Unsteady Viscous Flow Research Articles

A Multichamber Pulsating-Flow Device With Optimized Spatial Shear Stress and Pressure for Endothelial Cell Testing.

Design and analysis are presented for a new device to test the response of endothelial cells to the simultaneous action of cyclic shear stresses and pressure fluctuations. The design consists of four pulsatile-flow chambers connected in series, where shear stress is identical in all four chambers and pressure amplitude decreases in successive chambers. Each flow chamber is bounded above and below by two parallel plates separated by a small gap. The design of the chamber planform must ensure that cells within the testing region experience spatially uniform time-periodic shear stress. For conditions typically encountered in applications, the viscous unsteady flow exhibits order-unity values of the associated Womersley number. The corresponding solution to the unsteady lubrication problem, with general nonsinusoidal flowrate, is formulated in terms of a stream function satisfying Laplace's equation, which can be integrated numerically to determine the spatial distribution of shear stresses for chambers of general planform. The results are used to optimize the design of a device with a hexagonal planform. Accompanying experiments using particle tracking velocimetry (PTV) in a fabricated chamber were conducted to validate theoretical predictions. Pressure readings indicate that intrachamber pressure variations associated with viscous pressure losses and acoustic fluctuations are relatively small, so that all cells in a given testing region experience nearly equal pressure forces.

Study on the integrated self-priming process of a vehicle-mounted self-priming pump

In order to explore the self-priming characteristics of the self-priming pump at the mobile pump truck, this paper established a complete three-dimensional circulatory piping system including the self-priming pump, tank, valves, inlet pipe and outlet pipe. The UDF(User Defined Functions) was used to realize the acceleration-constant speed operation process of the impeller, thus reflecting the actual changing state of the rotational speed. Based on the VOF(Volume Of Fluid) multiphase flow model and the Realizable k-ε turbulence model, a coupled numerical calculation of unsteady incompressible viscous flow was conducted for its self-priming process. The results show that the self-priming process of the pump can be roughly divided into four stages: the rapid suction stage, the shock exhaust stage, the rapid exhaust period and the pump residual gas discharge stage. The proportion of each stage in the total self-priming time showed an increasing trend. During the rapid suction stage, the water level in the vertical section of the inlet pipe showed a slow and then fast-rising pattern. During the shock exhaust stage, the average gas-phase volume fraction in the volute is lower than that of the impeller, and the gas content at the volute outlet is lower than that of the impeller inlet. The region at the inlet and outer edge of the impeller consistently experience significant energy losses.

A high‐order pure streamfunction method in general curvilinear coordinates for unsteady incompressible viscous flow with complex geometry

AbstractIn this paper, a high‐order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier‐Stokes equations. By constructing the fourth‐order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth‐order mixed derivative terms, and applying a Crank‐Nicolson scheme for the second‐order temporal discretization, we extend the unsteady high‐order pure streamfunction algorithm to flow problems with more general non‐conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von‐Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non‐conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.

Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis

The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

An R-adaptive algorithm based on self-organizing maps for solving incompressible flows with high-order discontinuous Galerkin methods

Mesh quality is critical for the numerical accuracy of CFD (Computational Fluid Dynamics). Although various techniques have been developed to improve mesh applicability to complex flows, r-adaptive methods have received far too little attention. This paper introduces an r-adaptive algorithm based on the self-organizing maps (SOM) of Kohonen and applies it to unsteady CFD applications using the Discontinuous Galerkin (DG) method. Inspired by the properties of the DG method, the numerical discontinuity over the element interface is quantified as an adaptation indicator. The method requires only one adaptation, followed by solution projection onto the new mesh to save computational costs in unsteady cases. A significant advantage of this method is its higher efficiency without solving complex equations during the adaptation. The performance of the developed mesh adaptation algorithm is tested on the steady laminar viscous flow past a circular cylinder at Re=40 and the unsteady laminar viscous flow past a circular cylinder at Re=100 and two circular cylinders in a side-by-side arrangement at Re=200. Significant improvements in flow contours and coefficients are obtained after adaptation.

