Reynolds Numbers In Excess Research Articles

Qualification and Commissioning of Helium Flow Loop Experiment for Blanket Design Measurements

Sufficient cooling of plasma-facing materials remains an outstanding challenge in the design of fusion reactor blankets in commercial power demonstration plants. Due to its chemical inertness and low neutron interaction cross section, pressurized helium is a candidate coolant fluid for such systems; however, helium has a small thermal mass compared to liquid coolants, potentially reducing heat removal performance. To address this need, a number of heat transfer enhancements have been proposed to improve the cooling efficiency of such components, thereby decreasing pumping power needs and improving overall plant efficiency. Toward this end, a helium flow loop experiment (HFLE) has been designed and commissioned to test advanced passive heat transfer enhancements in unit-cell test sections, providing necessary data for model validation and subsequent system design. The HFLE is designed to provide flow of pressurized (up to 4 MPa) helium at flow rates up to 80 g/s, enabling heat transfer and pressure drop measurements in test pieces at Reynolds numbers in excess of 180 000. To explore the effects of novel and complex heat transfer enhancements, test sections are produced via additive manufacturing, providing geometries not typically obtainable by conventional machining. In this work, we present results from HFLE commissioning and the initial thermal-hydraulic tests of an additively manufactured rifled-rib test section. Results are compared to smooth pipe correlations, and plans are described for future HFLE measurements. These preliminary experiments indicate the utility of the HFLE for heat transfer enhancement testing and simulation validation activities.

Flow Patterns, Roller Characteristics, and Air Entrainment in Weak Hydraulic Jumps: Does Size Matter?

Abstract A hydraulic jump is a stationary transition from an upstream supercritical to a downstream subcritical flow. Hydraulic jumps with relatively low Froude numbers may be observed downstream of low-head hydraulic structures and their flow properties have not been not well documented. In this study, the hydraulic properties were investigated experimentally in weak hydraulic jumps with an inflow Froude number Fr1 = 2.1 and inflow depths 0.012 m < d1 < 0.130 m. Three novel features of the study were (1) the very wide range of inflow length scales tested systematically, (2) the relatively high Reynolds number Re = 3.05 × 105 achieved in the largest experiment, with the Reynolds number defined as Re = ρ × V1 × d1/μ, and (3) the broad range of inflow conditions. Although no air entrainment was observed at the lowest Reynolds numbers, some distinct air–water flow patterns were observed in the roller region, generally similar to those observed at higher Froude numbers. The ratio of downstream to upstream depths followed closely the analytical solution of the momentum principle irrespective of the inflow depth. On the other hand, noticeable scaling issues were observed in terms of the dimensionless roller length, length of air–water flow region, roller toe fluctuation frequency, and rate of air entrainment, with increasing dimensionless data with increasing inflow depths, hence Reynolds numbers. The present results have some practical implication in terms of physical modeling and upscaling of results for low-head hydraulic structures, including culverts and storm waterways, which typically operate with Reynolds numbers in excess of 105.

Two-phase air-water flows in hydraulic jumps at low Froude number: Similarity, scale effects and the need for field observations

A hydraulic jump is a region of rapidly-varied flow that is extremely turbulent. While the one-dimensional continuity and momentum principles have been successfully applied to express the relationships between upstream and downstream conditions, the three-dimensional equations cannot be resolved without some complicated turbulence closure, often involving two phases, i.e. air and water. Based upon a new dataset, the current investigation has the double objective of presenting a novel experimental investigation of the air-water flow characteristics in hydraulic jumps with a small Froude number (Fr1 = 2.1) and discussing the potential scale effects involving several Reynolds numbers (0.078 × 105 < Re < 3.05 × 105). Four unique features are the low inflow Froude number Fr1 = 2.1, the wide range of Reynolds numbers tested systematically, the broad amount of air-water flow properties investigated, and the relatively high Reynolds number (Re = 3.05 × 105) achieved in the largest experiment. More than two dozen of parameters were tested systematically under Froude similar conditions. All the data demonstrated that the selection of relevant (air-water) flow property(ies) used to assess similarity and scale effects is most essential. Further the concept of similarity and scale effects must be linked to specific flow conditions. At low Froude number (Fr1 = 2.1), the present results showed that many hydraulic jump properties could not be extrapolated from laboratory study to full scale hydraulic structures without substantial scale effects. These findings have profound implications for engineering design applications, often operating with Reynolds numbers in excess of 105.

