Longitudinal Pressure Gradient Research Articles

On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions

We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.

Subtidal hydrodynamics in a tropical lagoon: A dimensionless numbers approach

Observations in a tropical lagoon of the Yucatan peninsula motivated a non-dimensional number analysis to examine the relative influence of tidal stress, density gradients and wind stress on subtidal hydrodynamics. A two-month observation period in Chelem Lagoon covered the transition from the dry to the wet season. Chelem Lagoon is influenced by groundwater inputs and exhibits a main sub-basin (central sub-basin), a west sub-basin and an east sub-basin. Subtidal hydrodynamics were associated with horizontal density gradients that were modified seasonally by evaporation, precipitation, and groundwater discharge. A tidal Froude number (Fr0), a Wedderburn number (W), and a Stress ratio (S0) were used to diagnose the relative importance of dominant subtidal driving forces. The Froude number (Fr0) compares tidal forcing and baroclinic forcing through the ratio of tidal stress to longitudinal baroclinic pressure gradient. The Wedderburn number (W) relates wind stress to baroclinicity. The stress ratio (S0) sizes tidal stress and wind stress. S0 is a new diagnostic tool for systems influenced by tides and winds, and represents the main contribution of this research. Results show that spring-tide subtidal flows in the tropical lagoon had log(Fr0)≫0 and log(S0)>0, i.e., driven mainly by tidal stresses (advective accelerations). Neap tides showed log(Fr0)≪0 and log(S0)<0), i.e., flows driven by baroclinicity, especially at the lagoon heads of the east and west sub-basins. However, when the wind stress intensified over the lagoon, the relative importance of baroclinicity decreased and the wind stress controlled the dynamics (log(W)≫0). Each sub-basin exhibited a different subtidal response, according to the dimensionless numbers. The response depended on the fortnightly tidal cycle, the location and magnitude of groundwater input, and the direction and magnitude of the wind stress.

Numerical modeling of Stokes flows over a superhydrophobic surface containing gas bubbles

This paper continues the numerical modeling of Stokes flows near cavities of a superhydrophobic surface, occupied by gas bubbles, based on the Boundary Element Method (BEM). The aim of the present study is to estimate the friction reduction (pressure drop) in a microchannel with a bottom superhydrophobic surface, the texture of which is formed by a periodic system of striped rectangular microcavities containing compressible gas bubbles. The model proposed takes into account the streamwise variation of the bubble shift into the cavities, caused by the longitudinal pressure gradient in the channel flow. The solution for the macroscopic (averaged) flow in the microchannel, constructed using an effective slip boundary condition on the superhydrophobic bottom wall, is matched with the solution of the Stokes problem at the microscale of a single cavity containing a gas bubble. The 2D Stokes problems of fluid flow over single cavities containing curved phase interfaces with the condition of zero shear stress are reduced to the boundary integral equations which are solved using the BEM method.

A parametric study on the influence of boundary conditions on the longitudinal pressure gradient in CFD simulations of an automotive wind tunnel

Computational fluid dynamics (CFD) is an important and extensively used tool for aerodynamic development in the vehicle industry today. Validation of virtual methods by comparison to wind tunnel experiments is a must because manufacturers aim to substitute physical tests on prototype vehicles with virtual simulations. An appropriate validation can be performed only if the wind tunnel geometry with representative boundary conditions is included in the numerical simulation, and if the flow of the empty wind tunnel is accurately predicted. One of the important flow parameters to predict is the longitudinal pressure distribution in the test section, which is dependent on both the wind tunnel geometry and the settings of the boundary layer control systems. This study investigates the effects of flow angularity at the inlet and different boundary layer control systems, namely, basic scoop suction, distributed suction, and moving belts, on the longitudinal pressure distribution in the full-scale aerodynamic wind tunnel of Volvo Cars using CFD and a systematic design of experiments approach. The study shows that the different suction systems used to reduce boundary layer thickness upstream of the vehicle have statistically significant effects on the longitudinal pressure distribution in the test section. However, the estimated drag difference induced on a typical vehicle by the difference in horizontal buoyancy between the tested settings is within the test-to-test uncertainty of the physical wind tunnel, thereby leading to the conclusion that force calculations in simulations are fairly insensitive to the tested parameters on the investigated intervals.

