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Study of drag force on dendritic particles in highly viscous fluids is essential for understanding the dynamic sinking/floating behavior of particles in metallurgical systems. In this study, experiments were carried out to investigate the drag coefficient of simplified three-dimensional dendritic particles in silicone oil with a range of viscosities (20, 100 and 500 cSt). The experimental system was designed to represent the basic oxygen steelmaking (BOS) slag system based on a dynamic similarity approach. The drag coefficient of each dendritic particle was calculated from the measured terminal velocity based on a force balance and the known drag coefficient of its volume equivalent sphere. The drag coefficients were determined over a range of Reynolds numbers (~ 0.035 to 84) differing by two orders of magnitude accounting for various particle shape factors that included aspect ratio, sphericity, and particle orientation. Correlations between the drag coefficient and the shape factors were proposed for each viscosity.

A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.

Immersed granular collapses may encounter different flow regimes, such as free-fall (dry), fluid-inertial, and viscous regimes, depending on column geometry, particle size, particle density, fluid viscosity, and many other parameters. Understanding the controlling parameters of these regimes is important for both industrial and geological applications where grains and fluids coexist. It is also important to combine these parameters into dimensionless groups to guide down-scaled experiments and numerical simulations. In this work, we derive a set of dimensionless numbers (i.e., Stokes number, density ratio, and Reynolds number) based on typical time scales in the sedimentation of a sphere, and successfully verify the relevance of these numbers in determining flow regimes and maintaining dynamic similitude across length scales. The numerical method we use couples the computational fluid dynamics and discrete element method (CFD-DEM), which allows a wide variety of particle size and fluid viscosity to be chosen, keeping constant the Stokes number and density ratio. Quantitative data of front propagation and energy evolution are presented to characterize flow dynamics in different flow regimes. The collapse exhibits a transition from sliding-dominant to suspension-dominant behaviors as the Stokes number decreases, which gives rise to distinct deposit morphology in different regimes. Our findings enhance the understanding of inertial and viscous behaviors of immersed granular flows. The verified scaling rules and dimensionless parameters are of potential use in small-scale experiments and simulations where appropriate scaling is essential.

The dynamics of viscous fluid threads concurrently flowing with miscible solvents is experimentally investigated in square microchannels. Diffusive fluid threads are found to significantly swell at low flow velocities due to large specific interfacial area and hydrodynamic lubrication. An approach based on bounded function analysis of confined thread diameter is developed to model diffusive behavior of viscosity-differing fluids at the small scale. This work shows the determination of a critical flow rate associated with each fluid pair and the use of dynamic similarity to calculate diffusion coefficients between oils and organic solvents. The thread divergence is estimated based on the growth of diffusion layers and related to diffusion-induced buckling instabilities of viscous threads in parallel flows.

In this work, we proposed an upscaling methodology to extrapolate results from wind tunnel experiments with small-scale model to the full-size hydrokinetic turbine. Small-scale 1:20 wind tunnel experiments ( $${\hbox {Re}}\sim 10^4$$ ), with a three-blade horizontal axis turbine, were carried out looking to identify the characteristic curves of a full-size turbine operating in water ( $${\hbox {Re}}\sim 10^6$$ ). The lack of dynamic similarity due to unmatched Reynolds numbers is analyzed in the framework of blade element momentum theory arguments. A new semi-empirical power-law equation is achieved, uniquely based on the BEM theory which relates the power coefficients of model and full-size turbine to the Reynolds numbers and a power factor, specific to each turbine. Computational fluid dynamic CFD simulations for the same rotor geometry, simulating different runners with varying diameters from small-scale model to full-scale turbine are carried out to validate the upscaling arguments, and to verify the accuracy of the power coefficient curves predicted by proposed methodology.

Airfoil stall at low Reynolds numbers is a complex nonlinear dynamic phenomenon, which is characterized by catastrophe and hysteresis. It is difficult but important to mathematically describe the s...

A tidal bore is a positive surge or compression wave formed in an estuarine system during the early flood tide under macro-tidal conditions. A series of physical experiments were conducted in a large facility to investigate the unsteady free-surface properties, velocity characteristics and Reynolds shear stresses. Both instantaneous and ensemble-averaged measurements were performed. The results demonstrated the intense turbulence and turbulent mixing under breaking and undular tidal bores. A range of dimensionless unsteady turbulent properties were carefully compared based upon both Froude and Morton similitudes with two different Reynolds number ranges. The data showed that several parameters were affected by scale effects, including velocity and Reynolds stress fluctuations during the bore propagation. The finding implies that laboratory study data might not be up-scaled to prototype conditions without some form of scale effects.

