Steady Unidirectional Flow Research Articles

Flow and heat transfer performance of reciprocating oscillatory flow in a Stirling engine compared to steady unidirectional flow

The driving force of a Stirling engine comes from the thermal expansion and cold compression of working gas under reciprocating oscillating flow, the flow and heat transfer performance of which is significantly different with that of steady state unidirectional flow. In this work, the performance differences in a heating tube for a Stirling engine under steady state unidirectional and reciprocating oscillating flows were studied. The results indicate that the temperature distribution was mainly dependent on the inlet velocity for a steady unidirectional flow. For a reciprocating oscillatory flow, the temperature distribution was greatly affected by the working gas state in the previous period besides the inlet velocity. Furthermore, a slightly weaker of heat transfer was obtained for reciprocating oscillatory flow, accompanying with a slightly stronger pressure consumption. The change time of pressure difference, velocity and heat transfer for the reciprocating oscillatory flow were earlier than, substantially equal to, and later than that of the steady unidirectional flow. Finally, the entry-return asymmetric insert was suggested to prioritize the heat transfer enhancement in entry process of a heating tube under reciprocating oscillatory flow to achieve the excellent overall performance for a Stirling engine.

Experimental and Computational Evidence of Damped Axial Conduction with Reciprocating Flow

Abstract Axial conduction is a crucial performance deteriorating factor in miniaturized heat transfer devices, primarily due to the low fluid flow rates, high solid cross-sectional to free-flow area ratio, and use of high thermal conductivity materials. These causative factors, inherent to micro-scale systems, should be such that the axial conduction is minimum. The reciprocating flow of the convective fluid (instead of steady unidirectional flow) is proposed per se as an alternative, which directly alters the solid temperature profile, the root cause of axial conduction. An experimental setup is built as a proof of the concept. In the test rig, a double-acting reciprocating pump generates a fully reversing periodic flow of air through a flow channel carved into a steel block embedded with a heater. The experimental temperature profile in the solid at the cyclic steady state is bell-shaped, indicating a virtual adiabatic plane capable of restricting axial heat transfer. The experimental results are verified taking the help of an independent finite-element-based numerical analysis. Similarly, the non-dimensional interfacial flux ratio (?_0 ), integrally related to axial conduction, for unidirectional and reciprocating flow is significantly different. This ratio in the vicinity of the inlet is ~53% less with the reciprocating compared to the equivalent unidirectional flow. The optimal thermal performance with the reciprocating flow is correlated through a critical Strouhal number expression, Sr ≤ (pDh)/L. In thermal management applications employing reciprocating flow, the limiting relation can be used to determine flow parameters and optimum geometry design.

19th-century thermosiphon ventilation and its potential for heat recovery in buildings today

A forgotten thermosiphon scheme is found in Montreal's former Royal Victoria Hospital and traced back to the original Center Block of Canada's Parliament Hill. This discovery inspires an investigation into the fluid mechanics of heat recovery with buoyancy ventilation, where interior spaces are arranged in an open thermal loop with heat exchange through partition walls. Flow visualizations with physical models are used to corroborate the archival evidence and show how the historical scheme worked. The scheme is then generalized, defining a criterion for steady unidirectional flow and a heat recovery limit when room temperatures upstream and downstream reach equilibrium This mathematical model is validated experimentally, demonstrating steady flow close to the efficiency limit with a balanced thermal design . Further analysis shows significant heating savings are possible in mildly cold seasons compared to natural displacement (74%) and natural mixing (60%) ventilation.

Mathematical analysis of heat and mass transport under thermal radiations and dissipation for electrically conducting second-grade fluid

This research deals with heat and mass transport in 2D, steady laminar unidirectional flow of second-grade fluid inside converging/diverging stretchable channel with no slip effects. The similarity equations were engaged for the model development and acquired a model in the form of a joint system of ODEs comprising the innovative effects of thermal radiations, magnetic field and dissipation function. Then, mathematical treatment of the model was done via HAM Package and the results were furnished under the inspiration of physical constraints. It is pointed out that the fluid moves quite slowly in diverging cases than that of converging ones under multiple Re values, whereas magnetic field effects are almost negligible for the velocity profile. The temperature of the fluid can be enlarged by increasing Ec and Pr and Rd is not proven good in this study. Further, as far as the mass transport is concerned, the dominant contribution of Sc is observed for both stretching/shrinking walls.

