-------------------------------------------------------------------------- Data Bank contribution of the paper "Origin and Decay of Longitudinal Vortices in Developing Flow in a Curved Rectangular Duct" (Journal of Fluid Engineering, Vol. 116, Sep. 1993). -------------------------------------------------------------------------- NOTE: The annotated text of a symposium paper is here given because the experimental details were better documented in this paper. The figure numbers are changed to corresponding to the paper published in the Journal of Fluid Engineering. The name of the data file corresponding to each figure is given at the end of the paper. ----------------------------------------------------------------------------- ANNOTATED TEXT OF "AN EXPERIMENTAL STUDY OF BOUNDARY-LAYER FLOW IN A CURVED RECTANGULAR DUCT" PRESENTED AT THE SYMPOSIUM ON DATA FOR VALIDATION OF CFD CODES, ASME FLUIDS ENGINEERING DIVISION MEETING, 20-24 JUNE, 1993, WASHINGTON D.C. (FED-Vol. 146, pp.13-28) ---------------------------------------------------------------------------- by W. J. Kim and V. C. Patel -------- ABSTRACT -------- 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 measurements 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. ------------ INTRODUCTION ------------ Computational fluid dynamics (CFD) codes have come to occupy an important place among methods of analysis and design of fluids engineering systems and products. The validation of such codes for turbulent flows relies on compari- sons with carefully conducted experiments which highlight some particular fluid flow phenomenon or influence, the central uncertainty being the fidelity of the turbulence closure model employed in the code. Among the factors that have defied accurate representation in CFD codes are the influence of stream- wise surface and/or streamline curvature, and the development and decay of secondary motion, by either the Reynolds stresses or cross-stream pressure gradients associated with curvature. Many experiments have been carried out to understand the basic mechanisms involved, and some of the data have been considered refined enough for use in CFD code validation. This paper describes the results of an experiment designed to elucidate the development of secondary motion and vortices in turbulent boundary layers on the walls of a curved rectangular duct. Curved ducts of varying lengths and aspect ratios have been employed in the past to study the streamwise curvature effects and secondary motions. A review of the literature indicates basically two types of experiments. In one, devel- oping flow in curved ducts of "large" aspect ratio has been measured to study the effect of convex or concave curvature on a nominally two-dimensional tur- bulent boundary layer. In some cases, attempts were made to remove the attendant pressure gradients and isolate the effects of curvature, while in others, the pressure gradient effects were not documented and were generally ignored. In some others, two dimensionality was either not documented or the channel aspect ratio was not large enough to guarantee two dimensionality. Among experiments of this type are those of Smits et al. (1979), Gillis and Johnston (1983), Hoffman et al. (1985), and Muck et al. (1985). These studies in two-dimensional boundary layers indicate that convex curvature has a stabilizing influence (reduces turbulent transport) whereas concave curvature has a destabilizing effect (increases the turbulence). The differences between the two are not equal and opposite, however, and no turbulence model has yet succeeded in representing the effect of curvature with precision. The second type of experiments have been conducted mostly in ducts of square cross section, with short or long straight sections upstream of the curved portion, to study the evolution of the secondary motion in developing and fully-developed flows. Representative experiments of this type are those of Humphrey et al. (1981), Chang et al. (1983), and Iacovides et al. (1990). Measurements in fully-developed flow in a square duct clearly reveal that the secondary motion arise from curvature-induced pressure gradients which drive low-momentum fluid from the outer (concave) wall on to the inner (convex) wall. Strong and prolonged curvature leads to the formation of longitudinal vortices on the convex wall. The principal difference between developing (boundary layer) and fully-developed flow is that, in the former, the secondary motion is weaker and confined to the boundary layers. The effects of surface curvature on turbulence are obviously present in these flows as well but they are generally masked by those of the secondary motion. Also, the stress-driven secondary motion that is present in any straight upstream segment of the duct, interacts with the much stronger pressure-driven secondary motion in the curved section, resulting in a flow that is influenced by many factors. Because of these complexities, square-duct experiments have been used in CFD code validation to test not only the numerical capabilities but also to investigate the performance of turbulence models. Developing boundary-layer flow in curved