Streamwise Curvature Research Articles

Assessment of CHF Enhancement Mechanisms in a Curved, Rectangular Channel Subjected to Concave Heating

An experimental study was undertaken to examine the enhancement in critical heat flux (CHF) provided by streamwise curvature. Curved and straight rectangular flow channels were fabricated with identical 5.0 × 2.5 mm cross sections and heated lengths of 101.6 mm in which the heat was applied to only one wall—the concave wall (32.3 mm radius) in the curved channel and a side wall in the straight. Tests were conducted using FC-72 liquid with mean inlet velocity and outlet subcooling of 0.25 to 10 m s−1 and 3 to 29°C, respectively. Centripetal acceleration for curved flow reached 315 times earth’s gravitational acceleration. Critical heat flux was enhanced due to flow curvature at all conditions but the enhancement decreased with increasing subcooling. For near-saturated conditions, the enhancement was approximately 60 percent while for highly subcooled flow it was only 20 percent. The causes for the enhancement were identified as (1) increased pressure on the liquid-vapor interface at wetting fronts, (2) buoyancy forces and (3) increased subcooling at the concave wall. Flow visualization tests were conducted in transparent channels to explore the role of buoyancy forces in enhancing the critical heat flux. These forces were observed to remove vapor from the concave wall and distribute it throughout the cross section. Vapor removal was only effective at near-saturated conditions, yielding the observed substantial enhancement in CHF relative to the straight channel.

Single-phase heat transfer enhancement in a curved, rectangular channel subjected to concave heating

Experiments were performed to ascertain the single-phase heat transfer enhancement provided by streamwise curvature. Curved and straight rectangular flow channels were fabricated with identical 5.0×2.5 mm cross-sections and 101.6 mm heated lengths in which heat was applied to a 32.3 mm radius concave wall in the curved channel and a side wall in the straight. Reynolds number ranged from 9000 to 130 000 and centripetal acceleration for the curved flow reached 315 times the earths gravitational acceleration. Nusselt numbers defined with hydraulic and thermal diameters were consistently underpredicted by previous correlations developed for full-periphery-heated channels but were accurately predicted when defined with heated width. Convection coefficients were enhanced due to flow curvature for all conditions tested, and detailed experimental correlations are provided for both the straight and curved configurations. Increasing Reynolds number produced different enhancement trends for different locations along the heated wall, decreasing the enhancement near the inlet and increasing it elsewhere downstream. Mechanisms responsible for the curvature enhancement are believed to be Dean vortices and a shift in the maximum axial velocity toward the concave wall. These mechanisms require a finite distance to develop sufficient strength to influence heat transfer, which explains the different enhancement trends observed for different locations along the heated wall.

Competition of Coriolis instability with centrifugal instability and its effects on heat transfer in a rotating curved heated channel

The competition of the Coriolis instability with the centrifugal instability is examined numerically in terms of flow structure transitions by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square channel with streamwise curvature, spanwise rotation and wall heating. The competition is found to be of considerable effects on flow structures and heat transfer. Several hitherto unknown flow structures are revealed. The results cover both transitions in flow structures and effects of the flow transitions on flow resistance and heat transfer.

Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer

Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced by approximately 50%.

The Effect of Negative Spanwise Rotation on Dean Vortices

A finite-volume numerical analysis is performed to examine effect of spanwise rotation on Dean vortices. The specific problem considered is fully developed flow in a square channel with streamwise curvature and spanwise rotation in a negative sense, i.e., the Coriolis force counteracts the centrifugal force. The rotation of the channel is found to have a significant effect on the flow structure in general, and the Dean vortices in particular. The nonlinear interaction of the Coriolis instability and the centrifugal instability results in several new flow structures, including one with coexistence of Ekman, Dean, and corner vortices, one with coexistence of Ekman and corner vortices, one with one-pair vortices and an agostrophic, virtually inviscid core, and one with Coriolis vortices on the inner convex wall. These are in agreement with the experimental findings.

Effect of spanwise rotation on centrifugal instability in rotating curved non-isothermal flows

The effect of spanwise rotation on the centrifugal instability is examined numerically in terms of flow structure transitions by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square duct with a strong streamwise curvature, a spanwise rotation in both positive and negative directions and wall cooling. The rotation is found to be of considerable effect on flow structures. As well the effect is more complex for non-isothermal flows due to a buoyancy force which increases with the square of the rotation speed. Several hitherto unknown flow structures are revealed. The results cover both transitions in flow structures and effects of the flow transitions on temperature distributions.

Buoyancy-force-driven transitions in flow structures and their effects on heat transfer in a rotating curved channel

Buoyancy-force-driven transitions in flow structures are examined numerically by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square channel with streamwise curvature, spanwise rotation and wall heating or cooling. The buoyancy force is found to significantly affect the flow structures and heat transfer. Several previously unknown phenomena are revealed. Results include both transitions in flow structures and effects of the flow transitions on flow resistance and heat transfer.