Anisotropic slip boundary condition for three-dimensional lattice Boltzmann simulations of liquid microflows

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices.

Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme.

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.

Stochastic analysis of the variability of groundwater flow fields in heterogeneous confined aquifers of variable thickness

The problem of flow through heterogeneous confined aquifers of variable thickness is analyzed from a stochastic point of view. The analysis is carried out on the basis of the integrated equations of the depth-averaged hydraulic head and integrated specific discharge, which are developed by integrating the continuity equation and equation for the specific discharge over the thickness, respectively. A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge. However, the closed-form expressions are obtained under the condition of steady unidirectional mean flow in the horizontal plane. In developing stochastic solutions, the input hydraulic conductivity parameter is viewed as a spatial random field characterized by the theoretical spatial covariance function. The evaluation of the closed-form solutions focuses on the influence of the controlling parameters, namely as a geometrical parameter defining the variation of the aquifer thickness and the correlation scale of log hydraulic conductivity, on the variability of the fluid fields. The application of the present stochastic theory to predict the total specific discharge under uncertainty using the field data is also provided.

Electrokinetic energy conversion of fluids with pressure-dependent viscosity in nanofluidic channels

In this paper, electrokinetic flow of Newtonian fluids with pressure-dependent viscosity through a nanoslit is investigated. Under the assumption of unidirectional steady flow, taking the dimensionless pressure-viscosity coefficient ɛ as a small parameter, the asymptotic analytical solutions of velocity and pressure up to second order in ɛ, streaming potential and electrokinetic energy conversion (EKEC) efficiency are obtained based on the assumption that the viscosity has a linear dependence on the pressure in a high pressure. It is shown that the pressure-dependent viscosity slightly enhances the streaming potential and electrokinetic power output in smaller electrokinetic width K, which implies that more output electrical energy can be utilized to an external load. The increase of dimensionless pressure-viscosity coefficient could cause a decrease in electrokinetic energy conversion (EKEC) efficiency. However, it could cause an increase in pressure required to drive the flow. Last, within the given parametric regions, the maximum EKEC efficiency for different pressure-viscosity coefficients obtained is about 14% in present analysis.

Turbulence characteristics of oscillating flow through passive grid

The present work provides the turbulence characteristics of oscillating flow through passive grid under rigid boundary influence by adopting an experimental approach. The oscillations in the steady unidirectional flow were generated by plunger type wave-maker. This study attempts to analyse the turbulent length scales and local Reynolds numbers in order to characterise the different eddy sizes in the oscillating flow environment due to the interaction of grid and rigid boundary. The normalized phase averaged Shannon entropy is also presented to understand the degree of the randomness in oscillating flow environment through the passive grid. Further, to understand the deviation from the isotropic turbulence, the turbulence triangle, Eigen values, and the invariant functions are presented at the downstream of the grid for the three oscillating flow cases.

Approximations for Steady Unidirectional Slip Flows in Elliptic Microchannels

Abstract Consider steady flows in a channel whose cross section Ω is an ellipse, flows with the Navier slip boundary condition. Denote the volume flow rate by Q. We apply to elliptic cross section a recent simple approximation, a rigorous lower bound R on Q, requiring, along with the channel's area and perimeter, the calculation of just the torsional rigidity and two other domain functionals. This avoids the need for solving the partial differential equation repeatedly for differing values of the slip parameter.

