Developed Flow Region Research Articles

Numerical study of turbulent wall jet over multiple-inclined flat surface

In the present work flow field of a turbulent oblique wall jet with multiple flat inclined wall has been numerically investigated. The Reynolds averaged Navier–Stokes (RANS) equations for incompressible flow are solved in transformed geometry using boundary-fitted coordinate system. The aim of the work is to investigate the influence of three inlet conditions: uniform, parabolic and trapezoidal inlet velocity profiles, on the mean flow and turbulent characteristics of the jet flowing tangentially along a multiple inclined solid wall. The results show that the inlet conditions affect the flow in the vicinity of the nozzle exit area and also the far field region. Mean flow has been presented in terms of evolution of mean velocity profiles, jet spread, decay of streamwise maximum velocity, distribution of wall pressure and skin friction coefficients, and streamwise variations of integrated momentum and energy fluxes. Discontinuities in the boundary slope of the segmented wall produces oscillations in distribution of skin friction and pressure coefficients. Reduced pressure in the region of wall discontinuity appeared to be causing the deflected jet to remain attached to the wall. The growth of the inner layer of the jet is relatively high with uniform inlet velocity profiles in the near-field region, but in the far-field region the inner layer grows with higher rate for the trapezoidal and the parabolic profiles. The rate of decay of maximum streamwise velocity for oblique wall jet on segmented wall is higher than that of plane wall jet. The jet with parabolic and trapezoidal inlet profiles show higher rate of decay than that with a uniform inlet profile. Similarity of streamwise velocity and velocity component parallel to the oblique wall has been observed in the developed region of flow. The volume flow rate of the jet varies linearly along the flow direction due to entrainment of the fluid from the surrounding. Sudden change in slope of the wall causes a sharp rise in entrained volume of fluid. The distribution of near wall velocity in the inner coordinates of the boundary layer is grossly altered and the profiles do not conform to the universal velocity profiles in the form of the law of the wall. Relatively higher position of defect law data signifies comparatively lower turbulence in the outer mixing layer. Cross-stream distribution of Reynolds stresses shows that the effect of inlet velocity profiles is more pronounced in the near field region of flow. Self-similarity is observed in the normalized turbulent shear stress profiles whereas considerable scatter can be noticed in the profiles of turbulent normal stresses for all the inlet velocity conditions. Two distinct peaks in the normalized turbulent kinetic energy profiles characterize the two shear layers of the jet and shifting of the outer peak toward the wall suggests a strong interaction of the outer layer with the inner layer as the jet develops.

Effect of cylinder proximity to the wall on channel flow heat transfer enhancement

Heat-transfer enhancement in a uniformly heated slot mini-channel due to vortices shed from an adiabatic circular cylinder is numerically investigated. The effects of gap spacing between the cylinder and bottom wall on wall heat transfer and pressure drop are systemically studied. Numerical simulations are performed at Re=100, 0.1⩽Pr⩽10 and a blockage ratio of D/H=1/3. Results within the thermally developing flow region show heat transfer augmentation compared to the plane channel. It was found that when the obstacle is placed in the middle of the duct, maximum heat transfer enhancement from channel walls is achieved. Displacement of circular cylinder towards the bottom wall leads to the suppression of the vortex shedding, the establishment of a steady flow and a reduction of both wall heat transfer and pressure drop. Performance analysis indicates that the proposed heat transfer enhancement mechanism is beneficial for low-Prandtl-number fluids.

Second moment closure modelling of flow, turbulence and heat transfer in droplet-laden mist flow in a vertical pipe with sudden expansion

The gas and droplet mean velocities, gas turbulence modulation, droplet dispersion and heat transfer of a dilute gas–droplet two-phase flow in a vertical pipe with sudden expansion are predicted using a two-fluid Eulerian model. The effect of various particle mass loadings, inlet Reynolds numbers and particle diameters on these characteristics is investigated. The turbulence of the carrier phase is modelled using second-moment closure (SMC). The results obtained using SMC are compared with those derived with the k-ε̃ model. The presence of finely dispersed droplets in the flow attenuates gas-phase turbulence by up to 25% in the axis zone. In the wall area, the mass fraction of droplets is much lower than that in the axial region of the pipe due to droplet evaporation. Heat transfer in the gas–droplet separated flow increases (by more than twice that in single-phase air flow). Intensification of heat transfer is observed both in the recirculation zone and flow development region in the case of fine particles.

