Minimum Reynolds Number Research Articles

Motion of water drops on hydrophobic expanded polymer mat surfaces due to tangential air flow

Abstract Hydrophobic expanded polymer mats are used in a wide range of industries for many purposes. Their relatively low cost, availability in a wide range of polymer materials, and consistency of pore size distribution are advantageous for some applications such as the separation of liquid drops from gas streams. When fabricated of a non-wetting material, liquid drops tend to stay on one side of the mat and can move across the mat surface due to drag of the gas flow. The rate of movement of drops on the surface can affect the rate of coalescence, the drop size, the loading of drops on the surface of the mat, and ultimately the effectiveness of the mat to separate the drops from a gas stream. In this work the movements of water drops on the surfaces of expanded polymer mats due to tangential air flow are observed to determine the effects of mat material properties and geometrical characteristics, drop dimensions and air flow conditions. A correlation for a drag coefficient of drop movement on the mat surface is developed. A second correlation for the minimum Reynolds number of the gas to initiate the movement of drop on the surface of the mat is also developed.

Improvement in the performance of the vortex flowmeter using contraction cone

The present experimental study investigates a new configuration of vortex flowmeter to improve the turndown ratio and flow distortion sensitivity. An optimized contraction cone is introduced upstream to the vortex shedder to enhance the strength of the shed vortices and to suppress upstream flow distortion effects. A trapezoidal bluff body with two different blockage ratios (19% and 28%) is studied as a vortex shedder. The performance of this new configuration is studied under fully developed flow condition and also evaluated with various flow disturbances. The flow distortion is introduced with 90° degree in-plane and out-of-plane elbows. Transient wall pressure measurement technique is used to capture the vortex shedding frequency. It is found that 28% blockage ratio with optimized contraction cone is the best combination to improve the turn down ratio of vortex flowmeter. The installation of contraction cone helps in reducing the non-uniformity in the velocity profiles which improves the strength and stability of the shed vortices. Minimum measurable Reynolds number obtained with this technique is 5000 which is significantly lower than conventional vortex flowmeters. The turn down ratio achieved with this technique is 1:80 as opposed to 1:20 for conventional vortex flowmeters.

The stability of compressible swirling pipe flows with density stratification

We investigate the spatial stability of compressible, viscous pipe flows with radius-dependent mean density profiles, subjected to solid body rotations. For a fixed Rossby number $\unicode[STIX]{x1D716}$ (inverse of the rotational speed), as the Reynolds number $Re$ is increased, the flow transitions from being stable to convectively unstable, usually leading to absolute instability. If flow compressibility is unimportant and $Re$ is held constant, there appears to be a maximum $Re$ below which the flow remains stable irrespective of any rotational speed, or a minimum azimuthal Reynolds number $Re_{\unicode[STIX]{x1D703}}$ $(=Re/\unicode[STIX]{x1D716})$ is required for any occurrence of absolute instabilities. Once compressible forces are significant, the effect of pressure–density coupling is found to be more severe below a critical $Re$, where as rotational speeds are raised, a stable flow almost directly transitions to an absolutely unstable state. This happens at a critical $Re_{\unicode[STIX]{x1D703}}$ which reduces with increased flow Mach number, pointing to compressibility aiding in the instability at these lower Reynolds numbers. However, at higher $Re$, above the critical value, the traditional stabilizing role of compressibility is recovered if mean density stratification exists, where the gradients of density play an equally important role, more so at the higher azimuthal modes. A total disturbance energy-based formulation is used to obtain mechanistic understanding at these stability states, where we find the entropic energy perturbations to dominate as the primary instability mechanism, in sharp contrast to the energy due to axial shear, known to play a leading role in incompressible swirling flows.

Scale Effects on the Discharge Coefficient of Ogee Spillway with an Arc in Plan and Converging Training Walls

Dam spillways are the structures that lead rightly and safely the outflow downstream, so that the dam integrity can be guaranteed. Many accidents with dams have been caused by an inadequate spillway design or insufficient capacity. To accurately respond the hydraulic spillways, designers use physical modeling for designing this kind of structures. The scale effect in the spillway modeling, as a result, leads to the difference between the measured data and the prototype. In this study, an experimental model of Germi-Chay Mianeh dam spillway was made in three 1:100, 1:75, and 1:50 scales. Then, the water level in upstream of the spillway crest was measured in seven discharges and compared to 1:50 scale (basic scale), the percentage of water level difference on the crest was calculated in two physical models with 1:100 and 1:75 scales. Results revealed that as the scales of ogee spillway with an arc in plan and converging training walls decrease using Froude simulation, the effect of viscosity and surface tension increase in turn resulting in decreasing discharge coefficient. In this study, the scale effect in discharge coefficient ogee spillway was stated with K' equation. Using model family approved that the minimum Reynolds and Weber numbers which are 3.1×104 and 270, respectively indicated the minimum scale effect and thus, it is possible to avoid the effect of viscosity and surface tension in ogee spillway with an arc in plan and with converging training walls. Moreover, results obtained from the small scale which has been simulated using Froude simulation could be extrapolated to the prototype.