Detailed studies of modern large-scale wind turbines represent a significant challenge. The immense length scales characteristic of these machines, in combination with rotational effects, render numerical simulations and conventional wind tunnel tests unfeasible. Field experiments can give us important insight into the aerodynamics and operation, but they are always accompanied by large amounts of uncertainty, due to the changing nature of the inflow and the lack of accurate control of the test conditions. Here, a series of experiments is presented, using an alternative method that enables us to represent and study much of the physics governing the large-scale wind turbines in small-scale models. A specialized, compressed-air wind tunnel is used to achieve dynamic similarity with the field-scale, but under accurately controlled conditions of the laboratory. Power and thrust coefficients are investigated as a function of the Reynolds number up to ReD=14×106, at tip speed ratios representative of those typical in the field. A strong Reynolds number dependence is observed in the power coefficient, even at very high Reynolds numbers (well exceeding those occurring in most laboratory studies). We show that for an untripped rotor, the performance reaches a Reynolds number invariant state at Rec≥3.5×106, regardless of the tip speed ratio. The same model was also tested with scaled tripping devices, with a height of only 9μm, to study the effect of transition on the rotor performance. In the tripped case, the Reynolds number dependence was eliminated for all tested cases, suggesting that the state of the boundary layer is critical for correct predictions of rotor performance.

Summary For simulating freely moving problems, conventional immersed boundary-lattice Boltzmann methods encounter two major difficulties of an extremely large flow domain and the incompressible limit. To remove these two difficulties, this work proposes an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) in the arbitrary Lagragian–Eulerian (ALE) coordinates and establishes a dynamic similarity theory. In the ALE-based IB-LBFS, the flow filed is obtained by using the LBFS on a moving Cartesian mesh, and the no-slip boundary condition is implemented by using the boundary condition-enforced immersed boundary method. The velocity of the Cartesian mesh is set the same as the translational velocity of the freely moving object so that there is no relative motion between the plate center and the mesh. This enables the ALE-based IB-LBFS to study flows with a freely moving object in a large open flow domain. By normalizing the governing equations for the flow domain and the motion of rigid body, six non-dimensional parameters are derived and maintained to be the same in both physical systems and the lattice Boltzmann framework. This similarity algorithm enables the lattice Boltzmann equation-based solver to study a general freely moving problem within the incompressible limit. The proposed solver and dynamic similarity theory have been successfully validated by simulating the flow around an in-line oscillating cylinder, single particle sedimentation, and flows with a freely falling plate. The obtained results agree well with both numerical and experimental data. Copyright © 2016 John Wiley & Sons, Ltd.

In flutter wind tunnel test, the matching degree between scaled model and prototype would directly affect the reliability of test results. It is difficult to achieve completely dynamic similarity because of some material or technological constrains, and only lower order modes including mode shape and frequency are accurately simulated to construct a compromised model. Theoretical support would be necessary to answer the question which modes must be simulated to guarantee data validity of wind tunnel flutter test. An analytical study of a sweepback winghas been undertaken to estimate the flutter influence mode needed for accurate flutter prediction by analyzing generalized aerodynamic stiffness coefficient, unsteady aerodynamic force and flutter results. The results show that the aerodynamic stiffness coefficient with expression of mode shape could be taken as a quick criterion for mode selection in flutter model design and analysis.

The effects of percentage stenosis and Reynolds number (Re) on steady flow, and Womersley number (Wo) on pulsatile flow, of blood through a two-dimensional channel with stenosis are investigated, and the results are compared with the Newtonian case. We model blood using the shear-thinning relation proposed by Yeleswarapu, while the stenosis is approximated using a cosine-shaped taper. The vorticity–streamfunction formulation of the flow equations is solved using a finite difference scheme in conjunction with a full-multigrid algorithm that reduces computational time. The presence of stenosis leads to a recirculation zone immediately downstream of the stenosis. In steady flow, the shear-thinning fluid predicts higher peak wall shear stress than the Newtonian fluid: the difference between the predictions, expressed as a percentage of the Newtonian wall shear stress, decreases as percentage stenosis and Reynolds number increase. For a given percentage stenosis and Reynolds number, the percentage difference between the shear-thinning fluid and Newtonian fluid decreases, and remains negligible, as the Womersley number increases (corresponding to increasing pulsatile nature of the flow). This suggests that the Newtonian approximation can accurately model wall shear stress in the aortic flow of blood; however, for other variables (e.g. mean velocity) the shear-thinning model is more appropriate.

