Cross-stream Pressure Gradient Research Articles

Morphology of long gas bubbles propagating in square capillaries

We present the results of a systematic analysis of the morphology of the thin lubrication film surrounding a long gas bubble transported by a liquid flow in a square capillary. Direct numerical simulations of the flow are performed using the Volume-Of-Fluid method implemented in OpenFOAM, for a range of capillary and Reynolds numbers Ca=0.002−0.5 and Re=1−2000, and very long bubbles, up to 20 times the hydraulic diameter of the channel. The lubrication film surrounding the bubbles is always resolved by the computational mesh, and therefore the results are representative of a fully-wetting liquid. This study shows that when Ca ≥ 0.05, the long gas bubble exhibits an axisymmetric shape on the channel cross-section, whereas for lower capillary numbers the bubble flattens at the centre of the channel wall and thick liquid lobes are left at the corners. When Ca ≤ 0.01, the thin film at the centre of the wall assumes a saddle-like shape, which leads to the formation of two constrictions at the sides of the liquid film profile, where minimum cross-sectional values of the film thickness are observed. The resulting cross-stream capillary pressure gradients drain liquid out of the thin-film, whose thickness decreases indefinitely as a power-law of the distance from the bubble nose. Therefore, the film thickness depends on the length of the bubble, unlike flow in circular channels. We report detailed values of the centreline, diagonal and minimum film thickness along the bubble, bubble speed, and cross-sectional gas area fraction, at varying Ca and Re. Inertial effects retard the formation of the saddle-shaped thin-film at the channel centre, which may never form if the bubble is not sufficiently long. However, the film thins at a faster rate towards the bubble rear as the Reynolds number of the flow is increased.

Three-Dimensional Boundary Layer in a Turbine Blade Passage

The boundary layer on the end wall of a turbine blade cascade is subject to cross-stream pressure gradients in the blade passage, which generate a cross-stream velocity component to make it three dimensional. This distorts the turbulence relative to a two-dimensional boundary layer and impacts the end wall heat transfer. This study presents measurements of the three-dimensional boundary layer in a turbine cascade obtained with a laser Doppler velocimeter. In addition, two types of Reynolds-averaged Navier–Stokes models are compared to the measurements: the Shear Stress Transport model using the isotropic eddy viscosity assumption and a Reynolds stress model that allows for anisotropy of the Reynolds stress. Neither model fully captures the complexity of the three-dimensional boundary layer in a turbine blade passage, particularly for turbulence associated with the cross-stream flow and for the highly accelerated three-dimensional boundary layer at the passage exit. Measurements at the passage exit indicate a very thin boundary layer with laminarlike qualities. Because of the boundary-layer complexity, end wall heat transfer is not well predicted toward the pressure side and the exit of the blade passage.

Comparison of the Three-Dimensional Boundary Layer on Flat Versus Contoured Turbine Endwalls

The boundary layer on the endwall of an axial turbomachine passage is influenced by streamwise and cross-stream pressure gradients, as well as a large streamwise vortex, that develop in the passage. These influences distort the structure of the boundary layer and result in heat transfer and friction coefficients that differ significantly from simple two-dimensional boundary layers. Three-dimensional contouring of the endwall has been shown to reduce the strength of the large passage vortex and reduce endwall heat transfer, but the mechanisms of the reductions on the structure of the endwall boundary layer are not well understood. This study describes three-component measurements of mean and fluctuating velocities in the passage of a turbine blade obtained with a laser Doppler velocimeter (LDV). Friction coefficients obtained with the oil film interferometry (OFI) method were compared to measured heat transfer coefficients. In the passage, the strength of the large passage vortex was reduced with contouring. Regions where heat transfer was increased by endwall contouring corresponded to elevated turbulence levels compared to the flat endwall, but the variation in boundary layer skew across the passage was reduced with contouring.

Numerical investigation on synthetic jet flow control inside an S-inlet duct

The high degree of centerline curvature and cross-stream pressure gradient in S-inlet ducts gives rise to boundary layer separation and secondary flows, which result in poor pressure recovery and non-uniform flow in the outlet interface with the engine. The flowfield in ducts is three-dimensional due to the existence of secondary flow, so ordinary two-dimensional actuations have poor effect on reforming the flow. Synthetic jet actuations extended in different spanwise positions were employed to manipulate the flow, and compared with the two-dimensional actuation. The interaction mechanics between flow separation and secondary flow was studied at first. It was found that the secondary flow enhanced or weakened flow separation depending on the spanwise position of synthetic jet actuators. Moreover, the flow separation enhanced the secondary flow, thus causing lower pressure recovery and flow distortion in the duct outlet. The actuators located at different spanwise positions will weaken the secondary flows by improving the flow separation to get energetic and uniform main flow.

