Crossflow Reynolds Number Research Articles

Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Two-Phase Particulate Suspension Flow in Convergent and Divergent Channels: A Numerical Model

The problem dealing with the two-phase flow of particulate suspension in a converging diverging channel has been analyzed. The basic equations governing the flow are reduced to a set of ordinary differential equations by using the appropriate transformations for the velocity components. The numerical solutions are carried out using numerical technique and the results are presented graphically. The flow phenomena have been analyzed for different physical parameters, Reynolds number, cross flow Reynolds number, angle of the channel, ratios of densities fluid and particle phases and momentum inverse stokes number. The effects of parameters on the velocity of the fluid and the skin friction has been discussed.

Large eddy simulation of turbulent heat transfer from a rotating disk subjected to a forced parallel air stream

Nowadays, rotating disks are an important part of most industries such as turbo machines, heat exchangers, braking systems, rotating sawing machines, and computer disk drives. Working temperature and consequently heat transfer have a profound effect on performance and lifetime of rotating disks. There is a noticeable difference between numerical and experimental results in the studies of turbulent heat transfer from a rotating disk subjected to parallel air stream. The main objective of this study is numerical simulation of turbulent convective heat transfer from a rotating disk subjected to parallel air stream. In this study, the 2nd order finite volume scheme and large eddy simulation (LES) with the dynamic Smagorinsky procedure in sub-grid-scale is used. Two limit cases called rotating disk in still air (von Karman's swirling flow), stationary disk subjected to parallel air stream are investigated as well. The mean Nusselt number of the disk surface is obtained at statistical steady state for a wide range of rotational and cross flow Reynolds numbers. The influence of flow separation and finite disk thickness on heat transfer is investigated and followed by a detailed discussion. The effect of convection and diffusion on temperature field is illustrated. Comparison with experimental data shows that the LES dynamic Smagorinsky results are by far better than available numerical results. It is discussed in detail that there is a critical value for ratio of crossflow Reynolds number to rotational Reynolds number which above that the influence of disk rotation on mean Nusselt number is negligible.

Direct simulation of conjugate heat transfer of jet in channel crossflow

We present a DNS study of a hot, low momentum laminar water jet discharged into a cold turbulent channel stream through a circular orifice in one of the steel channel walls. The channel wall has a finite thickness and its outer side is cooled under Robin type thermal boundary conditions for a realistic external environment, leading to a conjugate heat transfer system. Nusselt number and r.m.s temperature fluctuations on the wall are compared with our earlier DNS results for the simpler iso-thermal and adiabatic conditions at the channel inner surface. Temperature fluctuations inside the channel wall are resolved to provide data for a conjugate heat transfer (CHT) thermal fatigue test case related to the ageing of pipe walls and welds studies, as found, for example, in power plant piping T-junctions. The crossflow Reynolds number is Re=3333, jet-to-crossflow velocity ratio is R=1/6 and fluid-to-solid conductivity ratio is 1/64.The near-wall mean flow structures, a horseshoe vortex ahead and on the sides of the jet orifice, a shallow recirculation behind the discharge and a counter-rotating vortex pair drawing in a blanket of cooler cross-flow, lead to a complex convective and turbulent wall heat transfer pattern around the orifice. The main findings are:(i)Wall maps of Nusselt number and r.m.s temperature, θr.m.s, for conjugate heat transfer are only qualitatively similar to the iso-thermal and adiabatic wall cases.(ii)Inside the solid θr.m.s and its dissipation, analysed from RANS modelling perspective, show that predicted thermal spot length scales are discontinuous on the interface, at variance with the 2-point spectrum-derived scales.(iii)At the high wavenumber range, the spanwise temperature spectra decrease according to exponential-decay spectral models for the fluid turbulence in the Kolmogorov range, but with large exponential coefficients increasing with depth inside the solid.

