Characteristic Reynolds Number Research Articles

Investigations on performance of valveless piezoelectric micropump with concave tuning diffuser/nozzle elements in transient flow

A diffuser/nozzle is one of the most frequently-used channels in a valveless piezoelectric micropump, but its efficiency has not been satisfactory. Hence, optimisation of the channel structure is of great significance. The concave tuning diffuser/nozzle element can obtain steady flow rectification under different Reynolds numbers, and its efficiency is much higher than the conventional diffuser/nozzle element whose diverging angle is >25°. Therefore, the application of concave tuning on the micropump is promising and worth anticipating. In this work, the experiment and numerical simulation were carried out under the conditions of voltage (50–250 vpp), excitation frequency (10–1000 Hz) and Rec (100–1000). The results show that the performance of a micropump with concave tuning is better than that with a straight sidewall, as the pump efficiency is improved significantly. The position and size of vortexes are of great significance to the pump efficiency of the micropumps. The distribution of pressure in the micropumps with concave tuning and straight sidewall was displayed. With the increase of characteristic Reynolds number, the adverse pressure gradient occurred. Compared with the straight sidewall, the concave tuning structure can better withstand adverse pressure gradient and delay the boundary layer separation in the channel.

Vortex-dynamical interpretation of anti-phase and in-phase flickering of dual buoyant diffusion flames

Anti-phase and in-phase flickering modes of dual buoyant diffusion flames were numerically investigated and theoretically analyzed in this study. Inspired by the flickering mechanism of a single buoyant diffusion flame, for which the deformation, stretching, or even pinch-off of the flame surface result from the formation and evolution of the toroidal vortices, we attempted to understand the anti-phase and in-phase flickering of dual buoyant diffusion flames from the perspective of vortex dynamics. The interaction between the inner-side shear layers of the two flames was identified to be responsible for the different flickering modes. Specifically, the transition between anti-phase and in-phase flickering modes can be predicted by a unified regime nomogram of the normalized flickering frequency versus a characteristic Reynolds number, which accounts for the viscous effect on vorticity diffusion between the two inner-side shear layers. Physically, the transition of the vortical structures from symmetric (in-phase) to staggered (anti-phase) in a dual-flame system can be interpreted as being similar to the mechanism causing flow transition in the wake of a bluff body and forming the Karman vortex street.

Steady Secondary Flow in a Plane Turbulent Free Jet

Asymptotic methods are applied to study a plane turbulent jet of a viscous incompressible fluid flowing out through a narrow slot into a space filled with a fluid. The complete Navier—Stokes equations are considered. The characteristic Reynolds number is assumed to be large, while the jet thickness is small. In analyzing the problem the method of many scales is used, which makes it possible to determine and investigate a steady secondary flow within the turbulent jet. The secondary steady solutions are analytically obtained for the normal and longitudinal velocity components and the pressure. It is shown that the self-induced fluid outflow of the jet core toward the jet periphery is the main secondary flow ensuring the supply of the kinetic energy from a maximum velocity zone into the turbulence production zone. The solutions obtained are in good agreement with the available experimental data.

Interaction of Water Droplets in Air Flow at Different Degrees of Flow Turbulence

Presented are results of experiments on high-speed video recording of collisions of water droplets in a gas medium as part of aerosol. Parameters of the gas (air) flow and aerosol cloud were monitored using cross-correlation complexes and optical methods of Particle Image Velocimetry, Particle Tracking Velocimetry, Interferometric Particle Imagine, and Shadow Photography. Conditions at different degrees of gas flow turbulence were considered. The characteristic Reynolds numbers ranged from 1100 to 2800. The relative probabilities of coagulation, scattering, and fragmentation of water droplets upon their collisions were calculated. Experimental dependences of probabilistic criteria on parameters of droplets and flow have been obtained for subsequent mathematical modeling. It has been shown that fragmentation and complete breakup of droplets can enable several-fold increase in the relative area of the liquid. The effect of the degree of gas flow turbulence on parameters of recorded processes of interaction of droplets has been established. The results of the experiments were subjected to criterion processing, theWeber and Reynolds numbers taken into account.

Steady secondary flow in a turbulent mixing layer

Turbulent mixing layer between the moving 2D viscous incompressible fluid and fluid in rest is studied. The characteristic Reynolds number of the flow is assumed to be large and the layer thickness being small. To analyze the problem, the method of multiple scales was applied, which allowed to find and investigate the steady secondary flow inside the turbulent mixing layer. Self-induced entrainment of fluid from the external stream is the main flow in this case, which ensures the supply of kinetic energy from the maximum speed zone to the turbulence generation zone. Secondary steady solutions were found analytically for the longitudinal velocity component. The found solutions were compared with the available experimental data. Understanding of turbulence nature has a principal value for mass and heat transfer in different flows.