Effect of point bar development on the local force balance governing flow in a simple, meandering gravel bed river

The patterns of depth, velocity, and shear stress that direct a river's morphologic evolution are governed by a balance of forces. Analyzing these forces, associated with pressure gradients, boundary friction, channel curvature, and along- and across-stream changes in fluid momentum driven by bed topography, can yield insight regarding the establishment and maintenance of stable channel forms. This study examined how components of the local force balance changed as a meandering channel evolved from a simple, flat-bedded initial condition to a more complex bar-pool morphology. A numerical flow model, constrained by measurements of velocity and water surface elevation, characterized the flow field for four time periods bracketing two floods. For each time increment, runs were performed for discharges up to bankfull, and individual force balance components were computed from model output. Formation and growth of point bars enhanced topographic steering effects, which were of similar magnitude to the pressure gradient and centrifugal forces. Convective accelerations induced by the bar reduced the cross-stream pressure gradient, intensified flow toward the outer bank, and routed sediment around the upstream end of the bar. Adjustments in the flow field thus served to balance streamwise transport along the inner bank onto the bar and cross-stream transport into the pool. Even in the early stages of bar development, topographically driven spatial gradients in velocity played a significant role in the force balance at flows up to bankfull, altering the orientation of the shear stress and sediment transport to drive bar growth. Copyright 2011 by the American Geophysical Union.

Ebb-Tide Dynamics and Spreading of a Large River Plume*

Abstract Momentum balances in the near-field region of a large, tidally pulsed river plume are examined. The authors concentrate on a single ebb tide of the Columbia River plume, using the Regional Ocean Modeling System (ROMS) configured to hindcast flow conditions on the Washington and Oregon shelves and in the Columbia River estuary. During ebb, plume-interior streamwise balances are largely between advection, pressure gradient, and frictional forces. Stream-normal balances in this region reduce to centrifugal, cross-stream pressure gradient, and Coriolis terms (i.e., the “gradient wind” balance commonly assumed in river plume bulge investigations). Temporal derivatives are most important at the plume front and as the ebb progresses. Winds were light and contributed little to the force balance. Midebb stress and vertical salt flux were largest at a midplume depth, where stratification and vertical shear were also high, consistent with shear-induced mixing. Internal stress slows the spreading plume considerably. A kinematic description of the spreading process relates lateral spreading to the momentum dynamics and illustrates that plume spreading is largely a competition between the cross-stream pressure gradient and Coriolis forces. However, the very near-field dome of buoyant water is instrumental in setting initial flow pathways.

The limiting form of inertial instability in geophysical flows

The instability of a rotating, stratified flow with arbitrary horizontal cross-stream shear is studied, in the context of linear normal modes with along-stream wavenumberkand vertical wavenumberm. A class of solutions are developed which are highly localized in the horizontal cross-stream direction around a particular streamline. A Rayleigh–Schrödinger perturbation analysis is performed, yielding asymptotic series for the frequency and structure of these solutions in terms ofkandm. The accuracy of the approximation improves as the vertical wavenumber increases, and typically also as the along-stream wavenumber decreases. This is shown to correspond to a near-inertial limit, in which the solutions are localized around the global minimum offQ, wherefis the Coriolis parameter andQis the vertical component of the absolute vorticity. The limiting solutions are near-inertial waves or inertial instabilities, according to whether the minimum value offQis positive or negative.We focus on the latter case, and investigate how the growth rate and structure of the solutions changes withmandk. Moving away from the inertial limit, we show that the growth rate always decreases, as the inertial balance is broken by a stabilizing cross-stream pressure gradient. We argue that these solutions should be described as non-symmetric inertial instabilities, even though their spatial structure is quite different to that of the symmetric inertial instabilities obtained whenkis equal to zero.We use the analytical results to predict the growth rates and phase speeds for the inertial instability of some simple shear flows. By comparing with results obtained numerically, it is shown that accurate predictions are obtained by using the first two or three terms of the perturbation expansion, even for relatively small values of the vertical wavenumber. Limiting expressions for the growth rate and phase speed are given explicitly for non-zerok, for both a hyperbolic-tangent velocity profile on anf-plane, and a uniform shear flow on an equatorial β-plane.

