Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

FLOW STRUCTURES AND FORCE CHARACTERISTICS FOR FLAT PLATE IN OSCILLATORY FLOWS WITH K_c NUMBER FROM 2 TO 40 AND IN COMBINED FLOWS

The evolution of wake structures and variation of the forces on a flat plate in harmonic oscillatory and in-line combined flows are obtained numerically by improved discrete vortex method. For the oscillatory oncoming flow cases, when K_c number varies from 2 to 40, the vortex pattern changes from a 'harmonic wave' shaped (in a range of small K_c numbers) to a slight inclined 'harmonic wave' shaped (in a range of moderate K_c numbers), then to inclined vortex clusters with an angle of 50 ° to the oncoming flow direction (at K_c = 20), at last, as K_c number becomes large, the vortex pattern is like a normal Karman vortex street. The well predicted drag and inertia force coefficients are obtained, which are more close to the results of Keulegan & Carpenter's experiment as compared with previous vortex simulation by other au- thors. The existence of minimum point of inertia force coefficient C_m near K_c = 20 is also well predicted and this phenomenon can be interpreted according to the vortex structure. For steady-oscillatory in-line combined flow cases, the vortex modes behave like a vortex street, exhibit a 'longitudinal wave' structure, and a vor- tex cluster shape corresponding to the ratios of U_m to U_0 which are of O (10^(-1)), O(1)and O (10), respectively. The effect on the prediction of forces on the flat plate from the disturbance component in a combined flow has been demon- strated qualitatively. In addition to this, the lock-in phenomenon of vortex shedding has been checked.

Research on the Effects of in-Line Oscillatory Flow on the Vortex-Induced Motions of A Deep Draft Semi-Submersible in Currents

A Deep Draft Semi-submersible （DDS） under certain flow conditions could be subjected to Vortex-Induced Motions （VIM）, which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular section columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics （CFD） method was conducted. The issues of the VIM of multi-column floaters can be con＇,＇eniently converted to the issues of oscillating cylinders in fluid cross flows. This paper looks into the CFD numerical simulation of infinite cylinders having rectangular sections in a two-dimensional sinusoidal time- dependent flow field coupled with a uniform current. The resulted hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in-plane motions of the DDS.

Hydrodynamic Forces on Smooth Inclined Cyh'nders in Oscillatory Flow

-The hydrodynamic forces on a smooth inclined circular cylinder exposed to oscillating flow were experimentally investigated at Reynolds number (Re) in the range 40000-200000 and Keulegan-Capenter number (KC) in the interval from 5-40. In the test, Re number and KC number were varied systematically. The inertia force coefficient (Cu) and the drag force coefficient (CD) in Morison equation were determined from the measured loads and the water particle kinematics. In this analysis a modified form of Morison equation was used since it uses the normal velocity and acceleration. Thus, the applicability of the Cross Flow Principle was assumed. This principle, simply stated, is as follows: the force acting in the direction normal to the axis of a cylinder placed at some oblique angle with the direction of flow is expressed in terms of the normal component of flow only, and the axial component is disregarded. Both the total in-line force coefficient (CF) and transverse force (lift) coefficient (Cf) were analyzed in terms of their maximum and root mean square values. All the in-line and lift force coefficients were given as a functions of Re and KC number. F'rom this research, it can be seen that the Cross-Flow Principle does not always work well. It seems valid for the total in- line force at high Re and large KC numbers. The Cu for a = 45 is larger and the CD for a = 45 is smaller than that for a = 90 ?and Re> 80000. The hydrodynamic force coefficients CD and Cu for the inclined cylinder are only the functions of the oblique angle (a) and KC number, but not of the Re number.

Streaming Caused by Oscillatory Flow in Peripheral Airways of Human Lung

Oscillatory flow facilitates gas exchange in human respiration system. In the present study, both numerical calculation and PIV (Particle Image Velocimetry) measurement indicate that, under the application of HFOV (High Frequency Oscillatory Ventilation), apparent steady streaming is caused and augmented in distal airways by the continuous oscillation, i.e., the core air moves downwards and the peripheral air evacuates upwards within bronchioles. The net flow of steady streaming serves to overcome the lack of tidal volume in HFOV and delivers fresh air into deeper lung region. Also, numerical calculations reveal that the intensity of steady streaming is mainly influenced by the geometry of airways with provided oscillatory frequency and tidal volume, and it rises with Re and Wo up to a Re of about 124 and Wo of about 5. Steady streaming is considered as an important factor for the ventilation efficiency of HFOV.

Mobile bed thickness in skewed asymmetric oscillatory sheet flows

A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.

