Hydraulic Reynolds Number Research Articles

Theoretical Approach for the Fast Estimation of the Turbulent Kinematic Viscosity for Internal Flows

Abstract An analytical expression for turbulent kinematic viscosity (νt), based solely on the hydraulic Reynolds number (Re), was derived and evaluated. The analytical expression is valid for the fast estimation of νt for internal, isotropic, fully developed flows. The expression was compared with experimental and simulation data for air, water, and liquid sodium, and was shown to provide reasonable values for 2100 ≤ Re ≤ 3.6 × 106 and Prandtl number (Pr) range of 0.0107 ≤ Pr ≤ 5.65. In addition, new expressions suitable for the central portion of internal flows, away from the wall, were derived for the turbulent Reynolds number (ReT), showing its relationship to Re, as well as to the ratio of νt and the molecular kinematic viscosity (ν).

A numerical evaluation of flows through an SMX-Plus mixer

A numerical investigation of the flow through an SMX+ mixer was undertaken in this study. Three elements were placed in series to assess various hydrodynamic parameters. Single-phase flows of different viscosities flowing at a hydraulic Reynolds number between 220 and 660 were considered to ensure turbulent conditions inside the mixer. The data was validated against pressure drop measurements collected under a wide range of hydrodynamic conditions.The results show that a three-dimensional velocity field dominate the flow within the mixer where the distribution of the strain rate and vorticity magnitudes undergo large fluctuations. The extensional efficiency was found to increase substantially in the first part of each mixer, indicating good dispersive behavior; however, its value decreased to values below 0.5 downstream of the last element. This was due to the presence of a significant rotational core as the fluid flowed farther from the last mixer. The core region of the flow spiraled on its axis as it moved downstream while the near-wall area whirled orthogonal to the flow direction. This also explained the persistence of a flatter velocity profile downstream of the mixing section. The energy dissipation rate and kinetic energy were also analyzed.

Advanced benchmark of the flow through a mixing vane grid – Large eddy simulation validation

Identifying what causes fuel assembly vibrations downstream of Mixing Vane Grids (MVG) in Pressurized Water reactor (PWR) is of paramount importance for nuclear community to understand grid-to-rod fretting wear. Experiments, called CALIFS, were carried out by the Atomic Energy Commission (CEA) on a 5 × 5 MVG at a hydraulic Reynolds number of 66,000, in order to measure the flow velocity and the pressure along the central rod. In parallel, a benchmark for Large Eddy Simulation (LES) was setup to compare the predictions of three different CFD codes: Star-CCM+, Code_Saturne and TrioCFD to experimental measurements. The computational domain is representative of a span of CALIFS mockup, composed of a 5 × 5 rod bundle with a MVG. The three computations overall give very satisfactory results, independently from the mesh created and the modelling options selected. It seems to suggest that whatever the software used, this kind of calculations has reached a significant level of robustness and accuracy. Nonetheless, some discrepancies remain concerning the predictions of pressure standard deviation decay far downstream of the mixing vane grid.

Interface capturing simulations of bubble population effects in PWR subchannels

As the computational power of high-performance computing (HPC) facilities grows, so too does the feasibility of using first principle based simulation to study turbulent two-phase flows within complex pressurized water reactor (PWR) geometries. Direct numerical simulation (DNS), integrated with an interface capturing method, allows for the collection of high-fidelity numerical data using advanced analysis techniques. The presented research employs the massively parallel, finite-element based, unstructured mesh code, PHASTA, to simulate a set of two-phase bubbly flows through PWR subchannel geometries including auxiliary structures (spacer grids and mixing vanes). The main objective of the presented work is to analyze bubble dynamics and turbulence interactions at varying bubble concentrations to support the development of advanced two-phase flow closure models. Turbulent two-phase flows in PWR subchannels were simulated at hydraulic Reynolds numbers of 81,000 with bubble concentrations of 3%–15% by gas volume fraction (768–3928 resolved bubbles, respectively) and compared against a 1% void fraction case (262 bubbles) that had been previously simulated. The finite element mesh utilized for the study at higher bubble concentrations was composed of 1.55 billion elements, compared to the previous study which employed 1.11 billion elements, ensuring all turbulence scales and individual bubbles within the flow are fully resolved. For each case, the resolved initial bubble size was 0.65 mm in diameter (resolved with 25 grid points across the diameter). The simulations were analyzed to find flow features such as the mean velocity profile, bubble relative velocity and the effect of the bubbles on the turbulent conditions.