ТЕЧЕНИЕ ТИПА КУЭТТА С УЧЕТОМ ИДЕАЛЬНОГО СКОЛЬЖЕНИЯ НА КОНТАКТЕ С ТВЕРДОЙ ПОВЕРХНОСТЬЮ

On the basis of a system of hydrodynamic equations, the unidirectional steady flow of a viscous incompressible fluid in a horizontal extended layer is studied. The solution to the governing equations is discovered in a distinguished class of functions that are linear in coordinates. The contact of the fluid with a lower hydrophobic solid boundary is described by the Navierslip condition. At the upper boundary of the layer, the temperature and pressure fields are assumed to be given, and a zero shear stress is specified. The system of boundary conditions is redefined due to the fact that all conditions for velocities are assigned as their derivatives. Zero flow rate is taken as an additional condition. The obtained exact solution to the boundary value problem is the only possible polynomial solution. The highest (eighth) degree of polynomials corresponds to a solution for background pressure. Analysis of the solution shows that it can describe a multiple stratification of kinetic-force fields. Since the analysis is carried out in a general form (without specifying physical constants that uniquely identify the fluid under study), the obtained results are applicable to viscous fluids of different nature.

Optimal configuration of a tidal current turbine farm in a shallow channel

This study investigates the macroscopic features of tidal farm layouts optimized to maximize power production in an idealized shallow channel with steady unidirectional flow. By varying the number of turbines and optimization constraints, numerical experiments were conducted using OpenTidalFarm, an open-source solver for tidal farm optimization using PDE-constraint gradient-based optimization. To alleviate the computational complexity for identifying a global optimum, a concept of quasi-global optimum was introduced, a local optimum that serves as a global optimum in a crude sense. From extensive numerical results, notable patterns in the shape of the quasi-global optimal layout were observed and explained by a nondimensional parameter, E, the ratio of the shortest hypothetical linear fence to the length of the lateral farm site constraint. The quasi-global optimal layout had a linear fence shape when E ≤ 1. The layout evolved into a downstream-concave parabola and subsequently into a V-shape as E increased beyond 1. Moreover, as more turbines were added to an array, the quasi-global optimal layout was no longer a single fence, and some turbines were separated from the main body. From the quantitative perspective, it is shown that the power production could be increased by up to 50% by tuning the optimization constraints.

Variational Approximations for Steady Unidirectional Slip Flows in Microchannels

Abstract Consider steady flows in a channel, cross section Ω, with the Navier slip boundary condition, and let the volume flowrate be denoted by Q. We present a new simple approximation, a rigorous lower bound on Q, requiring, along with the channel's area and perimeter, the calculation of just the torsional rigidity and two other domain functionals. This avoids the need for solving the partial differential equation repeatedly for differing values of the slip parameter. It also provides the opportunity to give tables for different shapes, requiring, for each shape, just its area and perimeter and the three domain functionals previously mentioned. We expect that for shapes used in practice, the approximation will be good for the entire range of slip parameter. This is illustrated with the case of Ω being rectangular.

Experimental study on the stable morphology and self-attraction effect of subaqueous barchan dunes

The evolutionary process of isolated dunes under the action of a unidirectional steady water flow is recorded from a bottom-up visual angle by optical synchronization imaging measurements. The morphological characteristics of dunes formed from different initial sand pile configurations are analyzed by an image-processing method. Results show that the trend of reproducing the crescent shape of the dune is shown in all sand piles, which is independent of the initial configuration. The triangular initial sand pile is found to be the first to stabilize to a crescent shape, whereas the square initial sand pile takes the longest time to form a stable crescent shape. This finding is essentially due to the shape effect of the triangle, which effectively reduces the amount of transverse moving sand particles. Based on the aspect ratio of the barchan dune that is stable at approximately 1, we determine that the evolution time required for the final stability of barchan dunes reproduced from different initial sand piles is approximately 200 s within the restriction of the present closed-water-tunnel experimental condition. Moreover, a dimensionless comparison of the profile curves of barchan dunes’ stable morphologies reveals a “streamwise–spanwise” dimension of the dune, which essentially synthesizes characteristic information about windward face and two horns. This “streamwise–spanwise” dimension ultimately presents the self-attraction effect of the crescent shape.