Effect of duct aspect ratio on heat transfer and friction in steam-cooled ducts with 60° angled rib turbulators

The effect of duct aspect ratio on heat transfer and friction characteristics is investigated experimentally and numerically. Heat transfer experiments as well as pressure drop measurements are carried out to get detailed local heat transfer coefficient distributions and friction factor data for steam-cooled ducts with 60° angled ribs. The test cases are also analyzed numerically by adopting the SSG turbulence model. Four different duct aspect ratios (AR) are studied: AR=1/4, 1/2, 1/1 and 2/1, the corresponding hydraulic diameter (D) is 32.0mm, 53.33mm, 40.0mm and 53.33mm, and the rib height-to-hydraulic diameter ratio (e/D) is 0.078, 0.047, 0.0475 and 0.047, respectively. The rib pitch-to-rib height ratio (p/e) is kept 10 for all the ducts. The investigated Re number ranges from 10,000 to 80,000. Both the experimental and numerical results show the similar trend on heat transfer and friction loss, but the prediction values are higher by 3–15% and 2–20%, respectively. The centerline heat transfer coefficient of steam on the ribbed side wall is gradually increased in the fully developed flow region because of the rib angle. The overall heat transfer coefficient is increased with increasing duct aspect ratio (except the duct of AR=1/1). The averaged heat transfer coefficient ratio of steam is higher by 12–25% than air at the same test conditions. The highest heat transfer enhancement accompanied by the highest friction factor is occurred at AR=2/1, however, the optimum thermal enhancement factor is found at AR=1/2.

An Experimental Investigation of Heat Transfer Enhancement Mechanisms in Microencapsulated Phase-Change Material Slurry Flows

This article investigates laminar heat transfer characteristic of two-phase microencapsulated phase-change material (MPCM) suspension flows within minichannels under a constant wall heat flux boundary. Capsules containing paraffin wax with phase-change temperature between 36.1°C and 38.1°C are examined and found to be well suited for electronics cooling applications using liquid cold plate technologies. In particular, it is shown that the large thermal capacity of MPCM slurries around the phase-change temperature can lead toward greater isothermality of isoflux systems, a characteristic of significant interest to telecommunication, laser and biomedical applications. The principal focus of the study is to examine heat transfer characteristics within standard tube flow geometries, quantify the heat transfer augmentation/degradation observed, and finally, elucidate the mechanisms from which these result. Through the study volume concentrations of the MPCM slurry were varied between 0% and 30.2%. High-resolution local heat transfer measurements were obtained using infrared thermography and results presented in terms of local Nusselt number versus inverse Graetz parameter. These spanned both the thermal entrance and the fully developed flow regions with inverse Graetz number ranging from 10−3 to 100. Results show that significant heat transfer enhancements are attainable via the use of MPCM slurries over conventional single-phase coolants. Overall, the study highlights mechanisms that lead to significant heat transfer enhancements in heat exchange devices employing microencapsulated phase-change material slurries.

Computational Modelling of Blood Flow Development and Its Characteristics in Magnetic Environment

Of concern in this paper is an investigation of the entrance length behind singularities in cardiovascular hemodynamics under magnetic environment. In order to get better interpretation of scan MRI images, the characteristics of blood flow and electromagnetic field within the circulatory system have to be furthermore investigated. A 3D numerical model has been developed as an example of blood flowing through a straight circular tube. The governing coupled nonlinear differential equations of magnetohydrodynamic (MHD) fluid flow are reduced to a nondimensional form, which are then characterized by four dimensionless parameters. With an aim to validate our numerical approach, the computational results are compared with those of the analytical solution available in the developed region far from the singularity. The hydraulic impedance by unit length within the developed flow region increases with the magnetic field. The time average entrance length with a greater precision on the unsteady case decreases with increasing magnetic field strength. The overall voltage characteristics do not depend on the developed flow field within the entry region.