A systematic set of flume experiments is used to investigate the features of velocity profiles within the body of coarse-grained debris flows and the dependence of the transport sediment concentration on the relevant parameters (runoff discharge, bed slope, grain size, and form). The flows are generated in a 10 m long laboratory flume, initially filled with a layer consisting of loose debris. After saturation, a prescribed water discharge is suddenly supplied over the granular bed, and the runoff triggers a debris flow wave that reaches nearly steady conditions. Three types of material have been used in the tests: gravel with mean grain size of 3 and 5 mm, and 3 mm glass spheres. Measured parameters included: triggering water discharge, volumetric sediment discharge, sediment concentration, flow depth, and velocity profiles. The dynamic similarity with full-sized debris flows is discussed on the basis of the relevant dimensionless parameters. Concentration data highlight the dependence on the slope angle and the importance of the quasi-static friction angle. The effects of flow rheology on the shape of velocity profiles are analyzed with attention to the role of different stress-generating mechanisms. A remarkable collapse of the dimensionless profiles is obtained by scaling the debris flow velocity with the runoff velocity, and a power law characterization is proposed following a heuristic approach. The shape of the profiles suggests a smooth transition between the different rheological regimes (collisional and frictional) that establish in the upper and lower regions of the flow and is compatible with the presence of multiple length scales dictated by the type of contacts (instantaneous or long lasting) between grains.

For numerical simulations of the turbulent cavitating flows, the volume fraction transport equations, namely cavitation models, are used widely to predict the dynamics of cavitation phenomenon. The cavitation models are empirical-based with tunable coefficients to dominate the evaporation and condensation rates. In order to assess the generality and sensitivity of the cavitation and turbulence models, steady attached and unsteady cloud cavitation conditions are simulated with different combinations of empirical coefficients systematically. Our goal is to improve the generality of coefficients and reduce their sensitivity while the good agreement with experimental measurements still can be satisfied. In this study, the original cavitation model is modified into a dimensionless form to maintain the dynamic similarity, and the sensitivity issue is improved by the filter-based turbulence model. Finally, by using a filter size between 6.25% and 8.125% of the characteristic length, it is found out that the evaporation coefficient Cv and condensation coefficient Cc within the range of 850–11,000 and 100–1900 respectively could reach our goals the best.

Glicksman’s viscous limit set of dimensionless parameters have been investigated using experimentally verifi ed computational fl uid dynamics model. Simulations have been performed for the two bubbling fl uidized beds with different particle sizes and densities. Dimensionless average pressure drops across the bed height, dimensionless pressure standard deviations and dimensionless relative pressures have been investigated as a function of dimensionless superfi cial gas velocities for the two beds. Fluctuation of solid volume fraction and contours of solid volume fraction have also been investigated at different dimensionless gas velocities. Time series data of the pressure fl uctuation and solid volume fraction are compared. The results indicate that the fl uid dynamic similarity between two beds holds up to particle Reynolds number of 15. After this, the bubble activities in the two beds start to deviate signifi cantly. The results of the work show that the analysis of solid volume fraction fl uctuation gives higher accuracy than time-series pressure fl uctuation when scaling the bubbling fl uidized bed within the viscous limit.

The present study highlights the need for using both the kinematic and dynamic similarities in scaled models of the critical submergence of vertical vortices at intake structures. A semi-theoretical approach, which is based on the principle of flow continuity, is used in combination with published experimental data. The present study shows that only the kinematic similarity is needed to model the ratio of the critical submergence to the diameter of the intake. For intakes that have an identical ratio of the intake velocity to the velocity at the critical spherical sink surface (CSSS), the ratio of the critical submergence to the diameter of the intake is identical regardless of the flow and the geometrical conditions. The new finding is that dynamic similarity is not required for the prediction of the ratio of the critical submergence to the intake diameter, provided that the ratio of the intake velocity to the velocity at the CSSS is kept the same.

This paper presents an analysis of flow parameters through a bottom outlet conduit with gated operation using physical and numerical models. A physical model of the regulating bottom outlet of Shahryar dam in Iran was used to investigate the hydraulic forces on the service radial gate and flow patterns within the conduit. The model was constructed from Plexiglas, and discharge and pressure data were recorded for different gate openings. The Froude law of similarity was satisfied in the hydraulic modelling, allowing for an investigation of the dynamic similarity of inertial and gravitational forces. The numerical scheme was based on using the natural-element method to study hydraulic forces and flow parameters within the conduit and the finite-element method to evaluate the natural frequencies of the radial gate. The results of the calculations for different radial gate openings showed good agreement with those from physical modelling for the pressure distributions throughout the flow domain and on the gate.

Flutter is a dynamic unstable phenomenon of elastic structure in airflow, the main objective of flutter analysis is to obtain the flutter critical speed and flutter frequency of flutter system. Numerical simulation and model test are two preliminary measures of determining the flutter characteristics of the system. According to the second theorem of similarity theory, it is proven by dimensional analysis that for any linear flutter system, if the geometrical size of the model is enlarged or reduced by n times while the material properties keep the same, the natural frequencies and flutter frequencies will be reduced or enlarged by n times accordingly, but the flutter critical speed remains unchanged. This finding is verified by formulations of the natural frequency for a simply supported uniform beam and a rectangular plate with simply supported edges, together with the numerical simulation example of the flutter critical speed and frequency of a curved panel. The special geometrical scaling effect in flutter reveals that in the model flutter wind tunnel tests, materials different from those of the prototype structure must be used considering that the flutter critical speed will be usually scaled.