Application of the method of near-wall boundary conditions to an investigation of turbulent flows with longitudinal pressure gradients

The dynamic and thermal characteristics of steady near-wall boundary layers in flow deceleration regions are studied on the basis of differential turbulencemodels. The method of transferring the boundary conditions from the wall into the flow is tested for flows with variable longitudinal pressure gradients. Using differential turbulence models in the transition and low-Reynolds-number regions near surfaces the effect of the parameters of highly turbulent free stream on the development of dynamic processes in the developed turbulent boundary layer in the flow deceleration region is studied. The calculated profiles of the velocity, the kinetic energy of turbulence, the friction and thermal conductivity coefficients, and the temperature factor are compared with the experimental data in the cases in which the boundary conditions are preassigned both on the wall and in the flow. The effect of an intermediate boundary condition on the results of the calculations is analyzed.

Research on deposition rate of TiZrV/Pd film by DC magnetron sputtering method

An accelerator storage ring needs clean ultra-high vacuum. A TiZrV non-evaporable getter (NEG) film deposited on interior walls of the chamber can realize distributed pumping, effective vacuum improvement and reduced longitudinal pressure gradient. But accumulation of pollutants such as N2 and O2 will decrease the adsorption ability of the NEG, leading to a reduction of NEG lifetime. Therefore, an NEG thin film coated with a layer of Pd, which has high diffusion rate and absorption ability for H2, can extend the service life of NEG and improve the pumping rate of H2 as well. In this paper, with argon as discharge gas, a magnetron sputtering method is adopted to prepare TiZrV-Pd films in a long straight pipe. By SEM measurement, deposition rates of TiZrV-Pd films are analyzed under different deposition parameters, such as magnetic field strength, gas flow rate, discharge current, discharge voltage and working pressure. By comparing the experimental results with the simulation results based on Sigmund’s theory, the Pd deposition rate C can be estimated by the sputtered depth.

Metachronal wave analysis for non-Newtonian fluid inside a symmetrical channel with ciliated walls

The main purpose of this article is to present a metachronal wave analysis for non-Newtonian fluid inside a symmetrical channel with ciliated walls. The governing equations of Sisko fluid for the two dimensional channel are simplified using the low Reynolds number and long wave-length approximations. Using the Homotopy perturbation method the reduced equations are solved for longitudinal velocity. Solutions are represented through graphs. Outcomes for the longitudinal velocity, pressure gradient, pressure rise and stream lines are analyzed graphically.

Heat transfer behind the backward-facing step under the influence of longitudinal pressure gradient

Results of an experimental and numerical study of the flow structure and turbulent heat transfer in a rectangular channel with longitudinal pressure gradient behind the backward-facing step. With the channel expansion the angle of rotation of the upper wall is 1.43; 2.86 and 4°, and with the channel convergence the rotation angle is 3; 5.7 and 7.6°. Experiments are carried out at Reynolds numbers, calculated on the step height and velocity in front of the backward-facing step, Re H = 4 000; 8 000; 12 000. It was determined, with the increase of pressure gradient the maximum value of Nusselt number increases for the converging channel and decreases for the expanding channel.

Physiological Flow of Jeffrey Six Constant Fluid Model due to Ciliary Motion

The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. Bk is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. in the history, the viscous-dissipation effect is usually represented by the Brinkman number.

Triple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness element

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number ($\mathit{Re}$) is large, we performed the Navier–Stokes calculations at $\mathit{Re}=4\times 10^{5}$ based on the distance of the roughness element from the leading edge of the flat plate. This $\mathit{Re}$ is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number $\mathit{Ma}_{\infty }=0.5$ and $\mathit{Ma}_{\infty }=0.87$. We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.

Analysis and characterization of ramp flow separation

Two-dimensional separation on 25°-ramp is studied experimentally in closed-loop wind tunnel. The analysis of the flow conditions and the separation is based on wall pressure distribution, velocity fields obtained by 2D-2C PIV measurements, and velocity profiles obtained by 2C LDV measurements. The boundary layer upstream and downstream the ramp is characterized. To control the longitudinal pressure gradient, a trailing edge flap is used and the flap angle effects are studied. When the flap angle is equal to +7.5°, the flow around leading edge is symmetric, but the separation is 3D. For the case where the flap is not slanted (0°), the separation is 2D. Proper orthogonal decomposition is used to characterize the separation unsteadiness.