High-Reynolds-number steady flow in a collapsible channel

We have studied steady flow in a two-dimensional channel in which a section of one wall has been replaced by an elastic membrane under dimensionless longitudinal tension T but possessing no bending stiffness. The dimensionless upstream transmural pressure takes a value P ext , the membrane section is assumed to be long compared with the channel width and its deformation is assumed to remain within the viscous boundary layers. Standard high-Reynolds-number asymptotic methods are applied to arrive at a coupled boundary-layer-membrane problem. A non-zero cross-stream pressure gradient, leading to flow perturbations upstream of the membrane, is included in the analysis. Linearization of the boundary-layer problem yields firstly an analytic solution at non-zero P ext and asymptotically high T. This takes the form of an expansion in T -1 for which the membrane shape and the flow decouple at each order. Extension of this solution branch to smaller values of the tension suggests a singularity at finite tension, where the deformation of the membrane becomes very large. Secondly, when the upstream transmural pressure is zero the trivial solution is valid for all values of the tension. However, we also obtain eigensolutions where the membrane tension plays the role of eigenvalue. There are thus non-trivial solutions of the problem at these particular values of the tension. The nonlinear coupled boundary-layer-membrane problem is then solved numerically. A finite-difference, Keller-box, marching scheme is used, together with a shooting algorithm to satisfy the boundary condition at the downstream end of the membrane. This reveals a variety of different solutions, showing the relation between the two cases captured by the linearized analysis and demonstrating the existence of parameter ranges for which no solutions exist under the specified constraints. Such parameter ranges appear not to exist if the downstream, rather than the upstream, transmural pressure is held constant. The relation to our results of solutions obtained by solving the two-dimensional Navier-Stokes equations directly is discussed. Reasonable agreement between parameters is obtained, once allowance is made for the finite Reynolds number and membrane length in those computations.

Characterizing the severe turbulence environments associated with commercial aviation accidents. Part 2: Hydrostatic mesoscale numerical simulations of supergradient wind flow and streamwise ageostrophic frontogenesis

Simulation experiments reveal key processes that organize a hydrostatic environment conducive to severe turbulence. The paradigm requires the juxtaposition of the entrance region of a curved jet streak, which is highly subgeostrophic, with the entrance region of a straight jet streak, which is highly supergeostrophic. The wind and mass fields become misphased as the entrance regions converge, resulting in significant spatial variation of inertial forcing, centripetal forcing, as well as along and cross-stream pressure gradient forcing over a meso-β scale region. Maxima of these forces are misphased where the two dissimilar jet streaks converge and geostrophic balance is disrupted. Velocity divergence within the subgeostrophic region of largest upstream-directed pressure gradient force and velocity convergence near the region of largest downstream-directed centripetal/inertial-advective forcing act to produce a mesoscale front due to spatially varying confluent flow flanked by zones of increasing velocity divergence. This results in frontogenesis as well as the along-stream divergence of cyclonic and convergence of cyclonic ageostrophic vertical vorticity. The nonuniform centripetally forced mesoscale front becomes the locus of large gradients of ageostrophic vertical vorticity along an overturning isentrope. This region becomes favorable for streamwise vorticity gradient formation enhancing the environment for the organization of horizontal vortex tubes in the presence of buoyant forcing. This is because the mesoscale convergence of vertical vorticity on an overturning isentropic surface creates vertical rotation for the development of horizontal vorticity in regions where isentropic surfaces overturn. Vorticity, shear, and buoyancy are focused in one location by this front thus favoring an environment favorable for microvortex formation leading to turbulence.