Three-Dimensional Velocity and Temperature Field Measurements of Internal and External Turbine Blade Features Using Magnetic Resonance Thermometry

Magnetic resonance thermometry (MRT) is a maturing diagnostic tool used to measure three-dimensional temperature fields. It has a great potential for investigating fluid flows within complex geometries leveraging medical grade magnetic resonance imaging (MRI) equipment and software along with novel measurement techniques. The efficacy of the method in engineering applications increases when coupled with other well-established MRI-based techniques such as magnetic resonance velocimetry (MRV). In this study, a challenging geometry is presented with the direct application to a complex gas turbine blade cooling scheme. Turbulent external flow with a Reynolds number of 136,000 passes a hollowed NACA-0012 airfoil with internal cooling features. Inserts within the airfoil, fed by a second flow line with an average temperature difference of 30 K from the main flow and a temperature-dependent Reynolds number in excess of 1,800, produces a conjugate heat transfer scenario including impingement cooling on the inside surface of the airfoil. The airfoil cooling scheme also includes zonal recirculation, surface film cooling, and trailing edge ejection features. The entire airfoil surface is constructed of a stereolithography resin—Accura 60—with low thermal conductivity. The three-dimensional internal and external velocity field is measured using an MRV. The fluid temperature field is measured within and outside of the airfoil with an MRT, and the results are compared with a computational fluid dynamics (CFD) solution to assess the current state of the art for combined MRV/MRT techniques for investigating these complex internal and external flows. The accompanying CFD analysis provides a prediction of the velocity and temperature fields, allowing for errors in the MRT technique to be estimated.

Flight tests of a supersonic natural laminar flow airfoil

A flight test campaign of a supersonic natural laminar flow airfoil has been recently completed. The test surface was an 80 inch (203 cm) chord and 40 inch (102 cm) span article mounted on the centerline store location of an F-15B airplane. The test article was designed with a leading edge sweep of effectively 0° to minimize boundary layer crossflow. The test article surface was coated with an insulating material to avoid significant heat transfer to and from the test article structure to maintain a quasi-adiabatic wall. An aircraft-mounted infrared camera system was used to determine boundary layer transition and the extent of laminar flow. The tests were flown up to Mach 2.0 and chord Reynolds numbers in excess of 30 million. The objectives of the tests were to determine the extent of laminar flow at high Reynolds numbers and to determine the sensitivity of the flow to disturbances. Both discrete (trip dots) and 2D disturbances (forward-facing steps) were tested. A series of oblique shocks, of yet unknown origin, appeared on the surface, which generated sufficient crossflow to affect transition. Despite the unwanted crossflow, the airfoil performed well. The results indicate that the sensitivity of the flow to the disturbances, which can translate into manufacturing tolerances, was similar to that of subsonic natural laminar flow wings.

Dynamo threshold detection in the von Kármán sodium experiment

Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of 10(6)). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field. We first show that a dynamo threshold can be estimated from analysis related to critical slowing down and susceptibility divergence, in configurations for which dynamo action is indeed observed. These approaches are then applied to flow configurations that have failed to self-generate magnetic fields within operational limits, and we quantify the dynamo capacity of these configurations.

