Pressure recovery in a radiused sudden expansion

Experiments on a steady flow through a nominally 2-D exit geometry with rounded edges are presented for the Reynolds number range 300<Re<25,000. The results indicate that the channel flow expands and decelerates upstream of the exit plane resulting in large pressure recovery, especially for turbulent channel flow. It is shown that pressure recovery is a function of the dimensionless edge radius and Re. Pressure recoveries of up to 20% are reported at large Re for dimensionless radii as small as r/h=0.625. It is also found that the rounded exit results in turbulence levels as much as 25% higher than sharp-edged exits.     

Boundary layer structure of oscillatory open-channel shallow flows over smooth and rough beds

The boundary layer structure of oscillatory shallow open channel flows has been studied in a wide flume. Fluorescence solution was released at a porous rough bed through a diffuser covered by gravel of 0.5 cm grain size. A planar laser-induced fluorescence (PLIF) system was used to visualise the dye plumes in both vertical and horizontal planes for a qualitative understanding of the roles of large-scale flow structures in mass transport. A variety of tests were conducted for a range of oscillatory periods (30–240 s), water depths (3–16 cm) and velocity amplitudes (0.027–0.325 m/s), which cover a wide range of oscillatory flows with Reynolds numbers Re _a varied from 0.3 × 10⁴ (laminar) to 2.1 × 10⁶ (fully turbulent). For quantitative investigation, a novel technique, namely combined laser-induced fluorescence (LIF) and 2D laser Doppler velocimetry (LDV) (LIF/LDV), was developed and used to measure the velocity and solute concentration simultaneously in a vertical plane over 50 cycles. From the dye plumes revealed by the PLIF in transitional flows, there are different patterns of flow structure and solute transport with three representative stages of acceleration, deceleration and flow reversal. In the acceleration stage, turbulence was suppressed with dye layers adhering to the surface with little vertical mass transport. In the deceleration stage, flame-like turbulent structures occurred when turbulence generation was prominent. This was investigated quantitatively by recording the percentage occurrence of the adhered smooth layers per cycle. For those smooth bed cases with Re _a < 1.8 × 10⁵, the adhered smooth dye layers type of boundary layer occupied 100% of the oscillation period. Over a sufficiently high Re _a , a rough bed can generate fully turbulent oscillatory flows without the appearance of adhering dye layers. Between these two extremes, a transitional flow regime occurs in a wide range of flow conditions: Re _a > 2.7 × 10⁴ over the rough bed and Re _a > 8.3 × 10⁶ over a smooth bed.     

Turbulent Transition in the Inlet Region of a Circular Pipe

Calculated and experimental data on turbulent transition in a circular pipe are analyzed. The calculations were performed using the three-parameter turbulence model. The dependence of the distance from the inlet to the point of minimum friction during transition on the Reynolds number for fixed inlet conditions and the distribution of the turbulence parameters over the pipe length and radius are obtained. The dependence of the maximum (critical) Reynolds number, Re^*, for which there is no transition in the pipe, on the inlet intensity and scale of turbulence is found. It is suggested that Re^* depends on the inlet perturbation parameters up to Re^* = 1000, where the friction coefficients for laminar and turbulent flows coincide.     

Simulations of Turbulent Flow in a Plane Asymmetric Diffuser

Large-eddy simulations (LES) of a planar, asymmetric diffuser flow have been performed. The diverging angle of the inclined wall of the diffuser is chosen as 8.5°, a case for which recent experimental data are available. Reasonable agreement between the LES and the experiments is obtained. The numerical method is further validated for diffuser flow with the diffuser wall inclined at a diverging angle of 10°, which has served as a test case for a number of experimental as well as numerical studies in the literature (LES, RANS). For the present results, the subgrid-scale stresses have been closed using the dynamic Smagorinsky model. A resolution study has been performed, highlighting the disparity of the relevant temporal and spatial scales and thus the sensitivity of the simulation results to the specific numerical grids used. The effect of different Reynolds numbers of the inflowing, fully turbulent channel flow has been studied, in particular, Re _b  = 4,500, Re _b  = 9,000 and Re _b  = 20,000 with Re _b being the Reynolds number based on the bulk velocity and channel half width. The results consistently show that by increasing the Reynolds number a clear trend towards a larger separated region is evident; at least for the studied, comparably low Reynolds-number regime. It is further shown that the small separated region occurring at the diffuser throat shows the opposite behaviour as the main separation region, i.e. the flow is separating less with higher Re _b . Moreover, the influence of the Reynolds number on the internal layer occurring at the non-inclined wall described in a recent study has also been assessed. It can be concluded that this region close to the upper, straight wall, is more distinct for larger Re _b . Additionally, the influence of temporal correlations arising from the commonly used periodic turbulent channel flow as inflow condition (similar to a precursor simulation) for the diffuser is assessed.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Simultaneous velocity and passive scalar concentration measurements in low Reynolds number neutrally buoyant turbulent round jets