Effects of trips on the oscillatory flow of an axisymmetric hypersonic inlet with downstream throttle

Experimental investigations are conducted on an axisymmetric hypersonic inlet to evaluate the effects of trips on oscillatory flows. The model exit is throttled with a fixed block to generate oscillatory flows at a freestream Mach number of 6 in a conventional wind tunnel and a shock tunnel. Schlieren imaging and pressure measurements are adopted to record unsteady flow features.Results indicate that trips with a 1 mm thickness prominently suppress external separations, shorten oscillatory cycles, and modify pressure magnitudes. Trips can reduce the upstream movement ranges of separated shocks from nose regions to locations axially 142 mm downstream. The oscillatory cycles are shortened from 3.75 ms to 3.25 ms and from 4 ms to 3.13 ms in two facilities.Tripped cases generally exhibit higher pressure magnitudes than those of untripped cases, of which the increment is up to 21 times the freestream static pressure for the farthest downstream transducer in the shock tunnel. The effects of trips are related to the streamwise vortexes in wake flows, in which interactions between external separations modify the separated flow patterns and enhance the sustainment of the forebody boundary layers to backpressure. Flow processes causing increments of oscillatory frequencies and pressure magnitudes are analyzed, while the flow mechanisms dominating the processes still need to be clarified in the future.

NUMERICAL STUDY OF AN OSCILLATORY TURBULENT FLOW OVER A FLAT PLATE

Oscillatory turbulent flow over a flat plate was studied by using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model was employed in LES and Saffman's turbulence model was used in RANS. The flow behaviors were discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime were also investigated for different Reynolds numbers. (Edited author abstract) 11 Refs.

INVESTIG ATIONS OF WAKE FLOWS OF A FLAT PLATE IN STEADY, OSCILLATORY AND COMBINED FLOWS

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns with K_c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for low K_c numbers (K_c<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments.

Oscillatory Couette flow of rotating Sisko fluid

The oscillatory Couette flow of a magnetohydrodynamic （MHD） Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.

ANALYSIS OF OSCILLATORY FLOW IN CONSIDERATION OF A PLASMA LAYER IN ARTERIAL STENOSES

This paper presents the influences of plasma layer on the oscillatory flow inarterial stenosis. The analysis demonstrates that the existence of the plasma layer mayobviously change the characteristics of flow such as velocity-profiles, longitudinalimpedance and pressure gradient, but hardly change the phase of longitudinalimpedance and pressure gradient. Besides. such influences vary with a and degree ofstenosis. These analyses have Special physiological significance in blood circulationsystem.

HYDRODYNAMIC FORCE ON SMOOTH HORIZONTAL CYLINDER IN UNIFORM OSCILLATORY FLOW

The hydrodynamic forces on a smooth horizontal circular cylinder exposed to oscillating flow have been experimentally investigated at Reynolds numbers (Re) in the range 20, 000 - 260, 000 (subcritical and transcritical regimes) and Keulegan- Carpenter numbers (Kc) in the interval from 5 to 40. In the tests, the Re number and Kc number were varied inertia systematically. The drag force coefficnent CD and inertia force coefficient CM in Morison equation have been determined through the use of Least Square Method. Both total in-line force coefficient CF and transverse force (lift) coefficient CL have been analysed in terms of their maximum and root mean square values. All the in-line and lift force coefficinets were given as a function of Re and Kc number, and also their deviations with the average value have been shown. The principal results are as follows: for the Re ≥80, 000, all the hydrodynamic force coefficients, including CD, CM, CP and CL,are at best very weak functions of Reynolds number, and each of them tends towards a certain constant with increasing Kc number; for the Re< 80, 000, the drag force coefficient CD decreases with increasing Re number, and inertia force coefficient CM increases with increasing Re number.The tendencies of drag and inertia coefficients versus Kc number for the Re ≥10￣5 are very similar to the others, which are very close to the Rodenbusch and Cutierrez's (1983) but are somewhat larger than the Sarpkaya's (1976 and 1986) and Bearman et al.' s(1985).

Computational Analysis of the Oscillatory Mixed Convection Flow along a Horizontal Circular Cylinder in Thermally Stratified Medium

The present work emphasizes the significance of oscillatory mixed convection stratified fluid and heat transfer characteristics at different stations of non-conducting horizontally circular cylinder in the presence of thermally stratified medium.To remove the difficulties in illustrating the coupled PDE’s,the finite-difference scheme with efficient primitive-variable formulation is proposed to transform dimensionless equations.The numerical simulations of coupled non-dimensional equations are computed in terms velocity of fluid,temperature and magnetic field which are computed to examine the fluctuating components of skin friction,heat transfer and current density for various emerging parameters.The governing parameters namely,thermally stratification parameter𝑆𝑆𝑡𝑡,mixed-convection parameter𝜆𝜆,Prandtl number Pr,magnetic force parameter𝜉𝜉and magnetic-Prandtl number𝛾𝛾are displayed graphically at selected values for velocity and heat transfer mechanism.It is computed that heat transfer attains maximum amplitude and good variations in the presence of thermally stratified parameter at each position𝛼𝛼=𝜋𝜋6⁄,𝛼𝛼=𝜋𝜋3⁄and𝛼𝛼=𝜋𝜋around the surface of non-conducting horizontally cylinder.The velocity of fluid attains certain height at station𝛼𝛼=𝜋𝜋6⁄for higher value of stratification parameter.It is also found that the temperature gradient decreases with stratification parameter𝑆𝑆𝑡𝑡,but it increases after a certain distance𝑌𝑌from the cylinder.The novelty of the current work is that due to non-conducting phenomena the magnetic effects are strongly observed far from the surface but exact at the surface are zero for each position.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