Packed bed pressure drop dependence on particle shape, size distribution, packing arrangement and roughness

Packed beds have been used or proposed for many different applications, including thermal storage in buildings and in solar thermal power plants. In order to size the blowers and predict the operating and capital cost, the packed bed pressure drop must be known. The Ergun equation, commonly used for predicting packed bed pressure drop, over-predicts the pressure drop through randomly packed or structured beds of smooth spheres at Ergun Reynolds numbers in excess of ≈ 700, and previous work has found it to under-predict the pressure drop through beds of rock by a factor as high as 5. Present measurements of the pressure drop for air flow through beds of rough spheres, smooth cylinders, cubes and crushed rock are significantly higher than those for smooth spheres, and all differ from the Ergun equation. Particle shape, arrangement (including packing method) and surface roughness are shown to influence the pressure drop. Recent correlations for non-spherical particles are shown to differ significantly from present measurements. Different pressure drop measurements obtained for irregularly shaped rock packed into the test section in two different directions relative to the flow direction show that random packing is not necessarily isotropic. In order to predict the pressure drop over a packed bed of irregular particles such as crushed rock with any degree of accuracy, an empirical equation must be obtained from a sample of the particles for a given packing arrangement.

NUMERICAL SIMULATIONS OF Z-PINCH EXPERIMENTS TO CREATE SUPERSONIC DIFFERENTIALLY ROTATING PLASMA FLOWS

The physics of accretion disks is of fundamental importance for understanding of a wide variety of astrophysical sources that includes protostars, X-ray binaries, and active galactic nuclei. The interplay between hydrodynamic flows and magnetic fields and the potential for turbulence-producing instabilities is a topic of active research that would benefit from the support of dedicated experimental studies. Such efforts are in their infancy, but in an effort to push the enterprise forward we propose an experimental configuration which employs a modified cylindrical wire array Z-pinch to produce a rotating plasma flow relevant to accretion disks. We present three-dimensional resistive magnetohydrodynamic simulations which show how this approach can be implemented. In the simulations, a rotating plasma cylinder or ring is formed, with typical rotation velocity ~30 km s–1, Mach number ~4, and Reynolds number in excess of 107. The plasma is also differentially rotating. Implementation of different external magnetic field configurations is discussed. It is found that a modest uniform vertical field of 1 T can affect the dynamics of the system and could be used to study magnetic field entrainment and amplification through differential rotation. A dipolar field potentially relevant to the study of accretion columns is also considered.

Sectional model investigation at high Reynolds number for a super tall building

This paper presents the results of an experimental study of the influence of Reynolds number on the vortex-shedding excitation of a super tall building with a quasi-circular cross-section, uniform with height. Sectional model tests were carried out on a large model in a large wind tunnel at high wind speeds to reach Reynolds number in excess of 3 million based on the model diameter. Stationary model tests and free-to-respond model tests were carried out for various azimuth angles, in smooth and turbulent flow. The study revealed that for this building cross-section, the dynamic excitation due to vortex shedding was equally important at high Reynolds numbers when compared to experiments performed in the sub-critical Reynolds number regime.

Preliminary Measurements on Grid Turbulence in Liquid 4He

A grid has been pulled through a column of liquid helium at speeds as high as 1 m/s and at temperatures as low as 90 mK. A 300 micrometer Ge thermometer with response time of less than 1 ms measured the temperature rise resulting from the decay of the turbulence generated. It is believed that homogeneous, isotropic quantum turbulence was formed, since mesh Reynolds numbers in excess of 100,000 were created. The rates and power spectra of the energy increases detected in the helium after grid-pulls are determined. The results are compared to other quantum and classical results, and to the theory of the Kelvin wave cascade in a viscosity-free fluid.

Steady and unsteady loading on a roughened circular cylinder at Reynolds numbers up to 900,000

This paper describes steady and unsteady loading in incompressible flow on a roughened circular cylinder in crossflow in the Reynolds number range from 50,000 to 900,000. The experiments were conducted on a cylinder of 38 mm diameter with aspect ratio 10. Measurements were made in smooth flow and in two levels of turbulence. Dynamic lift and drag measurements were made via two high-frequency force balances mounted at the ends of the model. The results demonstrate that with the level of roughness employed in this investigation, strong coherent shedding re-emerges in smooth flow for Reynolds numbers in excess of 750,000, whereas in smooth flow such shedding re-commences only for Reynolds numbers in excess of several million. It is also shown that turbulence serves to decrease the Reynolds number at which coherent shedding re-commences.