Non-Premixed Burner-Attached Jet Flames in Crossflow Pulsed at Resonance Frequency

The flame behavior, flow patterns, and thermochemical structures of a combusting propane gas jet in crossflow excited acoustically at resonance frequency were studied in a wind tunnel. The jet and crossflow Reynolds numbers were 1530 and 1399, respectively. The jet-to-crossflow momentum flux ratio was 0.192. The flame behavior was found to be closely related to the shear-layer vortical flow structures in the near-tube region. Six characteristic flame modes were observed in the domain of jet pulsation intensity . In flame modes 1 and 2 (), the shear-layer vortices were dominant. In flame modes 3–6 (), the flames were dominated by a puffing bent jet. Vortical structures increased in size with increasing . Temperature and combustion product measurements showed significant improvements in mixing and combustion, as well as a reduction of combustion-induced pollutants at the near-tube region of the flame. However, pulsing the jet flame in crossflow at pulsation intensities greater than 0.9 led to a significant increase in the maximum values of carbon monoxide and nitric oxide concentrations at the middle- to far-tube flame regions. Therefore, strongly pulsing a jet flame in crossflow may not necessarily lead to an improved combustion.

Effects of jet pulsation intensity on a wake-stabilized non-premixed jet flame in crossflow

The jet pulsation intensity effects induced by acoustic excitation on a non-premixed fuel jet flame in crossflow were experimentally studied in a wind tunnel at the crossflow Reynolds number Rew=1416, jet Reynolds number Rej=1550, jet-to-crossflow momentum flux ratio R=0.192, and excitation Strouhal number Stexc=0.21. The jet pulsation intensity Ipul varied from 0 to 0.9. The flame behaviors, stability mechanism of flame blowoff, flow patterns, and thermochemical fields were measured and discussed. The time-averaged and instantaneous flame appearances were photographed by a high speed camera. The instantaneous flow patterns were obtained by the laser-light-sheet-assisted particle-tracing method. The temperature and concentrations of combustion-induced pollutants (unburned HC, CO, and NO) were measured by a fine-wire R-type thermocouple and a gas analyzer, respectively. Analysis of the measured results showed that the flame and flow behaved differently within four ranges of jet pulsation intensities (slight, medium, strong, and over excitations). The flows presented different characteristic modes of enlarged shear-layer vortices, irregular puffs, up-down oscillating bent jet in different ranges of jet pulsation intensities, and therefore induced different flame behaviors in different ranges of jet pulsation intensities. The primary flow features leading to modifications of the flame behaviors were the upwind shear-layer vortices and the recirculation area around the leeward side of burner tube tip. Appling excitation to the combusting jet in crossflow at Ipul>0.55 could lead to significant improvement in mixing and combustion and reduction of combustion-induced pollutants.

Entropy generation in a porous annulus due to micropolar fluid flow with slip and convective boundary conditions

A numerical work has been performed to study the entropy generation of micropolar fluid flow and heat transfer in an annulus with porous walls under the transverse magnetic field associated with slip and convective boundary conditions. Assume that the injection velocity at one wall is same as the suction velocity at the other wall. The governing equations of the fluid flow are linearized using quasilinearisation method and further, solved by the Chebyshev spectral collocation method. The numerical data for velocity, microrotation and temperature fields are used to evaluate entropy generation and Bejan number. It has been found that the maximum entropy generation is observed at the inner cylinder and minimum entropy generation is observed at the outer cylinder. Also entropy generation increases with increase in coupling number, Hartman number, cross flow Reynolds number, Biot number and Brinkman number. Whereas it reduces with increase in slip parameter.

Effects of vortex generators on the jet impingement heat transfer at different cross-flow Reynolds numbers

Experiments are carried out to investigate the effects of vortex generators on the jet impingement heat transfer in cross-flow. This study is a continuation of our previous research (Wang et al., 2015). In the present paper, the jet Reynolds number is fixed at 15,000 and the cross-flow Reynolds number varies from 40,000 to 64,000. The nozzle-to-surface distance to jet diameter ratio is 4.0. A vortex generator pair (VGP), placed in the cross-flow channel and upstream of the jet exit, is to enhance the impingement heat transfer. Both delta winglet (DW) and rectangular winglet (RW) are applied with different heights. Measurements of detailed heat transfer distributions on the impingement wall are conducted. Results show that the presence of VGP substantially augments the impingement heat transfer in cross-flow for all the cases, and its effect depends on the shape of the VGP, the height of the VGP, and also the cross-flow Reynolds number. The RW provides better heat transfer enhancement than the DW due to stronger vortical flow. The enhancement also increases monotonically with the height of the VGP. In addition, the averaged Nusselt number and pressure drop of the jet and cross-flow at different cross-flow Reynolds numbers are included. It is found that the favorable effects of the VGP are more significant as the cross-flow Reynolds number increases. Some PIV measurements were carried out. The flow structures and heat transfer mechanisms are discussed.