The flow structure in a turbulent double-cavity flow has been studied experimentally and numerically. The dynamics of the two-component instantaneous velocity vector fields measured by an optical smoke image velocimetry method and calculated using the ANSYS Fluent 19.2 software has been derived. For a wide range of dynamic similarity numbers of shape factor and ReL, the flow resistance coefficients for the cavity and relative flow mass transfer with the cavities have been estimated; three characteristic flow regimes of double-cavity flow have been distinguished and described; the flow pattern map via the ReL number and shape factor has been obtained.

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers (criteria) based on turbulent kinetic and dissipation rates associated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged Navier-Stokes equations (RANS). The RNG k-ɛ models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to 107 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ⩾ 3 × 106. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.

A physical model of molten slag granulation by rotary disk was developed based on the mechanism of Newtonian liquid granulation. For geometrical similarity, the radius ratio of model disk to the prototype disk was chosen as 1 : 1. For dynamic similarity, equality of Ohnesorge number between the model and the prototype was achieved firstly by compounding rosin and paraffin wax with mass ratio of 1 : 1 as simulation liquid of molten blast furnace (BF) slag, and the simulation material can satisfy the similarity of liquid-solid transformation during falling in the medium; then equality of Reynolds number and Weber number was obtained by controlling the volumetric flow rate and the rotary speed, respectively. Model accuracy was verified by comparing the simulation data with the results reported in literature, which showed good agreement with the calculation results of empirical equation and the actual molten BF slag granulation from the view point of particle size. Furthermore, influences of disk radius, rotary speed and liquid flow rate on granulation were discussed using the developed model, and the Kitamura equation was modified according to the simulation data which can predict particle size more accurately. Using the modified equation, the operation parameters were predicted according to the flow rate of molten industrial BF slag.

[1] Coupled flows through and over permeable media, also known as obstructed shear flows, are ubiquitous to many environmental systems at different scales, including aquatic flows over sediment beds, and atmospheric flows over crops and cities. Despite their differences, such flows exhibit strong dynamic similarities among systems and scales, as evidenced by the recent finding of empirical universal scaling laws correlating relevant length and velocity scales. We propose a reduced complexity model for obstructed shear channel flows, which couples Brinkman with Reynolds equations to describe the flow within and above the obstruction. We derive scaling laws by intermediate asymptotic analysis of a Darcy-Brinkman type solution in the low permeability limit. The approach highlights the importance of the effective permeability of the obstruction as a critical parameter governing the system dynamical response. The model results are in good agreement with the scaling laws empirically calculated in other studies.

In this paper cross natural ventilation due to buoyancy assisted by wind is investigated with computational and laboratory simulation. The impact of the outlet's opening position is investigated, forming cross ventilation of variable distance h – namely, the vertical distance between midpoints of leeward and windward opening –, for three initial Froude numbers: (i) Fr 0 = 1.15, (ii) Fr 0 = 2.79, (iii) Fr 0 = 4.85. For the computational simulation a fluid dynamic software is used and the problem is solved by solving the 3D unsteady Reynolds Averaged Navier Stokes (RANS) equations in conjunction with the energy equation and the turbulence model RNG k-e. The laboratory simulation took place in an open channel and the experimental model represents a building form of orthogonal shape. The interior of the experimental model is filled with solution of ethanol at conditions of normalized gravity, but also with salted water at conditions of inversed gravity. The time taken for the indoor space to empty is calculated numerically and experimentally. Based on Froude number dynamic similarity, the experimental and computational results are characterized by good agreement and the functional process of natural ventilation is being explicated. In addition, the suggestion of using ethanol solution for the density difference between interior and exterior fluid in laboratory simulation of natural ventilation is verified successfully, as the results with use of ethanol solution are in good agreement with those using salted water.

The geodynamo is the process by which turbulent flow of liquid metal within Earth's core generates our planet's magnetic field. Numerical simulations of the geodynamo are commonly used to elucidate the rich dynamics of this system. Since these simulations cannot attain dynamic similarity with the geodynamo, their results must be extrapolated across many orders of magnitude of unexplored parameter space. For this purpose, scaling analysis is essential. We investigate the scaling behavior of the typical length scales, l , and speeds, U , of convection within a broad suite of geodynamo models. The model outputs are well fit by the scalings l ∝ E 1 / 3 and U ∝ C 1 / 2 E 1 / 3 , which are derived from a balance between the influences of rotation, viscosity, and buoyancy ( E is the Ekman number and C the convective power). Direct comparison with two previously proposed theories finds that the viscous scalings most favorably describe model data. The prominent role of viscosity suggested by these scaling laws may call into question the direct application of such simulations to the geodynamo, for which it is typically assumed that viscous effects are negligible.