Does shear induced demixing resemble a thermodynamically driven instability?

In the present paper, we continue our recent studies on a two-fluid Rolie-Poly approximation of entangled polymer solutions in simple shear flows. We review the existing literature on shear induced demixing (SID) in two-fluid models and highlight the apparent similarities to a thermodynamic model of demixing. Focusing on steady unidirectional simple shear flows driven by a constant applied shear stress, we show that when the frictional drag between solvent and polymer is asymptotically large, our two-fluid model is mathematically equivalent to a thermodynamic model in terms of its long-time concentration dynamics. In particular, we show that SID minimizes a Lyapunov functional L distinct from the system's free energy F. We apply our asymptotic model to make predictions regarding nucleation (finite amplitude instabilities) and coalescence phenomena in SID. Numerical calculations with the full model corroborate the asymptotic model predictions. Finally, we apply the same asymptotic analysis to two flows in which a thermodynamic mapping fails. First, we consider steady simple shear flows driven by a constant boundary velocity (as opposed to a constant boundary stress), wherein the hydrodynamic instability appears to have the same character but can no longer be mapped to an equivalent thermodynamic instability. Second, we consider unsteady simple shear flows driven by an oscillating boundary stress, wherein the nonlinear dynamics of demixing are totally distinct from what a thermodynamic model predicts.In the present paper, we continue our recent studies on a two-fluid Rolie-Poly approximation of entangled polymer solutions in simple shear flows. We review the existing literature on shear induced demixing (SID) in two-fluid models and highlight the apparent similarities to a thermodynamic model of demixing. Focusing on steady unidirectional simple shear flows driven by a constant applied shear stress, we show that when the frictional drag between solvent and polymer is asymptotically large, our two-fluid model is mathematically equivalent to a thermodynamic model in terms of its long-time concentration dynamics. In particular, we show that SID minimizes a Lyapunov functional L distinct from the system's free energy F. We apply our asymptotic model to make predictions regarding nucleation (finite amplitude instabilities) and coalescence phenomena in SID. Numerical calculations with the full model corroborate the asymptotic model predictions. Finally, we apply the same asymptotic analysis to two flows in...

Pressure drop analysis of oscillating flows through a miniature porous regenerator under isothermal and nonisothermal conditions

In this paper, we present an experimental study on the pressure, pressure drop, velocity and friction factor in a regenerator made from an array of pillars in reciprocating flow conditions. The fluid used in the experiment is air. We show that the pressure drop depends on the porosity, frequency and stroke. We observe a phase shift between the crank angle sinusoidal variation of the piston and the pressure variation that increases with frequency. We also observe that the instantaneous friction factor is higher in the discharge phase than in the suction phase, and higher in the acceleration than in the deceleration phase. Friction factor in oscillating flow appears to be higher than friction factor in steady unidirectional flow for the highest porosity. For the lower porosities, we observe that the pressure drop and friction factors are similar for maximum Reynolds numbers lower than 5000. An experimental correlation for the friction factor of the regenerator is derived in order to design a millimetric Stirling engine. The friction factor is compared with friction factors reported for woven screens, metal felts and involute foil regenerators.

Combined particle image velocimetry/digital image correlation for load estimation

Particle image velocimetry (PIV) and digital image correlation (DIC) are widely used experimental techniques in fluid mechanics and structural dynamics, respectively. PIV is capable of resolving detailed velocity fields around structures, from which the hydrodynamic loading can be reconstructed. However, PIV is ill-suited to capturing the structural response, which is critical for a complete understanding of the bidirectional coupling between the fluid flow and the structural dynamics. On the other hand, DIC can accurately quantify local deformation of the structure, but does not afford the precise identification of the hydrodynamic loading due to the ill-posed nature of the inverse load estimation process. Here, we explore the feasibility of a combined PIV/DIC technique for the investigation of fluid-structure interactions. Specifically, we study fluid-structure interactions associated with a flexible cantilever plate immersed in a steady unidirectional flow. We demonstrate that the combination of pressure estimation from PIV and deformation measurement through DIC enables the precise identification of the hydrodynamic loading and structural response. The proposed methodology may help in improving our understanding of a number of fluid-structure interaction problems, such as biomimetic propulsion, aeroelasticity of airfoils, and hydrodynamic impact on marine structures.