BE-BDF2 Time Integration Scheme Equipped with Richardson Extrapolation for Unsteady Compressible Flows

In this work we investigate the effectiveness of the Backward Euler-Backward Differentiation Formula (BE-BDF2) in solving unsteady compressible inviscid and viscous flows. Furthermore, to improve its accuracy and its order of convergence, we have equipped this time integration method with the Richardson Extrapolation (RE) technique. The BE-BDF2 scheme is a second-order accurate, A-stable, L-stable and self-starting scheme. It has two stages: the first one is the simple Backward Euler (BE) and the second one is a second-order Backward Differentiation Formula (BDF2) that uses an intermediate and a past solution. The RE is a very simple and powerful technique that can be used to increase the order of accuracy of any approximation process by eliminating the lowest order error term(s) from its asymptotic error expansion. The spatial approximation of the governing Navier–Stokes equations is performed with a high-order accurate discontinuous Galerkin (dG) method. The presented numerical results for canonical test cases, i.e., the isentropic convecting vortex and the unsteady vortex shedding behind a circular cylinder, aim to assess the performance of the BE-BDF2 scheme, in its standard version and equipped with RE, by comparing it with the ones obtained by using more classical methods, like the BDF2, the second-order accurate Crank–Nicolson (CN2) and the explicit third-order accurate Strong Stability Preserving Runge–Kutta scheme (SSP-RK3).

Numerical Assessment of the Resistance of a Solar Catamaran in Shallow Water

In this paper, a numerical assessment of the effect of shallow water on the total resistance of the solar catamaran SolarCat is carried out using computational fluid dynamics within the software package STAR–CCM+. The unsteady viscous fluid flow was modelled based on the Reynolds-averaged Navier–Stokes (RANS) equations with the application of the k−ω SST (k−ω Shear Stress Transport) turbulence model. The RANS equations were discretized by the finite volume method, and the position of the free surface is determined by the volume of fluid method. In shallow water conditions, a mesh morphing algorithm is applied. Numerical simulations were carried out for the deep water and limited depths corresponding to h/T=7.6, h/T=4, and h/T=2 at two speeds. The verification study was carried out and the total numerical uncertainty was calculated for the total resistance and sinkage of the catamaran. A detailed analysis of the flow around the catamaran was carried out.

Mathematical inspection of heat transfer and unsteady viscous flow in a tunnel with trapezoidal shaped slender wall

An exploration is made to investigate numerically and theoretically the time dependent flow of blood along with heat transfer through abnormal artery having trapezoidal shaped plaque. The flow is taken to be Newtonian, laminar, unsteady and incompressible. A suitable geometrical model is constructed to simulate the trapezoidal stenosis affected artery. The governed 2-dimensional momentum and heat transfer equations are conventionalized by assuming mild trapezoidal stenosis. The renovate partial differential equations are further converted into ordinary differential equations by assist of transformations. The novelty of the work is to consider unsteady blood flow through trapezoidal shape stenosed artery. A technique of finite difference is used to discretize the updated dimensionless model numerically. Comprehensive graphical outcomes for a flow of blood are obtained. The effect of trapezoidal plaque on blood velocity, pressure and temperature are shown by surface graph inside the artery and also shown with the help of line graph.

The acceleration effect of pump as turbine system during starting period

In order to reveal the influence of starting acceleration on starting process of a pump as turbine system, this paper carries out a numerical calculation of the three-dimensional viscous unsteady flow of pump as turbine circulating piping system under three starting acceleration conditions, and obtains the external and internal flow characteristics of each overflow component during the starting process, and also analyzes the energy loss of each component in the piping system in depth with the help of entropy production method and Q criterion method. The results show that during system start-up, the flow rate and outlet static pressure curves of the pump as turbine are hysteresis relative to the rotational speed, the head curve is similar to a linear rise during slow and medium speed start-up, while it shows a parabolic rise during rapid start-up, the entropy production and vorticity in the impeller domain of the pump as turbine are mainly distributed between the blades, and the distribution decreases during start-up. In addition, the pump similarity law does not apply to the performance prediction during the transient start of the pump as turbine.

