A Navier-Stokes code for S-shaped diffusers—a review

Three-dimensional, compressible, internal flow solutions obtained using a thin-layer Navier-Stokes code are presented. The code, formulated by P.D. Thomas, is based on the Beam-Warming implicit factorization scheme; the boundary conditions also are formulated implicitly. Turbulent flow is treated through the use of the Baldwin-Lomax two-layer, algebraic eddy viscosity model. Steady-state solutions are obtained by solving numerically the time-dependent equations from given initial conditions until the time-dependent terms become negligible. The configuration considered is a rectangular cross-section, S-shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. The Mach number at the duct entrance is 0.9, with a Reynolds number of 5.82 × 10⁵. Convergence to the final results required about 2700 time steps or 11 hours of CPU time on our CRAY-1M computer. The averaged residuals were reduced by about two orders of magnitude during the computations. Several regions of separated flow exist within the diffuser. The separated flow region on the upper wall, downstream of the second bend, is by far the largest and extends to the exit plane.     

Flow characteristics in the downstream region of a conical diffuser

Using the Navier-Stokes equations in conjunction with the k-? model of turbulence, the characteristics of flow in the region downstream of a conical diffuser with 5° angle of inclination are calculated. Two representative stations 1D₂ and 10D₂ after the diffuser exit are selected for comparison against experimental results. The calculations indicate an underestimation of mean velocity and turbulence kinetic energy at the first station, while satisfactory agreement is obtained for the mean velocity at the second station. The use of a modified k-? model sensitive to adverse pressure conditions improves the predictions considerably. The effect of inlet properties and Reynolds number on the flow characteristics at the above stations is studied using various inlet profiles and a range of Reynolds numbers based on the inlet diameter from 50 000 to 280 000.     

Turbulence measurements in the inlet plane of a centrifugal compressor vaneless diffuser

Detailed flow measurements at the inlet of a centrifugal compressor vaneless diffuser are presented. The mean 3-d velocities and six Reynolds stress components tensor are used to determine the turbulence production terms which lead to total pressure loss. High levels of turbulence kinetic energy were observed in both the blade and passage wakes, but these were only associated with high Reynolds stresses in the blade wakes. For this reason the blade wakes mixed out rapidly, whereas the passage wake maintained its size, but was redistributed across the full length of the shroud wall. Peak levels of Reynolds stress occurred in regions of high velocity shear and streamline curvature which would tend to destabilize the shear gradient. Four regions in the flow are identified as potential sources of loss - the blade wake, the shear layers between passage wake and jet, the thickened hub boundary layer and the interaction region between the secondary flow within the blade wake and the passage vortex. The blade wakes generate most turbulence, with smaller contributions from the hub boundary layer and secondary flows, but no significant contribution is apparent from the passage wake shear layers.     

Numerical prediction of turbulent flow in a conical diffuser usingk-ε model

Fully developed incompressible turbulent flow in a conical diffuser having a total divergence angle of 8° and an area ratio of 4∶1 has been simulated by ak-ε turbulence model with high Reynolds number and adverse pressure gradient. The research has been done for pipe entry Reynolds numbers of 1.16×10⁵ and 2.93×10⁵. The mean flow velocity and turbulence energy are predicted successfully and the advantage of Boundary Fit Coordinates approach is discussed. Furthermore, thek-ε turbulence model is applied to a flow in a conical diffuser having a total divergence angle of 30° with a perforated screen. A simplified mathematical model, where only the pressure drop is considered, has been used for describing the effect of the perforated screen. The optimum combination of the resistance coefficient and the location of the perforated screen is predicted for high diffuser efficiency or the uniform velocity distribution.     