rectangular ducts has not been studied to the same level of detail as that in a square duct. Some preliminary measurements were made in such a flow by Patel (1968) during the course of a study on curvature effects in nominally two-dimensional turbulent boundary layers. Mean velocity distributions measured at several spanwise stations in the boundary layers developing in a curved rectangular duct of aspect ratio six revealed not only Goertler type vortices on the concave wall but also much stronger longitudinal vortices on the convex wall some distance from the duct corners. These latter vortices are induced by the curvature-driven secondary motion. It was concluded that these vortices had to be reduced in order to realize two dimensionality of the flow along the duct centerplane. The authors are not aware of any other experiments in rectangular ducts of similar dimen- sions in spite of the fact they offer the opportunity to isolate and study, in a single simple geometry, two important flow features mentioned above, namely, the effects of streamwise curvature on the turbulence in a nearly two-dimensional flow, and vortex formation from a pressure-driven secondary flow. The latter feature is related to the so-called crossflow or open type of separation of a three-dimensional boundary layer. The present experiment is concerned with turbulent boundary layers developing in a curved rectangular duct. A computational study was conducted in parallel (Kim, 1991) to guide the experiments. As a result, special attention was paid to the three- dimensionality of the flow on the flat walls downstream of the wind tunnel contraction to properly document the flow conditions ahead of the curved section. The data from this experiment have been compared, by Kim (1991) and Sotiropoulos and Patel (1992), with two different numerical methods. Therefore , the authors are well aware of the need to present the experimental results in a form that is convenient for testing and validating computational methods. The experimental facilities are described, along with the instrumentation and measurement procedures. Measurement uncertainties were determined by the method of Kline and McClintock (1953). The quantities measured include the distributions of surface pressure and shear stress, the three components of the mean velocity vector, and all but one component of the Reynolds stress tensor. ---------------------- EXPERIMENTAL APPARATUS ---------------------- The experiments were conducted in the curved-wall wind tunnel shown in figure 1 (note: figure numbers have been changed according to JFE paper). This open-circuit, suction-type wind tunnel has a 90 deg. bend. A 0.25 in (6.35 mm) honeycomb and three 16-mesh screens are installed at the entrance, and these are followed by a two-dimensional lateral contraction with an area ratio of 6. The 5-ft (1.52 m) long straight upstream section provides a well- developed, flat-plate type turbulent boundary layer before the start of the curved section. The 17-ft (5.18 m) long downstream section enables the study of flow recovery following the curvature and attendant pressure gradients. The bend has an inner radius of 24 in (61.0 cm) and an outer radius of 32 in (81.3 cm). The tunnel cross section is rectangular, with a width of 8 in (20.3 cm) and a height of 48 in (121.9 cm). Thus, the duct aspect ratio is 6. In the design of the tunnel, the dimensions were determined after careful considera- tion of previous work on curvature effects on turbulent boundary layers, and the need to isolate the effects of curvature in the flow along the tunnel mid- section from those of secondary motion and vortex formation at the corners. The resulting configuration is versatile insofar as these effects can be studied either in isolation or together. The present experiments exploit both capabilities. The boundary layers on all walls of the test section were tripped by a one- inch (25.4 mm) wide, #80 sandpaper, just downstream (12.7 mm) of the contrac- tion. The air speed was controlled by adjusting the fan speed and monitoring the pressure difference along the contraction. A Pitot tube located in the freestream at the station marked U1 in figure 1 was used to calibrate the tunnel and establish the relation between the contraction pressure drop and the velocity in the tunnel. The wind-tunnel reference pressure had a maximum variation of 0.6% during a normal measurement time. A HP-1000 minicomputer was used to control the experiments and collect the data, and an Apollo workstation was used for post-processing and plotting. A computer-controlled, two-axis, probe-traversing unit was installed for rapid and accurate positioning of pressure and hot-wire probes. The traverse had two stepping motors which drive Unislide gears with an accuracy of 1/4000 inch. The traversing unit was mounted on the top of the tunnel, and could be manually moved from one section to another along the tunnel. Uniformity of the mean-velocity distribution at station U1, located 2 ft (61.0 cm) downstream of the turbulence stimulator, was ascertained by traversing a Pitot tube. The velocity was uniform outside the boundary layers, with a deviation from