For developing a scale-up method based on the kinematic and dynamic similarities of particle behavior, motion of particles in a commercial high shear mixer-granulator with different vessel sizes (2 to 112 L) were simulated using a three-dimensional discrete element method (DEM). Effects of the vessel size on the internal particle flow and the particle collision energy were analyzed. It was found that under the constant impeller tip speed magnitude of the internal particle shear flow can be nearly maintained at different vessel sizes. This implies that the constant impeller tip speed should be employed to achieve the kinematic similarity when scaling-up the high shear mixer-granulator. However, under the constant impeller tip speed the cumulative particle collision energy per unit time significantly decreased with an increase in the vessel size. This suggests that in order to achieve the dynamic similarity the granulation time should be adjusted so that the cumulative particle collision energy over the granulation time can be maintained at different vessel sizes. Based on the simulation results, we proposed a scale-up method in which the optimal granulation time can be determined to achieve the same cumulative particle collision energy at different vessel sizes while maintaining the same impeller tip speed. This method can provide both the kinematic and dynamic similarities between different vessel sizes. Validity of the proposed scale-up method was confirmed by an experiment of wet-granulation using a commercial high shear mixer-granulator with different vessel sizes (2 to 216 L).

We show that in an infinite straight pipe of arbitrary (sufficiently smooth) cross-section, a generalized non-Newtonian liquid admits one and only one fully developed time-periodic flow (Womersley flow) when either the flow rate (problem 1) or the axial pressure gradient (problem 2) is prescribed in analogous time-periodic fashion. In addition, we show that the relevant solution depends continuously upon the data in appropriate norms. As is well known from the Newtonian counterpart of the problem, the latter is pivotal for the analysis of flow in a general unbounded pipe system with cylindrical outlets (Leray's problem). It is also worth remarking that problem 1 possesses an intrinsic interest from both mathematical and physical viewpoints, in that it constitutes a (nonlinear) inverse problem with a significant bearing on several applications, including blood flow modelling in large arteries.

The characteristics of the fluid flows in tool joints were studied experimentally and theoretically in a laboratory scale. The goal of this study was to evaluate the pressure drop in accessories such as tool joints, placed along the drilling columns. The experimental fluid flow loop consisted of a 25-hp positive displacement pump, a 500-liter tank, a 3-HP mixer and a series of circular and annular pipes where the tool joints were installed. Based on the Reynolds number, the fluid flow loop was set to have dynamic similarity with respect to the real hydraulics of oil well fields. CFD simulations were implemented to aid in the design of the fluid flow loop. Pressure drop and fluid flow rate data were experimentally determined in a set of tool joints using water-based muds with non-Newtonian behavior. The CFD simulations showed a good performance on the tool joint simulations. Finally, the literature’s correlations originally employed by Petrobras were used to estimate the friction factor, and new parameters for these correlations were established. The evaluation of the parameters improved the predictive capacity mostly in the laminar regime.

Molecular dynamics (MD) method is used to simulate shear driven argon gas flows in the early transition and free molecular flow regimes to investigate surface effects as a function of the surface–gas potential strength ratio (ewf/eff). Results show a bulk flow region and a near wall region that extends three molecular diameters away from the surfaces. Within the near wall region the velocity, density, and shear stress distributions exhibit deviations from the kinetic theory predictions. Increased ewf/eff results in increased gas density, leading toward monolayer adsorption on surfaces. The near wall velocity profile shows reduced gas slip, and eventually velocity stick with increased ewf/eff. Using MD predicted shear stress values and kinetic theory, tangential momentum accommodation coefficients (TMAC) are calculated as a function of ewf/eff, and TMAC values are shown to be independent of the Knudsen number. Presence of this near wall region breaks down the dynamic similarity between rarefied and nanoscale gas flows.

The load dependent deformation responses and complex failure mechanisms of self-adaptive composite propeller blades make the design, analysis, and scaling of these structures nontrivial. The objective of this work is to investigate and verify the dynamic similarity relationships for the hydroelastic response and potential failure mechanisms of self-adaptive composite marine propellers. A fully coupled, three-dimensional boundary element method-finite element method is used to compare the model and full-scale responses of a self-adaptive composite propeller. The effects of spatially varying inflow, transient sheet cavitation, and load-dependent blade deformation are considered. Three types of scaling are discussed: Reynolds scale, Froude scale, and Mach scale. The results show that Mach scaling, which requires the model inflow speed to be the same as the full scale, will lead to discrepancies in the spatial load distributions at low speeds due to differences in Froude number, but the differences between model and full-scale results become negligible at high speeds. Thus, Mach scaling is recommended for a composite marine propeller because it allows the same material and layering scheme to be used between the model and the full scale, leading to similar 3D stress distributions, and hence similar failure mechanisms, between the model and the full scale.