Turbulent pipe flow of thixotropic fluids

In this work, aqueous suspensions of 1% and 1.5% by weight laponite and a blend of 0.5%/0.07% laponite/carboxymethil cellulose (CMC) are investigated in terms of their rheology and hydrodynamic behaviour in pipe flows. All fluids were shear-thinning, thixotropic and had an yield stress which was measured by direct and indirect methods. The oscillatory tests showed that the 1% laponite suspension was inelastic but the other two fluids exhibited some degree of elasticity. The turbulent pipe flow measurements showed a small amount of drag reduction for the pure laponite suspensions, which was basically accounted for by shear-thinning at Reynolds numbers in excess of 35,000, whereas for the polymer–clay blend the drag reduction was significantly more intense. This work confirmed findings in the literature that the equilibrium condition in the pipe flow was different from the equilibrium condition in the flow curve, which caused some difficulties in data interpretation. However, it found negligible drag reduction for the flow of pure 1.5% laponite suspensions at Reynolds numbers in excess of 60,000, in contradiction to previous findings.

Meta-Analysis of Gas Flow Resistance Measurements Through Packed Beds

Measurements of the resistance to flow through packed beds of inert spheres have been reported by a number of authors through relations expressing the coefficient of drag as a function of Reynolds number. A meta-analysis of the data using improved statistical methods is undertaken to aggregate the available experimental results. For Reynolds number in excess of 103 the relation log Fv = 0.49 + 0.90 log Re′ is shown to be a highly effective representation of all available data.

Animal cell culture in stirred bioreactors: Observations on scale-up

Scale-up of stirred tank bioreactors from 0.02 m3 to 0.3 m3 commercial plant is discussed for hybridoma suspension culture. Schemes for dissolved oxygen control with sparged air in serum containing media are described as well as mechanical breakage of foam in small and large bioreactors. Porous metal spargers (180−200×10−6 m) are found to produce foams which are hard to control. Aeration with larger (> 0.001 m) multihole spargers is recommended. Combined cell damage due to foam formation and control, and possible damage at mechanical seals or submerged bearings, are found to have no measurable effect on cell growth relative to roller bottle production. Hybridomas are shown to withstand significant impeller tip speed (> 1 ms−1) and fluid turbulence as evidenced by impeller Reynolds numbers in excess of 105. The size of the energy dissipating terminal eddies is calculated to be > 10-fold that of the hybridoma cells. Specific fluid turnover rate is employed as the scale-up criterion.

Animal cell culture in stirred bioreactors: observations on scale-up

The scale-up of stirred tank bioreactors from 0·02 m 3 to a 0·3 m 3 commercial plant is discussed for hybridoma suspension cultures. Schemes for dissolved oxygen control with sparged air in serum containing media are described, as well as mechanical breakage of foam in small and large bioreactors. Porous metal spargers (180–200 × 10 −6 m) were found to produce foams which were hard to control. Aeration with larger (≥ 0·001 m) multihole spargers is recommended. Combined cell damage due to foam formation and control, and possible damage at mechanical seals or submerged bearings, were found to have no measurable effect on cell growth relative to roller bottle production. Hybridomas are shown to withstand significant impeller tip speed ( > 1 m s −1) and fluid turbulence as evidenced by impeller Reynolds numbers in excess of 10 5. The size of the energy-dissipating terminal eddies was calculated to be greater than ten-fold that of the hybridoma cells. The specific fluid turnover rate was employed as the scale-up criterion.

Theoretical Basis for Extrapolation of Calibration Data of PTC 6 Throat Tap Nozzles

Equations for the extrapolation of calibration data for ASME/PTC 6 throat tap nozzles are derived from boundary layer theory. The results match published coefficients with a maximum difference of +0.03 percent. It is also shown that the effects of transition in the boundary layer extend to throat Reynolds numbers in excess of 10,000,000, far beyond the capacity of any known calibration laboratory. The present PTC 6 requirement that calibration data must be in the fully turbulent range cannot be met with current facilities.