A STUDY ON THE UNSTEADY FLOW IN A HELICAL PIPE

A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels, using the method of bi-parameter perturbation. The second order perturbation results were obtained and the characteristics were analyzed at different time of the axial velocity, of the secondary flow, and of the wall shearing stress. Also done the analysis of above-mentioned variables that varied along with time and Womersley number. The results indicate that for a helical pipe, the torsion exerts the main influence on the distribution of secondary flow velocity, especially when the absolute value of axial press gradient is rather small. The severe variation of stream function takes place within a very short period, during which time the stream function develops from positive value to negative value and vice versa, while in most cases in a cycle, the variation is smooth. The wall shearing stress changes severely with theta too.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

Effect of Gas Oscillation-Induced Irreversible Flow in Transitional Bronchioles of Human Lung

Gas exchange in human lungs is established by several flow mechanisms. In the present study, the features of gas displacement in the distal bronchioles of a human lung are investigated by both numerical calculation and experimental observation with particle image velocimetry. The effect of respiration frequency is considered, such as high frequency oscillatory ventilation. By comparing the obtained results, it has been found that the redistribution of gas is attributed to irreversible flow, which is remarkable in higher frequencies oscillation with even lower tidal volumes. Owing to the continuous driving, a time-averaged net flow was induced and intensified by the oscillation. Thus, the gas in the centre region penetrated the deeper region and the outer gas was evacuated to the upper region. Consequently, this streaming contributes to prompt gas replacement. Furthermore, we analysed the effect of the respiration wave form to consider the flow acceleration. From this inspection, it was found that the enhanced inertial force tends to encourage the irreversible flow.

Influences of oscillatory structural forces on dewetting of nanoparticle-laden ultrathin films

To understand the influences of nanoparticles on dewetting in ultra-thin films, both linear stability the- ory and numerical simulations are performed in the present study, with the consideration of oscillatory structural （OS） forces. Long scale approximation is utilized to simplify the hydrodynamic and diffusion equations to a nonlinear system for film thickness and nanoparticle concentration. Results show that the presence of nanoparticles generally suppresses the dewetting process. Two physical mechanisms responsi- ble for this phenomenon are addressed in the present study. When the oscillatory structural forces are relatively smaller, the essential feature of film evolution is similar to the case of particle-free flow. The reduction of the linear growth rate and the postponement of film rupturing can be attributed to the increment of the viscosity due to the presence of nanoparti- cles. On the other hand, when the intensity of the OS forces becomes stronger, the stepwise thinning of film can be ob- served which prevents the film from rupture. Numerical sim- ulations indicate that this phenomenon is caused by the ex- istence of a stable zone due to the oscillatory nature of the structural forces. Another interesting finding is that the non- uniformity of the distribution of nanoparticle concentration might destabilize a spinodally stable film, and trigger the oc- currence of film dewetting.

ANALYSIS OF OSCILLATORY BLOOD FLOW IN VARYING-AREA ELASTIC VESSEL

In this paper, by solving the fundamental e-qualions of periodicallyoscillatory blood flow, the distributions of pressure gradient and blood velocity in varying-areae-lastic vessel were obtained, and then the wall shear stress and its gradient were calculated. Asan example, the pulsatile blood flow in human carotid was analyzed and the effects of vessel taperangle on the distribution of wall shear stress and its gradient were discussed in detail. Numercialresults show that the wall shear stress will enlarge when the taper angle increases. Meantime, nomatter whether the vessel is converging or diverging, with the increase of the absolute value oftaper angle, the amplitude of wall shear stress gradient will enlarge significantly.

A Mathematical Study on Three Layered Oscillatory Blood Flow Through Stenosed Arteries

A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube （stenosed arteries）. The proposed model basically consists three layers of blood （viscous fluids with different viscosities） named as core layer （red blood cells）, intermediate layer （platelets/white blood cells） and peripheral layer （plasma）. The analysis was restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is larger compared to the radius of the arterial segment. The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces, average flow rate, mechanical efficiency, trapping and reflux are discussed with the help of numerical and computational results. This model is the generalized form of the preceding models. On the basis of present discussion, it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer, whereas, opposite effect is observed for viscosity of fluid in intermediate layer. Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers, however, the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.