Equal Reynolds Numbers Research Articles

Numerical Study on Heat Transfer and Pressure Loss Characteristics of Swirl Cooling in Elliptical Tubes With Tangential Jet Inlets

Abstract The paper presents a numerical study of the heat transfer, pressure loss, and flow characteristics of swirl cooling in elliptical tubes, which are compared to the counterpart of swirl cooling in a circular tube with a diameter of D = 50.0 mm under equal passage Reynolds numbers and equal jet Reynolds numbers. The swirl tubes with two kinds of fixed tube length of 12D and 20D are compared, where there are sequentially arranged three tangential jet inlets over the leading tube length of 12D. The numerical results show that the swirl tubes with the tube length of 12D has a much better heat transfer performance. Under equal passage Reynolds numbers, the elliptical swirl tubes with the tube length of 12D show appreciably higher Nusselt numbers by up to 22.8% and lower pressure loss coefficients by up to 69.0% than the circular tube. Under equal jet Reynolds numbers, the elliptical tubes can reduce the global heat transfer performance modestly by up to 25.6%, but reduce the pressure loss much significantly by up to 70.6%. Mostly due to much less pressure loss, the elliptical tubes have remarkably higher thermal performance in terms of the obtained heat transfer coefficient per unit pumping power for both L1 = 12D and L2 = 20D. The numerical simulations indicate that the suppression of elliptical tubes on the swirling flow development reduces the heat transfer on the wall between the jet inlets, and decreases the wall shear force and the pressure loss in the tube.

Energy redistribution dynamics in coupled Couette–Poiseuille flows using large-Eddy simulation

The problem of turbulent Couette flow driven by a statistically steady external wind is studied in the framework of spatially filtered Navier–Stokes equations. The phenomenon of wind-driven flow of water is represented by a layer of air modeled as Poiseuille flow (air sub-domain), coupled to a layer of water modeled as Couette flow (water sub-domain). We focus on changes in the statistics in either the air or the water sub-domain, due to the coupling with the other sub-domain. We also highlight dynamic flow structures forming near the air-water interface. Simulations based on different Reynolds numbers in the air and the water sub-domains are compared to computationally less demanding simulations with equal Reynolds numbers. Results of these simulations indicate strong similarities, i.e., the flow is well approximated by simulating air and water at the same Reynolds numbers. Further analysis shows that the flow in the water domain shares important features with classical Couette flows. The horizontal turbulent mixing renders a thinner boundary layer in the water sub-domain. Moreover, an increased intermittency in the flow velocities is observed, which may be linked to so-called splat events near the air-water interface. These splats characterize the interaction of coherent structures across the interface, being stronger in the water phase. An analysis of the pressure-strain correlation near the air-water interface on the water side shows that such splats are responsible for redistributing energy from the streamwise and spanwise directions, to the vertical direction. This behavior, although qualitatively similar to wall-bounded flows, differ mainly on the fact that most of the energy drained comes from the streamwise direction: in wall-bounded the main contributor is the spanwise direction. The boundary layers near the air-water interface show inclined vortical structures. Unlike in coupled Couette–Couette flow, the peak in the Reynolds stress is displaced from the channel’s center into the buffer region of the water sub-domain.