Validation of Theory with Experiments for Local Mass Transfer at Parallel Plate Electrodes under Laminar Flow Conditions

Theoretical equations are reported to calculate the local Sherwood number for a parallel plate electrochemical reactor with a developing flow region under laminar flow conditions. These equations were deduced from analytical velocity profiles according to different proposals, which are compared with the velocity profiles given by the numerical solution of the Navier-Stokes equations. A comparison between the theoretical mass transfer equations with experimental results is also given.

Particle clusters and drag coefficients in gas–solid downer units

This manuscript reports “individual” particle cluster information obtained using a Chemical Reactor Engineering Centre Gas–Solid Optical Probe (CREC-GS-Optiprobe) equipped with a Graded Refractive Index (GRIN) lens. The CREC-GS-Optiprobe is used to study the fluid dynamics in the developed region of a co-current gas solid down flow fluidized bed unit. The CREC-GS-Optiprobe forms a 118±34μm diameter highly illuminated light region at 8.05mm distance in front of the sensor tip. Experiments are carried out in a circulating fluidized bed downer cold model unit of 3.0m height and 0.0257m internal diameter. The solid used is a fluid catalytic cracking (FCC) catalyst with a mean particle diameter of 84.42μm and a particle density of 1722kg/m3. The superficial gas velocity and solid mass fluxes are varied from 0.95 to 2.53m/s and from 10 to 106kg/m2s, respectively. Analysis of the data obtained involves a rigorous methodology for setting the data baseline in compliance with solid mass balances. The application of this method allows the simultaneous measurement of (i) cluster solid concentrations, (ii) individual cluster slip velocities and (iii) individual cluster sizes. These data also allow calculation of cluster size frequency distribution at various radial positions in the downer unit. On the strength of these experimental data, particle cluster drag coefficients are calculated as a function of the cluster Reynolds’ number and average particle number in the cluster. Drag coefficients determined using the proposed method provide close range values. These findings support a particle string configuration for clusters in downer units.

Infra-red thermography of laminar heat transfer during early thermal development inside a square mini-channel

Infra-red thermography (IRT) has been employed to experimentally scrutinize the thermo-hydrodynamics of very early part of hydrodynamically fully developed, but thermally developing, internal laminar flow of water (850⩾Re⩾100) in a mini-channel of square cross-section (5mm×5mm; aspect ratio=1.0; Dhyd 5mm). The channel is machined on that face of an aluminum substrate whose dimensions are 11mm×140mm; the total width of the substrate being 45mm. A constant heat flux boundary condition is provided on the substrate face which is opposite to that on which the mini-channel is machined. Thus, the mini-channel receives heat from three sides; the fourth side being covered by an insulating poly-carbonate material. IRT provides non-intrusive and high-resolution spatial measurement of local wall temperature in the streamwise direction. By assuming a one-dimensional heat transfer model in the transverse direction, the local value of heat flux and therefore the Nusselt number, in the thermally developing region, can be estimated. Moreover, a 3D conjugate heat transfer numerical model, exactly corresponding to the real experimental conditions, has also been developed. The conjugate effects in the experiment arising due to the substrate, as well as the high heat transfer coefficient in the early thermal development zone, are analyzed. The errors and discrepancy in the in situ boundary conditions which may creep in due to such effects, especially in the estimation of transport coefficients in the developing flow region, are scrutinized and delineated. It is concluded that experimental estimation of local heat flux is a primary requirement for minimizing the errors in estimating local Nusselt number in developing flows. This in turn, necessitates the use of non-intrusive field measurement techniques, such as IRT.

Impact of Internals on the Heat-Transfer Coefficient in a Bubble Column

The effect of heat exchanging internals on the heat-transfer coefficient has been investigated in a 0.19 m diameter bubble column. An air–water system was used with superficial gas velocities varying from 3 to 20 cm/s, which cover both the bubbly and churn-turbulent flow regimes. Internals occluding 0% (empty column), 5% (simulating methanol synthesis), and 22% (simulating Fischer–Tropsch synthesis) of the column cross-sectional area were implemented. A fast response heat-transfer probe was utilized to measure the radial profile of the heat-transfer coefficient in the fully developed flow region. The results indicate that the presence of a high percentage of internals causes an increase in the heat-transfer coefficient at the same actual gas velocity on the basis of the open cross-sectional area. Also, the heat-transfer coefficient increases with an increase in the gas velocity. The heat-transfer coefficients in the column center for all of the studied conditions are larger than those near the wall of the column.