Permeability models affecting nonlinear stability in the asymptotic suction boundary layer: the Forchheimer versus the Darcy model

The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability and of the wall suction , whereas the Darcian wall permeability is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of both models produce almost identical TW solutions. However, when both increasing the suction to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for , with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, , for which the Navier–Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of the TW solutions is assessed using a three-dimensional linearized direct numerical simulation (DNS). Low-frequency unstable modes are found for both permeability models; however, the Darcy model is found to overpredict the growth rate, and underpredict the streamwise extension of the most unstable mode. These results indicate that a careful choice of the underlying permeability model is crucial for accurately studying the transition to turbulence of boundary-layer flows over porous walls.

Water drop movement on woven fiber mat surfaces due to flow of diesel fuel

Abstract Fuel contamination by water is one of the major factors of engine failures. Separation of water from diesel fuel is often achieved by coalescing or depth filter media. The separation performance is strongly related to the motion of drops on the surface and in the depth of a filter medium. The dynamics of the motions of drops on a filter surface are influenced by many factors such as the wetting properties of the media. Direct observations of drop movements on fiber surfaces are not well documented. Of particular interest in this work are the dynamics of drops on surfaces of hydrophobic mats that resist drop movement into the interior of the mat, forcing the drops to move on the surface of the mat. Such materials function as barriers to the dispersed phase and allow the continuous phase to move through the mat. In this paper, the motions of water drops were studied on surfaces of mats woven of polypropylene, nylon and Teflon™ (ie, polytetrafluoroethylene) fibers. Pore sizes of the mats ranged from 100 to 1000 μm and drop sizes ranged from 200 to 6000 μm. The flow of ultra low sulfur diesel fuel parallel to the mat surface provided a drag force that induced the movement of the drops. The effects of surface wettability, flow velocity, drop size, fiber size, fiber mat pore size, fiber mat orientation were considered. A correlation for a drag coefficient to estimate the average velocity of drops moving on the woven mats surfaces was derived from the flow and the material’s characteristics. In addition, another correlation was obtained for estimating the minimum velocity, or minimum Reynolds number, required to initiate the drop motion on the woven mat surfaces.

Turbulence generation through intense kinetic energy sources

Direct numerical simulations (DNS) are used to systematically study the development and establishment of turbulence when the flow is initialized with concentrated regions of intense kinetic energy. This resembles both active and passive grids which have been extensively used to generate and study turbulence in laboratories at different Reynolds numbers and with different characteristics, such as the degree of isotropy and homogeneity. A large DNS database was generated covering a wide range of initial conditions with a focus on perturbations with some directional preference, a condition found in active jet grids and passive grids passed through a contraction as well as a new type of active grid inspired by the experimental use of lasers to photo-excite the molecules that comprise the fluid. The DNS database is used to assert under what conditions the flow becomes turbulent and if so, the time required for this to occur. We identify a natural time scale of the problem which indicates the onset of turbulence and a single Reynolds number based exclusively on initial conditions which controls the evolution of the flow. It is found that a minimum Reynolds number is needed for the flow to evolve towards fully developed turbulence. An extensive analysis of single and two point statistics, velocity as well as spectral dynamics and anisotropy measures is presented to characterize the evolution of the flow towards realistic turbulence.

Barrel shaped droplet movement at junctions of perpendicular fibers with different orientations to the air flow direction

Abstract Droplet movements on surfaces are of significant interest in a wide range of practical applications. In contrast to the widely studied motion of droplets on rough and smooth surfaces in a flat configuration, knowledge of the motion across fiber junctions is sparse, despite its significance in filters. Crossed fibers at various angles to flow are a fundamental structure within a complex fibrous medium. This work presents the experimental results of a microscopic study of liquid droplet movement on crossed fibers when subjected to air flow. The crossed fibers were positioned to create different angles, within a plane, relative to the airflow direction. Crossed fibers at various angles to flow are a fundamental structure within a complex fibrous medium. The liquid droplets were placed on the intersection point using a previous method developed by the authors for single fibers. A comparison was made between different fiber layouts in terms of Reynolds number of the gas flow. A mathematical correlation for the minimum Reynolds number of gas at which the droplets began to move was developed. This correlation predicts the gas flow conditions required to start the movement of drops at the fiber junction.