Measurements in the vaneless diffuser of a radial flow compressor

Results from an experimental study of flow behaviour at the inlet of a vaneless diffuser of a centrifugal compressor are presented. Measurements from a crossed hot-wire probe are given for operating points having inlet flow coefficients ranging from 0.006 to 0.019 at different Reynolds numbers. Instantaneous, time-averaged, and phase-averaged absolute velocity and flow angle at the diffuser inlet are deduced from the hot-wire signals after correction for mean density variations. These results show how flow behaviour varies in stable, rotating stall and surge regimes of compressor operation     

Sensitivity of an asymmetric 3D diffuser to vortex-generator induced inlet condition perturbations

Modifications of the turbulent separated flow in an asymmetric three-dimensional diffuser due to inlet condition perturbations were investigated using conventional static pressure measurements and velocity data acquired using magnetic resonance velocimetry (MRV). Previous experiments and simulations revealed a strong sensitivity of the diffuser performance to weak secondary flows in the inlet. The present, more detailed experiments were conducted to obtain a better understanding of this sensitivity. Pressure data were acquired in an airflow apparatus at an inlet Reynolds number of 10,000. The diffuser pressure recovery was strongly affected by a pair of longitudinal vortices injected along one wall of the inlet channel using either dielectric barrier discharge plasma actuators or conventional half-delta wing vortex generators. MRV measurements were obtained in a water flow apparatus at matched Reynolds number for two different cases with passive vortex generators. The first case had a pair of counter-rotating longitudinal vortices embedded in the boundary layer near the center of the expanding wall of the diffuser such that the flow on the outsides of the vortices was directed toward the wall. The MRV data showed that the three-dimensional separation bubble initially grew much slower causing a rapid early reduction in the core flow velocity and a consequent reduction of total pressure losses due to turbulent mixing. This produced a 13% increase in the overall pressure recovery. For the second case, the vortices rotated in the opposite sense, and the image vortices pushed them into the corners. This led to a very rapid initial growth of the separation bubble and formation of strong swirl at the diffuser exit. These changes resulted in a 17% reduction in the overall pressure recovery for this case. The results emphasize the extreme sensitivity of 3D separated flows to weak perturbations.     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

Moderate Reynolds number axisymmetric jet development downstream an extended conical diffuser: Influence of extension length

Low-velocity (bulk velocity of 4.4 m/s) and moderate Reynolds (7350) axisymmetrical jet development is studied by hot-film single sensor anemometry. The jet issues from a conical convergent-divergent diffuser with uniform extension (diameter 25 mm). Decreasing the length-to-diameter ratio of the extension tube from 20 down to 0.4 is shown to alter severely the mean velocity profile at the tube outlet from Blasius to top-hat whereas turbulence intensities increases from 6 up to 50%. Next, the influence of the initial velocity profile at the tube outlet on axisymmetrical jet development is assessed. The velocity development exhibits a self-similar far field characteristic for axisymmetrical jet development. Although, the jet centerline decay constant increases and the jet spreading rate decreases as length-to-diameter ratios are increased from 0.4 up to 7.2 for which the initial centerline velocity decreases. Therefore, scaling of the centerline decay constant and inverse scaling of the spreading rate with initial centerline velocity U₀ or initial velocity Reynolds number Re₀ reported for moderate Reynolds numbers and low initial turbulence levels [18,22] does not hold as the turbulence level exceeds a threshold value in the range 12–27%. In addition, the influence of initial conditions on near and far field turbulence properties is shown. A transition in near field behaviour is observed for length-to-diameters around 3.6. Flow and geometrical configurations under study are relevant to e.g. upper airway flow.     

LES of supersonic turbulent flow in nozzles and diffusers

Large-eddy simulations of supersonic nozzle and diffuser flows with circular cross-sections using high-order compact schemes and an explicit filtering version of the approximate deconvolution method are presented in this paper. Two flow cases each for nozzle and diffuser having different outlet to inlet area ratios are presented. The effect of the geometry variations on the Reynolds stresses as well as on the production and pressure-strain terms in their transport equations is demonstrated. A Green’s function analysis of the Poisson equation for pressure fluctuations using LES data is presented and the results show similar trends as found in previous analyses using DNS data. The effects of geometry changes on the rapid and slow parts of pressure-strain correlations is also demonstrated.     