Heat transfer analysis of bi-viscous ciliary motion fluid

The impulsion system of cilia motion is deliberated by biviscosity fluid model. The problem of two-dimensional motion of biviscosity fluid privileged in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolute by the supremacy of viscous effects above inertial possessions by the long-wavelength and low Reynolds approximation. Closed-form solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the biviscosity are also premeditated. The flow possessions for the biviscosity fluid resolute as a function of the cilia and metachronal wave velocity.

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Self-similar flows of an incompressible fluid in a turbulent boundary layer, when the free-stream velocity is a power function (with the exponent m) of the longitudinal coordinate, have been studied. It has been shown that there are four different self-similar flow regimes corresponding to four individual similarity parameters one of which is the known Clauser parameter and the three other parameters have been established for the first time. At adverse pressure gradient, when the exponent m lies in a certain range depending on Reynolds number, the problem has two solutions with different values of the boundary-layer thickness and skin friction; consequently, hysteresis in a pre-separation flow is possible. Separation occurs not at the minimal value of m that corresponds to the strongest adverse pressure gradient, but at m = −0.216 −0.4 Rep−1/3 + O(Rep−2/3), where Rep is the Reynolds number based on longitudinal pressure gradient. The theoretical results are in good agreement with experimental data.

Development of correlations for the flow of agricultural residues as slurries in pipes for Bio-refining

Pipeline hydrotransport of agricultural residue in a carrier liquid could be an economically viable alternative to replace truck delivery of biomass materials, as well as encouraging the increase in scale of bio-refineries. The feasibility of this concept, together with friction loss behaviour and corresponding mechanisms of biomass slurry flows through pipelines, was previously studied by the authors. A 50 mm diameter, 25 m long pipeline facility was used to measure the longitudinal pressure gradient of wheat straw and corn stover slurries over a range of particle dimensions, slurry solid mass fractions, and slurry velocities. Econometric software and a nonlinear least square regression model were used to analyse the measured pressure gradients and an empirical correlation was proposed to predict slurry pressure gradients as a function of slurry specifications and operating conditions. The correlation was then modified using scale-up methods to account for the effects of pipe diameter. The pressure gradient was found to be proportional to the pipe diameter to the power of −1.2. The final correlation was able to predict the longitudinal pressure gradient of the flow of agricultural residues (i.e., non-wood fibres) as biomass slurries in pipes and, with a small uncertainty (<10%), could be applied to design commercial pipelines to hydraulically transport various agricultural residue biomass slurries. This knowledge of the slurry flow pressure gradient is essential to specify slurry pumps, determine the number of booster stations, and estimate the capital and operational costs of a slurry pipeline. • Slurries of agricultural residue biomass were pumped into a closed-circuit pipeline. • Slurry longitudinal friction losses in the pipe were measured over a range of variables. • Econometric software and an NLS regression model were used to analyse measurements. • An empirical correlation was developed based on measurements and scale-up methods. • An empirical correlation can predict slurry pressure drop for all sizes of pipes.

Hall effects on peristaltic flow of couple stress fluid in an inclined asymmetric channel

Effect of Hall current on peristaltic transport of couple stress fluid in an inclined asymmetric channel is investigated. An incompressible fluid is conducting in the presence of inclined magnetic field. Problem formulation is developed through heat and mass transfer aspects. Soret and Dufour effects are present. Long wavelength and low Reynolds number approaches are adopted. Closed form expression for longitudinal velocity, pressure gradient, temperature and concentration are presented. Important results reflecting the influence of embedded parameters in the problems have been pointed out. Pumping and trapping phenomena are especially focused.

Metachronal beating of cilia under influence of Hartmann layer and heat transfer

The propulsion system of cilia motion is investigated considering a viscous fluid model. The problem of the two-dimensional fluid motion in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolved by the supremacy of viscosity effects over inertial control by the long-wavelength and low-Reynolds-number approximation. Exact solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the flow parameters are also predicted. The flow possessions for the viscous fluid are solved as a function of the cilia and metachronal wave velocity.