Velocity and scalar concentration characteristics of low Reynolds number (Re) neutrally buoyant turbulent round jets were studied using coupled particle image velocimetry and laser induced fluorescence. Experiments were conducted on a jet with a fully developed pipe exit profile at Re = 1,500 and Re = 4,000. Measurements were made in the far field (60 < x/D < 80). Results show that the centerline velocity decay constant increases with Re and the virtual origin is located far from the jet exit. The Re does not have such an influence on the scalar concentration decay constant and scalar field virtual origin. Centerline turbulent intensities show evidence of becoming self-similar past x/D ≈ 75 but the same is not observed in the scalar fluctuations. The latter are strongly influenced by the Re, increasing as entrainment of ambient flow on the jet axis increases as the flow approaches laminar conditions. Scalar fluxes showed a marked Re dependence as well. Results were used to estimate the turbulent Schmidt number which decreases as the Re decreases.     

Oil mist transport process in a long pipeline on turbulent flow transition region

Internal gas velocity fluctuations and their effects on the mist diffusion process were examined in a long horizontal pipe to understand oil mist transportation, particularly in the laminar-to-turbulent flow transition region. Three hot-wire anemometers and aerosol concentration monitors were used to deduce these effects as the two-phase mist flow gradually developed in the stream-wise direction. We found significant axial mist diffusion at Reynolds numbers (Re) < 1000 because of passive scalar transport by Poiseuille flow. However, this diffusion was restricted by the non-zero inertia of the mist at a Stokes number, O(10⁻⁵), relying on the Brownian motion of the mist. At Re > 2400, a sharp mist waveform was maintained by a turbulent flow with active radial mixing. New data were obtained within the range of 1000 < Re < 2400, which cannot be explained by interpolation between the above-mentioned two states. The mist concentration displays multiple temporal peaks at Re < 2000 owing to perturbations of localized turbulence as well as radial anisotropy as being conveyed more than 2000-diameters in distance. This behavior is caused by intermittent disturbances induced by the pipe wall roughness, which sharply distorts the wall-aligned laminar mist layer left by parabolic axial stretching of local laminar flow.     

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.     

Mixed convection from upward flow of hot air to a cooled vertical pipe

An experimental study had been carried out to investigate the buoyancy-opposed mixed convection from an upward flow of hot air to a vertical pipe with a cooled surface. The investigation covered a wide range of flow regime, ranging from the “free convection significant” to the “forced convection significant” conditions. Reynolds number of the flow extended from 966 to 14780, whereas the Buoyancy parameter, Ω [=Gr_d/(Re_d)²], varied from 0.008 to 2.77. A steady stream of hot air at a moderate pressure and a Prandtl number of 0.707 was arranged to flow upward through a vertical steel pipe, whose external wall was cooled uniformly by ambient air at 20°C. Test section of the vertical pipe was 1625 mm long with an internal diameter of 156 mm and an external diameter of 166 mm. Air temperature at inlet of the test section was varied from 40°C to 70°C. Both radial temperature and velocity profiles of the airflow were measured at inlet and exit of the test section respectively. Temperatures along the pipe wall were also measured. Non-dimensional expression for the prediction of the average heat transfer coefficient of the mixed convection from an upward flow of hot air to a vertical pipe with a cooled surface was developed from the experimental results. Convection heat transfer was found to impair when the flow is laminar and was enhanced for turbulent flow condition. Received on 20 July 1998     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Numerical study of oscillating boundary layer flow over a flat plate using k–kL–ω turbulence model