Influence of particle properties on convective heat transfer of nanofluids

An experimental study is performed in order to examine how particle properties such as size and thermal conductivity affect the convection heat transfer of nanofluids. For this purpose, we prepare and study self-synthesized water-based nanofluids with different kinds of particles: polystyrene, SiO2, Al2O3 and micelles. Concentrations of the nanofluids vary in the range of 0.1–1.8 vol-% and particle sizes between 8 and 58 nm. Full-scale convective heat transfer experiments are carried out using an annular tube heat exchanger with the Reynolds numbers varying in the range of 1000–11000. The pressure losses are also taken into account in the analysis in order to assess the feasibility of the nanofluids for practical forced convection heat transfer applications. The fluids are thoroughly characterized: viscosities, thermal conductivities, densities, particle size distributions, shapes and zeta potentials are all determined experimentally. In many previous studies, anomalous enhancement in convective heat transfer is observed based on comparison of the Nusselt numbers with equal Reynolds numbers. Also in this work, the nanofluids exhibit Nusselt numbers higher than water when compared on this basis. However, this comparison neglects the impact of differences in the Prandtl numbers, and therefore the altered thermal properties of nanofluids are not properly taken into account. In this study, no difference in Nusselt numbers is observed when the Prandtl number is properly considered in the analysis. All nanofluids performed as the Gnielinski correlation predicts, and the widely reported anomalous convective heat transfer enhancement was not observed with any nanoparticle types. Instead, we show that the convection heat transfer behavior of nanofluids can be explained through the altered thermal properties alone. However, addition of any type of nanoparticles was observed to change the fluid properties in an unfavorable manner: the viscosity increases significantly, while only moderate enhancement in the thermal conductivity is obtained. The more viscous nanofluids reach lower Reynolds numbers than water with equal pumping powers resulting in lower heat transfer coefficients. However, the increase in viscosity, and therefore also the deterioration of the convective heat transfer, is less pronounced for the nanofluids with smaller particle size indicating that small particle size is preferable for convective heat transfer applications.

Thermal properties and convective heat transfer of phase changing paraffin nanofluids

Fluids containing micro-sized solid-liquid phase changing particles have been proposed to be promising candidates as future heat transfer fluids. In addition, smaller nano-sized particles have been claimed to enhance the heat transfer performance of fluids even if the phase change is not exploited. For the first time, we conduct full scale convection heat transfer measurements combining these two consepts. Three water-based paraffin mixture nanofluids with particle mass fractions of 5–10% are prepared and measured with an annular tube heat exchanger with Reynolds numbers varying in the range of 700–11000. In addition, the fluids are characterized: latent heats, specific heats, viscosities, thermal conductivities, densities and particle size distributions are all determined experimentally. In agreement with previous studies of solid-particle nanofluids and nanoemulsions, also the phase changing nanofluids are found to exhibit Nusselt numbers clearly higher (up to ∼60% in the turbulent regime) than water when compared on the basis of equal Reynolds numbers. However, the differences in Prandtl numbers are shown to explain these deviations in Nusselt numbers. Indeed, the well-known Gnielinski correlation is able to explain the results and thus, significant anomalies in the convection heat transfer caused by neither the melting of the phase change material nor the presence of the nanoparticles are observed. However, the nanofluids have systematically slightly higher Nusselt numbers than the correlation would predict, but the deviations are within the accuracy of the correlation (10%). When compared by using equal pumping powers, the nanofluids exhibit heat transfer performance poorer than that of water. The positive impact of the latent heat is outweighed by the negative effects of the increased viscosity and decreased specific heat.

Heat transfer and pressure loss in swirl tubes with one and multiple tangential jets pertinent to gas turbine internal cooling

This paper presents a comparative experimental and numerical study of heat transfer and pressure loss characteristics in swirl tubes with one (S1) and five (S5) tangential inlet jets, respectively. Transient liquid crystal thermography has been used in the experiments to obtain detailed local and globally averaged heat transfer data in the swirl tubes with the two different inlet jet configurations. Comparisons of the experimental data for the heat transfer and pressure loss characteristics of the swirl tubes are analyzed under equal mass flow rates and under equal inlet jet Reynolds numbers, respectively. With equal overall mass flow rates in the two configurations the experiments showed that the heat transfer patterns of the swirl tube S1 are substantially different from those of the swirl tube S5. The swirl tube S1 shows significantly higher heat transfer and pressure loss than the swirl tube S5. The heat transfer in the swirl tube S1 reaches peak values under the inlet jet and then continuously decreases to the end of the tube, while the heat transfer in the swirl tube S5 is increased under each inlet jet along the tube length. The swirl tube S5 shows a more uniform heat transfer pattern than the swirl tube S1 along the tube length. However, under equal inlet jet Reynolds numbers, the globally averaged heat transfer of swirl tube S5 is higher than that of swirl tube S1 over the whole tube length. The heat transfer of the swirl tube S5 can be regarded as a combination of repeated heat transfer patterns along the tube, each of which is dominated by a single jet induced swirling flow over a shorter tube length between the jets. The cross flow does not show detrimental effects on the heat transfer of the downstream inlet jets in the swirl tube S5. In support of the experiments, three-dimensional numerical computations are presented to provide more insight into the flow structure in the swirl tubes.

