The effect of mixed convection on the structure of channel flow at low Reynolds numbers

An experimental study was conducted to investigate the effect of bottom wall heating on the flow structure inside a horizontal square channel at low Reynolds numbers (Re) and high Grashof numbers (Gr). The flow field was found to be complex and three-dimensional due to the interactions of buoyancy-induced rising plumes of warm fluid, falling parcels of cold fluid and the shear flow. The mean streamwise velocity profiles were altered by bottom wall heating; and back flow was induced in the upper half of the channel when Gr/Re² > 55. The bottom wall temperatures were found to have more significant influence on the turbulent velocity magnitudes than the flow rate. The Reynolds stress became negative in the channel core region indicating the momentum transfer from the turbulent velocity field to the buoyancy field. The POD analysis revealed the presence of convective cells primarily in the lower half of the channel.     

On the effect of Reynolds number on von Kármán’s constant

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10×10³ to 350×10³ with a hot-wire anemometer and a Pitot tube. Comparisons were made with the experimental results of previous work. The mean velocity profile and the turbulent intensity in the experiments indicate that for the mean velocity profile, in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number, i.e. κ increases slowly with the Reynolds number. The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow. The project supported by the Deutscher Akademische Austauschdienst (DAAD)     

Experimental study on heat transfer of thermally developing and developed, turbulent, horizontal pipe flow of dilute air-solids suspensions

Heat transfer characteristics of a turbulent, dilute air-solids suspension flow in thermally developing/developed regions were experimentally studied, using a uniformly heated, horizontal 54.5 mm-ID pipe and 43-μm-diameter glass beads. The local heat transfer was measured at 27 locations from the inlet to 120-dia downstream of the heated section over a range of Reynolds numbers 3×10⁴−1.2×10⁵ and solids loading ratio 0–3, and the fully developed profiles of air velocity/temperature and particle mass flux were measured at a location 140-dia downstream of the heated section using specially designed probes, inserted into the suspension flow. The effects of the Reynolds number, solids loading ratio, and azimuthal/longitudinal locations on the heat transfer characteristics and their interactions are discussed through comparison of the present results with the data obtained by other investigators. Received on 14 October 1996     

Numerical simulation and visualization of fiber suspension in a turbulent round jet

The turbulent properties of the fiber suspension in a turbulent round jet are numerically simulated and visualized, and some of the results are compared with the experimental data. The effects of the Reynolds number, fiber volume fraction, and aspect ratio are analyzed. The results show that the fiber injection in the flow has a delay effect on the streamwise velocity decay along the jet axis, and such an effect becomes more obvious with the increases in the fiber volume fraction and aspect ratio and the decrease in the Reynolds number. The flow with fibers shows an increase in the streamwise velocity along the radial direction, and the increase magnitude is directly proportional to the fiber volume fraction and aspect ratio and inversely proportional to the Reynolds number. The presence of fibers makes the turbulent kinetic energy and Reynolds stress increase, and the extent increases with the fiber volume fraction, Reynolds number, and fiber aspect ratio.     

Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation(LES) is considered as a better simulation model. However, the sub-grid scale(SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder(SC)at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square(RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls.The instantaneous factor of swirling strength intermittency(FSI) exhibits some laminated structure involved with vortex shedding.     

Time-resolved velocity and concentration measurements in variable-viscosity turbulent jet flow