Rivulet flow of generalized Newtonian fluids

Steady unidirectional gravity-driven flow of a uniform thin rivulet (i.e. a rivulet with small transverse aspect ratio) of a generalised Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the shear rate, and the explicit solution for any generalised Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behaviour of these two fluids. In addition, the general behaviour of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux, as well as the behaviour of rivulets of strongly shear-thinning Carreau and Ellis fluids, are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three non-dimensional parameters and of an Ellis fluid on two of its three non-dimensional parameters leads to the expected dependence of the behaviour of the rivulet on these parameters (namely that increasing the viscosity of the fluid leads to a larger rivulet), the non-monotonic dependence of the viscosity of an Ellis fluid on the non dimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behaviour of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shear-thinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of non-zero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a non-constant power-law viscosity, leading to a plug-like velocity profile with large magnitude in the narrow central region of the rivulet.

Fluid shear stress regulates the expression of Lectin-like oxidized low density lipoprotein receptor-1 via KLF2-AP-1 pathway depending on its intensity and pattern in endothelial cells

Background and aimsVascular endothelial cells (ECs) are exposed to fluid shear stress (FSS), which modulates vascular pathophysiology. Lectin-like oxidized low-density lipoprotein receptor-1 (LOX-1) is crucial in endothelial dysfunction and atherosclerosis. We elucidated the mechanism regulating LOX-1 expression in ECs by FSS. MethodsHuman umbilical vein endothelial cells were exposed to laminar shear stress (LSS) of indicated intensities using a unidirectional steady flow, or to oscillatory shear stress (OSS) using a bidirectional disturbed flow. In vivo studies were performed in a mouse model of partial carotid ligation and human pulmonary artery sections. ResultsWithin ECs, OSS upregulated LOX-1 expression, while LSS (20 dyne/cm2) downregulated it. We confirmed that OSS-induced LOX-1 expression was suppressed when the mechanotransduction was inhibited by knockdown of the mechanosensory complex. In addition, we demonstrated that Kruppel-like factor 2 (KLF2) has an inhibitory role on OSS-induced LOX-1 expression. Next, we determined that activator protein-1 (AP-1) was the key transcription factor inducing LOX-1 expression by OSS, which was inhibited by KLF2 overexpression. To explore whether the intensity of LSS affects LOX-1 expression, we tested three different intensities (20, 60, and 120 dyne/cm2) of LSS. We observed higher LOX-1 expression with high shear stresses of 120 dyne/cm2 compared to 20 and 60 dyne/cm2, with OSS-like KLF2-AP-1 signaling patterns. Furthermore, ECs within disturbed flow regions showed upregulated LOX-1 expression in vivo. ConclusionsWe concluded that LOX-1 expression on ECs is regulated via FSS depending on its intensity as well as pattern. Furthermore, this is mediated through the KLF2-AP1 pathway of mechanotransduction.

Microfluidic flow actuation using magnetoactive suspensions

The rheological behavior of magnetotactic bacterial suspensions is analyzed using a continuum kinetic theory. In both unbounded and confined geometries, the response of these suspensions under simple external flows can be controlled by applying a magnetic field and hinges in a subtle way on the interplay of magnetic alignment, rotation under shear, and wall-induced accumulation under confinement. By tuning magnetic field strength and direction, the apparent viscosity can either be enhanced or reduced, and the mechanisms for these trends are elucidated. In the absence of any applied flow, we further demonstrate the ability of magnetoactive suspensions to internally drive steady unidirectional flows upon application of a magnetic field, thus suggesting novel avenues for the design of microfluidic pumps and flow actuation devices.