemble-averaged properties of the flow. The computed mean velocity field accurately satisfies mass conservation. A thin, curved shear layer oriented parallel to the surface is responsible for most of the turbulence production with the turbulence intensity decaying rapidly away from the toe of the breaker (location of largest surface curvature) with both increasing depth and downstream distance. The reverse-flow region, localized about the ensemble-averaged free surface, is characterized by a weak downslope mean flow and entrainment of water from below. The Reynolds shear stress is negative in the breaker shear layer, which shows that momentum diffuses upward into the shear layer from the flow underneath, and it is positive just below the mean surface indicating a downward flux of momentum from the reverse-flow region into the shear layer. The turbulence structure of the breaker shear layer resembles that of a mixing layer originating from the toe of the breaker, and the streamwise variations of the length scale and growth rate are found to be in good agreement with observed values in typical mixing layers. All evidence suggests that breaking is driven by a surface-parallel adverse pressure gradient and a streamwise flow deceleration at the toe of the breaker. Both effects force the shear layer to thicken rapidly, thereby inducing a sharp free surface curvature change at the toe.

Improved Prediction of Plane Transverse Jets in Supersonic Crossflows

THE flowfield due to transverse injection of a round sonic jet into a supersonic flowis a configuration of interest in the design of supersonic combustors or thrust vector control of supersonic jets. The flow is also of fundamental interest because it presents separation from a smooth surface, embedded subsonic regions, curved shear layers, strong shocks, an unusual development of the injected jet into a kidney-shaped streamwise vortex pair, and a wake behind the jet. Although the geometry is simple, the flow is complex and is a good candidate for assessing the behavior of turbulence models for high-speed flow, beginning with the corresponding two-dimensional flow shown in Fig. 1. At the slot, an underexpanded sonic jet expands rapidly into the supersonic crossflow. Expansion waves reflect at the jet boundary, coalesce, and give rise to a Mach surface (Mach disk for round jets).

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.

Structure, Penetration, and Mixing of Pulsed Jets in Crossflow

Effects of periodic disturbances on the structure and mixing of a transverse jet have been investigated through chemically reactive laser-induced fluorescence experiments in a water model. Flow visualization experiments with a steady, round jet in crossflow revealed a distinct vortex loop merging pattern among the vortices that make up the curved shear layer around the jet. As the vortex loops are stretched and distorted, certain parts of the neighboring loops with the opposite or the same sign of vorticity merge, resulting in cancellation or intensification of the vorticity in the corresponding regions of the jet. When the flow rate of this jet was periodically modulated by a square wave, however, distinct vortex rings were created whose spacing and strength were dictated by the pulsing frequency for a given jet and crossflow combination. At low pulsing rates, these rings penetrated into the crossflow significantly deeper than the steady jet. An optimum pulsing frequency was found at which closely spaced vortex rings were observed, which penetrated as discrete vortices into the crossflow in the near field. Strong interactions among neighboring rings were observed farther downstream

The effects of curvature on wake-dominated incompressible free shear layers

Instability characteristics of curved incompressible free shear layers, with mean velocity profiles having a wake component, are studied using linear inviscid stability theory in spatial formulation. Both two- and three-dimensional disturbances are considered. The shear layer mode and the wake mode, previously found in a plane shear layer with a wake component in the mean velocity profile, are also found in the corresponding curved shear layer. Results of unstably curved shear layers with a wake component are consistent with those of previous investigations of a curved shear layer without a wake component. Results for a stably curved shear layer with a wake component show that the growth rate of the wake mode increases with increasing shear layer curvature and an oblique wake mode can become dominant compared to its corresponding two-dimensional wake mode. A wake-dominated shear layer, therefore, can become unstable as its curvature increases, regardless of whether the shear layer is stably or unstably curved regarding the corresponding monotonic mixing layer profile. The amplification rates of the shear layer mode and the wake mode could become comparable by varying the free-stream density ratio. For a wake-dominated shear layer under three-dimensional disturbances, the centrifugal modes are found. These modes are developed out of the wake mode for a stably curved shear layer and developed out of the shear layer mode for an unstably curved shear layer. Since the stability behavior is governed by the wake behavior, the wake-dominated shear layer could support the centrifugal instability regardless of the sense of curvature regarding the corresponding monotonic mixing layer profile.