Violent water entry of spheres

Water entry is an impulsive two-phase flow often met in nature and in industrial processes. Violent vertical entries are observed when the projectile is heavy and when the Froude number is high enough: they form a distinct category characterized by an elongated cavity trailed by the projectile. The guiding idea in the present approach is to regard the union of the deep cavity caped by the sphere as a composite deformable body relevant to the theory of flows past slender bodies. This process allows linearization, making the problem analytically tractable when air behaves as a passive component, a case occurring very often due to the contrast in density between air and water. Asymptotic analysis shows that the length of the slender body is of the order of RF 2∕3, with F=U(gR)−12 the Froude number, R being the radius, U the speed at entry and g the gravity. That gives rise to a parameter scaling the importance of the air flow inside the cavity, D=(ρa∕ρ)F4∕3, with ρ and ρa the water and air densities. In what follows we adopt the mathematical symbols o and O , with D=o(1) when D≪1 and D=O(1) when D is of the order of 1 but cannot become ≪1. As long as water and air are considered as inviscid, the dimensionless parameters governing the flow are F, D and ρb∕ρ, with ρb the projectile density. In the present contribution we introduce the concept of ideal deep cavity, which does not take into account some transitory perturbations occurring just after impact. Access is obtained to the water velocity potential and to the equations governing the shape of the cavity and the air flow filling the cavity. The problem is solved for D=o(1), which is met in most cases owing to the smallness of ρa /ρ, even if F is very high. Water velocity and air pressure are expressed in terms of the sectional area S of the slender body. Still for D=o(1), a full solution including friction, turbulence and separation is obtained afterward provided the characteristic Reynolds number Re is high. However, transient unsteadiness instigated by a sudden impingement, or transition from laminar to turbulent regimes cannot be characterized by quantitative criteria put in advance, making the task difficult. One of significant features revealed by the present contribution is the important role of friction, which has been generally ignored in previous investigations. The cavity seal appears to be closely connected to friction and instability through the way how separation occurs. The theoretical model is consistent with separation taking place above the equator. A typical property arises: violent cavity sealing occurs in the first third of the distance between atmosphere and the sphere. Present results come complete past entry models elaborated at moderate Froude number. Finally, validation is based on results obtained almost seventy years ago at the Naval Ordnance Laboratory, USA.

IMEX based multi‐scale time advancement in ODTLES

AbstractIn this paper we overcome a key problem in an otherwise highly potential approach to study turbulent flows, ODTLES (One‐Dimensional Turbulence Large Eddy Simulation). From a methodological point of view, ODTLES is an approach in between Direct Numerical Simulations (DNS) and averaged/filtered approaches like RANS (Reynolds Averaged Navier‐Stokes) or LES (Large Eddy Simulations). In ODTLES, a set of 1D ODT models is embedded in a coarse grained 3D LES. On the ODT scale, the turbulent advection is modeled as a sequence of stochastic eddy events, also known as triplet maps, while the other (deterministic) terms are fully resolved in space (along the ODT‐line) and time. Schmidt et al. first (2008) introduced ODTLES and Gonzalez et al. (2011) applied the model for a variety of wall‐bounded flow problems. Although the results were notable for a first proof of concept, the numerical methods used are subject to debate. First of all, an unstable discretization for the large scale 3D advective terms was used, as shown by Glawe (2015). This scheme can be stabilized by reducing the CFL number for the explicitly discretized LES terms down to the order of the small scale ODT time step, but this of course reduces the advantage of the ODTLES multi‐scale approach. The stochastic ODT eddies were also allowed to overlap two LES cells introducing an artificial smoothing (stabilizing) effect. Glawe (2015) limited the overlap consistently to one LES cell and used a stable Runge Kutta (RK) discretization, maintaining, however the low CFL number problem. In this paper we adapt a new implicit/explicit (IMEX) time scheme to ODTLES in order to remedy the small CFL number issue. For the problems investigated, the results indicate a performance increase of the IMEX scheme by a factor of 17 based on the ratio of applied CFL numbers. This allowed simulations of a turbulent channel flow with characteristic friction Reynolds number on one Banana Pi single board computer. We compare results to available DNS data and discuss in general the efficiency and potential of ODTLES for high Reynolds number flows.