Computational fluid dynamics analysis of diffuser performance in gas-powered jet pumps

Jet pump diffuser performance is analyzed, both in terms of past experimental work dealing with the high inlet flow distortions involved and in the sense that this problem is amenable to predictive investigation by computational fluid dynamics techniques. In these highly nonuniform flow conditions, diffusers are seen to justify their inclusion in a jet pump design, for regaining static pressure downstream of the vacuum chamber, even though their performance in effectiveness terms is lowered by about two thirds at high inlet glow distortion levels. A satisfactory correlation has been found between outlet and inlet conditions and diffuser area ratio, extending well beyond past experimental published results for diffuser geometry and distorted inlet flows.     

Behavior of homogeneous turbulence in channels with variable cross-sectional area

On the basis of the equation describing the behavior of the spectral tensor of the energy of the pulsation velocity for one-dimensional flow in a channel with variable cross-sectional area, we obtained a system of equations for the meansquare components of the pulsation velocity vector and integral scales of the turbulence length in various directions, enabling us to use these parameters in the initial section of the channel for determining their behavior along the channel. We made use of some ideas of A. N. Kolmogorov and J. Rotta concerning the possibility of describing viscous and nonlinear terms in the equations for the components of the tensor of Reynolds stresses in terms of the energy of pulsation motion and the integral scale of the turbulence length. The resulting system, in the special cases of very low intensity of turbulence, leads to the results of the linear theory; for constant cross-sectional area (or for a very high intensity of turbulence, when the damping affects the turbulence much more strongly than does the deformation effect) it describes the known empirical laws of the degeneration of turbulence beyond grids. We made a comparison with the data available in the literature on the behavior of the characteristics of turbulence in channels with variable cross-sectional area.     

不同参数下环形通道内湍流旋流流动的模拟

应用一种合理考虑湍流一旋流相互作用及湍流脉动各向异性的新的代数ＲｅｙｎｏｌｄＳ应力模型,对环形通道内的湍流旋流流动进行了数值模拟．研究了旋流数、进口轴向速度和内外半径比等参数对环形通道内湍流旋流流动的影响,以及由此产生的流场变化对强化环形通道内传热的作用．     

Flow in a simple swirl chamber with and without controlled inlet forcing

Results are presented from a swirl chamber with and without controlled inlet forcing. The controlled inlet forcing is induced using arrays of vortex generators placed along one wall of the swirl chamber inlet duct. Flow visualization results are given, along with surveys of circumferential mean velocity, static pressure, and total pressure, at Reynolds numbers (based on inlet duct characteristics) as high as 8000. The controlled inlet forcing provides means to alter and control: (i) the spacing and number of Görtler vortices across the span of the swirl chamber, (ii) the amount of vortex development at a particular Reynolds number and circumferential location, (iii) the circumferential location and Reynolds number of initial Görtler vortex development, and (iv) the circumferential location and Reynolds number of Görtler vortex breakup into more chaotic flow.     

Turbulent flow in a conical diffuser: A review

This is a review of experimental studies of turbulent flow in a conical diffuser by eight Ph.D. students, eleven M.Sc. students, one M.Eng. student, and myself in the past 29 years. During this time, two conical diffusers were constructed: the first was of cast aluminum construction, and the second was of plastic fabrication. These two diffusers were basically the same in geometry except that the pipe section was constructed as an integral part of the plastic diffuser to avoid the lip at the junction of the inlet pipe and the diffuser. The conical diffuser had a total divergence angle of 8°, an area ratio of 4:1, and an inlet diameter of 0.1016 m (4 in.).

The flow at the inlet of the diffuser was usually fully developed pipe flow, but sometimes it was boundary layer grown on the pipe wall. Hot-wire and pulse-wire anemometry together with computer facilities were used to obtain the results of complex flow present in the conical diffuser. Mean velocity profiles were obtained throughout the diffuser, which in turn were used to obtain strain rates and their principal direction. Turbulence moments up to fourth order were measured. The results were used to assess momentum, turbulent kinetic energy, and shear stress equations. Other features such as instantaneous flow reversals in the wall region, relative strength of large eddies, extra strain rate, and the production of kinetic energy also were investigated to find the dynamical picture in the diffuser flow.     