DNS of compressible pipe flow exiting into a coflow

Direct numerical simulations were conducted of a fully turbulent canonical nozzle/jet configuration. For all cases, the target Reynolds number, based on the jet velocity and diameter, was specified as 7500 and the jet Mach number and coflow Mach number were varied. Turbulence statistics at the nozzle exit are shown to collapse with fully developed turbulent pipe flow profiles when using the wall shear-stress, and in the case of higher Mach number cases also the wall density, from the fully developed flow region upstream in the nozzle. Predictions of flow variables in the near-nozzle region obtained from asymptotic theory are found to agree qualitatively with Direct Numerical Simulation data. The data from the different cases are shown to collapse in the potential core region when scaling with the appropriate mixing layer parameter while further downstream the appropriate parameter is the non-dimensional local velocity excess. For all scalings investigated, including virtual-origin correction of the streamwise axis, the case with the highest coflow magnitude did not agree well with the other cases implying that self-similarity of coflowing jets is restricted to low coflow values. Finally, it is shown that the acoustic field is resolved by the simulations making the data suitable for subsequent aeroacoustic analysis.

Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: Forces, deformation, and detachment. I: Theoretical and numerical analyses

Water management is critical to achieving/maintaining high performance of polymer electrolyte fuel cells (PEFCs); and elucidating the dynamic behavior of liquid water droplets in a PEFC channel is essential to water management. In this work, the dynamics of liquid water droplets in a single PEFC gas flow channel is investigated through theoretical and numerical analyses. Forces on water droplet, droplet deformation and detachment are examined. The pressure and viscous drags are computed and compared at different flow regimes (which exhibit different droplet-dynamic scenarios) such as that in the entrance and fully developed flow regions. The expression for describing droplet shape change is derived, and it is found that the droplet can deform significantly at high gas-flow rates and when the droplet is relatively large (relative to the channel dimension). The detachment velocity is analyzed by comparing the wall adhesion and drag forces, and an expression relating the Weber number to the Reynolds number using the detachment velocity is developed. Follow-on work is also briefly discussed.

3D Modeling and Simulation of a Two-Phase Mixing Jet Flow

Gas-solid mixing jet flows are an essential feature of typical chemical engineering processes. A proper analysis of the mixture flow optimizes process qualities and efficiencies. In this contribution, a numerical study of the solids dispersion in a two-phase jet flow is presented. The mathematical model treats the gas and the solid phases with an Eulerian approach. Radial profiles of the solid-phase mean velocity were computed on five axial levels, subdivided in five cases, in the mixing jet flow using a two-phase 3D computational fluid dynamics model. The computed solids velocities were compared with experimental data on a jet with an internal diameter of 12mm, at different inlet conditions of solid mass load for rates (3 to 7) and velocities (8 to 16m/s). The mean particle diameter used was 50μm and a density of 2500kg/m3.Three different drag models were applied to evaluate the solids dispersion, Wen and Yu [1], Gidaspow [2] and Massarani [3] correlations, the latter being a continuous one. The two-equation (k-e) turbulence model was employed to describe the gas-phase, while the zero-equation (kinematic viscosities analogy) turbulence model describing the solid-phase in a jet flow. The mathematical model predicts a developed flow regions similar to that found experimentally.