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.

A free-surface flow can change from a supercritical to subcritical flow with a strong dissipative phenomenon called a hydraulic jump. Herein the progress and development in turbulent hydraulic jumps are reviewed with a focus on hydraulic jumps operating at large Reynolds numbers typically encountered in natural streams and hydraulic structures. The key features of the turbulent hydraulic jumps are the highly turbulent flow motion associated with some intense air bubble entrainment at the jump toe. The state-of-the-art on the topic is discussed based upon recent theoretical analyses and physical data.

An unstructured finite volume method coupled with a fractional-step projection method is developed for the numerical solution of the incompressible Navier–Stokes equations. Based on the use of the proposed method, numerical investigations are performed for a pulsatile flow through a stenotic channel. The geometry of the stenotic segment is assumed to be asymmetric, which can mimic the deformations in the diseased arteries. The numerical results reveal that for the pulsatile flow, the Womersley and Reynolds numbers have a great influence on the vortex generation and the wall shear stress distributions. The size and number of vortices depend largely on the Womersley number but less on the Reynolds.

SUMMARY In this paper, a modified projection method is combined with a self-adaptive time step procedure to develop numerical scheme for large eddy simulation (LES) of low Ma number turbulent reactive flows. The projection method introduced by Chorin is modified in this study to satisfy the simulation requirement of low Ma number reactive flow. The time step in this computation is automatically determined according to the time scales of both chemical reaction and turbulent fluctuations. This enables the simulation to capture detailed flow structures with less computational time. Numerical simulation of methane‐air jet flames is carried out as an example to validate the developed numerical scheme. The mechanism of a simplified 4-step chemical kinetics is applied for the methane‐air reaction. The dynamic model is adopted for the turbulent motion of sub-grid scale (SGS). The dynamic similarity model is used as the SGS model for the reaction rate. The LES results satisfactorily depict the ignition process of the turbulent jet flames and illustrate lucid and detailed coherent structures of the fully developed turbulent reactive jet flow. The LES results also exhibit the mechanism and characteristics of local extinction. The method developed in this study provides an effective way to capture more flow details with less computational time. In addition the method also helps one to investigate the mechanism of ignition and local extinction in jet flames. Copyright q 2008 John Wiley & Sons, Ltd.

We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude σh where σ ~ O(1), but long-wavelength variations λ, with h/λ ≪ 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel's wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.

Recent work on fully opened rubber-lined diaphragm valves showed that due to the lack of geometric similarity, dynamic similarity could not be established. The laminar flow loss coefficient constant therefore becomes diameter dependent as is the case of turbulent flow loss coefficients. The purpose of this work was to establish if this is the case for all types of diaphragm valves, by testing diaphragm valves from a different manufacturer. Accurate loss coefficient data is critical for energy efficient hydraulic design. Saunders type straight-through diaphragm valves ranging from 40 mm to 100 mm were tested in the fully open, 75%, 50% and 25% open positions, using a range of Newtonian and non-Newtonian fluids. It was found that the laminar flow loss coefficient constant suggested by Hooper (1981) is sufficient for all valve diameters at Reynolds numbers below 10. However, for transitional and turbulent flow the same loss coefficients cannot be applied for more accurate designs for diaphragm valves from different manufacturers. A new correlation has therefore been developed to predict the loss coefficients for straight-through Saunders diaphragm valves at various openings from laminar to turbulent flow regimes.

The interaction of flow with an erodible bed in alluvial rivers and deep-sea channels gives rise to a wide range of self-formed morphologies, including channels, ripples, dunes, antidunes, alternate bars, multiple-row bars, meandering and braiding. As the flow is invariably turbulent in field manifestations of these morphologies, there has been a tendency to assume that turbulence is necessary for them to form. While turbulence undoubtedly has an important influence when it is present, it is not necessary for any of these features. Indeed, all of these features can be formed by the morphodynamic interaction of purely laminar or nearly laminar flow with an erodible bed. This paper provides a survey and synthesis of a wide range of laminar or near-laminar flow analogues of morphologies observed in the field. Laminar-flow analogues of turbulent-flow morphologies cannot and should not be expected to satisfy dynamic similarity in terms of all relevant dimensionless parameters. What is of more significance is the convergence of the underlying physics. It is illustrated in this paper that many existing theoretical frameworks for the explanation of turbulent-flow morphodynamics require only relatively minor modification in order to adapt them to laminar flows.