FLOW DEVELOPMENT OF CO-FLOWING STREAMS IN RECTANGULAR MICRO-CHANNELS

The diffusion and flow development characteristics of two co-flowing, laminar streams in a high aspect ratio rectangular micro-channel have been examined. A long, thin splitter plate initially separates the two streams such that fully developed flow in each of the two channels is established prior to merging. The co-flowing micro-channel has an aspect ratio of 16 with a width of 1006 μm and a height of 63 μm. Micro-Particle Image Velocimetry (μPIV) was utilized to observe the interaction between the streams for a range of flow rate ratios ranging from one to nine, for Reynolds numbers of one and ten. For flow rate ratios greater than one, a cross-stream pressure gradient exists immediately downstream of the splitter plate, which results in a strong lateral flow of the faster moving fluid into the slower moving fluid. Despite this rapid expansion, the fluids in the two streams do not mix. The two streams eventually recover a fully developed velocity profile across the entire channel. A model is presented to predict this development length based on the pressure imbalance between the two streams. The model is expressed in terms of the flow rate ratio between the streams, which is shown to be a function of channel aspect ratio. An asymptotic condition for the development length is found for high flow rate ratios and high aspect ratio channels. It is shown that existing entrance length relationships greatly underpredict this development length.

DIFFUSION AND FLOW DEVELOPMENT IN CO-FLOWING MICROCHANNEL STREAMS

A study of the momentum diffusion and flow development of two co-flowing streams in a microchannel is presented. The microchannel has a high-aspect-ratio (20) rectangular cross section with a height of 50 w m and a width of 1,000 w m. A splitter plate is used to obtain fully developed flow in each of two channels prior to the flows merging. Experimental results are obtained illustrating the streamwise variation of the interface between the streams for a range of flow rate ratios ranging from 1 to 9. Numerical simulations were used to determine details of the velocity and pressure fields in the region of momentum mixing. When there is a velocity difference between each stream there is a cross-stream pressure gradient just downstream of the splitter plate that causes the faster-moving stream to expand very rapidly into the slower-moving stream. The faster-moving stream is shown to recirculate into the slower-moving stream, resulting in a stagnation region. The two streams do not mix during this process, although mass diffusion is observed. The merged streams, although unmixed, have a fully developed velocity profile within approximately 4 to 14 hydraulic diameters downstream of the end of the splitter plate, depending on the flow rate ratio. This is shown to be significantly further than predicted using existing entrance length relationships in the literature.

Curvature Effects on Discrete-Hole Film Cooling

A numerical study has been conducted to investigate the effects of surface curvature on cooling effectiveness using three-dimensional film cooling geometries that included the mainflow, injection hole, and supply plenum regions. Three surfaces were considered in this study, namely, convex, concave, and flat surfaces. The fully elliptic, three-dimensional Navier–Stokes equations were solved over a body-fitted grid. The effects of streamline curvature were taken into account by using algebraic relations for the turbulent viscosity and the turbulent Prandtl number in a modified k–ε turbulence model. Computations were performed for blowing ratios of 0.5, 1.0, and 1.5 at a density ratio of 2.0. The computed and experimental cooling effectiveness results were compared. For the most part, the cooling effectiveness was predicted quite well. A comparison of the cooling performances over the three surfaces reveals that the effect of streamline curvature on cooling effectiveness is very significant. For the low blowing ratios considered, the convex surface resulted in a higher cooling effectiveness than both the flat and concave surfaces. The flow structures over the three surfaces also exhibited important differences. On the concave surface, the flow involved a stronger vorticity and greater mixing of the coolant jet with the mainstream gases. On the convex surface, the counterrotating vortices were suppressed and the coolant jet pressed to the surface by a strong cross-stream pressure gradient.

The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial effects

A localized, insoluble, surfactant monolayer, spreading under the action of surface-tension gradients over a thin liquid film, has at its leading edge an integrable stress singularity which renders conventional thin-film approximations locally non-uniform. Here high-Reynolds-number asymptotics are used to explore the quasi-steady two-dimensional developing flow near the monolayer tip, assuming that gravity keeps the free surface almost flat, that weak ‘contaminant’ surfactant regularizes the singularity and that the monolayer spreads fast enough for inertial effects to be important in a region which is long compared to the film depth but which is short compared to the length of the monolayer. It is shown how downward displacement of the inviscid core flow by the subsurface viscous boundary layer yields a non-uniform pressure distribution which, when the monolayer is spreading fast enough for cross-stream pressure gradients to be significant at its tip, creates a short free-surface hump which is the thin-film version of a Reynolds ridge. The ridge and other singular flow structures are smoothed as the monolayer slows and levels of contaminant are increased. The conditions under which lubrication theory provides a uniformly accurate approximation for this class of surfactant-spreading flows are established.

Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model

Recent research into river channel confluences has identified confluence geometry, and particularly bed discordance, as a control on confluence flow structures and mixing processes, and this has been illustrated using both field measurements in natural confluences and laboratory measurements of simplified confluences. Generalization of the results obtained from these experiments is limited by the number of confluence geometries that can be examined in a reasonable amount of time. This limitation may be overcome by numerical models, in which confluence geometry is more readily varied, and data acquired more rapidly. This paper aims to: (i) validate the application of a three-dimensional numerical model to a simple confluence geometry; (ii) simulate the effects of different boundary condition values upon flow structures; and (iii) interpret the implications of these simulations for river channel confluence dynamics. The model used in this research solves the three-dimensional form of the Navier–Stokes equations and is used to simulate the flow in a parallel confluence of unequal depth channels and to investigate the effect of different combinations of velocity and depth ratio between the two tributaries. The results generally agree with empirical evidence that secondary circulation is generated in the absence of streamline curvature, but only for specific combinations of depth and velocity ratio. This research shows how understanding of the interaction of these controls is enhanced if pressure gradients are considered. The velocity ratio is the prime determinant of the cross-stream pressure gradient that initiates cross-stream velocities. However, for significant secondary circulation to form, cross-stream velocities must lead to significant transfer of fluid in the cross-stream direction. This depends on the vertical extent of the cross-stream pressure gradient which is controlled by the depth ratio. In this study, strong secondary circulation occurred for a depth differential of 25% or more, as long as the velocity in the shallower tributary was at least as great as that in the deeper channel. This provides an important context for interpretation of previous work and for the design of new experiments in both the field and the laboratory. © 1998 John Wiley & Sons, Ltd.

Counterflow Thrust Vector Control of Subsonic Jets: Continuous and Bistable Regimes

Fluidic thrust vectoring of a subsonic jet was examined by the asymmetric application of countere ow to the jet shear layers. When countere ow is applied to one side of a 4:1 aspect ratio rectangular jet in the proximity of a control surface, the shear-layer entrainment characteristics are altered asymmetrically giving rise to a cross-stream pressure gradient and e ow vectoring. Thrust vector control up to 20 deg was possible at Mach numbers up to 0.5 using countere ow. Two regimes of e uidic control were identie ed, a continuous regime and a bistable one. During continuous vectoring, proportional control could be achieved between jet response and the pressure conditions established in the countere owing stream. However, under certain circumstances, proportional control was lost leading to jet bistability. Since such bistability is undesirable for aircraft control applications, the phenomenon was studied in detail. A parametric study of the collar geometry was used to minimize jet attachment and expand the operating domain over which proportional control could be maintained.

Comparison of series expansions and finite-difference computations of internal laminar flow separation

We present computed results for steady viscous flow in a two-dimensional channel with one plane wall and the other wall parallel far upstream but not parallel elsewhere. The particular example studied most fully is that of gradual exponential divergence. The main aim is to see whether a series expansion approach is as good as a finite difference method in computing flow separation in a diverging channel at moderately large values of the Reynolds number Re. It is assumed that the wall slope parameter e is small but that eRe is not. The leading term of the series expansion is that given by lubrication theory, and the expansion proceeds in powers of eRe; two versions of the series are considered, one based on the boundary layer equations and one in which the leading effect of cross-stream pressure gradient is included. Convergence of the series is enhanced by the use of Pade approximants. Estimates are made of the position of the separation point, x s , at various values of eRe (= 1, 3, 5); the values of x s on the two walls are somewhat different if the cross-stream pressure gradient is included. The results are compared with those of finite difference solutions of ( a ) the boundary layer equations and ( b ) the full Navier-Stokes equations. The boundary-layer and series-expansion results (with no cross-stream pressure gradient) agree extremely well, but to use the series method for more general wall geometries would be forbiddingly cumbersome, especially with cross-stream pressure gradient included. The Navier Stokes computations fail to provide a converged symmetric solution in which separation occurs at approximately the same value x s of on each wall, but gives two converged solutions with the first separation point on one wall or the other. If too crude a convergence criterion had been used, a ‘symmetric’ solution would have been found. Such non-uniqueness is to be expected; the ‘symmetric’ flow (the only one achieveable by the series method) would presumably be unstable. None of the computed solutions predict that separation occurs as early as has been seen experimentally in a slightly different geometry.