Efficiency Prediction of Centrifugal Pump Using the Modified Affinity Laws

Abstract This research is a continuation of efforts aimed at establishing the modified affinity laws for viscosity to predict the pump performance directly from a plot in terms of dimensionless numbers, i.e., flow coefficient, Reynolds number, head coefficient, and efficiency. The group has earlier proposed modified head coefficient affinity law. This work proposes and validates a similar efficiency plot that completes the set of modified affinity laws that include all the input and output parameters for a specific pump design and type. A wide range of viscosities and flow rates are considered for CFD analysis to have a comprehensive set of data that includes enough data points to comment on both the laminar and turbulent flow cases categorized based on the hydraulic Reynolds number (2300). Initial analysis shows some inconsistency based on laminar versus turbulent simulation model selection which is addressed in the latter part of this work. In general, two curves can be constructed for laminar and turbulent flow cases. These curves have different axes parameters (exponents of the dimensionless numbers) depending on the plot being for a laminar or a turbulent flow case. Validation with established experimental data shows good agreement in terms of the variation of axes parameters (their exponents) depending on the pump type for a single suction impeller and a double suction impeller pump. The distinction between laminar and turbulent flow cases is found to be applicable to established experimental data as well.

Wall-Modeled Large Eddy Simulation of the Flow Through PWR Fuel Assemblies at ReH = 66 000—Validation on CALIFS Experimental Setup

The EDF aims to identify what causes fuel assembly vibrations in pressurized water reactors. The present work focuses on the validation of pressure fluctuations along the central rod of a 5 × 5 configuration for wall-modeled large eddy simulations. New experiments, called CALIFS, have been carried out by the Atomic Energy Commission (CEA) on a 5 × 5 mixing vane grid (MVG) in the framework of the Fuel Assembly EDF/CEA/FRAMATOME tripartite project. In addition to pressure drop and velocity measurements using particle image velocimetry, pressure measurements have been performed along the central rod. The computational domain is representative of a span of the experimental mock-up composed of a 5 × 5 rod bundle equipped with a split-type MVG. The hydraulic Reynolds number is equal to 66 000 and periodic boundary conditions are imposed in the streamwise direction. The mesh is fully hexahedral and conformal. Computations give very satisfactory results for the pressure drop, the mean velocity, and the Reynolds stresses at different locations. The root-mean-square of the pressure along the central rod is also compared to experimental data at different heights. The behavior is in very good agreement up to five hydraulic diameters downstream of the MVG.

Dynamics of the removal of viscoplastic fluids from inclined pipes

The dynamics of the removal of a viscoplastic fluid by a Newtonian fluid is investigated experimentally and theoretically in an inclined pipe based on our previous studies on near-horizontal and highly inclined configurations. The fluids are miscible. The displacing Newtonian fluid is heavier than the displaced viscoplastic one i.e. the configuration is density-unstable. In our earlier work it was found that two major flow regimes, namely center-type and slump-type, might occur depending on the density difference. These flows are explored in great details through measurements of the displacement speeds and hydraulic Reynolds numbers. The residual viscoplastic layer unevenness is characterized revealing that the flows are in the range of large roughness regimes. Through an integrated experimental-theoretical approach, estimates of the interfacial and wall shear stresses are given which is of great importance in designing the displacement and cleaning processes involving fluids with yield stress. Accompanied by Ultrasonic Doppler Velocimetry (UDV) data, the dynamics of the removal of the viscoplastic fluid from a pipe is elucidated suggesting three distinct phases in the displacement process namely a plug flow, inertial multi-dimensional flow at the displacing front and steady multi-layer developed flow. Finally, the viscoplastic displacement flow results are compared against the predictions of the closure model, previously proved successful for Newtonian and shear-thinning fluids displacement in pipe. It is found that in the case of viscoplastic fluids the closure model always over predicts the displacing front velocity due to the inertial stresses present at the front not captured in the model.