This paper addresses the ability to reliably measure the fluctuating velocity field in variable-viscosity flows (herein, a propane–air mixture), using hot-wire anemometry. Because the latter is sensitive to both velocity and concentration fluctuations, the instantaneous concentration field also needs to be inferred experimentally. To overcome this difficulty, we show that the hot-wire response becomes insensitive to the concentration of the field, when a small amount of neon is added to the air. In this way, velocity measurements can be made independently of the concentration field. Although not necessary to velocity measurements, Rayleigh light-scattering technique is also used to infer the local (fluctuating) concentration, and, therefore, the viscosity of the fluid. Velocity and concentration measurements are performed in a turbulent propane jet discharging into an air–neon co-flow, for which the density and viscosity ratios are 1.52 and 1/5.5, respectively. The Reynolds number (based on injection diameter and velocity) is 15400. These measurements are first validated: the axial decay of the mean velocity and concentration, as well as the lateral mean and RMS profiles of velocity and concentration, is in full agreement with the existing literature. The variable-viscosity flow along the axis of the round jet is then characterized and compared with a turbulent air jet discharging into still air, for which the Reynolds number (based on injection diameter and velocity) is 5400. Both flows have the same initial jet momentum. As mixing with the viscous co-flow is enhanced with increasing downstream position, the viscosity of the fluid increases rapidly for the case of the propane jet. In comparison with the air jet, the propane jet exhibits: (1) a lower local Reynolds number based on the Taylor microscale (by a factor of four); (2) a reduced range of scales present in the flow; (3) the isotropic form of the mean energy dissipation rate is first more enhanced and then drastically diminishes and (4) a progressively increasing local Schmidt number (from 1.36 to 7.5) for increasing downstream positions. Therefore, the scalar spectra exhibit an increasingly prominent Batchelor regime with a ~ k ^?1 scaling law. The experimental technique developed herein provides a reliable method for the study of variable-viscosity flows.     

Turbulent transport of particles in a straight square duct

Turbulent flow through a duct of square cross-section gives rise to off-axis secondary flows, which are known to transfer momentum between fluid layers thereby flattening the velocity profile. The aim of this study is to investigate the role of the secondary flows in the transport and dispersion of particles suspended in a turbulent square duct flow. We have numerically simulated a flow through a square duct having a Reynolds number of Re_τ = 300 through discretization of the Navier–Stokes equations, and followed the trajectories of a large number of passive tracers and finite-inertia particles under a one-way coupling assumption. Snapshots of particle locations and statistics of single-particle and particle pair dispersion were analyzed. It was found that lateral mixing is enhanced for passive tracers and low-inertia particles due to the lateral advective transport that is absent in straight pipe and channels flows. Higher inertia particles accumulate close to the wall, and thus tend to mix more efficiently in the streamwise direction since a large number of the particles spend more time in a region where the mean fluid velocity is small compared to the bulk. Passive tracers tend to remain within the secondary swirling flows, circulating between the core and boundary of the duct.     

Heat transfer in turbulent pipe flow based on a new mixing length model

A new model for the heat transfer in turbulent pipe flow is presented based on a modified form of the mixing length theory developed by Cebeci [1] for boundary layer flow problems. The model predicts the velocity and temperature distributions and the Nusselt number for fluids with low, medium and high Prandtl numbers (Pr=.02 to 15) and fits the available experimental data very accurately for values of Reynolds number exceeding 10⁴. Expressions for the eddy conductivity and for the turbulent Prandtl number are presented and shown to be dependent upon the Reynolds number, the Prandtl number, and the distance from the tube wall.     

Experimental study of the velocity field in a vortex-flow heat exchanger with isothermal conditions

The velocity field in a vortex heat cell was investigated experimentally using laser Doppler velocimetry for a wide range of flow conditions. Experimental results point out the three dimensionality of the exchanger's flow, which is composed into a main vortex flow developing along the side walls. The strength of the flow increases up to a limiting value reached for a Reynolds number ranging between 15,000 and 30,000; a secondary flow, caused by interaction between centrifugal and inertial forces, extends perpendicularly to the main flow and remains Reynolds number dependent. It is composed of multiple counter-rotating structures occurring at the exchanger periphery with low inlet Reynolds numbers, thus reducing the rate of centripetal momentum transfer. With increasing inlet Reynolds number, the secondary flow extends across the whole exchanger radius, thus increasing the rate of mixing of the treated fluid. The appearance of so-called Taylor–Görtler vortices tends to reduce the z- and r-axis vorticity transfer.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