the mean less than 1.0% . As will be discussed more fully later, the two-dimensional contraction introduced secondary motion in the boundary layers on top and bottom flat walls of the tunnel. However, the boundary layers on the wider, vertical walls were two dimensional over the middle 32 in (81.3 cm). Figure 1 also shows the coordinates employed in the presentation of experimental results; X is the longitudinal distance along the inside wall, Y is the outward distance from the inside wall, and Z is the distance measured downward from the top inside corner. The origin of the coordinate system is located at the start of the bend at the top inside corner. The mean and fluctuating velocity components in the (X,Y,Z) directions are (U,V,W) and (u,v, w), respectively. Thus, U represents the longitudinal component whose direction follows the duct curvature, while V and W are the transverse components. The reference station U1 is at X = - 4.5 H, upstream of the bend, H being the duct width. Station U2 is at X = - 0.5 H, just inside the influence of the pressure gradients induced by the duct curvature. The following three stations are located at 15, 45, and 75 degrees along the bend, and are so designated. Two downstream stations, D1 and D2 which are 0.5 H, 4.5 H downstream of the bend, respectively, were selected to study the recovery of the flow following the curvature. In the following discussion, all velocity components are nondimensionalized by the freestream velocity Uo (16 m/sec) at station U1 and the duct width H. ---------------------- MEAN-FLOW MEASUREMENTS ---------------------- The mean-velocity field was measured with a five-hole pressure probe. Using this probe, it was possible to measure the three components of mean velocity at any location in the tunnel without yawing and pitching the probe. The overall diameter of the probe was 0.13 in (3.30 mm) and it had five 0.023 in (0.584 mm) holes: one on the flat surface facing upstream and four equally- spaced on 45 deg. facets. All pressure measurements were made with a Validyne pressure transducer (+/- 0.125 psi range) which was calibrated against a micro- manometer, having a resolution of 0.001 in (0.0254 mm) of alcohol. The pressure measurements were accurate to within 2 % of the freestream dynamic pressure. The five-hole pressure probe was calibrated in the freestream at station U1 against a standard Pitot tube, following Treaster and Yocum (1979). A specially designed probe-holder base enabled the probe to be yawed and pitched in desired positions, in the range +/- 35 deg., in 5 deg. intervals. For each pressure measurement, a sampling rate of 200 samples/second and a measuring period of 3 seconds was used by suitably programming the A/D converter of the computer. Thus, the mean pressure was obtained by averaging 600 samples. The pressures measured by the probe were converted to the calibration coefficients defined in Treaster and Yocum, and the calibration charts were used, with fourth-order polynomials for interpolation, to calculate the yaw and pitch angles, velocity magnitude, and static pressure. The velocities components were then calculated. Errors from the approximation of the calibration chart were estimated to be 1 deg. in flow angle when the yaw and pitch angles were less than 25 deg. Most of the measurements were found to be within this range. The overall uncertainty in the mean-velocity measurements was estimated to be 1.5% in the streamwise components (U) and 3% in the transverse components (V and W) of the reference velocity. -------------------------------------------------- MEASUREMENT OF WALL PRESSURE AND WALL SHEAR STRESS -------------------------------------------------- The pressure distribution on the tunnel walls was measured by pressure taps. Along the centerline of the side walls of the wind tunnel, 80 taps were placed on the inside wall and 106 taps were placed on the outside wall. The location of these taps and the measured pressures are plotted in figure 2. Additional pressure taps were provided in the spanwise direction at several streamwise sections but these were used mainly to check the flow symmetry about the tunnel centerplane. The wall shear stress was determined by employing two different types of pressure probes at the same location. A total-head tube with inner and outer diameters of 0.047 and 0.065 in (1.19 and 1.65 mm), respectively, was used in the manner of a Preston tube. However, the static pressure at the same point was obtained from a separate static-pressure probe. The difference between the readings of the two probes was used, along with the Preston-tube calibration of Patel (1965), to obtain the wall friction coefficient. This method of determining the static pressure (instead of using wall taps) enabled wall-friction measurements to be made rapidly and at closely-spaced positions. However, it should be pointed out that, due to the relative insensitivity of the probes to yaw, this method gives the magnitude of the wall shear but not its direction. This limitation should be kept in mind in future use of these data. ----------------------- TURBULENCE MEASUREMENTS ----------------------- A constant-temperature