Effect of a time dependent stenosis on flow of a second order fluid through constricted tube with velocity slip at wall using integral method

The effect of time dependent axially symmetric constriction in a tube of constant cross section through which a non Newtonian fluid is flowing steadily is modeled and the analysis was made using integral approach The present article is stationed on second order fluid model The study is made applicable for mild constriction by using an order of magnitude analysis The effect of different parameters non Newtonian characteristics Reynolds number and time looming in the model on velocity distribution wall shear stress separation and reattachment and pressure gradient are reviewed graphically It is observed that Reynolds number gives a mechanism to oversight the attachment and de attachment data Constricted tube Non Newtonian fluids Time dependent stenosis Slip velocity Shear stress

Mechanisms in the hypersonic laminar near wake of a blunt body

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

Asymptotic Analysis of Viscous Fluctuations in Turbulent Boundary Layers

A two-dimensional boundary layer of an incompressible viscous fluid is investigated in the presence of velocity and pressure fluctuations. The characteristic Reynolds number is high and, as a consequence, the unsteady (turbulent) boundary layer is thin. An asymptotic approach is used to analyze the complete unsteady Navier–Stokes equations, which makes it possible to separate out the characteristic viscous and inviscid flow zones in the boundary layer and to solve the corresponding problems. The analytical expressions for the viscous fluctuations governed by the Hamel equation with a large value of the parameter are derived.

Effects of piezoelectric fan on overall performance of air-based micro pin-fin heat sink

Due to the lack of studies on the thermal and hydraulic performances of roughed surfaces subjected to the piezoelectric fan in the presence of forced channel flow, an experimental investigation is performed for a micro pin-finned heat sink integrated with a specific piezoelectric fan in the current study. Some influence factors, such as characteristic Reynolds number of vibrating fan, fan tip-to-heated surface clearance and channel flow Reynolds number, are taken into considerations for two specific micro pin-fin configurations having the same pin-fin height. Particular attention is focused on evaluating the role of piezoelectric fan in the design of an active heat sink. It is confirmed that the micro pin-fin surface with a larger pin diameter (H250D400) provides a stronger heat transfer enhancement but greater additional flow losses than H250D250. The integration of piezoelectric fan into micro pin-fin heat sink is a highly efficient means for improving thermal performance. Its role on heat transfer enhancement behaves more significantly under a higher characteristic Reynolds number of vibrating fan and smaller fan tip-to-surface distance. With the presence of piezoelectric fan, the overall thermal performance parameter is generally bigger than the corresponding one without the piezoelectric fan except for the micro pin-fin type H250D400 under high channel flow Reynolds numbers. The linear relationships of heat transfer coefficient and overall thermal performance parameter are derived with respect to the total Reynolds number combining the channel flow and piezoelectric fan. It is demonstrated that the influence weighting of piezoelectric fan on the overall thermal performance parameter is weaker than that on the pure thermal performance of micro pin-fin heat sink.

Human Cough as a Two-Stage Jet and Its Role in Particle Transport.

The human cough is a significant vector in the transmission of respiratory diseases in indoor environments. The cough flow is characterized as a two-stage jet; specifically, the starting jet (when the cough starts and flow is released) and interrupted jet (after the source supply is terminated). During the starting-jet stage, the flow rate is a function of time; three temporal profiles of the exit velocity (pulsation, sinusoidal and real-cough) were investigated in this study, and our results showed that the cough flow’s maximum penetration distance was in the range of a 50.6–85.5 opening diameter (D) under our experimental conditions. The real-cough and sinusoidal cases exhibited greater penetration ability than the pulsation cases under the same characteristic Reynolds number (Rec) and normalized cough expired volume (Q/AD, with Q as the cough expired volume and A as the opening area). However, the effects of Rec and Q/AD on the maximum penetration distances proved to be more significant; larger values of Rec and Q/AD reflected cough flows with greater penetration distances. A protocol was developed to scale the particle experiments between the prototype in air, and the model in water. The water tank experiments revealed that although medium and large particles deposit readily, their maximum spread distance is similar to that of small particles. Moreover, the leading vortex plays an important role in enhancing particle transport.

A numerical investigation of shock propagation in three-dimensional microducts

In the present work, shock propagation and attenuation in three-dimensional microducts with rectangular cross-sections of differing aspect ratios are numerically investigated. The simulations are performed using the Navier–Stokes equations with no-slip wall boundary conditions. The post-shock flow in such microducts resembles a pipe flow, with the extent of the boundary layers comparable with the lateral dimension of the duct. The shock attenuation data are explained on the basis of the viscous dissipation characteristics in the post-shock flow-field, in addition to the behaviour of the boundary layers. It is shown that the three-dimensional effects are adequately modelled using a two-dimensional axisymmetric model or a two-dimensional model, depending on the aspect ratio of the microduct. The data for the shock attenuation are presented in the form of correlations involving the initial Mach number of the shock and a dimensionless parameter that includes the characteristic Reynolds number and the dimensionless shock travel.