Oscillating boundary layer flow over an infinite flat plate at rest was simulated using the k–k_L–ω turbulence model for a Reynolds number range of 32 ⩽ Re_δ ⩽ 10,000 ranging from fully laminar flow to fully turbulent flow. The k–k_L–ω model was validated by comparing the predictions with LES results and experimental results for intermittently turbulent and fully turbulent flow regimes. The good agreement obtained between the k–k_L–ω model prediction with the experimental and LES results indicate that the k–k_L–ω model is able to accurately simulate transient intermittently turbulent flow and as well as accurately predict the onset of turbulence for such oscillatory flows.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Oscillating flow in a 2-D diffuser

Separating oscillating flows in an internal, adverse pressure gradient geometry are studied experimentally. Simultaneous velocity and pressure measurements demonstrate that the minor losses associated with oscillating flow in an adverse pressure gradient geometry can be smaller or larger than those for steady flow. Separation is found to begin high in the diffuser and propagate downward. The flow is able to remain attached further into the diffuser with larger Reynolds numbers, small displacement amplitudes, and smaller diffuser angles. The extent of separation grows with L ₀/h. The minor losses grow with increasing displacement amplitude in the measured range 10 < L ₀/h < 40. Losses decrease with increasing Re _δ in the measured range of 380 < Re _δ < 740. It is found that the losses increase with increasing diffuser angle over the measured range of 12° < θ < 30°. The nondimensional acoustic power dissipation increases with Reynolds number in the measured range and decreases with displacement amplitude.     

Near Field Round Jet Flow Downstream from an Abrupt Contraction Nozzle with Tube Extension

Round air jet development downstream from an abrupt contraction coupled to a uniform circular tube extension with length to diameter ratio L/D?=?1.2 and L/D?=?53.2 is studied experimentally. Smoke visualisation and systematic hot film velocity measurements are performed for low to moderate Reynolds numbers 1130?<?Re _b ?<?11320. Mean and turbulent velocity profiles are quantified at the tube exit and along the centerline from the tube exit down to 20 times the diameter D. Flow development is seen to be determined by the underlying jet structure at the tube exit which depends on Reynolds number, initial velocity statistics at the tube exit and the presence/absence of coherent structures. It is shown that the tube extension ratio L/D as well as the sharp edged abrupt contraction influence the initial jet structure at the tube exit. For both L/D ratios, the presence of the abrupt contraction results in transitional jet flow in the range 2000?<?Re _b ?<?4000 and in flow features associated with forced jets and high Reynolds numbers Re _b ?>?10⁴. The tube extension ratio L/D downstream from the abrupt contraction determines the shear layer roll up so that for L/D?=?1.2 flow visualisation suggests the occurrence of toroidal vortices for Re _b ?<?4000 whereas helical vortices are associated with the transitional regime for L/D?=?53.2. Found flow features are compared to features reported in literature for smooth contraction nozzles and long pipe flow.     

Parametric study of unsteady laminar flows

Results of a parametric study of unsteady laminar flows are analyzed. Three-dimensional unsteady equations of hydromechanics for a compressible medium are solved. The range of the characteristic Reynolds number Re = 400–900 is considered. It is demonstrated that the laminar flow in a plane channel ceases to be steady at Re = 415. As the Reynolds number increases, the unsteady processes become more intense, disturbances penetrate inward the channel, and separation zones lose their stability. In the vicinity of the channel exit, however, the flow tends to stabilize, though it remains unsteady. No transition to a turbulent flow occurs in the examined range of Reynolds numbers.     

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.     

High-resolution imaging of turbulence structures in jet flames and non-reacting jets with laser Rayleigh scattering

A comparative study of the length scales and morphology of dissipation fields in turbulent jet flames and non-reacting jets provides a quantitative analysis of the effects of heat release on the fine-scale structure of turbulent mixing. Planar laser Rayleigh scattering is used for highly resolved measurements of the thermal and scalar dissipation in the near fields of CH₄/H₂/N₂ jet flames (Re _d  = 15,200 and 22,800) and non-reacting propane jets (Re _d  = 7,200–21,700), respectively. Heat release increases the dissipation cutoff length scales in the reaction zone of the flames such that they are significantly larger than the cutoff scales of non-reacting jets with comparable jet exit Reynolds numbers. Fine-scale anisotropy is enhanced in the reaction zone. At x/d = 10, the peaks of the dissipation angle PDFs in the Re _d  = 15,200 and 22,800 jet flames exceed those of non-reacting jets with corresponding jet exit Reynolds numbers by factors of 2.3 and 1.8, respectively. Heat release significantly reduces the dissipation layer curvature in the reaction zone and in the low-temperature periphery of the jet flames. These results suggest that the reaction zone shields the outer regions of the jet flame from the highly turbulent flow closer to the jet axis.     

Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers

The phenomenon of low amplitude self-sustained pitch oscillations in the transitional Reynolds number regime is studied numerically through unsteady, two-dimensional aeroelastic simulations. Based on the experimental data, simulations have been limited in the Reynolds number range 5.0×10⁴<Re_c<1.5×10⁵. Both laminar and URANS calculations (using the SST k–ω model with a low-Reynolds-number correction) have been performed and found to produce reasonably accurate limit cycle pitching oscillations (LCO). This investigation confirms that the laminar separation of the boundary layer near the trailing edge plays a critical role in initiating and sustaining the pitching oscillations. For this reason, the phenomenon is being labelled as laminar separation flutter. As a corollary, it is also shown that turbulence tends to inhibit their existence. Furthermore, two regimes of LCO are observed, one where the flow is laminar and separated without re-attachment, and the second for which transition has occurred followed by turbulent re-attachment. Finally, it is established that the high-frequency, shear instabilities present in the flow which lead to von Kármán vortex shedding are not crucial, nor necessary, to the maintaining mechanism of the self-sustained oscillations.     

Effects of magnetic field on nanofluid forced convection in a partially heated microchannel

This paper numerically examines the laminar forced convection of a water–Al₂O₃ nanofluid flowing through a horizontal microchannel. The middle section of the microchannel is heated with a constant and uniform heat flux. The middle section is also influenced by a transverse magnetic field with a uniform strength. The effects of pertinent parameters such as the Reynolds number (0≤Re≤1000), the solid volume fraction (0≤?≤0.04) and the Hartmann number (0≤Ha≤100) on the flow and temperature fields and the heat transfer performance of the microchannel are examined against numerical predictions. The results show that the microchannel performs better heat transfers at higher values of the Reynolds and Hartmann numbers. For all values of the Reynolds and Hartmann numbers considered in this study, the average Nusselt number on the middle section surface of the microchannel increases as the solid volume fraction increases. The rate of this increase is considerably more at higher values of the Reynolds number and at lower values of the Hartmann number.     

Flows in the initial sections of channels with permeable walls

Calculations of two types of flows in the initial sections of channels with permeable walls are carried out on the basis of semiempirical turbulence theories during fluid injection only through the walls and during interaction of the external flow with the injected fluid. Experimental studies of the first type [1–3] show that at least within the limits of the lengths L/h<30 and L/a< 50 (2h is the distance between permeable walls of a flat channel anda is the tube radius) the velocity distributions in the laminar and turbulent flow regimes differ little and are nearly self-similar for solutions obtained in [4]. For sufficiently large Reynolds numbers, Re₀>100 (Re₀=v₀h/ or Re₀=v₀ a/, where v₀ is the injection velocity), and small fluid compressibility, the axial velocity component is described by the relations for ideal eddying motion: u=(/2)x× cos (y/2) in a flat channel and u=x cos (y²/2) in atube (the characteristic values for the coordinates are, respectively, h anda). Measurements indicate the existence of a segment of laminar flow; its length depends on the Reynolds number of the injection [3]. In the turbulent regime the maximum generation of turbulent energy occurs significantly farther from the wall than in parallel flow. Flows of the second type in tubes were studied in [5–7]. These studies disclosed that for Reynolds numbers of the flow at the entrance to the porous part of the tube Re=u₀ a/<3.10³ fluid injection with v₀/u₀>0.01 leads to suppression of turbu lence in the initial section of the tube. An analogous phenomenon was observed in the boundary layer with v₀/u₀>0.023 [8, 9]. Laminar-turbulent transition in flows with injection was explained in [10, 11] on the basis of hydrodynamic instability theory, taking into account the non-parallel character of these flows. The mechanisms for the development of turbulence and reverse transition in channels with permeable walls are not theoretically explained. Simple semiempirical turbulence theories apparently are insufficient for this purpose. In the present work results are given of calculations with two-parameter turbulence models proposed in [12, 13] for describing complex flows. Due to the sharp changes of turbulent energy along the channel length, a numerical solution of the complete system of equations of motion was carried out by the finite-difference method [14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 43–48, September–October, 1976.