Process engineering optimization of nanofiltration unit for the treatment of textile plant effluent in view of solution diffusion model

A nanofiltration (NF) based separation process is used to treat the effluent from a textile plant to allow for water reuse and fulfill environmental standards. The wastewater effluent contains reactive black (RB5)- and disperse (DR60) dyes. A NF-unit model E2 series with HL 2521 TF spiral wound module was used to carry out experiments. 90 & 93% color removal and COD reduction for RB5 and 98 & 95% for DR60 were achieved. A parametric study of the separation process is undertaken to characterize the effects of the operating variables, e.g., trans-membrane pressure, dye/salt concentration in the feed, temperature, and cross flow velocity. The solution diffusion model was used to develop power correlations to calculate the permeate side solute mass transfer coefficient as a function of effective cross-flow Reynolds number. In contrast to the commonly assumed constant hydraulic solvent permeability, a non-linear relationship was developed over the applied trans-membrane net driving pressure. The latter correlates exponentially with salt permeability for both dyes. The effects of feed salt-content on solute mass transfer coefficient, water and salt permeability, concentration polarization, dye hydrophobicity and ionic strength were studied. Results were used to assess engineering specifications of a commercial size NF-plant (500m3/d capacity).

Film Cooling Effectiveness Enhancement Applying another Jet in the Upstream Neighbor of the Main Jet-Using LES Approach

Flow hydrodynamic effects and film cooling effectiveness of placing a coolant port (upstream jet) just upstream of the main cooling jet were numerically investigated. The upstream jet was added such that the total cooling cross section (cross sections of the main and upstream jets) remains constant, in comparison to the case of ordinary cooling jet. The finite volume method and the unsteady SIMPLE algorithm on a multiblock non-uniform staggered grid arrangement were applied. The large eddy simulation (LES) approach with the one equation subgrid scale model was used. The jet to cross flow velocity ratio (for both of the main and the upstream jets) is 0.5 and the cross flow Reynolds number (based on the main jet parameters) is equal to 4700. The obtained results showed a significant improvement in the flow control capability and both centerline and span-wise averaged film cooling effectiveness applying the new cooling configuration. Effects of the upstream jet dimensions are also studied here. The obtained results showed that the span-wise width of the upstream jet has more essential influence on the cooling performance than that of its stream-wise width. Moreover, it is demonstrated that the film cooling performance could be enhanced even by applying an upstream jet which its temperature is as same as the cross-flow temperature, i.e. applying a hot upstream jet. Finally, it is shown that presence of the upstream jet decreases the stream-wise component of the velocity near the wall, which decreases the wall shear stress and the skin friction drag coefficient significantly.

Numerical investigation of laboratory tested cross-flow tidal turbines and Reynolds number scaling

The cross-flow, or vertical axis tidal turbine, is a prominent configuration of marine renewable energy device aimed at converting tidal currents into electrical energy. This paper highlights the hydrodynamic limitations of laboratory testing such devices and uses numerical simulation to explore the effect of device scaling. Using a 2D Reynolds-Averaged Navier–Stokes (RANS) numerical approach, a single turbine blade is initially modelled and validated against published data. The resultant numerical model is then expanded to emulate an experimental cross-flow tidal turbine designed and tested by the University of Oxford. The simulated turbine achieves a close quantitative match for coefficients of power, torque and thrust, forming the basis of a study exploring the effects of Reynolds number scaling in three alternative operating conditions. It is discovered that the coefficient of power (CP) increases with Re¯ without a ubiquitous correlation until an Re¯ of ∼350,000. Above this Re¯ the CP values for all three operation conditions become both proportional and predictable. The study represents a significant contribution to understanding the application of detailed numerical modelling techniques to cross-flow tidal turbines. The findings, with regard to scaling from laboratory data, could reduce uncertainty and development costs for new and existing devices.