Anode flooding characteristics as design boundary for a hydrogen supply system for automotive polymer electrolyte membrane fuel cells

An automotive fuel cell is investigated to define the design boundaries for an automotive hydrogen supply system with regard to anode flooding. The flooding characteristics of the fuel cell anode at various operating conditions (hydrogen flow rate, pressure, temperature, current density) are analyzed by in-situ and ex-situ measurements. Stable operation conditions are identified and a relation to the operating conditions is established. For adequate water removal, a minimum Reynolds number in the gas channels has to be adjusted. Using this information, different hydrogen supply system designs are compared in their compliance with the stability requirements. It is shown that passive hydrogen supply systems do not achieve all fuel cell requirements regarding power density, lifetime and robustness.

Drop movement along a fiber axis due to pressure driven air flow in a thin slit

The movements of liquid drops on fibers commonly occur in fabrics used in household and commercial applications. The fundamental mechanisms controlling the movement of drops on the fibers are basically the same as those for flat surfaces, but the differences in the geometries cause different kinematic behaviors. Drops on surfaces are widely discussed but fewer publications discuss drops on fibers. The results of pressure driven air flow experiments to move liquid drops along a fiber axis are presented here. Data from these new experiments are used to revise a drag coefficient correlation previously reported with data from a Couette flow device. The revised correlation combines the data sets from the Couette flow and the pressure driven flow experiments and significantly extends the range of the Reynolds number in the correlation. Also, a new correlation is obtained to predict the minimum Reynolds number of the gas flow necessary to initiate the movement of the drops on the fibers. The second correlation gives an estimate of the gas flow conditions necessary to start the movement of drops on fibers. The first correlation provides a drag coefficient to estimate the average speed of drops moving on the fibers.

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Reth(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Reth(p) → ∞, only at p = p k = k, p = p 1/k = 1/k, and $p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2$ , where k = 1, 2, 3, …. The minimum Reynolds number Reth(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Reth = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.

Экспериментальное определение параметров гидротрансформатора в условиях недостаточной мощности приводного двигателя

The paper is devoted to the issue of conducting experimental studies of torque converters for accurate determination of their external and internal parameters of operating in conditions of low-power drive motor by selecting the optimal gear ratio and rotational speed of the impeller n 1 . On the basis of the graphical optimization method the algorithm was developed based on imposing the constraints for the maximum motor power, the minimum Reynolds number and the resonance speed of impeller rotation. The theoretical issue of experimental studies of the torque converter in the area of quadratic losses of the VTI graph is resolved. The graph for the coefficient of hydraulic friction losses depending on several flow sections and the Reynolds number is shown. The diagram of dependence of the coefficient of hydraulic friction losses for several flow sections on the gear ratio λmn=f (i) is presented.

Numerical Simulation and Modeling of Laminar Developing Flow in Channels and Tubes With Slip

Analytical solutions for slip flows in the hydrodynamic entrance region of tubes and channels are examined. These solutions employ a linearized axial momentum equation using Targ's method. The momentum equation is subjected to a first order Navier slip boundary condition. The accuracy of these solutions is examined using computational fluid dynamics (CFD) simulations. CFD simulations utilized the full Navier–Stokes equations, so that the implications of the approximate linearized axial momentum equation could be fully assessed. Results are presented in terms of the dimensionless mean wall shear stress, τ⋆, as a function of local dimensionless axial coordinate, ξ, and relative slip parameter, β. These solutions can be applied to either rarefied gas flows when compressibility effects are small or apparent liquid slip over hydrophobic and superhydrophobic surfaces. It has been found that, under slip conditions, the minimum Reynolds number should be ReDh>100 in order for the approximate linearized solution to remain valid.