Influence of the fluid density on the statistics of power fluctuations in von Kármán swirling flows

Here, we report experimental results on the fluctuations of injected power in confined turbulence. Specifically, we have studied a von Kármán swirling flow with constant external torque applied to the stirrers. Two experiments were performed at nearly equal Reynolds numbers, in geometrically similar experimental setups. Air was utilized in one of them and water in the other. With air, it was found that the probability density function of power fluctuations is strongly asymmetric, while with water, it is nearly Gaussian. This suggests that the outcome of a big change of the fluid density in the flow-stirrer interaction is not simply a change in the amplitude of stirrers’ response. In the case of water, with a density roughly 830 times greater than air density, the coupling between the flow and the stirrers is stronger, so that they follow more closely the fluctuations of the average rotation of the nearby flow. When the fluid is air, the coupling is much weaker. The result is not just a smaller response of the stirrers to the torque exerted by the flow; the PDF of the injected power becomes strongly asymmetric and its spectrum acquires a broad region that scales as f−2. Thus, the asymmetry of the probability density functions of torque or angular speed could be related to the inability of the stirrers to respond to flow stresses. This happens, for instance, when the torque exerted by the flow is weak, due to small fluid density, or when the stirrers’ moment of inertia is large. Moreover, a correlation analysis reveals that the features of the energy transfer dynamics with water are qualitatively and quantitatively different to what is observed with air as working fluid.

Blending of miscible liquids with different densities and viscosities in static mixers

The homogenization of two liquids of different densities and viscosities in a pipeline equipped with a corrugated plate SMV static mixer is investigated by RANS-based CFD simulations. The blending effectiveness of the mixer is compared at different Richardson numbers and viscosity ratios for equal Reynolds numbers. The mixedness level is found to be a function of the Richardson number. As a result, depending on the pipeline scale, equal density differences require a different number of pipe diameters for the achievement of the same level of homogenization. The dynamic viscosity differences give rise to less marked effects, unless back-mixing becomes significant. Besides the coefficient of variation of the scalar concentration, which is often adopted as a measure of the intensity of segregation in turbulent static mixers, novel definitions of the scale and of the rate of change of segregation are proposed, in order to add deeper insight into the evaluation of the mixing features.

An experimental and numerical study of the structure and stability of laminar opposed-jet flows

Experiments, simulations, and numerical bifurcation analysis are used to study the incompressible flow between two opposed tubes with disks mounted at their exits. The experiments in this axisymmetric geometry show that for low and equal Reynolds numbers, Re, at both nozzles, the flow remains symmetric about the plane halfway through the nozzle exits and the stagnation plane is located halfway between the two jets. When Re is increased past a critical value, asymmetric flow fields are obtained even when the momentum fluxes of the two opposed streams are equal. For unequal Re at the jet exits, when the fixed velocity (and the corresponding Reynolds number, Re 1 ) of one stream is low, the stagnation plane location, SPL, changes smoothly with the Re 2 . For high enough Re 1 , a hysteretic jump of SPL is observed. Particle Image Velocimetry and flow visualization demonstrate that within the hysteretic range, the two stable flow fields are anti-symmetric. The experimental setup is also studied with transient incompressible flow simulations using a spectral element solver. It is found that to accurately model the flow, we either need to extend the domain into the nozzles, or impose experimental velocity profiles at the nozzle exits. As in the experiments asymmetric flows are obtained past a critical Re. Finally, bifurcation analysis using a Newton–Picard method shows that the transition from symmetric to asymmetric flows results from the loss of stability of the symmetric flows at a pitchfork bifurcation.