Numerical simulation and regression analysis of MHD dissipative and radiative flow of a Casson nanofluid with Hall effects

The magnetohydrodynamic (MHD) flow of Casson nanofluid has several applications in engineering and medical processes. The present research work is performed to examine the unsteady viscous dissipative and radiative flow of a Casson nanofluid over a stretching sheet under the influence of a transverse magnetic field with a view to highlight the impact of Hall current. The mathematical model comprising of nonlinear coupled PDE is transformed into a set of coupled ODEs using appropriate similarity transformation. The reduced mathematical model in a similar form is then solved by adopting the successive linearization method (SLM). The residual analysis is used to validate the solutions. A parametric study is performed to inquire about the impacts of Hall current, nonlinear thermal radiation, viscous dissipation, and other pertinent flow parameters such as temperature ratio, Brownian movement, thermophoresis on the nanofluid velocities, temperature, and concentration. The effects of pertinent flow parameters are also examined on the skin-friction coefficients, Nusselt number, and Sherwood number. A quadratic regression analysis is presented to estimate the skin-friction coefficient and Nusselt number for different values of effecting parameters. Results reveal that the increasing values of Casson parameter decrease the fluid velocity and temperature, whereas a converse trend is detected in concentration profile, rate of heat transfer and mass transfer.

On the Unsteady Rotationally Symmetric Flow Between a Stationary and a Finite Rotating Disk With a Given Change in the Axial Velocity

Abstract We consider the scenario of an unsteady viscous flow between two coaxial finite disks, one stationary and the other rotating with an axial velocity changing impulsively from zero to a constant value. The three-dimensional (3D) incompressible Navier–Stokes equations are analytically solved by postulating the polynomial profiles for the axial and circumferential velocity components and by employing the open-end condition of zero pressure difference and an integral approach. It is shown that the time-dependent squeezing of the fluid between the disks and the edge effects of the finite open-ended disks in the flow domain are determined by the compressing Reynolds number and the rotating Reynolds number for the case of laminar flow at low Reynolds numbers and small aspect ratios. The general explicit formulae are derived for the velocity and pressure distributions as a function of the compressing and rotating Reynolds numbers in this unsteady flow process (and the steady-state solutions are then obtainable as the compressing Reynolds number vanishes). A simple theoretical relationship between the radial and axial pressure gradients is deduced to hinge the radial and circumferential velocity components together. The values of the compression and rotation Reynolds numbers suitable to this theory are also suggested for the problem of rotating disk flows at low Reynolds numbers. The validity of the theoretical predictions for the circumferential, radial, and axial velocity components is partially verified through comparison with previous steady experimental and numerical results. These analytical results have the immediate engineering applications of fluid flows with varying gap widths, including wet brakes, wet clutches, hydrostatic bearings, face seals, and rotating heat exchangers.

A GPU-based 2D viscous flow model with variable density and heat exchange

Numerical simulation of unsteady viscous flow over variable topography under the influence of temperature changes is a challenge. In order to apply the model to large domains with complex topography, it becomes mandatory to reduce the model complexity from 3D to 2D by depth averaging the equations and to apply massive parallelization techniques for an efficient simulation. The depth averaged mass continuity, momentum and internal energy equations, combined with suitable friction laws, can be used for this type of flows. Variations in temperature can be accounted for from internal energy changes with density changing accordingly. The resulting system is solved using a finite volume technique on unstructured triangular grids well suited for problems over variable topography. A generic model applicable to a wide range of viscous fluids and validated with synthetic cases is presented to evaluate the performance of the numerical solution in presence of both external thermal forcing functions and discontinuous initial conditions. Finally, the model is applied to a realistic application and calibration to a particular case of lava flow taking into consideration variable density, viscosity and yield stress with temperature . A heat transfer with the air is included to consider the lava cooling. The numerical results of the lava front advance are compared to the Copernicus satellite observations at different dates. The efficiency of the GPU implementation allows to simulate a 11 day event in less than 1.7 h of simulation.