Resistance of particle beds at Reynolds numbers up to Re ≈ 10 4

In a paper previously published, a coherent representation of pressure drop in fixed beds and of fluidized bed expansion, both with spherical particles was presented. The theoretical treatment was based on an analysis of the Navier-Stokes equations. A semi-empirical formula, which combines an Euler number, a Reynolds number and a characteristic dimensional ratio r 0δ was quantitatively verified from the analysis of experimental results with Reynolds numbers not exceeding Re=200 in the case of fixed bed percolation. Recently, fixed bed percolation was investigated up to Reynolds numbers in excess of Re=10 4 with particle packings as dense as ε≈0.35 at pressures up to 25 bar. Unsatisfactory prediction of these new measurement results necessitated reexamination of the theoretical treament, resulting in an extension of the previously suggested approximation for pressure drop behaviour with packings of monodisperse spherical particles. Introduction of a pressure drop shape factor Φ D enabled the extension of the same concept to packings of non spherical polydisperse particles. The underlying idea is based on the simple consideration that it is always possible to find a packing of spherical particles with a smaller particle diameter which has the same dimensionless pressure drop behaviour as the real packing with irregularly shaped material. A practical way is shown to simply evaluate the pressure drop shape factor using a single pressure drop measurement point at any bed porosity and any gas velocity. A quantitative verification of the validity of the underlying concept has been obtained from the analysis of experimental results.

Boiling Incipience in Plane Rotating Water Films

Knowledge of heat transfer in rotating liquid films is of paramount importance for evaluating the thermal efficiency of gas turbines with water-cooled blades. Centrifugal forces constitute the primary driving forces for liquids flowing in radial rotating channels. Coriolis forces, on the other hand, tend to thin out the flow in the form of a film that covers one side of the channel. Fully developed motion of the film is determined by a balance between centrifugal and shear forces. Thus, rotating film motion resembles that of a free-falling gravity-driven film since both are characterized by a balance between shear and body forces. However, Coriolis forces can strongly influence interfacial waves and turbulent velocity fluctuations of rotating films. This is evident from the results of Kirkpatrick (1980), who compared film thickness measurements for the cases of free-falling and rotating films. His data indicate profound waviness at higher Reynolds numbers for the case of gravity-driven films. On the other hand, interfacial waves in rotating films were found to stabilize at Reynolds numbers in excess of 8,000. This paper focuses on the effects of Coriolis forces and wall roughness on the convective heat transfer coefficient and the incipient boiling heat flux in thin rotatingmore » films.« less

On the scaling of the turbulence energy dissipation rate

From an examination of all data to date on the dissipation of turbulent energy in grid turbulence, it is concluded that, for square-mesh configuration, the ratio of the time scale characteristic of dissipation rate to that characteristic of energy-containing eddies is a constant independent of Reynolds number, for microscale Reynolds numbers in excess of about 50. Insufficient data available for other grid configurations suggest a possibility that the ratio could assume different numerical values for different configurations. This persistent effect of initial conditions on the time scale ratio is further illustrated by reference to the jet-grid data of Gad-el-Hak and Corrsin.

The Numerical Prediction of Viscous Flow and Heat Transfer in Tube Banks

A scheme for handling the numerical analysis of viscous flow and heat transfer in tube banks is presented. It involves the use of a cylindrical network of nodes in the vicinity of the tubes with a Cartesian mesh covering the remainder of the flow domain. The approach has been incorporated into the numerical solving algorithm for the Navier Stokes equations of Gasman, et al. [8]. A number of demonstration calculations is presented including a numerical simulation of the staggered square bank for which Bergelin and co-workers [4, 9] have reported experimental results for pressure drop and heat transfer rate. Agreement between predicted and measured characteristics is satisfactory when account is taken of end and entry effects that are present in the experiments but necessarily omitted from the calculations. Indeed the close agreement of the laminar predictions with measurements extends to Reynolds numbers in excess of 1000, a level at which it has hitherto been supposed that turbulent motion in the fluid made a substantial contribution to friction and heat transfer.