Effect of channel geometry in regular ceramic packings on the hydrodynamics of heat and mass exchange

It is noted that regular structured packings, which permit maximum development of the contact surface, are coming into increasingly greater use in the chemical, petroleum-refining, petrochemical, and other branches of industry for implementation of heat-and mass-exchange processes in liquid-vapor (gas) systems. It is demonstrated that for equal surface areas of the elements of irregular and regular granular beds and equal Reynolds numbers, the coefficients of mass exchange are approximately equal, while the coefficient of hydraulic resistance of the regular packing is three orders lower. A simple packing in the form of a block with parallel through channels (passages) is investigated on a structural and production basis. A relationship is presented for the specific surface of the channel and the size of the cell, and it is established that the specific surface, and of course, the active surface decreases by a factor of 30 as the size of the cell increases from 0.5 to 15 mm. The influence exerted by the cross section of the channel on head loss is also demonstrated.

Shear driven solitary waves on a liquid film

Long nonlinear two-dimensional traveling waves on a film driven by laminar gas flow are investigated numerically via solving Navier-Stokes equations. The evolution of their shape, amplitude, and speed with increasing Reynolds number is studied. The existence of solitary waves is demonstrated. A comparison between shear driven and gravity-capillary waves is made and discussed. It is shown that shear driven waves as compared to gravity driven waves are much higher for equal film Reynolds numbers and much slower for equal wave amplitudes.

Mixing Characteristics in a Conical Taylor-Couette Flow System at Low Reynolds Numbers

Mixing behaviors in a conical Taylor–Couette flow system were investigated at low Reynolds numbers using flow-visualization and salt-solution tracer techniques. Owing to sensitivity during the start-up procedure, the acceleration rate of the inner conical cylinder was precisely controlled by computer. Two different flow modes were observed in the laminar flow regime. When the inner conical cylinder was accelerated at a low rate (0.05 rad/s2), the whole fluid column was filled with helical vortices. In the case of a high acceleration rate (0.5 rad/s2), an upward traveling motion of the Taylor vortices was observed. The vortices started to display a global upward motion due to the strong meridional circulation. These two flow modes showed quite different mixing behaviors even at nearly equal Reynolds numbers. In the case of the upward traveling motion, the tracer substance was convected with the traveling vortices in the main flow cross-section and with the meridional flow at the outer-edge cell boundaries. In the helical motion, on the other hand, the tracer was transported by diffusion-like motion along the helical vortex filament and by convection along the secondary flow streamlines at outer-edge cell boundaries.

Multiplicity of Steady Two-Dimensional Flows in Two-Sided Lid-Driven Cavities

The two-dimensional steady incompressible flow in rectangular cavities is calculated numerically by a finite volume method. The flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves. Depending on the cavity aspect ratio and the two side-wall Reynolds numbers different flow states exist. Their range of existence and the bifurcations between different states are investigated by a continuation method accurately locating the bifurcation points. When both side walls move in opposite directions up to seven solutions are found to exist for the same set of parameters. Three of these are point-symmetric and four are asymmetric with respect to the center of the cavity, if the side-wall Reynolds numbers have the same magnitude. When the walls move in the same direction, up to five different flow states are found. In this case only a single mirror symmetric solution exists for equal Reynolds numbers.

Perforated Trapezoidal Fins for Tube-in-Fin Heat Exchangers: Heat Transfer and Pressure Drop Characteristics

The paper reports the heat transfer and pressure drop characteristics of an air-cooled tube-in-fin heat exchanger equipped with novel fins that prove effective in low Reynolds number flows. The fins have many perforations and are configured into trapezoidal corrugations. The air-side heat transfer coefficient is about 1.4 ∼ 2.2 times that of a plain-fin heat exchanger at equal Reynolds numbers. An analytical model to predict the air-side performance of the heat exchanger is developed, dividing the flow field into potential flow cores on the upstream sides of the tubes and the wake zones behind the tubes. Experimental data of heat transfer coefficient and pressure drop are compared with the predicted values. The both are found in reasonable agreement.