Enhanced diffusion for oscillatory viscoelastic flow

This paper examines the enhanced axial solute dispersion of a linear viscoelastic fluid, subjected to a longitudinal pressure gradient sinusoidal oscillation, in a duct between parallel walls. The viscoelastic fluid follows the material law of the Jeffrey fluid. An extension of Watson’s theory, developed in 1983, is used to solve the problem analytically. The diffusivity enhancement results are shown in dimensionless form and are presented as functions of the dimensionless group β = h(2ω/ν)1/2 as defined by Watson, the dimensionless retardation time, and the Schmidt, elasticity, and Euler dimensionless numbers. This paper compares the dispersion enhancement of the Jeffrey fluid, in relation to the Newtonian one, for several intervals of the dimensionless parameters. The results indicate very high dispersion enhancement in several cases, especially for high realistic Schmidt number values, and peaks appear at certain dimensionless parameter β values.

Erratum to: Turbulent velocity, sediment motion and particle trajectories under breaking tidal bores: simultaneous physical measurements

A tidal bore is a hydrodynamic discontinuity propagating upstream in an estuarine zone with a funnel shape as the tide starts rising under spring tidal conditions. The transient sediment motion beneath tidal bores was investigated in laboratory under controlled flow conditions by measuring simultaneously the fluid and sediment particle velocities. Although no sediment transport was observed in the initially steady flow and in undular bores, a transient sheet flow motion was observed beneath the breaking bores. The sediment transport was initiated during the passage of the bore roller toe by the large longitudinal pressure gradient force, and the sediment particles were subjected to large horizontal accelerations. About 5 % of all particles were accelerated in excess of 1 g. The sediments were advected upstream with an average velocity close to the instantaneous fluid velocity. The time evolution of instantaneous particle velocity for each trajectory was analysed, using the starting point of particle trajectory corresponding to the entrainment point, and the end point to the particle stoppage point. The present data provided some quantitative data in terms of force terms acting on sediment particles beneath a tidal bore and their trajectory characteristics.

An Analysis of Peristaltic Flow of Finitely Extendable Nonlinear Elastic- Peterlin Fluid in Two-Dimensional Planar Channel and Axisymmetric Tube

We have investigated the peristaltic motion of a non-Newtonian fluid characterized by the finitely extendable nonlinear elastic-Peterlin (FENE-P) fluid model. A background for the development of the differential constitutive equation of this model has been provided. The flow analysis is carried out both for two-dimensional planar channel and axisymmetric tube. The governing equations have been simplified under the widely used assumptions of long wavelength and low Reynolds number in a frame of reference that moves with constant wave speed. An exact solution is obtained for the stream function and longitudinal pressure gradient with no slip condition. We have portrayed the effects of Deborah number and extensibility parameter on velocity profile, trapping phenomenon, and normal stress. It is observed that normal stress is an increasing function of Deborah number and extensibility parameter. As far as the velocity at the channel (tube) center is concerned, it decreases (increases) by increasing Deborah number (extensibility parameter). The non-Newtonian rheology also affect the size of trapped bolus in a sense that it decreases (increases) by increasing Deborah number (extensibility parameter). Further, it is observed through numerical integration that both Deborah number and extensibility parameter have opposite effects on pressure rise per wavelength and frictional forces at the wall. Moreover, it is shown that the results for the Newtonian model can be deduced as a special case of the FENE-P model

Effect of bulk viscosity in supersonic flow past spacecraft

In this paper, we consider the effect of bulk viscosity in various hydrodynamic problems. We numerically study this effect on the front structure of the one-dimensional stationary shock wave and on the flow past blunt body. We estimate the effect of the bulk viscosity coefficient (BVC) on the heat transfer and drag of a sphere in a supersonic flow, apparently for the first time, by the numerical solution of parabolized Navier–Stokes equations. The solution is obtained by an original fast convergent method of global iterations of the longitudinal pressure gradient. The directions of further investigations of bulk viscosity are suggested.