Particle dispersion and turbulence modification in a dilute mist non-isothermal turbulent flow downstream of a sudden pipe expansion

Flow, particles dispersion and heat transfer of dilute gas-droplet turbulent flow downstream of a pipe sudden expansion have been numerically investigated for the conditions of heated dry wall. An Euler two-fluid model with additional turbulence transport equations for gas and particulate phases was employed in the study. Gas phase turbulence was modelled using the elliptic blending Reynolds stress model of Fadai-Ghotbi et al. (2008). Two-way coupling is achieved between the dispersed and carrier phases. The partial equations of Reynolds stresses and temperature fluctuations, and the turbulent heat flux equations in dispersed phase by Zaichik (1999) were applied. Fine droplets get readily entrained with the detached flow, spread throughout the whole pipe cross-section. On the contrary, large particles, due to their inertia, do not appear in the recirculation zone and are presented only in the shear layer region. The presence of fine dispersed droplets in the flow attenuates the gas phase turbulence of up 25 %. Heat transfer in the mist flow increased (more than twice in comparison with the single-phase air flow). Intensification of heat transfer is observed both in the recirculation zone and flow development region in the case of fine particles. Large particles enhanced heat transfer only in the reattachment zone. Comparison between simulated results and experimental data of Hishida et al. (1995) for mist turbulent separated flow behind a backward-facing step shows quite good agreement.

Prediction of fully developed turbulent heat transfer of internal helically ribbed tubes – An extension of Gnielinski equation

Turbulent heat transfer and friction factors are measured in this paper for 16 internally grooved tubes with different geometrical parameters. Experiments are conducted for the 16 tubes with the Reynolds number range from 10,000 to 100,000 and Prandtl number from 4.98 to 8.22. Other parameter ranges are: 1 ⩽ N s ⩽ 45, 0.016 ⩽ e/ d i ⩽ 0.04, 13 ⩽ α ⩽ 45, where N s is the number of circumferential micro-fins (number of starts), e and α are the height and helix angle of the micro-fin, respectively, and d i is the inner diameter of the embryo tube. An equation for predicting the average heat transfer of the inner helically ribbed tubes is presented based on Gnielinski equation with the friction factor in the numerator of the original Gnielinski equation being replaced by the measured friction factor in the fully developed flow region of the internally grooved tubes. For all data of the 16 tubes, most of the relative deviation is within ±10%. Comparison of this equation with other data available in the literature is also provided, and the deviation of more than 93% of the compared data is within ±20%, 99% within ±40%. Since the friction factor is easier to be measured, the proposed correlation equation is practically very applicable and its accuracy is also acceptable for the engineering design.

Thermal performance of developing flow in a radially rotating parallelogram channel with 45° ribs

An experimental study was performed to measure the full-field Nusselt number ( Nu) distributions over two opposite leading and trailing ribbed walls, the pressure drop coefficients ( f) and the overall thermal performance factors (TPF) of a rotating parallelogram channel with radially outward flow. The test conditions in terms of Reynolds ( Re), rotation ( Ro) and buoyancy ( Bu) numbers were respectively in the ranges of 5000 ≤ Re ≤ 15,000, 0 ≤ Ro ≤ 0.3 and 0.001 ≤ Bu ≤ 0.23. The full-field Nu data generated by the infrared thermography method were examined to study the isolated and interdependent Re, Ro and Bu impacts on the detailed Nu distributions as well as on the rib-wise averaged Nusselt numbers ( N u ¯ ) at rib and mid-rib locations over the leading and trailing walls. With rotation, the Nu distribution over the trailing wall followed the Nu 0 pattern in the static channel; but underwent considerable modification from the Nu 0 pattern on the leading wall by generating a haloed high Nu region at the obtuse entry corner. A parametric analysis which examined the detailed Ro and Bu impacts on N u ¯ at rib and mid-rib locations enlightened the streamwise developments of rotational effects on heat transfer performances over leading and trailing walls. This parametric analysis led to the generation of a set of physically consistent empirical N u ¯ correlations which assisted to evaluate the individual and interdependent Ro and Bu effects on N u ¯ at rib and mid-rib locations over the developing flow region. As an indication of the combined effects of Coriolis force, rotating buoyancy and the geometric features emulated by the present parallelogram ribbed channel, the area-averaged Nusselt numbers on the leading and trailing walls were modified to the respective ranges of 0.78–1.34 and 1.09–1.38 times of the non-rotating Nusselt numbers; while the f coefficients were raised to 1.05–5.2 times of the stationary levels, leading the TPF factors to the range of 0.979–1.575.