hot-wire system was employed to measure the fluctuating velocity components. At the beginning of this study, it was thought that a triple-sensor probe could be used to obtain all the necessary information in a single set of experiments. However, more detailed consideration of the flow to be measured soon led to the conclusion that commercially available triple-sensor probes were much too large to properly resolve the near-wall flow. Therefore, a miniature two-sensor (X-wire) probe, whose overall size is less than 2 mm (DISA 55P61), was employed. The probe had a 1.25-mm long, 5-mm diameter platinum-plated tungsten wires, giving a length-diameter ratio of 250. It was used in two orientations, with the sensors in the XY plane, and then in the XZ plane, to obtain all except one (-vw)) component of the Reynolds stress tensor. Each sensor was connected to a DISA 55P10 Constant Temperature Anemometer bridge operating with an overheat ratio of 1.5. The probe was speed-calibrated to obtain the calibration constants before and after each experiment. This was intended to monitor the drift in the calibration due to variations in ambient temperature or deposits accumulating on the sensors. Since the wind tunnel is of the open-circuit type, temperature increases inside the tunnel were usually quite small (less than 2 deg. Celsius during a one to two hour period). However, the temperature was monitored and corrections were made in the calibration. The modified King's law was used to relate the anemometer voltage E to the effective cooling velocity Ue: 2 n E / (Tw - Ta) = A + B (Ue) where Tw is the constant wire temperature, Ta is the ambient temperature, A and B are calibration constants, and n = 0.5. The instantaneous effective cooling velocity was converted to instantaneous in-plane velocity in the laboratory frame using the cosine law and a constant directional sensitivity coefficient, k = 0.2, with cooling by the out-of-plane velocity component ignored. The main source of error comes from the out-of-plane velocity cooling. The overall uncertainty in the measured Reynolds stresses was estimated as 5% in uu and 10% in other stresses. The data-acquisition procedure was similar to that used for the five-hole pressure probe. Voltages from the hot-wire sensors and the tunnel temperature were sampled simultaneously for 5 seconds with a sampling rate of 200 Hz, and processed to determine the instantaneous velocity components and then the Reynolds stresses. Although the hot-wire measurements also yielded the mean- velocity components, the measurements with the pressure probe are considered more reliable. Therefore, only the pressure-probe data are presented for the mean velocities. ------------------------------------ INFLUENCE OF WIND-TUNNEL CONTRACTION ------------------------------------ From the measurements at station U1 it became apparent quite early that the flow on the flat top (and bottom) wall was influenced by the two-dimensional contraction of the wind tunnel. Figure 3 shows selected data. It is clear that a pair of vortices exists inside the top-wall boundary layer, rendering it highly three dimensional. As observed by Mokhtari and Bradshaw (1983), these vortices are induced by the lateral pressure gradients that exist on the top wall of the wind-tunnel contraction. These gradients deflect the slow-moving boundary-layer fluid toward the vertical centerplane more strongly than the inviscid fluid outside the boundary layer, inducing a pressure-driven secondary motion. The secondary flows collide at the vertical centerplane of the top wall, forming a pair of vortices with the common flow between them away from the wall. However, in the present case, the roll-up process was not sufficiently advanced to form vortices with identifiable cores of velocity defect. The data in figure 3 indicate that the secondary flow magnitude reaches almost 5% of the freestream velocity, while the longitudinal velocity contours indicate that the boundary layer thickness at the center of the top wall is almost three times that near the corners. This extraordinarily thick boundary layer leads to the large vertical component of velocity near the center. The contours of turbulent kinetic energy and the Reynolds shear stress -uw), which is principally responsible for the transport of X-momentum in the vertical direction, normal to the top wall, indicate that the flow is approximately symmetric about the vertical centerplane. A more careful study of the secondary motion and the various contours indicates that there may be yet another pair of counter-rotating vortices forming under the primary pair. These secondary vortices produce a flow towards the wall in the centerplane and lead to increased axial velocity, turbulent kinetic energy, and Reynolds stress very close to the wall. The downstream persistence of the top-wall vortices observed in figure 3 can be clearly seen from the friction coefficients measured at stations U1, U2, 15, and 45, which are shown in figure 4. First of all, the higher friction coeff- icient near the centerplane at U1 is indicative of a local flow divergence associated with the counter-rotating secondary vortices