Simple and double microemulsions via the capillary breakup of highly stretched liquid jets

We present an exhaustive experimental and theoretical study of the shapes of simple and compound jets formed when one (simple) or two (compound) immiscible liquids are injected into another liquid. The viscosity of the co-flowing external liquid is chosen to vary the characteristic Reynolds number of the outer stream, $Re_{o}$, over a wide range of values. Our slender-body theory in Gordillo et al. (J. Fluid Mech., vol. 738, 2014, pp. 335–357) is extended to predict the shapes of simple jets when $Re_{o}$ is such that $Re_{o}\gg 1$ and also to predict the shapes of compound jets in the case of $Re_{o}\lesssim O(1)$. The validity of our theoretical results, applicable to describe the dynamics of simple or compound jets within an outer carrier fluid in a wide variety of practical situations, is tested using a set-up where the liquids flow from a pressurized chamber towards an extraction tube, finding a very good agreement between the predicted and the observed shapes. Moreover, when $Re_{o}\lesssim O(1)$, and thanks to the fact that the liquid jets produced using our method are highly stretched in the downstream direction, we find that the values of the critical capillary number above which a steady stretched jet is produced, with the capillary number defined here using the outer stream velocity and viscosity, is well below the corresponding critical values characterizing other similar procedures, like flow focusing. This experimental result, which is supported by a spatio-temporal stability analysis in which the axial gradients of the unperturbed solution are retained in the dispersion relation, imply a substantial saving of energy and of the volume of outer liquid necessary to generate a steady capillary jet from which drops are regularly produced. Additionally, making use of continuity arguments and of the fact that drops are formed as a consequence of the growth of a capillary instability, we provide closed expressions for the drop diameters and their production frequencies when the capillary number is above the critical one, in very good agreement with experiments. The simple or double microemulsions generated by the capillary disintegration of the type of simple or compound highly stretched steady jets described here might find applications in biotechnology, pharmacy, cosmetics or materials science.

A Numerical Simulation Algorithm of the Inviscid Dynamics of Axisymmetric Swirling Flows in a Pipe

Current simulations of swirling flows in pipes are limited to relatively low Reynolds number flows (Re < 6000); however, the characteristic Reynolds number is much higher (Re > 20,000) in most of engineering applications. To address this difficulty, this paper presents a numerical simulation algorithm of the dynamics of incompressible, inviscid-limit, axisymmetric swirling flows in a pipe, including the vortex breakdown process. It is based on an explicit, first-order difference scheme in time and an upwind, second-order difference scheme in space for the time integration of the circulation and azimuthal vorticity. A second-order Poisson equation solver for the spatial integration of the stream function in terms of azimuthal vorticity is used. In addition, when reversed flow zones appear, an averaging step of properties is applied at designated time steps. This adds slight artificial viscosity to the algorithm and prevents growth of localized high-frequency numerical noise inside the breakdown zone that is related to the expected singularity that must appear in any flow simulation based on the Euler equations. Mesh refinement studies show agreement of computations for various mesh sizes. Computed examples of flow dynamics demonstrate agreement with linear and nonlinear stability theories of vortex flows in a finite-length pipe. Agreement is also found with theoretically predicted steady axisymmetric breakdown states in a pipe as flow evolves to a time-asymptotic state. These findings indicate that the present algorithm provides an accurate prediction of the inviscid-limit, axisymmetric breakdown process. Also, the numerical results support the theoretical predictions and shed light on vortex dynamics at high Re.

Aerodynamic separation and cleaning of pomegranate arils from rind and white segments (locular septa)