Prandtl and capillary effects on heat transfer performance within laminar liquid–gas slug flows

This paper investigates a two-phase non-boiling slug flow regime for the purposes of enhancing heat transfer in microchannel heat sinks or compact heat exchangers. The primary focus is upon understanding the mechanisms leading to enhanced heat transfer and the effect of using different Prandtl number fluids, leading to variations in Capillary number. Experimental work was conducted using Infrared thermography and results are presented in the form of Graetz solution, spanning both the thermal entrance and fully developed flow regions. Nusselt numbers enhancements were observed throughout when data was reduced to account for void fraction. However, the gaseous void was also noted to demonstrate an artificial increase with greater thicknesses of the liquid film, due to higher Capillary numbers. Up to 600% enhancement in heat transfer rates were observed over conventional Poiseuille flow. This was verified through Nusselt number measurements over inverse Graetz number ranges from 10 −4 to 1 and slug length to channel diameter ratios from 0.88 to 32. Varying Prandtl and Capillary numbers caused notable effects in the transition region between entrance and fully developed flows. Significant Nu oscillations were observed for low Pr fluids due to internal circulation within the slug. However, these oscillations are observed to be damped out when higher Prandtl number fluids are employed. The thickness of the liquid film surrounding the gas bubbles is shown to have a significant influence on heat transfer performance. Overall, this study provides a greater understanding of the mechanisms leading to significant enhancements in heat exchange devices employing two-phase gas–liquid flows without boiling.

Influence of Radial Rotation on Heat Transfer in a Rectangular Channel With Two Opposite Walls Roughened by Hemispherical Protrusions at High Rotation Numbers

Detailed heat transfer distributions over two opposite leading and trailing walls roughened by hemispherical protrusions were measured from a rotating rectangular channel at rotation number up to 0.6 to examine the effects of Reynolds (Re), rotation (Ro), and buoyancy (Bu) numbers on local and area-averaged Nusselt numbers (Nu and Nu¯) using the infrared thermography. A set of selected heat transfer data illustrates the Coriolis and rotating buoyancy effects on the detailed Nu distributions and the area-averaged heat transfer performances of the rotating channel. The Nu¯ for the developed flow region on the leading and trailing walls are parametrically analyzed to devise the empirical heat transfer correlations that permit the evaluation of the interdependent and individual Re, Ro, and Bu effect on Nu¯.

Experimental Study of Near-Field Entrainment of Moderately Overpressured Jets

Particle image velocimetry (PIV) experiments have been conducted to study the velocity flow fields in the developing flow region of high-speed jets. These velocity distributions were examined to determine the entrained mass flow over a range of geometric and flow conditions, including overpressured cases up to an overpressure ratio of 2.83. In the region near the jet exit, all measured flows exhibited the same entrainment up until the location of the first shock when overpressured. Beyond this location, the entrainment was reduced with increasing overpressure ratio, falling to approximately 60% of the magnitudes seen when subsonic. Since entrainment ratios based on lower speed, subsonic results are typically used in one-dimensional volcanological models of plume development, the current analytical methods will underestimate the likelihood of column collapse. In addition, the concept of the entrainment ratio normalization is examined in detail, as several key assumptions in this methodology do not apply when overpressured.

Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms

In this paper, a bottom-up approach is used to construct random rough bottom walls for trapezoidal silicon microchannels with hydraulic diameters Dh from 47 μm to 241 μm. The top and side walls are set to be smooth. A computational fluid dynamics solver is used to solve the 3D Navier–Stokes equations for the water flow through the rough trapezoidal microchannels. No-slip and periodic boundary conditions are applied to achieve the fully developed flow characteristics. The effects of Reynolds number Re (75–600), relative roughness height H/Dh (1.66–5.39%), aspect ratio β (0.13–1), and base angle θ (30–90 deg) on the Poiseuille number Po are investigated. It is found that the roughness strongly affects the flow near the bottom wall but does not have significant effect on the center flow. The Po number in the developing flow region increases with the Re number and in the fully developed region tends to be independent of the Re number. The entrance length Le is found to be smaller than that in smooth channels because the roughness reduces hydraulic diameter Dh of the microchannel. It is also observed that with a certain H/Dh, the Po number has a larger deviation from the theoretical value with a smaller β, and with the same H/Dh and β, θ can also change the Po number, especially at small base angles.