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Measurements of the velocity characteristics of the flows in two curved diffusers of rectangular cross section with C and S-shaped centerlines are presented and related to measurements of wall heat transfer coefficients along the heated flat walls of the ducts. The velocity results were obtained by laser-Doppler anemometry in a water tunnel and the heat transfer results by liquid crystal thermography in a wind tunnel. The thermographic technique allowed the rapid and inexpensive measurement of wall heat transfer coefficients along flat walls of arbitrary boundary shapes with an accuracy of about 5 percent. The results show that an increase in secondary flow velocities near the heated wall causes an increase in the local wall heat transfer coefficient, and quantify the variation for maximum secondary-flow velocities in a range from 1.5 to 17 percent of the bulk flow velocity.

An experimental investigation of developing flows through a combination of out-of-plane S-bend ducts was conducted to gain insight into the redirection of flow in geometries similar to those encountered in practical aircraft wing-root intake ducts. The present double S-bend was fabricated by placing previously investigated S-ducts and S-diffusers in series and with perpendicular planes of symmetry. Laser-Doppler anemometry was employed to measure the three components of mean velocity, the corresponding rms quantities, and Reynolds stresses in the rectangular cross-section ducts. Due to limited optical access, only two mean and rms velocity components were resolved in the circular cross-section ducts. The velocity measurements were complemented by wall static pressure measurements. The data indicates that the flows at the exit are complex and asymmetric. Secondary flows generated by the pressure field in the first S-duct are complemented or counteracted by the secondary flows produced by the area expansion and the curvature of the S-diffuser. The results indicate the dominance of the inlet conditions and geometry upon the development of secondary flows and demonstrate that the flows are predominantly pressure-controlled. The pressure distribution caused by the duct geometry determines the direction and magnitude of the bulk flow while the turbulence dictates the mixing characteristics and profiles in the near wall region.

Developing flows in two out-of-plane double S-bend configurations have been measured by laser-Doppler anemometry. The first duct had a rectangular cross-section 40mmx40mm at the inlet and consisted of a uniform area 22.5 deg. - 22.5 deg. S-duct upstream with a 22.5 deg.- 22.5 deg. S- diffuser downstream. The second duct had a circular cross-section and consisted of a 45 deg. - 45 deg. uniform area S-duct upstream with a 22.5 deg. -22.5 deg. S-diffuser downstream. In both configurations the ratio of the mean radius of curvature to the inlet hydraulic diameter was 7.0, the exit-to-inlet area ratio of the diffusers was 1.5 and the ducts were connected so that the centerline of the S-duct lay in a plane normal to that of the S-diffuser. Streamwise and cross-stream velocity components were measured in laminar flow for the rectangular duct and in turbulent flow for both configurations; measurements of the turbulence levels, cross-correlations and wall static pressures were also made in the turbulent flow cases. Secondary flows of the first kind are present in the first S-duct and they are complemented or counteracted by the secondary flows generated by the area expansion and by the curvature of the S-diffusers downstream. Cross-stream velocities with magnitudes up to 0.19 and 0.11 of the bulk velocity were measured in the laminar and turbulent flows respectively in the rectangular duct and six cross-flow vortices were evident at the exit of the duct in both flow cases. The turbulent flow in the circular duct was qualitatively similar to that in the rectangular configuration, but the cross-stream velocities measured at the exit plane were smaller in the circular geometry. The results are presented in sufficient detail and accuracy for the assessment of numerical calculation methods and are listed in tabular form for this purpose.

Laser-Doppler velocimetry measured the laminar and turbulent streamwise flow in a S-duct. The wall pressure distribution and one component of cross-stream velocity were also obtained for the turbulent flow case. Boundary layers near the duct inlet were about 25 percent of the hydraulic diameter in the laminar flow and varied around the periphery of the pipe between 10 percent and 20 percent in turbulent flow. Pressure-driven secondary flows develop in the first half of the S-duct and are attenuated and reversed in the second half. For both Reynolds numbers there is a region near the outer wall of the second half of the duct where the sign of the radial vorticity results in an enforcement of the secondary flow which was established in the first half of the S-duct. The core flow migrates, for both Reynolds numbers, to the outside wall of the first half and lies towards the inside wall of the second half of the S-duct at the outlet. The thinner inlet boundary layers in the turbulent flow give rise to weaker secondary motion.