mentioned above. By station U2, these secondary vortices have disappeared and the friction distribution is that associated with only the primary pair, the low friction at the centerplane being due to the flow convergence induced by the primary pair of vortices. There exists some asymmetry due to the fact that some radially inward pressure gradient exists at station U2 (see figure 2). This asymmetry is obvious at station 15, where the curvature related radial pressure gradient drives low-momentum fluid in the top wall boundary layer from the inside to the outside corner. The effect of the thickened boundary layer (due to the vortices) is still in evidence at station 15 in the dip in the friction coefficient. By station 45, however, there is little evidence of the contraction-induced vortices. Measurements similar to those shown in figure 4 were made along the vertical side walls of the duct at station U1. These revealed that the boundary layers on the two walls were essentially two dimensional except for a short region close to the corners. The boundary layer thickness at midspan of the vertical walls was 0.08H (Reynolds number based on boundary thickness was 18,000), and wall friction coefficient [Cf = 2*(shear stress at the wall)/(density*Uo*Uo)] was 0.0038. While these two integral parameters are usually sufficient to prescribe the initial conditions (under the assumption of a flat-plate boundary layer) for the calculation of the subsequent flow, the observed contraction- induced vortical flow should be taken into account to properly model the flow in the corners. The measured data can be used to construct realistic inlet condition for such computations. ---------------------- RESULTS AND DISCUSSION ---------------------- The experiment was conducted with the freestream velocity Uo, outside the boundary layers at the reference section U1 (figure 1), of 16 m/s. In the presentation of results, this is used as the reference velocity. With these values, the duct Reynolds number, UoH/(kinematic viscosity) = 224,000 and the corresponding Dean number [UoRh/(kinematic viscoity)]*sqrt[Rh/(Ri+0.5H)] = 95,000, where the hydraulic radius Rh = 0.857H and the inner radius of the duct Ri = 3.0 H. However, it should be noted that these are not particularly meaningful for the developing boundary layers that are of interest in the present situation. Instead, it is the state of the boundary layer in the upstream section, at station U1, say, that determines the effects of surface curvatures and pressure gradients that are imposed on the boundary layers as they negotiate the curve and recover from it. At this station, the boundary layers on the vertical walls have essentially the same characteristics as they have developed in identical circumstances. Measurements indicated that, at the center of these walls, the momentum-thickness Reynolds number, was 1650. The boundary layers on these walls were found to be essentially two-dimensional in regions out of the immediate influence of the corners. However, as described above, the boundary layers on the top and bottom walls are not two dimensional. Measurements were made in the upper half of the duct cross section, the symmetry of flow in the upper and lower halves of the duct being assumed following some preliminary measurements. Mean pressure and velocity fields ================================= The pressure distribution [Cp = 2(P-Po)/(density*Uo*Uo)] along the channel walls in the plane of symmetry, is presented in figure 2, where Po represents pressure at (0,0,3) and Uo is the freestream velocity at U1. The pressure gradients induced by the curvature are clearly seen. On the convex side, the boundary layer is subjected to a favorable pressure gradient starting upstream of the bend, and this is followed by an adverse gradient around the bend exit. The boundary layer on the concave side is subjected to pressure gradients of similar magnitude but opposite signs. The mean-velocity field measured by the pressure probe is shown in figure 5 . The longitudinal vorticity shown in figure 5(b) was obtained by numerical differentiation of the measured secondary velocity components and non- dimensionalized by the freestream velocity at U1 and the duct width H. The top-wall vortices are clearly seen, particularly in the vorticity plots, at station U2 and they are still in evidence at station 15. Thereafter, they are smeared out by the curvature-driven secondary motion, which is directed from the outer to the inner corner. The experiments indicate that, near the center of the duct, the boundary layers remain relatively thin and there exists an inviscid region in which the velocity gradient is small . Near the top wall , however, the boundary layer on the convex wall thickens as it is fed by fluid coming down from the top-wall boundary layer, and by station 75, there appears a longitudinal vortex with its core approximately at Y = 0.08 and Z = 0.7. Vortical flow now begins to fill the top of the channel. The vortex on the convex wall grows in size and is pushed away from the top. The vortex persists even after the end of curvature. At station D2, the core of the vortex, identified by low axial