Pressure losses and flow patterns in 3D axial flow between corrugated plates

Pressure losses as friction factor, and flow patterns in 3D axial flow between sinusoidal corrugated parallel plates with perpendicular directions of corrugation is numerically studied. The flow is assumed to be steady and laminar in the studied range. The numerical procedure is Chorin’s artificial compressibility method with finite difference second order central discretization. Results show that in moderate Reynolds numbers, vortices are formed and they put a great effect on pressure drop. The size of vortices grows with increase in Reynolds number, and also their cores tend to shift toward the flow direction and away from the walls. These vortices are not closed loops, and the streamlines slightly swirl in the circulating zone of vortices. This means that there can be a little convection in these regions and they are not closed dead zones anymore. The linear curve fit of the friction factor diagrams versus Reynolds number in logarithmic scale, shows that friction factor almost obeys a power function of hydraulic Reynolds number in the investigated geometries. With a slight error, this can be assumed as a rough estimation for the product of friction factor and hydraulic Reynolds number. The friction factor grows larger with increase in wave amplitude or decrease in wavelength. Also, when the gap between two plates decreases, friction factor increases. The least friction factor among the investigated geometries is for flat parallel plates.

Residence time distribution and liquid holdup in Kenics ® KMX static mixer with hydrogenated nitrile butadiene rubber solution and hydrogen gas system

A Kenics ® KMX static mixer that has curved-open blade internal structure was investigated to study its hydrodynamic performance related to residence time distribution and liquid holdup in a gas/liquid system. The static mixer reactor had 24 mixing elements arranged in line along the length of the reactor such that the angle between two neighboring elements is 90°. The length of the reactor was 0.98 m with an internal diameter of 3.8 cm and was operated cocurrently with vertical upflow. The fluids used were hydrogen (gas phase), monochlorobenzene (liquid phase) and hydrogenated nitrile butadiene rubber solution (liquid phase). In all the experiments, the polymer solution was maintained as a continuous phase while hydrogen gas was in the dispersed phase. All experiments were conducted in the laminar flow regime with the liquid side hydraulic Reynolds number in the range of 0.04–0.36 and the gas side hydraulic Reynolds number in the range of 3–18. Different polymer concentrations and different operating conditions with respect to gas/liquid flow rates were used to study the corresponding effects on the hydrodynamic parameters such as Peclet number ( Pe) and the liquid holdup ( ε L ) . Empirical correlations were obtained for the axial dispersion coefficient ( D a ) and liquid holdup in liquid system alone and for the gas/liquid system separately. It was observed that the Peclet number decreased with the introduction of gas in to the reactor while in the liquid system alone, an increase in viscosity decreased the Peclet number. The liquid holdup was empirically correlated as a function of the physical properties of the fluids used in addition to the operating flow rates.

Numerical study of two-dimensional multi-layer spacer designs for minimum drag and maximum mass transfer

Based on the insights gained from previous published works, a series of multi-layer spacer designs for use in spiral wound membrane modules are proposed and evaluated via computational fluid dynamics simulations. The filament diameter to channel height ratio of traditional cylindrical filaments is reduced from 0.6 to 0.4 and 0.3, and one or two layers of elliptical filaments with various attack angles are introduced in the middle region of the channel. The mass transport equations are solved in conjunction with the momentum and continuity equations for a solute with Schmidt number of 600, and the hydraulic Reynolds number is varied from 50 up to 800. Spacer performance is evaluated via a basic permeate processing cost analysis. The proposed designs did not lower processing costs when operating at hydraulic Reynolds numbers above 200, but showed potential for reducing costs in the steady laminar flow regime, at hydraulic Reynolds numbers equal to or less than 200. Implications for design improvements of spacer meshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, and changes to the filament profiles to reduce form drag are discussed.