Origin of Streamwise Vortices in Supersonic Jets

Our purpose is to clarify the initial conditions necessary for the development of streamwise vortices observed in underexpanded jets. In particular, we examine whether the Taylor-Gortler instability established in the curved shear layers of an underexpanded jet is a sufficient condition for the formation of streamwise vortices

Laser-diagnostic and numerical study of strongly swirling natural gas flames

This study is focused on the experimental and numerical investigation of the reacting flow field of a strongly swirling, unconfined 150-kW natural gas flame. This work is embedded in the TECFLAM swril burner project in which five research groups currently are involved with various tasks. The final goal is the accurate prediction of complex combustion systems with advanced models based on a complete data set of the governing turbulent flow and reaction field. At this point, attention is paid to the influence of the turbulence structure on the mixing process. A two-component Laser-Doppler Velocimetry (LDV) system is used for the determination of mean and fluctuating velocity components. Two-dimensional temperature fields and fuel-gas distributions are measured via Rayleigh scattering. Three-dimensional temperature distributions and flamefront surfaces are obtained via simultaneous measurements of Rayleight scattering and OH Laser-Induced Fluorescence (LIF) in three adjacent planes. An advanced numerical simulation, based on a nonlinear second moment closure is presented to be in good agreement with experimental data. The mean values of axial and circumferential velocity reconfirm a substantial reverse flow surrounded by a curved shear layer. High strain rates yield an intensive turbulent mixing process. It can be concluded from measured temperature fluctuations in this region that reaction takes place in this inner part of the shear layer. The entraining ambient air cannot penetrate through this highly strained area, thus isolating the hot core and providing a stabilizing mechanism to the flame. The 3-D time-resolved measurements of the flamefront give evidence that its structure is disconnected for strongly swirling flames.

Calculation of curved shear layers with two-equation turbulence models

Three extensions of the k-ε turbulence model were tested for shear-layer flows with streamline curvature. The first version is an algebraic-stress model which was derived by simplification of modeled Reynolds-stress equations and does not contain curvature-specific empiricism. The other two versions use a modified form of the dissipation-rate equation. The test cases considered are a convexly curved boundary layer, a curved mixing layer, and wall jets on logarithmic spiral surfaces. The results show that the algebraic-stress model gives the best overall agreement in the curved part of the flow but predicts too fast a recovery after the removal of curvature.

Evidence of imbedded vortices in a three-dimensional shear flow

Vortex phenomena encountered in an investigation of the streamwise development of the three-dimensional wake region behind the tip of a three-dimensional wedge model are reported. Pressure profiles were measured by pitot probes downstream of a tip with a nearly constant surface pressure level and a nearly continuous surface curvature in a blowdown air tunnel operating at Mach 6. Rather than the simple three-dimensional quasi-parallel shear flow expected, the measurements indicated the presence of a flow with large deficits in longitudinal pitot pressure, which are usually associated with the core region of quasi-steady longitudinal vortices. Vapor screen flow visualizations also support the presence of longitudinal vortices located primarily in the tip region and evidently forming in the vicinity of the wake neck. An increase in overall wake thickness by 100% is also observed. The origin of the vortices as quasi-steady Taylor-Gortler vortices generated in the concavely curved shear layer near the wake neck is considered. It is pointed out that the existence of longitudinal vortexes suggests that three-dimensional turbulence modeling may be much more difficult than previously supposed.

An Approximate Method for Curved Shear Layers

Steady, incompressible two-dimensional laminar boundary layers on curved surfaces with spanwise rotation are investigated using an approximate method. A fourth-degree polynomial is assumed for the velocity profiles and they are found to constitute a three-parameter family of curves characterized by a pressure factor, a curvature parameter and a rotational parameter. The results obtained for constant surface velocity flow with/without rotation on plane/curved surfaces are found to be consistent with those reported in the literature.

Momentum Integral for Curved Shear Layers

If the exact metric influence of curvature is retained and the displacement effect neglected, it can be shown that the momentum integral for two-dimensional, curved boundary-layer flows is identical to the von Karman momentum integral. As a result, attempts by previous researchers to account for longitudinal curvature effects by adding more terms to the momentum integral are shown to be correct.

The analogy between streamline curvature and buoyancy in turbulent shear flow

A formal algebraic analogy is drawn between meteorological parameters, such as the Richardson number, and the parameters describing the effect of rotation or streamline curvature on a turbulent flow. The analogy between thephenomenais a good first approximation. Semi-quantitative use of the analogy to apply meteorological data to curved shear layers shows that the effects of curvature on the apparent mixing length are appreciable if the shear-layer thickness exceeds roughly 1/300 of the radius of curvature; larger effects may occur in compressible flow. Application of the Monin-Oboukhov formula considerably improves the agreement between prediction and experiment in boundary layers on curved surfaces.