This paper deals with the numerical analysis of kinematic and dynamic similarities of particle behavior in high shear mixer granulators with different vessel sizes. The three-dimensional particle motion in high shear mixer granulators with four different vessel sizes was calculated using a discrete element method (DEM). The geometrically similar mixer granulators equipped with a flat-shaped impeller blade were used as simulated mixer granulators. Kinematic and dynamic similarities of particle behavior in various vessel sizes under a constant normalized agitation power were numerically analyzed. In various vessel sizes, dynamic similarity expressed by the particle collision energy was confirmed under a constant normalized agitation power, while kinematic similarity expressed by the particle velocity was not confirmed. These results indicate that the dynamic similarity should be maintained for successful scale-up of high shear mixer granulators.

A solar chimney power plant derives its mechanical power from the kinetic power of the hot air which rises through a tall chimney, the air being heated by solar energy through a transparent roof surrounding the chimney. In our previous studies, the achievement of complete dynamic similarity between a prototype and its models imposed the use of different solar heat fluxes between them. It is difficult to conduct an experiment by using dissimilar heat fluxes with different physical models. Therefore, this study aimed to maintain dynamic similarity for a prototype and its models while using the same solar heat flux. The study showed that, to achieve the same-heat-flux condition, the roof radius between the prototype and its scaled models must be dissimilar, while all other remaining dimensions of the models are still similar to those of the prototype. In other words, the models are ‘partially’ geometrically similar to the prototype. The functional relationship that provides the condition for this partial similarity is proposed and its validity is proved by scaling the primitive numerical solutions of the flow. Engineering interpretations of the similarity variables are also presented.

Colloque avec actes et comité de lecture. Internationale.; International audience; Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is proposed and quantitatively verified against the DNS data.

The principle of multiple solutions of the Navier-Stokes and energy equations discussed in this paper is not directed at any particular problems in fluid dynamics and heat transfer, or at any specific applications. The non-uniqueness principle states that the Reynolds number, above its critical value, is insufficient to uniquely determine a flow field for a given geometry, or for similar geometries. It is a generic principle for all fluid flows and its transportation properties, but is not well known. It compliments the current popular bifurcation theories by the fact that multiple solutions can exist on each stable bifurcation branch.

In high-velocity free-surface flows, air entrainment is common through the interface, and intense interactions take place between turbulent structures and entrained bubbles. Two-phase flow properties were measured herein in high-velocity open channel flows above a stepped chute. Detailed turbulence measurements were conducted in a large-size facility, and a comparative analysis was applied to test the validity of the Froude and Reynolds similarities. The results showed consistently that the Froude similitude was not satisfied using a 2:1 geometric scaling ratio. Lesser number of entrained bubbles and comparatively greater bubble sizes were observed at the smaller Reynolds numbers, as well as lower turbulence levels and larger turbulent length and time scales. The results implied that small-size models did underestimate the rate of energy dissipation and the aeration efficiency of prototype stepped spillways for similar flow conditions. Similarly a Reynolds similitude was tested. The results showed also some significant scale effects. However a number of self-similar relationships remained invariant under changes of scale and confirmed the analysis of Chanson and Carosi (Exp Fluids 42:385-401, 2007). The finding is significant because self-similarity may provide a picture general enough to be used to characterise the air–water flow field in large prototype channels.

In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.

Hydrodynamics and scale-up of liquid–solid circulating fluidized beds (LSCFBs) are investigated using similitude method and computational fluid dynamics (CFD) technique. Similitude method is applied to establish the dynamic similarity among LSCFBs by tuning physical properties of liquids and solids, operating conditions and bed dimensions to match several scaling sets of dimensionless groups. The hydrodynamic behaviors in these constructed LSCFBs are simulated by a validated CFD model [Cheng, Y., Zhu, J., 2005. CFD modeling and simulation of hydrodynamics in liquid–solid circulating fluidized beds. Canadian Journal of Chemical Engineering 83, 177–185] and compared in terms of the axial and radial flow structures characterized by the solids fraction, particle and liquid velocities and solids mass flux. The results demonstrate that only the full set scaling parameters obtained from similitude method, i.e., five dimensionless groups together with fixed bed geometry, particle sphericity, particle size distribution as well as particle collision properties, can ensure the similarity of hydrodynamics in the fully developed region of different LSCFBs. Developing flow structures in LSCFBs are strongly influenced by some parameters such as turbulent kinetic energy at the inlet so that the proposed similitude method may not always be applicable.

Sensitivity of flow and sediment transport in a meandering river to variations in scaling and flow rate was studied. The FLUENT™ code was used for evaluating the river flow characteristics, including the mean velocity field and the Reynolds stress components, as well as for particle trajectory analysis. Particular attention was given to the sensitivity of the sedimentation patterns of different size particles in the river bend for various scales. Simulation studies were performed for both a model river and a physical river. The physical river was geometrically similar to the model river, with a scaling ratio of 1:100, but with identical Froude number. The flow and particle deposition patterns in the physical and model rivers were compared. It was shown that the mean flow quantities exhibit dynamic similarity, but the turbulence parameters and the particle sedimentation features in the physical river were different from the model. The secondary flows and particle transport patterns were also found to be se...