Using boundary-layer coordinates to compute unsteady laminar two-dimensional viscous and convective flows

In this paper, the use of boundary-layer coordinates to compute various unsteady laminar two-dimensional viscous flows is discussed. Three illustrative examples are provided, including flow around a corner, free convective flow from a heated corner, and mixed convective vortex flow. A numerical solution procedure to solve the transformed equations is also outlined. Various results and comparisons are presented and discussed. Good agreement is found with well-known documented studies.

Electro-osmosis modulated periodic membrane pumping flow and particle motion with magnetic field effects

Theoretical studies of micro-electro-mechanical systems provide important insight into the mechanisms and optimization of such devices for a range of applications, including biomedical and chemical engineering. Inspired by emerging applications of microfluidics, unsteady viscous flow in a microchannel with periodic membrane pumping modulated by electro-magnetohydrodynamics is analyzed in a mathematical framework. The membrane kinematics induces the pressure inside the microchannel, where an electric field enhances the capability of the pumping flow rate. This model is formulated based on the Navier–Stokes equations, the Poisson equation, and the Maxwell electromagnetic equations and is further simplified using the lubrication approximations and Debye–Hückel linearization. The transformed dimensionless conservation equations under appropriate boundary conditions are analytically solved and the graphical results are illustrated through MATLAB (2019b) software. From the computational results, it is found that the Hartmann number enhances the fluid pressure uniformly throughout the microchannel, while the electric field parameter enforces the direction of the pressure-driven flow. The time-averaged flow rate exhibits a linear decay with axial pressure gradient, and it is strongly elevated with electric field parameter whereas it is weakly increased with electric double layer thickness parameter. It is further observed that the fluid is driven unidirectionally by the membrane contractions via a particle tracking simulation method. This study is relevant to provide the parametric estimation in designing the magnetic field-based microfluidics devices for microlevel transport phenomena.

Dual Solution with Heat Transfer through Moving Porous Plate of an Unsteady Incompressible Viscous Fluid

We examine graphically the behavior of the dual solution of an unsteady incompressible viscous flow with heat transfer due to a moving porous surface. The mathematical model is developed with the implementation of conservation laws which are then tackled numerically, and the simulations are performed through the Keller–Box technique. Application of the Keller–Box technique allows the non-linear differential equations to transform to a scheme of linear differential equations which are easier to illuminate. Outcomes of velocity and thermal behavior are shown graphically for certain values of the dimensionless parameters. It is obvious from the results that temperature of fluid decreases with the increasing values of dimensionless Prandtl number Pr, whereas the velocity enhances for blowing situations.

Weighted Moving Square-Based Solver for Unsteady Incompressible Laminar Flow Simulations

For computational fluid dynamics simulations, grid systems are generally used in the Eulerian frame for both structured and unstructured grids and solvers designed for the chosen grid systems. In contrast to the grid-based method, in which the connection information with neighboring grids must be maintained, gridless methods do not require an underlying connectivity in the form of control volumes or elements. Hence, gridless methods are feasible and robust for the problems with moving boundary and/or complicated boundary shapes. In this study, a Eulerian gridless solver is proposed, and its application for simulating two-dimensional unsteady viscous flows in low Reynolds number regions is investigated. The solver utilizes the weighted moving square method to obtain the spatial derivatives of the governing equations and solve the pressure Poisson equation iteratively. Simple remedies to satisfy the boundary conditions in the finite difference method are applied. The fractional step method with the second-order Adams–Bashforth method is used for time integration. Some benchmark problems were solved using the developed solver, and the results were compared with those of other experimental and computational methods. Good agreement with the results of other methods confirmed the validity of the proposed solver.

Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects

The present study examines the impact of unsteady viscous flow in a squeezing channel. Silver–gold hybrid nanofluid particles with different shapes are inserted in the base fluid engine oil. Flow and heat transfer mechanism is detected in the presence of magnetohydrodynamics between the two parallel infinite plates. The thermal conductivity models, that is, Yamada–Ota and Hamilton–Crosser models are used to investigate various shapes (Blade, platelet, cylinder, and brick) of hybrid nanoparticles. The model is made up of paired high nonlinear partial differential equations that are then transformed into ordinary differential equations which are coupled and strong nonlinear using the boundary layer approximation. The MATLAB solver bvp4c package is used to solve the numerical solution of this coupled system. The influence of different parameters on the physical quantities is addressed via graphs. A comparison with already reported results is given in order to confirm the current findings. The analysis shows that surprisingly the Yamada–Ota model of the Hybrid nanofluid gains high temperature and velocity profile than the Hamilton–Crosser model of the hybrid nanofluid. Also, both the models show increasing trends toward increasing the volume fraction rate of silver‐gold hybrid nanoparticles. It is also inferred that the hybrid‐nanoparticles performance is far better than the common nanofluids.