Experimental investigation of highly effective plate-fin heat exchanger surfaces

Results are presented of an experimental investigation of a new convective rational heat transfer augmentation law in plate-fin heat exchanger surfaces. This law is characterized by Nu/Nu sm ≥ ξ/ξ sm by comparing channels (heat transfer surfaces) with vortex promoters with similar smooth channels at equal Reynolds numbers. For experimental confirmation and investigation of this law, heat exchanger cores having three different plate-fin surfaces were developed and manufactured. Two surfaces are formed by short offset channels (interrupted surfaces) of equilateral triangular and rectangular cross sections. The third surface has channels of isosceles triangular cross sections, with transverse projections and grooves along the channel length direction. The experimental results and correlations are reported for the three surfaces. The experiments were conducted in a wind tunnel with specially developed precise instrumentation that ensured experimental uncertainties of δξ = ± 2.3% and δRe = 1.7% at a 0.997 confidence level. Analysis of the results indicated that the fundamental character and causes limiting rational heat transfer augmentation to Nu/Nu sm ≥ ξ/ξ sm depend upon the heat transfer surface configuration. This paper consolidates the author's research on the subject reported in the Russian language over the last 25 years.

The hydrodynamics of conodont elements

Accurate palacobiological interpretation of the fossil record requires an assessment of biostratinomic processes. Samples which have undergone significant post-mortem sorting reflect only the hydrodynamic regime prevalent at the time of deposition and not the original faunal composition. Conodont bedding plane assemblagcs are rare and many conodont taxa are known only through reconstructions of apparatuses using empirical techniques. These methods require large collections where the elements have undergone no significant post-mortem transportation. In this paper measurements of settling velocities are used to predict relative hydrodynamic behaviour in a current. The settling velocity of a particle is of about the same magnitude as the current required to entrain that particle. Conodont elements rotate during fall, spinning about a central axis. Elements with equal Reynolds numbers may have different drag coefficients indicating that shape is an important factor in determining conodont element hydrodynamics. In a current of increasing velocity the predicted order of entrainment of elements of the same equivalent size is as follows: Polygnathus S. Ancyrodella Pa. Polygnathus Pa. Palmatolepis Pa. Polygnathus Pb. lcriodus Pa. Conodont elements grow by accretion of lamellae; to the first approximation. length is a satisfactory indication of size. Length can therefore be used to predict the settling velocities of elements, and which elements will sort together. Measurement of element lengths allows a rapid estimation of the degree of post-mortem sorting undergone by a sample and therefore its suitability for use in palaeobiological analysis. □Conodont hydrodynamics, biostratinomy, drag coefficient, settling velocity. sorting.

SCOUR UNDER A VERTICALLY OSCILLATING LEG

Mishaps with jack-up oil rigs could be caused by scour beneath their legs as they oscillate vertically, either on site or when being shifted to or from site. This action was replicated in the laboratory by moving cylindrical feet to and from a sandy bed at frequencies appropriate to the scale of the model. By retaining equal Reynolds numbers for the sand grains, whose size was commensurate with prototype material, the period of oscillation had to vary with the leg diameter. By adopting a suitable size scale, a range of periods was determined from knowledge of resonant motions of rigs in relatively deep water. Erosion was recorded which appeared sufficient to cause mal-distribution of load in the structure. Even when oscillations occurred in a leg penetrating the bed, no support was available due to liquifaction of the soil. The two pilot studies herein described indicate the need for a comprehensive research program on the subject, due to the large investments in jeopardy.