Animals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of a dimensionless parameter (DP) called the Froude number. Consequently, the Froude number has been widely used for defining equivalent speeds and predicting speeds of locomotion by extinct species and on other planets. However, experiments using simulated reduced gravity have demonstrated that equality of the Froude number does not guarantee dynamic similarity. This has cast doubt upon the usefulness of the Froude number in locomotion research. Here we use dimensional analysis of the planar spring-mass model, combined with Buckingham's Pi-Theorem, to demonstrate that four DPs must be equal for dynamic similarity in bouncing gaits such as trotting, hopping and bipedal running. This can be reduced to three DPs by applying the constraint of maintaining a constant average speed of locomotion. Sensitivity analysis indicates that all of these DPs are important for predicting dynamic similarity. We show that the reason humans do not run in a dynamically similar manner at equal Froude number in different levels of simulated reduced gravity is that dimensionless leg stiffness decreases as gravity increases. The reason that the Froude number can predict dynamic similarity in Earth gravity is that dimensionless leg stiffness and dimensionless vertical landing speed are both independent of size. In conclusion, although equal Froude number is not sufficient for dynamic similarity, it is a necessary condition. Therefore, to detect fundamental differences in locomotion, animals of different sizes should be compared at equal Froude number, so that they can be as close to dynamic similarity as possible. More generally, the concept of dynamic similarity provides a powerful framework within which similarities and differences in locomotion can be interpreted.

Dimensionless variables are proposed to guide the experimental study of flow in a small-scale solar chimney: a solar power plant for generating electricity. Water and air are the two working fluids chosen for the modeling study. Computational fluid dynamics (CFD) methodology is employed to obtain results that are used to prove the similarity of the proposed dimensionless variables. The study shows that air is more suitable than water to be the working fluid in a small-scale solar chimney model. Analyses of the results from CFD show that the models are dynamically similar to the prototype as suggested by the proposed dimensionless variables.

Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.

In this experimental study a thorough analysis of the steady and unsteady flow field in a realistic transparent silicone lung model of the first bifurcation of the upper human airways will be presented. To determine the temporal evolution of the flow time-resolved particle-image velocimetry recordings were performed for a Womersley number range 3.3 ≤ α ≤ 5.8 and Reynolds numbers of ReD = 1,050, 1,400, and 2,100. The results evidence a highly three-dimensional and asymmetric character of the velocity field in the upper human airways, in which the influence of the asymmetric geometry of the realistic lung model plays a significant role for the development of the flow field in the respiratory system. At steady inspiration, the flow shows independent of the Reynolds number a large zone with embedded counter-rotating vortices in the left bronchia ensuring a continuous streamwise transport into the lung. At unsteady flow the critical Reynolds number, which describes the onset of vortices in the first bifurcation, is increased at higher Womersley number and decreased at higher Reynolds number. At expiration the unsteady and steady flows are almost alike.

International audience; The influence of wall transverse pulsation on the viscous incompressible fluid flow in a channel under the action of pressure and gravity is studied under approximation of the small amplitudes. It is found that for the large values of the Womersley numbers the pulsations decrease the flow rate, rather than increase it, as it was found in the previous studies for the small Womersley numbers.

In this chapter, we begin the discussion of how computational methods can be used to study various biofluid mechanics problems. We begin by presenting various computational methods, such as the large eddy simulations and direct numerical simulations. The use of various computational programs is illustrated with a diverging channel and then the human left main coronary artery. We then move into a discussion of the need for and the difficulty of fluid structure interaction modeling, in which the movement of blood vessels can be coupled to the fluid flow through the blood vessel. Particle trajectories and the calculation of the shear history on particles are presented. The development of the Buckingham Pi Theorem is discussed, to derive salient dimensionless numbers. Some of the important dimensionless numbers for biofluid mechanics are presented. These numbers can be used to develop dynamically similar conditions.

Large eddy simulations (LES) of two-dimensional turbulent convection within the anelastic approximation are presented for Rayleigh number Ra = 109, Prandtl number Pr = 1 with free-slip boundary conditions. Various subgrid-scale (SGS) models are investigated such as a similarity model, a dynamic similarity model, a dynamic eddy-viscosity model, a hyperdiffusion model and a hybrid model (dynamic similarity hyperdiffusion model). To study the effects of density stratification on the models, we have also carried out simulations for a Boussinesq flow. The SGS models are compared to direct numerical simulation (DNS) data on the basis of kinetic energy and entropy variance spectra, mean entropy profiles, r.m.s. entropy profiles and r.m.s. kinetic energy density profiles. The results show that for the Boussinesq flow, all the SGS models agree fairly well with the high resolution DNS data. However, for the strongly density-stratified flow, only the hyperdiffusion and the hybrid model show good performance.