velocity and high longitudinal vorticity, is located around Y = 0.17 and Z = 1.0. Previous studies of the flow in curved ducts of square section, mentioned in the Introduction, indicated two vortices forming near the convex wall, colliding at the centerline, and lifting from the wall. In the present case, however, the longitudinal vortex develops without interference from a similar vortex in the other half of the duct. The wall shear stresses are shown in figure 7. A circle, a triangle and a square denote the values on the convex, concave and top walls, respectively. As expected from the longitudinal velocity contours of figure 5(a), flow symmetry about the vertical centerplane is observed until station U2, where the radial pressure gradient begins. In general, near the duct center, the friction coefficient on the convex wall first increases due to the favorable longitudinal pressure gradient and then decreases due to the adverse pressure gradient near the exit. The opposite is found on the concave side. The top-wall vortices are seen at station U2 through the dip in the friction distribution. The data also show similar dips on both vertical walls near the corners. Unfortunately, the resolution of the velocity measurements was not sufficient to identify these with corner vortices. As the flow progresses downstream, the most prominent feature of the measurements is a significant drop in the friction coefficient on the convex wall. This begins around station 45, where the minimum is located at Z = 0.45, and moves downward to about Z = 1.5 at station D2. At the last three stations, this minimum in friction is preceded by another local minimum, and the entire spanwise distribution acquires a characteristic shape. This shape of the friction distribution is associated with the flow convergence and divergence induced by the longitudinal vortex. Yet another interesting feature of the measured friction coefficients is found on the top wall near the junction with the convex wall at station D2. The pronounced trough in the local friction distribution suggests the development of yet another vortex which arises from the strong inflow towards the convex wall. The corner vortex rotates in a sense opposite to that of the vortex on the convex wall described above. Figure 8 shows the profiles of the longitudinal velocity component (U) across the duct, from the inner to the outer wall, at six positions: Z = 0.25, 0.50, 0.75, 1.00, 2.00 and 3.00, the last being the symmetry plane of the duct. These results represent only a small sample of the total database. The corres- ponding distributions of the transverse components (V and W) are not shown. The velocity profiles at stations U1 and U2 show flat-plate type boundary layers on the vertical walls except at Z = 0.25, which is under the influence of the secondary flow on top wall. The longitudinal velocity outside the boundary layers at station 45 decreases from the inner to the outer wall, as required by inviscid-fluid theory. Further downstream, at stations D1, much fuller longitudinal velocity profiles are observed in the outer-wall boundary layer in the two-dimensional flow region near the duct center. This is consistent with the effect of concave curvature, which acts to increase turbulent mixing, and leads to increased velocity close to the wall and larger friction. This effect persists on the straight wall, even after removal of the curvature. The longitudinal vortex on the convex wall is seen through the profiles of U at Z = 0.50 and 0.75 at station D1, and at Z = 0.75 and 1.00 at station D2, which depict the two peaks commonly observed in vortical flows. Reynolds-stress distributions ============================= The effect of surface curvature on the boundary layers on the convex and concave walls in the two-dimensional flow near the plane of symmetry of the duct, and the growing three-dimensionality associated with the vortex on the convex wall were already evident from the mean-velocity field. These two effects combine to produce a quite complex distribution of the Reynolds stresses. The hot-wire measurements were made at four streamwise stations and included all except one (-vw)) component of the Reynolds stress tensor. Figure 9 and 10 show the turbulent kinetic energy (k) and the primary Reynolds stress (-uv). At each station, profiles are shown at six sections (Z = 0.25 - 3.00) across the duct. Figure 9 shows that, at the reference station U1, there are thin, two-dimensional boundary layers on the inner and outer walls and a large inviscid core. The vortex pair on the top wall is not seen at Z = 0.25. Within the boundary layers in the central portion of the duct (Z = 0.75 - 3.00, say), the kinetic energy and the primary Reynolds shear stress -uv behave as expected, with peak values near the wall. The structure parameter (a1=-uv/k) attains a value of about 0.3, which is generally accepted for fully turbulent flows. The standard flat-plate turbulent boundary layer behavior over much of station U1 and the details of the flow near the top was provided in a previous section are sufficient to specify proper inlet conditions for a CFD code applied to calculate the subsequent