Turbulence parameters in a stirred tank

tirred tanks are widely used in the chemical indusS try for effecting mixing, but their design has so far been empirical. A theoretical treatment of the flow within a stirred tank is rendered intractable by the inherent randomness and three-dimensionality of the flow and non-linearity of the governing equations of motion. Experimental studies of the large- and small-scale turbulence characteristics in stirred vessels may be expected to lead to formulation of realistic models of the flow. These models can then be used to predict such quantities of engineering interest as the mixing efficiency, pumping capacity, power requirements, etc. It was the objective of this work to measure the turbulence characteristics of the high speed stream issuing from a turbine type impeller in a fully baffled tank. Turbulence parameters were measured using a constant-temperature hot-wire anemometer with air as the fluid within the tank. The hot-wire technique was chosen because of the ease of operation and extremely good frequency response. Use of mr as working fluid Cooper‘” recently showed that the temporal mean velocity distribution in the impeller stream is the same with air and water as the fluid in the tank. We have assumed that the small-scale turbulence characteristics would also be similar at equal Reynolds numbers irrespective of the fluid in the tank. There exists sufficient confirmation in the literature for air and water flows in circular pipes and circular jets, and also grid-generated turbulent flows in wind and water tunnels. Chuang and Cermak“’ have compared their measurements of turbulent intensities, shear stress and energy spectra in the pipe flow of distilled water for a Reynolds number of 5 x lo4 with those of Sandborn‘J) and Laufer“) who studied the flow of air in a pipe at the same Reynolds number. The agreement between the air and water data is remarkable

Mass Transfer of Rough Hailstone Models in Flows of Various Turbulence Levels

Abstract The convective mass transfer of smooth and rough sphere test particles over a range of Reynolds numbers between 3 × 103and 105 was studied by means of an electrochemical method at a Schmidt number of 2170. The experiments were carried out in a liquid tunnel where the electrolyte is forced past the stationary test particles at variable flow rates. Three distinctly different levels of turbulence intensity of the flow allowed an evaluation of the turbulence effect on the transfer rates. An extrapolation of the results to the heat and mass transfer coefficients of hailstone models in the atmosphere shows that surface roughness may account for increases in the transfer rates of up to a factor of 2. For relatively large roughness elements (cluster Particles) the increase in the convective transfer coefficients at equal Reynolds numbers (based on equal volume diameters) is approximated by the increase in surface area. Atmospheric turbulence is not expected to change these transfer coefficients significa...

Interferometric Studies of Supersonic Flows about Truncated Cones

Fringe shifts on interferograms of flows at M = 2.45 about variously truncated 15° (half-angle) cone cylinders in free flight in a pressurized range have been examined for similarity of the flow fields, occurrence of scale effects, and convergence to conical flow. It was found that flows over similar objects with equal tip Reynolds numbers were similar and that convergence to conical flow occurred before the disturbance at the tip had been reflected the second time along characteristics to the body. Density distributions have been determined, and a number of comparisons have been made with theoretical predictions.

Some Effects of Surface Curvature on Laminar Boundary-Layer Flow

The laminar flow of a viscous incompressible fluid over a twodimensional curved surface is investigated for two cases, one in which the curvature is large and the other in which it is moderate. The boundary-layer equations applicable to these cases are obtained as approximations from the exact equations of motion by an order-of-magnitude analysis. These equations are solved for flow over a particular surface with zero surface pressure gradient. In this analysis, the pressure gradient normal to the surface is included, and the boundary conditions are modified in accordance with the requirements of flow over a curved surface. The results indicate tha t for equal Reynolds Numbers, the stress on convex surfaces is less than the flat-plate value, while the stress on concave surfaces is greater than for a flat plate. The most important effect of surface curvature, for the cases considered, is the modification of the shape of the velocity profile near the outer of the boundary layer. The requirement tha t a smooth transition exist between the viscous flow and the potential flow at the edge of the layer causes the profile to have a negative slope near the edge for convex surface curvature and a positive slope for concave surface curvature. X= CONSTANT