A novel control of jet impingement heat transfer in cross-flow by a vortex generator pair

Jet impingement is an effective heat transfer method while the favorable performance is usually degraded by the cross-flow. In this article, a novel control of the impinging jet in cross-flow has been proposed. A delta winglet vortex generator pair (VGP) is installed in the cross-flow channel upstream of the jet nozzle. The jet and the cross-flow Reynolds numbers are 15,000 and 40,000, respectively. The ratio of nozzle-to-surface distance to jet diameter is 4.0. Experimental measurements are conducted to study the characteristics of heat transfer with liquid crystal thermography (LCT). Results indicate that the VGP with common-flow-up (CFU) configuration promotes the jet penetration in cross-flow and augments the impingement heat transfer greatly on the target wall compared to the baseline case without the VGP. In addition, the enhancement increases monotonically with the angle of attack of the VGP varying from α=15° to 45°. The spacing between the VGP l1=1.2d is preferred with the highest heat transfer augmentation of jet impingement among l1=0.5–2.0d. The optimal value of spacing between the VGP and the jet nozzle l2 is suggested to be 4d in terms of enhancing the heat transfer, for the measurement range from l2=2d to l2=8d. The VGP with common-flow-down (CFD) configuration is also tested, but it leads to slightly lower heat transfer than without the VGP. Pressure drop of the jet in cross-flow with VGP is measured and analyzed.

Improving cooling effectiveness by use of chamfers on the top of electronic components

A Computational Fluid Dynamic (CFD) study based on Reynolds Averaged Navier–Stokes (RANS) approach is carried out to predict the mean velocity field and the heat transfer rate of an impinging jet in cross-flow configuration on a heated wall-mounted cube. Targeting an electronic cooling configuration, the aim is to investigate the effect of geometrical modification of the component on the cooling effectiveness. For the same cross flow Reynolds number ReH=3410, three levels of impinging jets are computed as well as a case without impinging jet that will serve as baseline case for comparison. The results from the RANS computation are compared to experimental data from published scientific literature. The validation shows qualitatively good agreement and almost all flow structures are well reproduced by the computation. In an attempt to optimize the wall heat flux over the cube surface, a new geometry is proposed without sharp corners on the top cube face. Numerical results show that with minor geometrical modification (chamfer), the fluid flow structure around the electronic component is radically transformed and the heat transfer rate can be improved. The highest cooling effectiveness improvement is realize for the highest Reynolds number ratio Rej/ReH=1.5 and for the chamfer height of 4mm.

Trapping of embolic particles in a vessel phantom by cavitation-enhanced acoustic streaming

Cavitation clouds generated by short, high-amplitude, focused ultrasound pulses were previously observed to attract, trap, and erode thrombus fragments in a vessel phantom. This phenomenon may offer a noninvasive method to capture and eliminate embolic fragments flowing through the bloodstream during a cardiovascular intervention. In this article, the mechanism of embolus trapping was explored by particle image velocimetry (PIV). PIV was used to examine the fluid streaming patterns generated by ultrasound in a vessel phantom with and without crossflow of blood-mimicking fluid. Cavitation enhanced streaming, which generated fluid vortices adjacent to the focus. The focal streaming velocity, uf, was as high as 120 cm/s, while mean crossflow velocities, uc, were imposed up to 14 cm/s. When a solid particle 3–4 mm diameter was introduced into crossflow, it was trapped near the focus. Increasing uf promoted particle trapping while increasing uc promoted particle escape. The maximum crossflow Reynolds number at which particles could be trapped, Rec, was approximately linear with focal streaming number, Ref, i.e. Rec = 0.25Ref + 67.44 (R2 = 0.76) corresponding to dimensional velocities uc = 0.084uf + 3.122 for 20 < uf < 120 cm/s. The fluidic pressure map was estimated from PIV and indicated a negative pressure gradient towards the focus, trapping the embolus near this location.

Study of shear-thinning/thickening effects on plane Couette-Poiseuille flow with uniform crossflow

The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theoretical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shearthickening circumstance is discovered.