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature - II. Experiment

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature - II. Experiment

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature - I. Theory

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature - I. Theory

Development of square nozzles for supersonic low-disturbance wind tunnels

Two Mach 2.4 nozzles with square test sections have been designed and analyzed, as part of an effort to develop low-disturbance facilities for laminar-flow control for high-speed civil transport. The mean flows have been simulated using a finite volume, central-differencing scheme to solve the thin-layer NavierStokes equations. Substantial crossflow exists in the boundary layers of both nozzles. The crossflow changes direction about halfway between the throat and exit, because of a change in the sign of the crossflow pressure gradient. S-shaped crossflow profiles are present in this region, just as on a swept wing. Both the standard crossflow Reynolds number and the new Reed and Haynes transition estimator predict transition to occur in the throat as well as near the exit. An analysis of the crossflow pressure gradients in the transonic throat region indicates that streamwise curvature has only a weak effect on the crossflow pressure gradient. Further research on crossflow-induced transition will have to be carried out before these nozzles will be suitable for low Mach number quiet-tunnel designs.

Turbulence characteristics of a boundary layer over a swept bump

The evolution of the turbulent boundary layer over a bump defined by three tangential circular arcs and swept at 45° was examined. The flat-plate boundary layer approaching the swept bump had a momentum thickness Reynolds number of approximately 3800. The ratios of upstream boundary-layer thickness to bump height and convex radius of curvature were 1.5 and 0.06, respectively. The boundary layer was influenced by alternating signs of streamwise pressure gradient, wall curvature, and mean crossflow, which resulted in a complex boundary-layer flow that grew rapidly on the downstream side of the bump. The mean flow profiles deviated significantly from typical logarithmic layer behaviour, but the flow remained attached. The evolution of the Reynolds stress components was explained by the growth of two internal layers triggered by discontinuities in wall curvature near the leading and trailing edges of the bump. The shear stress vector was found to lag the velocity gradient vector, despite the spanwise flow changing direction above the bump. The measurements were compared to the previous results from a two-dimensional bump with the same profile shape and Reynolds number. Contrary to previous studies, the addition of mean crossflow to this complex flow field did not reduce the vertical mixing relative to the turbulent kinetic energy.

Visualization of Flows in Curved Channels with aModerate or High Rotation Speed

Flows in channels with streamwise curvature and spanwise rotation are visualized in terms of end‐view near the exit of the test sections through injecting smoke into the flows. Two test sections are used, i.e. the rectangular channels with the aspect ratio of and 10, respectively. The work focuses on visualization of Dean and Coriolis vortices under the effects of secondary instabilities and flows in the region with a relatively high rotation speed. The results show that the secondary instabilities cause the Dean and Coriolis vortices oscillating in various forms and the flows at high rotation speeds are controlled by the secondary instabilities rather than the primary instability. In particular, the secondary instabilities lead the flows to be unsteady and turbulent somewhat like the bursting flow in the turbulent boundary layers.

Numerical Prediction of Three-Dimensional Turbulent Structure through a Circular-to-Rectangular Transition Duct.

Numerical analysis is used to investigate three-dimensional turbulent structure and fluid flow behavior in a circular-to-rectangular transition duct. Turbulent flow through a circular-to-rectangular duct is characterized by streamwise curvature and streamwise vorticity embedded in the boundary layer. In the calculation, an algebraic Reynolds stress model together with a boundary-fitted coordinate system is applied to to a circular-to rectangular duct in order to solve anisotropic turbulent flow precisely. The calculated results are compared with the experimental results to examine the validity of the present method. As a result of this calculation, it is found that the present method predicts well a secondary flow pattern which develops into a discrete vortex pair along the duct sidewalls. This secondary flow arises as a result of lateral skewing of the near-wall flow in the vicinity of the sidewall induced by transverse pressure gradients associated with wall curvature. Moreover, the calculated contours of six Reynolds stress components are shown for comparison with the experiment. The distortion of Reynolds stresses by the vortex pair is clearly observed as well as the primary flow. Although agreement is not perfect, the main features are reproduced by the present method using the algebraic Reynolds stress model.

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature—I. Theory

We study the combined action of particle inertia and thermophoresis in boundary layer aerosol flows over surfaces with streamwise curvature, in the limit of small particle Stokes number, Stk, when the interaction between these two transport mechanisms is expected to be most significant. The governing dimensionless parameter controlling inertial effects is found to be Stk • Re x 1 2 , which can be large enough to cause dramatic changes in deposition rates even when Stk ⪡ 1, due to the largeness of the streamwise Reynolds number, Re x in boundary layer flows. Predictions are presented for concave/convex surfaces either ‘colder’ or ‘hotter’ than the mainstream.

Inertial effects on thermophoretic transport of small particles to walls with streamwise curvature—II. Experiment

Directing a high-speed, high-temperature, seeded jet generated by a micro-combustor past the concave side of a ‘cold’, platinum circular foil whose temperature is actively controlled, we investigate the simultaneous action of inertial and thermophoretic effects on particle deposition from curved, laminar boundary layer flows. Although particle Stokes numbers in these experiments are of O (10 −2), much smaller than the values customarily thought to signal the onset of inertial effects, we observe a significant increase of particle deposition rates over those expected based on ‘pure thermophoresis’ theory, in agreement with a recently developed theory of inertially modified thermophoresis in such flows.