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.     

Measurements of pore scale flows within and exiting ceramic foams

LDA was used to measure the mean velocities and pore scale turbulence intensity of air flowing through ceramic foams having pore sizes between 0.8 and 2.5 mm in diameter. The stream-wise and transverse velocity components were measured near the exit plane, in a region between two foams separated by 5 mm, and within a section of ceramic foam. Mean velocities ranged from 0.25 m/s to 1.5 m/s, corresponding to pore Reynolds numbers between 20 and 200. A transition to a fully developed pore turbulence was achieved at pore Reynolds numbers above approximately 150.Support for this work was provided by the Texas Advanced Research Program and The Center for Energy Studies of The University of Texas at Austin.     

Sensitivity of an asymmetric 3D diffuser to plasma-actuator induced inlet condition perturbations

Experiments were conducted for the flow in a straight-walled 3D diffuser fed by a fully developed turbulent duct flow. Previous work found that this diffuser has a stable 3D separation bubble whose configuration is affected by the secondary flows in the upstream duct. Dielectric barrier discharge plasma actuators were used to produce low-momentum wall jets to determine if the separation behavior could be modified by weak forcing. Actuators producing a streamwise force along the wall where separation occurred in the baseline flow had a relatively small effect. However, spanwise acting plasma actuators that produced a pair of streamwise vortices in the inlet section of the diffuser had a strong effect on the diffuser pressure recovery. The diffuser performance could be either improved or degraded depending on the actuation parameters, including the actuator modulation frequency, duty cycle, and drive voltage. Velocity profile measurements in the diffuser inlet showed that the streamwise vortices affect the uniformity of the streamwise mean velocity accounting for some of the performance changes. However, phase-locked hotwire measurements at the diffuser exit indicate that the periodic nature of the forcing also plays an important role for cases with enhanced pressure recovery.     

Influence of adverse pressure gradient on rough-wall turbulent flows

This paper presents an experimental investigation of adverse pressure gradient turbulent flow over two rough surfaces and a reference smooth surface. The adverse pressure gradient was produced in an asymmetric diffuser whose opening angle was 3°. The rough surfaces comprised sand grains and gravels of nominal mean diameters of 1.55 mm and 4.22 mm, respectively. The tests were conducted at an approach flow velocity of 0.5 m/s and the momentum thickness Reynolds number varied from 900 to 3000. A particle image velocimetry technique was used for the velocity measurements. Profiles of the mean velocity, turbulent intensities, Reynolds stress ratios, mixing length, eddy viscosity and the production terms were then obtained to document the effects of adverse pressure gradient (APG) on low Reynolds number rough-wall turbulent boundary layers. The results indicate that APG thickens the boundary layer and roughness sublayer. The APG and surface roughness also enhanced the production of turbulence as well as the turbulence level when compared with the smooth-wall data.     

An experimental study of ice-layer transition phenomena in a rectangular duct containing water flow

Measurements of both the velocity and turbulence-intensity distributions above an ice-layer surface along flow direction have been performed to clarify the ice-layer transition phenomena observed in a rectangular duct. The test duct which has a lower cooled wall kept less than the freezing temperature of water with cross-sectional dimension of 50 mm by 19 mm was used in the present measurements. The velocity and turbulence-intensity distributions in the test duct were measured using Laser Doppler Velocimeter set up on the two-dimensional traversing table. The freezing experiments were carried out under the condition of uniform water-flow rate even after the ice layer has developed in the test duct. It was found that inlet water flow tended to be laminarized under an influence of developing ice layer, and that onset of the ice-layer transition phenomena might be closely related to an increase in turbulence intensity in the water flow above the developing ice-layer surface.