development of the flow through the duct. Comparison of the profiles of k and -uv at stions U2 and 45 near the symmetry plane show the direct effects of surface curvature. At U2, the profiles near the two walls are quite similar, but at 45, they develop marked differences. Both k and -uv are suppressed near the convex wall and greatly amplified near the concave wall. For example, at station 45, Z = 3.00, the peak value of k near the concave wall is almost three times that near the convex wall, and there is a similar difference in the shear stress. It is again confirmed that production of the turbulence energy is enhanced by the concave curvature, while it is suppressed by convex curvature. However, as discussed in Richmond and Patel (1991), most commonly used two-equation turbulence models fail to predict this asymmetric behavior of turbulence production in curved wall boundary layers. The measurements of k and the individual Reynolds stresses at the last station, D1, which is just downstream of the bend in the duct, continue to indicate the curvature effects described above in the boundary layer near the duct center (Z = 2.00 - 3.00, say). Although the evolution of the longitudinal vortex on the convex wall near the top of the duct is evident from the turbulence profiles at station D1 in the region Z = 0.50 - 1.00, the global features of the vortex are more conveniently visualized from the contour plots shown in figure 11. It is clear that the two shear stresses change sign in the region where the longitudinal velocity contours are most distorted, indicating a more vigorous transport of momentum and energy by the vortex. A high level of turbulent kinetic energy is also observed near Z = 0.825, because the boundary layer fluid near the convex wall is lifted outward by the vortical flow. The distributions shown in figure 11 are typical of a longitudinal vortex inside a boundary layer. ------------------ CONCLUDING REMARKS ------------------ Measurements in developing turbulent boundary-layer flow in a 90 deg. curved duct of rectangular cross section with an aspect ratio of six were presented and discussed. Despite the relatively simple geometry this flow offers two challenges to physical and computational modeling. First, there is an extensive region of nominally two-dimensional boundary layers subjected to strong streamwise curvatures and related pressure gradients, and second, the data document the development of the pressure-driven secondary motion in the corner region which eventually leads to the formation of a longitudinal vortex on the convex wall. The duct aspect ratio was such that these two features develop more or less independently, without interaction. Together, these features of a complex turbulent flow present a formidable challenge to any CFD code that claims a high level of generality. Calculations carried out by the authors (Kim, 1991; Sotiropoulos and Patel, 1992) suggest that prediction of the details of such a flow require methods that solve the Reynolds-averaged Navier-Stokes equations with an advanced turbulence model capable of resolving the joint effects of curvature and pressure gradients. The data were obtained in such detail, with respect to the location of measurement points, that they can be used to test or validate computational methods and turbulence models. In particular, special care was given to documenting the flow at an upstream section so that realistic initial boundary conditions could be provided for computational studies. Tabulated experimental data are available from the JFE data bank (subdirectory DB93???). --------------- ACKNOWLEDGMENTS --------------- This study was sponsored by the Office of Naval Research under Grant N00014-89-J-1342 in support of the DARPA Subtech Program, and Grant N00014-91-J-1204. 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(1979), "The Calibration and application of five-hole probes," ISA Trans., vol. 18, pp. 23-34. ------------------------------------------------------------------------------- Names of data file related to each figure (read "readme.doc" for description) ------------------------------------------------------------------------------- Figure 2 : pressure.dat (pressure.dir) Figure 3 : mu1up1.dat (mean.dir), tu1up1.dat (turb.dir) Figure 4 : su1up.dat, su2up.dat, s15up.dat, s45up.dat (friction.dir) Figure 5 : mu2up1.dat, mu2in1.dat, mu2ou1.dat, mu2in2.dat, mu2ou2.dat, m15up1.dat, m15in1.dat, m15ou1.dat, m15in2.dat, m15ou2.dat, m45up1.dat, m45in1.dat, m45ou1.dat, m45in2.dat, m45ou2.dat, m75up1.dat, m75in1.dat, m75ou1.dat, m75in2.dat, m75ou2.dat, md1up1.dat, md1in1.dat, md1ou1.dat, md1in2.dat, md1ou2.dat, md2up1.dat, md2in1.dat, md2ou1.dat, md2in2.dat, md2ou2.dat (mean.dir) Figure 7 : su2up.dat, su2in.dat, su2out.dat, s15up.dat, s15in.dat, s15out.dat, s45up.dat, s45in.dat, s45out.dat, s75up.dat, s75in.dat, s75out.dat, sd1up.dat, sd1in.dat, sd1out.dat, sd2up.dat, sd2in.dat, sd2out.dat (friction.dir) Figure 8 : mu2sel.dat, m45sel.dat, md1sel.dat (sel.dir) Figure 9 : tu2sel.dat, t45sel.dat, td1sel.dat (sel.dir) Figure 10 : tu2sel.dat, t45sel.dat, td1sel.dat (sel.dir) Figure 11 : mdiin1.dat (mean.dir), td1in1.dat (turb.dir)