In the process of pomegranate arils pneumatic separation, the aerodynamic characteristics of pomegranate aril, rind and locular septa are essential. The main aim of this study was to measure and compare the aerodynamic characteristics of these materials to provide the data and to facilitate the design and adjustment of machines that perform separation of pomegranate arils from rind and locular septa based on aerodynamic characteristics (terminal velocity, drag coefficient and Reynolds number). To achieve this objective, Ashraf variety pomegranate fruit during its maturity stages was studied. The obtained results showed that the variation in maturity stage significantly influenced the terminal velocity, drag coefficient and Reynolds number (P<0.05). During the fruit maturity, the terminal velocity of locular septa, rind and pomegranate aril increased from 1.05 to 1.16, 3.16 to 3.73 and 5.89 to 6.70ms−1, respectively. The corresponding value of drag coefficient of the three studied materials decreased from 0.92 to 0.79, 0.75 to 0.59 and 0.53 to 0.36, respectively with advancing fruit maturity. Also these ranges for Reynolds number were 403.24–617.75, 1213.44–1986.37 and 2261.76–3568.02, respectively. Consequently, aerodynamic separation of pomegranate aril from locular septa and rind is theoretically possible if the air velocity value is adjusted according to the terminal velocity of pomegranate aril. Also the obtained equations can be used for calculating the parameters of pomegranate aril movement in pneumatic tunnels or in the design and development of air conveyor and pneumatic separator of pomegranate aril.

Effect of viscosity and wall heat conduction on shock attenuation in narrow channels

In the present work, the effects due to viscosity and wall heat conduction on shock propagation and attenuation in narrow channels are numerically investigated. A two-dimensional viscous shock tube configuration is simulated, and heat conduction in the channel walls is explicitly included. The simulation results indicate that the shock attenuation is significantly less in the case of an adiabatic wall, and the use of an isothermal wall model is adequate to take into account the wall heat conduction. A parametric study is performed to characterize the effects of viscous forces and wall heat conduction on shock attenuation, and the behaviour is explained on the basis of boundary layer formation in the post-shock region. A dimensionless parameter that describes the shock attenuation is correlated with the diaphragm pressure ratio and a dimensionless parameter which is expressed using the characteristic Reynolds number and the dimensionless shock travel.

On recent developments in marginal separation theory.

Thin aerofoils are prone to localized flow separation at their leading edge if subjected to moderate angles of attack α. Although ‘laminar separation bubbles’ at first do not significantly alter the aerofoil performance, they tend to ‘burst’ if α is increased further or if perturbations acting upon the flow reach a certain intensity. This then either leads to global flow separation (stall) or triggers the laminar–turbulent transition process within the boundary layer flow. This paper addresses the asymptotic analysis of the early stages of the latter phenomenon in the limit as the characteristic Reynolds number , commonly referred to as marginal separation theory. A new approach based on the adjoint operator method is presented that enables the fundamental similarity laws of marginal separation theory to be derived and the analysis to be extended to higher order. Special emphasis is placed on the breakdown of the flow description, i.e. the formation of finite-time singularities (a manifestation of the bursting process), and on its resolution being based on asymptotic arguments. The passage to the subsequent triple-deck stage is described in detail, which is a prerequisite for carrying out a future numerical treatment of this stage in a proper way. Moreover, a composite asymptotic model is developed in order for the inherent ill-posedness of the Cauchy problems associated with the current flow description to be resolved.

Estimating the effective Reynolds number in implicit large-eddy simulation

In implicit large-eddy simulation (ILES), energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter out unresolved scales and to implicitly model subgrid scale effects. From an applied perspective, it is highly desirable to estimate a characteristic Reynolds number (Re)-and therefore a relevant effective viscosity-so that the impact of resolution on predicted flow quantities and their macroscopic convergence can usefully be characterized. We argue in favor of obtaining robust Re estimates away from the smallest scales of the simulated flow-where numerically controlled dissipation takes place and propose a theoretical basis and framework to determine such measures. ILES examples include forced turbulence as a steady flow case, the Taylor-Green vortex to address transition and decaying turbulence, and simulations of a laser-driven reshock experiment illustrating a fairly complex turbulence problem of current practical interest.

Orientation of a cone settling in a vertical duct

The orientation of a cone settling in a vertical duct has been numerically investigated by using the direct-forcing fictitious domain method. Our results indicate that with the characteristic Reynolds number Re being 30, the cone settles with apex pointing upward if the cone apex angle is smaller than 48°, irrespective of the initial orientation. For the apex angle larger than 48°, the cone also turns upward as long as the releasing angle is smaller than a critical one, otherwise it either turns to an inclined angle if the apex angle is smaller than (or equal to) 52°, or turns downward for the apex angle larger than 52°. The fluid inertial effect helps to turn the cone downward and both the critical apex angle for the unanimous upward-turning and the releasing angle for the turning direction at a fixed apex angle become smaller for a higher Reynolds number, although the effects of the Reynolds number on the critical angles are not enormous. The hairpin-like vortex structures are observed in the wake of the settling cone at Re = 400, accompanied by the persistent oscillation of the orientation angle. Both stable tilted and apex-upward orientations for the cone with the apex angle of 50°, depending on the releasing angle, are confirmed in our experiments.