Developing laminar and turbulent flows have been measured in two diffusers with S- and C-shaped center-lines, small divergence angle and moderate curvature. The square inlet cross-section expanded in the plane of curvature to a rectangle with an exit-to-inlet area ratio of 1.5. Laser-Doppler anemometry was used to measure three velocity components and, in turbulent flow, the associated fluctuations and cross-correlations. Wall static pressure measurements are also reported. Flow visualization did not reveal the presence of any recirculation regions. Pressure-driven secondary flows are present in both ducts, but are generally smaller than those measured in similar ducts of uniform cross-section area.

Two orthogonal components of velocity and associated Reynolds stresses are determined in a square-sectioned, 90 degree bend of 2.3 radius ratio by utilizing laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. Results show that boundary layers at the bend inlet of 0.25 and 0.15 of the hydraulic diameter create secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity, respectively. It is concluded that the boundary layer thickness is important to the flow development, mainly in the first half of the bend, especially when it is reduced to 0.15 of the hydraulic diameter. Smaller secondary velocities are found for turbulent flow in an identical duct with a radius ratio of 7.0 than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. In addition, the detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models.

Laser-Doppler velocimetry was used to measure the laminar and turbulent flow in an S-duct formed with two 22.5 deg sectors of a bend with ratio of mean radius of curvature to hydraulic diameter of 7.0. The boundary layers at the inlet to the bend were about 25% and 15% of the hydraulic diameter for the laminar and turbulent flows, respectively. Pressure-driven secondary flows develop in the first half of the S-duct and persist into the second half but are largely reversed by the exit plane as a consequence of the change in the sense of curvature. There is, however, a region near the outer wall of the second bend where the redistribution of the streamwise isotachs results in a reinforcement of the secondary flow which was established in the first half of the S-duct. The net redistribution of the streamwise isotachs is comparable to that occurring in unidirectional bends of stronger curvature. The wall pressure distribution was also measured for the turbulent flow and quantifies the expected large variations in the longitudinal pressure gradient distributions which occur at different radial locations.

The streamwise components of velocity in the flow through a ninety degree bend of circular cross section for which the ratio of radius of curvature to diameter is 2.8 were measured. The development of strong pressure driven secondary flow in the form of a pair of counter rotating vortices in the steamwise direction is shown. Refractive index matching at the fluid wall interface was not employed; the displacement of the measurement volume due to refraction is allowed for in simple geometrical calculations.

The velocity characteristics of laminar and turbulent developing flow in an S-duct formed from two 22.5-deg bends of rectangular cross-section have been studied experimentally using laser Doppler velocimetry. It is shown that pressure-driven secondary flows arise in the first bend of the duct and reach maxima of 0.22 and 0.15 of the bulk velocity in the laminar and turbulent flows, respectively. The velocities are greater in the laminar flow, mainly because of the thicker inlet boundary layers. On passing through the second half of the S-duct, a secondary flow is established over most of the section in the direction opposite to that in the first half. Near the outer wall of the second bend, however, the secondary flow generated in the first bend is sustained because of the local sign of radial vorticity. This effect contributes to a redistribution of the streamwise isotachs, by the end of the duct, comparable with that in unidirectional bends.

Measurements of turbulent flow in a duct with a cross sectional transition from square to round are presented. Laser Doppler velocimetry was used to measure the mean velocity components, turbulence levels and shear stresses. The boundary layers at the inlet and exit of the transition were approximately 13 percent and 20 percent of the hydraulic diameter respectively, becoming thicker near the corner fillets. The development of secondary flow, of magnitudes up to 7 percent of the bulk velocity is shown. This flow is directed away from the corner fillets and along the periphery of the duct and is associated with the longitudinal curvature of the wall and the related pressure gradients.

The merits of small-scale, water-flow experiments with measurements by laser-Doppler anemometry are indicated in relation to previously reported results. New measurements are reported in a square-to-round transition duct and show that, for example, the pressure forces overwhelm any small normal-stress driven secondary flows in the inlet plane to given maximum values of around 0.07 of the bulk velocity in the exit plane. The precision of manufacture of the ducts means that the geometric boundary conditions are accurately known and the results are therefore suitable for calculation purposes. Similarly, the instrumentation allows the flow boundary conditions to be accurately determined.