Convex Curvature Effect on the WakeIncluding Recovery from the Curvature

Streamwise convex‐curvature effect including recovery process is discussed. Previous studies have demonstrated that even mild streamwise curvature has a marked effect on turbulence structure, heat transfer and skin friction coefficient. This effect is further investigated in the present study with Coles wake law. Coles previously reported that flows in or near equilibrium have a constant wake parameter depending on the strength of streamwise pressure gradient. Turbulent boundary layers on the curved and following recovery wall may not be in or near equilibrium and the wake parameter may depend upon the strength of curvature, δ/R. Different streamwise curvature strength, ranging 0.01–0.1, is tested to confirm the validity of the wake law. The ratio of wake parameter between the curved and flat wall is found to be proportional to that of skin friction coefficient for the flows in both convexly curved and recovery sections. This relationship describes the deviation of wake behavior from the flat‐plate turbulent boundary layer due to convex curvature.

Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution

The three-dimensional structure and streamwise evolution of two-stream mixing layers at high Reynolds numbers (Reδ ∼ 2.7 × 104) were studied experimentally to determine the effects of mild streamwise curvature ($\delta/ \overline{R}$ < 3%). Mixing layers with velocity ratios of 0.6 and both laminar and turbulent initial boundary layers, were subjected to stabilizing and destabilizing longitudinal curvature (in the Taylor–Görtler sense). The mixing layer is affected by the angular momentum instability when the low-speed stream is on the outside of the curve, and it is stabilized when the streams are reversed so that the high-speed stream is on the outside. In both stable and unstable mixing layers, originating from laminar boundary layers, well-organized spatially stationary streamwise vorticity was generated, which produced significant spanwise variations in the mean velocity and Reynolds stress distributions. These vortical structures appear to result from the amplification of small incoming disturbances (as in the straight mixing layer), rather than through the Taylor–Görtler instability. Although the mean streamwise vorticity decayed with downstream distance in both cases, the rate of decay for the unstable case was lower. With the initial boundary layers on the splitter plate turbulent, spatially stationary streamwise vorticity was not generated in either the stable or unstable mixing layer. Linear growth was achieved for both initial conditions, but the rate of growth for the unstable case was higher than that of the stable case. Correspondingly, the far-field spanwise-averaged peak Reynolds stresses were significantly higher for the destabilized cases than for the stabilized cases, which exhibited levels comparable to, or slightly lower than, those for the straight case. A part of the Reynolds stress increase in the unstable layer is attributed to ‘extra’ production through terms in the transport equations which are activated by the angular momentum instability. Velocity spectra also indicated significant differences in the turbulence structure of the two cases, both in the near- and far-field regions.

Origin and Decay of Longitudinal Vortices in Developing Flow in a Curved Rectangular Duct (Data Bank Contribution)

Developing turbulent flow in a 90 deg curved duct of rectangular cross-section, and an aspect ratio of 6, was investigated. Mean-velocity and Reynolds-stress components were measured using a five-hole pressure probe and two-sensor hot-wire probes, respectively, in the boundary layers on the duct walls to document the pressure-driven secondary motion and the formation of a longitudinal vortex near the corner on the convex wall. Special attention was paid to the three-dimensionality of the flow exiting the two-dimensional contraction of the wind tunnel in order to provide proper inlet boundary conditions for future computational work. The mean velocities and wall shear stresses were measured at seven sections and turbulence measurement were made at four sections. The data provide insights into the development of three-dimensional turbulent boundary layers under the influence of strong streamwise curvature, both convex or concave, and attendant pressure gradients, and clearly elucidate the mechanism by which strong pressure-driven secondary motion results in a longitudinal vortex.

Flow characteristics of slot jet impingement on a wedge

An experimental investigation is made to study the flow characteristics of slot jet impingement on a wedge whose included angle is 90 degrees. The aim of this investigation is to study the characteristics of the flow field near the wedge surface for various parameters. The different parameters like, jet velocity, slot width, distance of wedge vertex from the jet exit and the inclination of the wedge to jet axis are systematically varied to see their effect on the flow field. The flow field near the wedge vertex is similar to stagnation point flow. Far away from the vertex, the flow field is like that of wall jet. Near the vertex, very large variations of static pressure are observed in streamwise and transverse directions. This is due to large streamwise curvature and stagnation of flow. The transverse pressure gradient slowly decays in the streamwise direction, as a result, the velocity profiles are different from the similarity profiles of stagnation point flow and wall jet in the respective regions. Experiments are conducted for slot widths of 10 mm, 15 mm and 30 mm each for the distance between slot and wedge vertex of 80 mm, 120 mm and 240 mm. The static pressure and velocity profiles are measured by calibrated disk type static pressure probe and pitot tube respectively at various streamwise locations.

The development of an axisymmetric curved turbulent wall jet

An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.