Hydrodynamic and thermal fields analysis in gas-solid two-phase flow

The present work aims to investigate numerically the flowfield and heat transfer process in gas-solid suspension in a vertical pneumatic conveying pipe. The Eulerian-Lagrangian model is used to simulate the flow of the two-phases. The gas phase is simulated based on Reynolds Average Navier-Stokes equations (RANS) with low Reynolds number k-ε model, while particle tracking procedure is used for the solid phase. An anisotropic model is used to calculate the Reynolds stresses and the turbulent Prandtl number is calculated as a function of the turbulent viscosity. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. Comparisons between different models for turbulence modulation with experimental data are carried out to select the best model. The model is validated against published experimental data for velocities of the two phases, turbulence intensity, solids concentration, pressure drop, heat transfer rates and Nusselt number distribution. The comparisons indicate that the present model is able to predict the complex interaction between the two phases in non-isothermal gas-solid flow in the tested range. The results indicate that the particle-particle collision, turbulence dispersion and lift force play a key role in the concentration distribution. In addition, the heat transfer rate increases as the mass loading ratio increases and Nusselt number increases as the pipe diameter increases.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Effect of the shape of a body on the intermittency of turbulent flow in an axisymmetrical wake

Experimental data regarding the distribution of the intermittency coefficient of the turbulent flow of an incompressible liquid in the axisymtnetrical wakes behind a sphere or a solid of revolution with an elongation of 8∶1 are presented. The original measurements were carried out at a Reynolds number of Re=U_∞D/v=10⁴ (U_∞) is the velocity of the incident flow, D is the diameter of the middle cross section). The shape of the solid is shown to have a considerable effect on the form of intermittency in the far automodel wake.     

Turbulent heat transfer characteristics of water flow in a rotating pipe

Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 ≤ N ≤ 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined.     

An application of the k-ɛ model with variable Prandtl number to heat transfer computations in air flows

The two-equation `low Reynolds number' k-? model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Pr_t in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 10⁴?4. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.     

Turbulent Couette–Taylor flows with endwall effects: A numerical benchmark

The accurate prediction of fluid flow within rotating systems has a primary role for the reliability and performance of rotating machineries. The selection of a suitable model to account for the effects of turbulence on such complex flows remains an open issue in the literature. This paper reports a numerical benchmark of different approaches available within commercial CFD solvers together with results obtained by means of in-house developed or open-source available research codes exploiting a suitable Reynolds Stress Model (RSM) closure, Large Eddy Simulation (LES) and a direct numerical simulation (DNS). The predictions are compared to the experimental data of Burin et al. (2010) in an original enclosed Couette–Taylor apparatus with endcap rings. The results are discussed in details for both the mean and turbulent fields. A particular attention has been turned to the scaling of the turbulent angular momentum G with the Reynolds number Re. By DNS, G is found to be proportional to Re^α, the exponent α = 1.9 being constant in our case for the whole range of Reynolds numbers. Most of the approaches predict quite well the good trends apart from the k–ω SST model, which provides relatively poor agreement with the experiments even for the mean tangential velocity profile. Among the RANS models, even though no approach appears to be fully satisfactory, the RSM closure offers the best overall agreement.     

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ^° pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (R e _d =32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10^°. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.     

Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates

Analytical solutions are presented using method of separation of variables for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson–Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of half channel width to Debye length, the periodic EOF electric oscillating Reynolds number Re and normalized relaxation time λ₁ω on velocity profiles and volumetric flow rates are presented. Results show that for prescribed electrokinetic width K, lower oscillating Reynolds number Re and shorter relaxation time λ₁ω reduces the plug-like EOF velocity profile of Newtonian fluids. For given Reynolds number Re and electrokinetic width K, longer relaxation time λ₁ω leads to rapid oscillating EOF velocity profiles with increased amplitude. With the increase of the K, the velocity variations are restricted to a very narrow region close to the EDL for small relaxation time. However, with the increase of the relaxation time, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. As far as volume flow rates are concerned, for given electrodynamic width K, larger oscillating Reynolds number Re results in a smaller volume flow rates. For prescribed oscillating Reynolds number Re, with the changes of relaxation time λ₁ω, volume flow rates will produce some peaks no matter how the electrodynamic width K varies. Moreover, the time periodic evolution of the velocity profiles provides a detail insight of the flow characteristic of this flow configuration.     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.