On flow uniformity in various interconnects and its influence to cell performance of planar SOFC

This paper investigates flow uniformity in various interconnects and its influence to cell performance of a planar SOFC. A transparent hydraulic platform was used to measure flow uniformity in different rib-channel modules of interconnects. Several 3D numerical models implemented by CFD-RC packages were established to first simulate these hydraulic experiments and then used to evaluate the cell performance of a single-cell stack using different designs of interconnects with different flow uniformity over a wide range of a hydraulic Reynolds number ( Re) based on a hydraulic diameter of rib-channels. Numerical flow data are found in good agreement with experimental results. It is proposed that a new design, using simple small guide vanes equally spaced around the feed header of the double-inlet/single-outlet module, can effectively improve the degree of flow uniformity in interconnects resulting in 11% increase of the peak power density (PPD) which can be further increased when applying a Ni-mesh on anode. Numerical analyses demonstrate a strong influence of Re on cell performance, of which appropriate ranges of Re in both anode and cathode sides are identified for achieving a reasonably good PPD while remaining an economic fuel utilization rate and having less temperature variations in the single-cell stack.

Numerical study of mass transfer in three-dimensional spacer-filled narrow channels with steady flow

A Computational Fluid Dynamics (CFD) model was used to simulate steady fluid flow with mass transfer in three-dimensional narrow channels containing non-woven spacers with a d f/ h ch ratio of 0.6, and a l m/ h ch ratio of 4, positioned at 45° and 90° angles against the flow direction. A solute with a Schmidt number of 600 dissolving from the wall and hydraulic Reynolds numbers up to 200 for 3D geometries, and up to 500 for 2D geometries were considered. Greater mass transfer enhancement was found for the 3D geometries modeled, when compared with 2D geometries, due to wall shear perpendicular to the bulk flow and streamwise vortices. The regions of high mass transfer were found to correlate mainly with those regions where the fluid flow is towards the wall. The relationship between 3D flow effects, pressure drop and mass transfer was investigated. Form drag was identified as the main component of energy loss for the flow conditions analyzed. Implications for the design of improved spacer meshes are discussed.

Flow resistance and forced convective heat transfer effects for various flow orientations in a packed channel

This study explores the flow resistance and forced convective heat transfer effect for three types of flow orientation in a packed channel. Experimental parameters include the copper bead diameter (dp=3, 4, 5, and 6 mm) and the hydraulic Reynolds number (Re=1349, 2697, 4046, 5394, and 6743). The results indicate that flow resistance approaches a minimum in O-II due to its inlet/outlet design, and the O-I case produces the largest friction in the three orientations. While the influence of flow orientation on convective heat transfer is not as strong as that of as flow resistance, O-I and O-II show almost the same performance, and O-III case can acquire a higher average Nusselt number value for its two outlets. Therefore, two dominated parameters (ε, Re) need to be compromised for their positive/negative effects in the abovementioned Cf and Nu. An empirical correlation equation of Nu― vs. Re for O-I–O-III and dp=3–6 mm is also proposed herein to offer a rapid and efficient guide in specifying appropriate parameters in relational applications.