Late-time quadratic growth in single-mode Rayleigh-Taylor instability

The growth of the two-dimensional single-mode Rayleigh-Taylor instability (RTI) at low Atwood number (A=0.04) is investigated using Direct Numerical Simulations. The main result of the paper is that, at long times and sufficiently high Reynolds numbers, the bubble acceleration becomes stationary, indicating mean quadratic growth. This is contrary to the general belief that single-mode Rayleigh-Taylor instability reaches a constant bubble velocity at long times. At unity Schmidt number, the development of the instability is strongly influenced by the perturbation Reynolds number, defined as Rep≡λsqrt[Agλ/(1+A)]/ν. Thus, the instability undergoes different growth stages at low and high Rep. A new stage, chaotic development, was found at sufficiently high Rep values, after the reacceleration stage. During the chaotic stage, the instability experiences seemingly random acceleration and deceleration phases, as a result of complex vortical motions, with strong dependence on the initial perturbation shape (i.e., wavelength, amplitude, and diffusion thickness). Nevertheless, our results show that the mean acceleration of the bubble front becomes constant at late times, with little influence from the initial shape of the interface. As Rep is lowered to small values, the later instability stages, chaotic development, reacceleration, potential flow growth, and even the exponential growth described by linear stability theory, are subsequently no longer reached. Therefore, the results suggest a minimum Reynolds number and a minimum development time necessary to achieve all stages of single-mode RTI development, requirements which were not satisfied in the previous studies of single-mode RTI.

Scale Effects of Impulse Wave Run-Up and Run-Over

AbstractHydraulic models differing from prototype scale are affected by model effects. Despite these effects, which are often negligible, they may become important in very small scales involving, for instance, small water depths. A scale family is a convenient method to detect these effects in a new test setup to demonstrate the equipment applicability. The scale family investigated here involves a previously installed test setup concerning the impulse wave run-up and overland flow. Solitary waves as a typical wave type of slide-generated impulse waves were analyzed using a pneumatic piston-type wave generator. Free surface profiles were measured to investigate the maximum flow depths and the flow front velocities. The observed scale effects led to the definition of the minimum Reynolds and Weber numbers for the considered test setup, above which scale effects can be neglected.

Linear spatio-temporal instability analysis of ice growth under a falling water film

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.

Scalar energy fluctuations in Large-Eddy Simulation of turbulent flames: Statistical budgets and mesh quality criterion

Large-Eddy Simulation (LES) provides space-filtered quantities to compare with measurements, which usually have been obtained using a different filtering operation; hence, numerical and experimental results can be examined side-by-side in a statistical sense only. Instantaneous, space-filtered and statistically time-averaged signals feature different characteristic length-scales, which can be combined in dimensionless ratios. From two canonical manufactured turbulent solutions, a turbulent flame and a passive scalar turbulent mixing layer, the critical values of these ratios under which measured and computed variances (resolved plus sub-grid scale) can be compared without resorting to additional residual terms are first determined. It is shown that actual Direct Numerical Simulation can hardly accommodate a sufficiently large range of length-scales to perform statistical studies of LES filtered reactive scalar-fields energy budget based on sub-grid scale variances; an estimation of the minimum Reynolds number allowing for such DNS studies is given. From these developments, a reliability mesh criterion emerges for scalar LES and scaling for scalar sub-grid scale energy is discussed.

208 二次元チャンネル流の限界レイノルズ数付近の撹乱構造について(OS2-2 乱流現象の実験とシミュレーション2,OS2 乱流現象の実験とシミュレーション)

208 二次元チャンネル流の限界レイノルズ数付近の撹乱構造について(OS2-2 乱流現象の実験とシミュレーション2,OS2 乱流現象の実験とシミュレーション)

209 二次元チャンネル流における乱流維持する限界レイノルズ数について(OS2-2 乱流現象の実験とシミュレーション2,OS2 乱流現象の実験とシミュレーション)

209 二次元チャンネル流における乱流維持する限界レイノルズ数について(OS2-2 乱流現象の実験とシミュレーション2,OS2 乱流現象の実験とシミュレーション)

Enhanced mixing of Newtonian fluids in a stirred vessel using impeller speed modulation

AbstractThis paper reports on an experimental study of mixing intensification using speed modulation of a six‐blade Rushton turbine in a stirred vessel. Mixing times were measured using a non‐intrusive technique based on direct visualisation of an acid‐base reaction in a Newtonian fluid. The impeller speed modulation was achieved by using two waveforms: a square wave and a sine wave. The amplitude was fixed between a maximum Reynolds number of Remax = 60 and minimum Reynolds numbers of Remin = 40 or 30. The wave periods were varied (10, 20, or 40 s) in order to compare the effects of unsteady stirring on mixing performance. It was observed that a square wave protocol with the shortest wave period and the larger amplitude resulted in the shortest time to destroy the observed isolated mixing regions (IMRs), which are known to exist in stirred vessels operating at low Reynolds number. However, the sine wave protocol led to a slow diffusive mechanism in which IMR structures reached an asymptotic volume and remained visible even after several hours. The results are presented and discussed using digital photographs taken at different time intervals during experimentation.