Membrane scaling and flux decline during fertiliser-drawn forward osmosis desalination of brackish groundwater

Fertiliser-drawn forward osmosis (FDFO) desalination has been recently studied as one feasible application of forward osmosis (FO) for irrigation. In this study, the potential of membrane scaling in the FDFO process has been investigated during the desalination of brackish groundwater (BGW). While most fertilisers containing monovalent ions did not result in any scaling when used as an FO draw solution (DS), diammonium phosphate (DAP or (NH4)2HPO4) resulted in significant scaling, which contributed to severe flux decline. Membrane autopsy using scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDS), and x-ray diffraction (XRD) analysis indicated that the reverse diffusion of DAP from the DS to the feed solution was primarily responsible for scale formation during the FDFO process. Physical cleaning of the membrane with deionised water at varying crossflow velocities was employed to evaluate the reversibility of membrane scaling and the extent of flux recovery. For the membrane scaled using DAP as DS, 80–90% of the original flux was recovered when the crossflow velocity for physical cleaning was the same as the crossflow velocity during FDFO desalination. However, when a higher crossflow velocity or Reynolds number was used, the flux was recovered almost completely, irrespective of the DS concentration used. This study underscores the importance of selecting a suitable fertiliser for FDFO desalination of brackish groundwater to avoid membrane scaling and severe flux decline.

Effects of shear-thinning/thickening nature on the stability of Couette-like flow with uniform crossflow

The linear stability of wall-injected pressuredriven Couette-like flow in power-law fluids is studied. Previous study on this kind of flow for Newtonian fluids by Nicoud and Angilella [Phys. Rev. E 56, 3000 (1997)] was extended to power-law fluids to understand the effects of shear-thinning/thickening nature on the flow stability. A related expression between the critical crossflow Reynolds number for Newtonian fluids and that for power-law fluids is obtained as the streamwise Reynolds number is large enough based on numerical computations, and verified theoretically in the case of a limiting condition with the power-law index.

Theoretical analysis on the laminar flow of an elastico- viscous fluid between a moving elliptic plate with constant injection and the ground

A theoretical study is presented for the problem of injection of an elastico-viscous fluid through a moving elliptic plate. The governing equations are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations for the velocity components. The resulting boundary value problem is solved numerically using the Matlab solver singular boundary value problem (SBVP). The current numerical analysis encompasses the range of cross-flow Reynolds number R as . The results are compared with those known from the literature and an excellent agreement is found. Perturbation solutions are also obtained for small R. A comparison of the numerical solutions with the perturbation solutions is made. The comparison shows that the perturbation solutions give acceptable results for and , where N is the viscoelastic fluid parameter. The influence of the viscoelastic fluid parameter on the velocity, load-carrying capacity and friction force has been examined carefully. Key words: Elasticoviscous fluid, porous slider, load-carrying capacity, friction force.

Heat transfer and vortical structures around a rotating cylinder with a spanwise disk and low-velocity crossflow

In this paper, we study the flow field characteristics and heat transfer of a rotating cylinder with a spanwise disk attached and subjected to low-velocity crossflow with a disk-cylinder diameter ratio, Dd/Dc=3.06. Reynolds Averaged Navier–Stokes (RANS) simulations using the k-∊ realizable turbulence model with enhanced wall treatment were performed for various crossflow and rotational velocities. We were particularly interested in the case of a rotating cylinder, with a spanwise disk attached, in an air stream with a crossflow Reynolds number, ReU=23,560, and rotational Reynolds numbers, ReΩ, ranging from 5500 to 109,800. Large-eddy simulations (LES) using the dynamic kinetic energy subgrid-scale model were performed for ReΩ=54,900 and 109,800. Heat transfer results from the RANS simulations were compared to results from previous studies. Flow statistics computed from the LES calculations were compared to results measured by particle image velocimetry experiments. Unsteady flow patterns and thermal behaviours are discussed with reference to the instantaneous LES results.

Pulsating flow of a couple stress fluid in a channel with permeable walls

The paper is concerned with an analytical study of the oscillatory flow of a couple stress fluid in a channel, bounded by two permeable walls. The couple stress fluid is considered to be injected into the medium through one of the walls with a given velocity and to be sucked off by the other wall with an equal velocity. The problem is solved by using a perturbation technique. Analytical expressions for the velocity and volumetric flow rate are derived for the oscillatory flow of the couple stress fluid flowing in the channel. By using the method of parametric variation, distribution of the velocity of the couple stress fluid, change in velocity profiles at different instants of time, change in volumetric flow rate with change in frequency and cross-flow Reynolds number are computed, by considering an illustrative example. The study reveals that both the velocity and the volumetric flow rate are quite sensitive to the couple stress parameter, the frequency of oscillation and also to the cross-flow Reynolds number. The study will be immensely useful in resolving different problems associated with oil industries.