Progress in Understanding the Physical Processes Inside Spinning Cone Columns

The dynamics of gas flow through spinning cone columns (SCCs) have been studied through Computational Fluid Dynamics (CFD) simulations, and the liquid flow characteristics on the rotating surfaces have been correlated through dimensional analysis. The CFD simulations have been carried out in the absence of liquid flow. Flow instabilities are predicted above a critical value of the hydraulic Reynolds number (Re hyd , based on the minimum passage size between the cones) of about 100. Highfrequency oscillations of the velocity components and pressure are predicted to occur about their mean values. The flow regime is an unsteady laminar one, not a turbulent one, for small-scale SCCs, as shown by the discrete nature of the pulsation spectrum across the entire range of the column operation (200 < Re hyd < 2000) irrespective of whether or not the inner cone is rotating (as in normal operation). The pulsations are synchronised with the rotor motion for normal (rotating) operation and are likely to cause mechanical vibrations as a consequence of the flow instability. The actual pressure drop through the column stage is predicted by the CFD model to within 1015%. Key parameters determining mass transfer characteristics and overall performance of SCCs include the thickness and velocity of the thin liquid films flowing up a rotating cone surface. The turbulent flow conditions of commercial-scale equipment make laminar model predictions for these devices inapplicable. Dimensionless empirical models for the average thickness and radial velocity of wavy film have been developed based on thickness measurements on a laboratory-scale cone. These measurements were made using the intensity of induced fluorescence of a flowing film illuminated by an ultraviolet light source. The film is modelled as a wavy layer on top of a laminar sub-layer attached to the disk surface, with the thickness of the film being an additive modification of the Nusselt model thickness 3 3 / 2 95

CFD analysis of spinning cone columns: prediction of unsteady gas flow and pressure drop in a dry column

Computational fluid dynamics (CFD) simulations have been carried out on the gas flow patterns and pressure distribution in a laboratory-scale (0.15 m diameter) spinning cone distillation column (SCC) in the absence of liquid flow. These simulations show that the flow becomes unstable at a hydraulic Reynolds number ( Re hyd, based on the minimum passage size between the cones) above a critical value of about 100. The instability leads to high-frequency oscillations of the velocity components and pressure about their mean values. The discrete nature of the pulsation spectrum indicates that the flow regime is an unsteady laminar one for the small-scale SCC considered here, not a turbulent one. This unsteady regime occurs across the entire range of the column operation (200< Re hyd<2000). The instability develops regardless of whether the inner cone is rotating (as in normal operation) or not. For normal (rotating) operation, the pulsations are synchronised with the rotor motion. Comparison of time-average pressure values with experiment shows that the actual pressure drop through the column stage is predicted by the CFD model to within 10–15%. The pressure pulsations are likely to cause mechanical vibrations and are a consequence of the flow instability.

Catheter obstruction effect on pulsatile flow rate--pressure drop during coronary angioplasty.

The coupling of computational hemodynamics to measured translesional mean pressure gradients with an angioplasty catheter in human coronary stenoses was evaluated. A narrowed flow cross section with the catheter present effectively introduced a tighter stenosis than the enlarged residual stenoses after balloon angioplasty; thus elevating the pressure gradient and reducing blood flow during the measurements. For resting conditions with the catheter present, flow was believed to be about 40 percent of normal basal flow in the absence of the catheter, and for hyperemia, about 20 percent of elevated flow in the patient group. The computations indicated that the velocity field was viscous dominated and quasi-steady with negligible phase lag in the delta p(t)-u(t) relation during the cardiac cycle at the lower hydraulic Reynolds numbers and frequency parameter. Hemodynamic interactions with smaller catheter-based pressure sensors evolving in clinical use require subsequent study since artifactually elevated translesional pressure gradients can occur during measurements with current angioplasty catheters.

Electrochemical wall mass transfer in liquid particulate systems

AbstractIonic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion‐controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100.The developed fluidization mass transfer coefficient for 41 &lt; DT/dp &lt; 105 were correlated by iD E = 0.274 ReH−0.38 for 10 &lt; ReH &lt;1600 and by JD E = 0.455 ReH−0.44 for 16.7 &lt; DT/dp &lt; 27 and 50 &lt; ReH &lt; 3500. ReH is the hydraulic Reynolds number = dH up/μE and dH is DT E/[1 + (3/2) ((1–E)) (DT/dp)).The distinct effect of DT/dp ratio is attributed to wall effects and the non‐particulate behaviour of the fluidized bed for DT/dp &lt; 27.Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given ReH.