Numerical and Experimental Analysis of Transient Flow Field and Pressure Pulsations of an Axial-Flow Pump Considering the Pump–Pipeline Interaction

The internal flow in a vertical axial-flow pump is a complex unsteady three-dimensional viscous flow. An unstable flow often produces complex flow phenomena such as flow separation, vortices, and secondary reflux, which reduces the operating efficiency of the pump and can endanger safety and stability. In this paper, computational fluid dynamics is used to calculate the flow characteristics in an axial-flow pump using the shear stress transport and curvature correction (SST-CC) model for turbulence modified to account for the rotational curvature. Furthermore, the dependability of the numerical results was confirmed by a test with an actual model of a pump. The transient deviation angle at the impeller inlet of the pump, the stream field attributes in various spanwise parts of the impeller and guide vane, and the velocity distributions at the impeller inlet and outlet were analyzed. The omega method was utilized to recognize the vortex structure inside the guide vane. Moreover, the development of the transient vortex structure inside the guide vane was studied. As the flow rate increased, the scale and turbulent kinetic energy of the vortex structure gradually decreased. The time-domain graph for the impeller inlet is clearly periodic, with three peaks and three troughs in an impeller rotational period. The dominant frequency in the spectrum at each monitoring point was basically the blade frequency, and the secondary dominant frequency was twice the blade frequency.

ОПРЕДЕЛЕНИЕ ГИДРОДИНАМИЧЕСКИХ СИЛ, ДЕЙСТВУЮЩИХ НА ТЕЛО В НЕСТАЦИОНАРНОМ ПОТОКЕ, ПО ХАРАКТЕРИСТИКАМ ТЕЧЕНИЯ НА УДАЛЕННОЙ КОНТРОЛЬНОЙ ПОВЕРХНОСТИ

ОПРЕДЕЛЕНИЕ ГИДРОДИНАМИЧЕСКИХ СИЛ, ДЕЙСТВУЮЩИХ НА ТЕЛО В НЕСТАЦИОНАРНОМ ПОТОКЕ, ПО ХАРАКТЕРИСТИКАМ ТЕЧЕНИЯ НА УДАЛЕННОЙ КОНТРОЛЬНОЙ ПОВЕРХНОСТИ

Shape effect of Cu, Al2O3 and TiO2 nanoparticles on stagnation point nanofluid flow in a microgravity environment

The unsteady viscous nanofluid flow near a three-dimensional stagnation point was studied numerically under microgravity environment. g-Jitter is one of the effects occurs under microgravity environment that producing a fluctuating gravitational field. Three different types of nanoparticles were induced in the study that is copper (Cu), alumina (Al2O3), and titania (TiO2) which then produce a water-based typed of nanofluid. In addition, different shape of nanoparticle was applied on the study in analyzing the performance of each types of nanoparticle. The fluid system was then mathematically formulated into a system of partial differential equation based on physical law and principle such as conservation of mass, Newton’s second law and conservation of energy. The system of equation then undergoes semi-similar transformation technique in reducing the complexity of the problem into non dimensionless form. Keller box method was applied into the dimensionless system of equations in solving the problem numerically. The problem was analyzed in term of velocity and temperature profiles together with skin friction coefficient and Nusselt number. The results shown that temperature profile, skin friction coefficient and Nusselt number were increase while velocity profile decreased as nanoparticle volume fraction decreased. The results indicated that, the needle-shaped nanoparticles give the highest enhancement on the heat transfer of the nanofluid compared to sphere and disk-shaped nanoparticles with more than 14% significant different. In addition, alumina hold the highest velocity profile while copper hold the lowest velocity profile.