The structure of instantaneous reversals in highly turbulent flows

Structure of instantaneous flow reversals has been measured in a highly turbulent axisymmetric diffuser flow using pulsed-wire anemometry. In this 8° nominal included angle conical diffuser, the adverse pressure gradient (APG) is strong enough to cause appreciable instantaneous flow reversals (instantaneous backflow up to 30% of the time), but the time-averaged flow is non-separated. The results are compared with the other severe APG separating flows reported in literature. An increase in entry Reynolds number indicated a decrease in the size of near-wall instantaneous reversals region as well as a decrease in the magnitude of instantaneous backflow. Also, the region of instantaneous reversals moves slightly downstream at appreciably higher Reynolds numbers. The initiation and growth of instantaneous reversals in a conical diffuser was found to strongly influence the wall-layer and the central region. Present results also suggest that the instantaneous backflow should be considered for modelling of instantaneously-separating diffuser flows. In the final stages of a conical diffuser, the magnitudes of cross-stream pressure gradient were found to be appreciably larger than that of the longitudinal pressure gradient, indicating that accurate representation of a conical diffuser flow can not be achieved without considering V-momentum equation. A comparison of various separating flows revealed remarkable similarity of instantaneous reversals regions and distributions even in different flow configurations.

Upstream influence and the form of standing hydraulic jumps in liquid-layer flows on favourable slopes

Steady planar flow of a liquid layer over an obstacle is studied for favourable slopes. First, half-plane Poiseuille flow is found to be a non-unique solution on a uniformly sloping surface since eigensolutions exist which are initially exponentially small far upstream. These have their origin in a viscous–inviscid interaction between the retarding action of viscosity and the hydrostatic pressure from the free surface. The cross-stream pressure gradient caused by the curvature of the streamlines also comes into play as the slope increases. As the interaction becomes nonlinear, separation of the liquid layer can occur, of a breakaway type if the slope is sufficiently large. The breakaway represents a hydraulic jump in the sense of a localized relatively short-scaled increase in layer thickness, e.g. far upstream of a large obstacle. The solution properties give predictions for the shape and structure of hydraulic jumps on various slopes. Secondly, the possibility of standing waves downstream of the jump is addressed for various slope magnitudes. A limiting case of small gradient, governed by lubrication theory, allows the downstream boundary condition to be included explicitly. Numerical solutions showing the free-surface flow over an obstacle confirm the analytical conclusions. In addition the predictions are compared with the experimental and computational results of Pritchardet al.(1992), yielding good qualitative and quantitative agreement. The effects of surface tension on the jump are also discussed and in particular the free interaction on small slopes is examined for large Bond numbers.

Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend

A three-dimensional turbulent boundary layer (3DTBL) was generated on the floor of a low-speed wind tunnel by the imposition of a cross-stream pressure gradient using a 30° bend in the horizontal plane. The surface streamlines were deflected by as much as 22° relative to the local tunnel centreline. Downstream of the bend, the 3DTBL gradually relaxed towards a 2DTBL; this was an impulse-and-recovery experiment which focused on the outer layer. Mean velocities were measured with a three-hole yawmeter and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer. The experiment isolated the effects of crossflow from those of adverse streamwise pressure gradients, which may have clouded interpretations of previous 3DTBL experiments. In particular, the detailed developments of the cross-stream shear stress and of the stress/energy ratio become clearer. The shear-stress vector lagged behind the velocity-gradient vector as crossflow developed; however, the two vectors became more closely aligned downstream of the bend. Reductions in the stress/energy ratio implied that crossflow made shear-stress production less efficient. Another effect of three-dimensionality was a change of sign in the vertical transport of turbulent kinetic energy by turbulence, in the inner part of the boundary layer.

Measurements in a Pressure-Driven Three-Dimensional Turbulent Boundary Layer During Development and Decay

Measurements of the turbulence structure in the outer layer of a three-dimensional turbulent boundary layer were made in an open-circuit low-speed blower tunnel. The three-dimensional turbulent boundary layer on the floor of the tunnel was generated by a cross-stream pressure gradient using a 30-deg bend in the horizontal plane. Downstream of the bend, the three-dimensional turbulent boundary layer gradually relaxed toward a two-dimensional turbulent boundary layer as the crossflow decayed slowly after the cross-stream pressure gradient was removed. Mean velocities were measured with a three-hole pressure probe, and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer