Non-steady Flow Research Articles

A wavenumber parallel computational code for the numerical integration of the Navier–Stokes equations

A parallel computational code for the numerical integration of the Navier–Stokes equations has been developed. The system of partial differential equations describing the non-steady flow of a viscous incompressible fluid in three dimensions is considered and applied to the channel flow problem. A mixed spectral-finite difference technique for the numerical integration of the governing equations is devised: Fourier decomposition in both streamwise and spanwise directions and finite differences in the direction orthogonal to the solid walls are used, while a semi-implicit procedure of Runge–Kutta and Crank–Nicolson type is utilised for the advancement in time. A wavenumber parallelism is implemented for the execution of the calculations. Within each time step of integration, the computations are executed in two distinct phases, each phase corresponding to a different way of decomposing the computational domain, vertically and horizontally, respectively; in both phases of the whole calculation process, each portion of the computing domain is handled by a different CPU on a Convex SPP 1200/XA parallel computing system. Results are presented in terms of performance of the calculation procedure with the use of 2,4,6 and 8 processors respectively and are compared with the single-processor performance. Also the accuracy of the parallel algorithm has been tested, by analysing the evolution in time of small amplitude disturbances of the mean flow; a satisfactory agreement with the theoretical solution given by the hydrodynamic stability theory is found, provided that a given number of grid points in the y direction are present.

Effects of oscillation on the arteries measured by arterial impedance during left ventricular assistance

Oscillating blood flow has effects on the arteries similar to the effects of pulsatile blood flow at lower frequencies. Alternating-current theory is useful to study the pulse in the circulatory system. Arterial impedance is a good index to estimate the frequency characteristics of the artery. In this study, total vascular resistance and arterial impedance were studied in animal experiments during left ventricular assistance. A centrifugal pump was used for comparison with a VFP (vibrating-flow pump). Left ventricular assistance was performed in animal experiments using goats. Total vascular resistance and arterial impedance were studied to estimate the frequency characteristics of the artery. Total vascular resistance during steady flow assistance decreased compared with that during nonassistance. Arterial walls were extended by the blood flow assistance at steady flow. The resistance during oscillating blood flow was different at each driving frequency, showing the frequency dependency, or pulse effect, of the arterial system under nonsteady flow. Arterial impedance was also studied during oscillating blood flow and showed a slight increase at a driving frequency of 25 or 30 Hz. These fluctuations in impedance are influenced by the reflection of the pulse. Arterial impedance should be taken into consideration when analyzing pulsatile blood flow because the pulse reflection may have some effects on the arterial wall. Some variation of blood pressure and blood flow might be necessary for stable support with artificial circulatory assistance.

Free boundary problem of non-steady state seepage flow

Along with the vigorous developing construction, the number of various underground engineerings is greatly increasing. Such as: the foundations of dams and high- rise multistoried houses, subways and tunnels, water and oil wells etc., where the close attention is always payed to the seepage behaviour in the media around the structures. The Variational Inequality formulation and its FEM solution for the free boundary problem of 2D steady state seepage flow was given by the authors. In this paper a further investigation is made on the non-steady state seepage problem, taken the seepage flow of wells as an example. The presented approach—Variational Inequality and its FEM solution- is also very beneficial to the non-steady state problems, where the transient free boundary can also be defined directly without conventional iterations.

Effect of Operational Pressure on Periodic Oscillation of Secondary Circulation near the Bottom of the Thermal Diffusion Column

A computational code has been developed to analyze the non-steady flow field of the thermal diffusion column in the higher pressure region. Numerical analyses for H2-HT are performed for the thermal diffusion column with an effective height of 1,500 mm, a hot wire of 0.15 mm and a cold wall of 15 mm in radius. In the condition that temperatures of cold wall and hot wire are 77.35 and 1,277.35 K at the pressure less than 0.112 MPa, the flow fields reach the steady state. However, a secondary circulation observed near the bottom of the column moves periodically at the pressure of 0.112 MPa or more. The frequency of the flow fields becomes larger as the gas pressure increases. The marginal pressure to make flow field apart from the steady state to the periodic state is predicted with the present analyses.

Commentary on Russo [1991], Serrano [1990, 1998], and other applications of the water‐content‐based form of Richards' Equation to heterogeneous soils

Commentary on <i>Russo</i> [1991], <i>Serrano</i> [1990, 1998], and other applications of the water‐content‐based form of Richards' Equation to heterogeneous soils

Variability of black hole binary systems

X-ray light curves of black hole candidate systems reveal a variety of transient activity including quasi-periodic oscillations, dips, and bursts. These X-ray behaviors likely arise from nonsteady mass flow modulations in an accretion disk surrounding the compact object. The possible origin of the variabilities are discussed in terms of dynamical, viscous, and thermal instabilities in the accretion disk. The comparison of results from the global evolution of disks with X-ray observations can be used to provide constraints on proposed theoretical models, thereby, facilitating an understanding of the structure of the inner regions of accretion disks in these systems.

Experiments on steady and oscillatory flows at moderate Reynolds numbers in a quasi-two-dimensional channel with a throat.

The study of steady and unsteady oscillatory static fluid pressures acting on the internal wall of a collapsible tube is essential for investigation of the complicated behavior observed when a flow is conveyed inside a tube. To examine the validity of two one-dimensional nonsteady theoretical flow models, this paper presents basic experimental observations of flow separation and reattachment and measured data on the static pressure distributions of the flow in a quasi-two-dimensional channel with a throat, together with information on the corresponding shape of the wall deflection and motion. For combinations of moderate Reynolds numbers and angles of the divergent segment of the channel, a smooth flow is separated from the wall downstream of the minimum cross section and reattached to the wall farther downstream. The measured data are compared with numerical results calculated by the two flow models.

Integrable unsteady motion with an application to ocean eddies

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

Nonsteady Flow of Viscous Fluid in a Tube of Triangular Cross-Section

By superposing of one-dimensional solutions an exact solution is obtained for the nonsteady two-dimensional problem of the motion of an incompressible viscous fluid in a rigid tube whose cross-section is a regular triangle. The fluid is driven by a time-dependent pressure gradient. The fluid particles may have a nonuniform initial velocity distribution over the tube cross-section. Solutions are obtained in the form of series for the cases in which the fluid is accelerated from rest by a varying pressure gradient and also in the stationary oscillating regime under the action of a periodically pulsating pressure gradient.

Nonevolutionary discontinuous magnetohydrodynamic flows in a dissipative medium

Magnetohydrodynamic discontinuities in a dissipative medium are considered from the view point of the principle of evolutionarity. For a nonevolutionary discontinuity, the problem of time evolution of a small perturbation does not have a unique solution. This means that an infinitesimal perturbation results in finite variation of the initial flow. Such a discontinuity cannot exist as a stationary configuration and it must disintegrate or transform to some other nonsteady flow. Using the kinematic properties of weakly damping high-frequency perturbations of a dissipative medium, the sufficient conditions of nonevolutionarity of the dissipative discontinuities are obtained. These conditions are shown to strengthen the known criterion of a discontinuous profile of inviscid shocks. It is suggested that time evolution of the nonevolutionary shock that contains the nonevolutionary internal discontinuity is a superposition of two oscillation processes with different characteristic times corresponding to internal disintegration and disintegration of the shock as a whole.

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established.

Prediction of the steady and non-steady flow performance of a highly loaded mixed flow turbine

This paper describes a method for predicting the performance under both turbine inlet steady state and non-steady state flow conditions of a mixed flow turbine used for turbocharged internal combustion engines. The mixed flow turbine steady state performances computed with the steady state performance prediction method are in good agreement with the experimental results obtained in the Imperial College turbocompressor cold air test rig. The unsteady state performance is computed using a one-dimensional model based on the solution of the unsteady one-dimensional flow equations. These equations are solved in the volute by a finite difference method using a four-step explicit Runge—Kutta scheme. The instantaneous volute exit condition is provided by the steady state rotor performance prediction model with the assumption of a quasi-steady state flow in the rotor. The computed instantaneous performances are in reasonable agreement with published experimental data for the same mixed flow turbine. The unsteady flow model is also used to study the effects of the frequency and the amplitude of the pulse on the performances of the mixed flow turbine.

Problem of constructing conservative finite-difference schemes for differential equations of nonsteady flow in a nonprismatic channel

Problem of constructing conservative finite-difference schemes for differential equations of nonsteady flow in a nonprismatic channel

Mixed convective non-steady 3-dimensional micropolar fluid flow at a stagnation point

The problem of mixed convective non-steady three dimensional flow of a micropolar fluid near the stagnation point of a blunt nosed body has been discussed. The governing set of differential equations are solved using the Finite Element Method. The velocity and microrotation distribution are shown graphically to depend upon four parameters namely the micropolar parameter, Grashof number, buoyancy parameter and the degree of acceleration. The conclusions are quite interesting from the application point of view.

Oscillatory disintegration of nonevolutionary magnetohydrodynamic discontinuities

Trans-Alfvenic shock waves are considered in the approximation of small amplitude and almost parallel propagation of the magnetic field. Such shocks are nonevolutionary, since the problem of time evolution of their small perturbation does not have a unique solution. Therefore, they cannot exist as stationary configurations and must disintegrate or transform to some more general, nonsteady flow. The disintegration configuration necessarily includes an Alfven discontinuity that is also nonevolutionary. It is shown that the contradiction inherent in the nonevolutionary configuration is removed if its time evolution has the form of oscillatory disintegration, i.e., reversible transformation of one type of discontinuity to the other. In this process fast and slow shock or rarefaction waves as well as contact discontinuities are emitted.

Pressure-transient analysis of two-layers fractal reservoirs

In this article based on the discussion and nonsteady flow of two-layers fractal reservoirs, the solution of generalized C-D equations in Laplace space, and then the solution under different boundary conditions with considering or not considering wellbore storage and skin effects are found out. At last, the nature of the solution under not considering wellbore storage and skin effects is taken under discussion.

Comportamiento reológico no estacionario de emulsiones aceite en agua estabilizadas con un palmitato de sacarosa.

Non-steady flow properties of concentrated oil in water emulsions containing oil (60-80% wt.), water and sucrose palmitate (1-5% wt.) of high hydrophilic-lypophilic balance were investigated. Stress growth, steady flow and linear viscoelastic measurements were carried out for this study. The emulsions studied exhibited a thixotropic behavior showing a very rapid stress overshoot. The stress decay was fitted to a Figoni-Shoemaker model using two exponentials. An stress undershoot was also produced under certain conditions. Shear brought about strong structural changes, such as droplet size redistribution at high oil content and temperature. Thus, the steady state viscosity does not fit an Arrhenius type equation with temperature. A shear thinning behavior was found for the steady state viscosity and the peak viscosity.

Water table draw down during drainage with evaporation/evapotranspiration

Groundwater table behavior in drained lands in addition to tile flow depends upon several other factors. Evaporation/evapotranspiration (E/ET) from the shallow water table is one of them. The Boussinesq equation for non-steady state groundwater flow with variable drainable porosity was suitably modified by incorporating a non-linear function simulating E/ET from the shallow water table. The modified equation was solved numerically for predicting the groundwater table behavior with respect to space and time. Column studies and soil tank model experiments were conducted to find out the functional relationship between the evaporation rate and water table height as well as for determination of other parameters required in the mathematical model. The water table fluctuation data were recorded in the soil tank model when both the process of evaporation and drainage were operative. The result of this study revealed that groundwater table behavior, predicted by modified Boussinesq equation was quite comparable with corresponding observed data. The quality of the predictions were much better compared to the conventional approach in which drainable porosity is assumed constant and the process of E/ET is neglected.

Vorticity Jump in Surface Coordinates Across a Shock in Nonsteady Flow

We obtain Hayes'formulas in the coordinates attached to an arbitrarily moving and deforming shock surface that occurs in nonsteady flows. The formulas given here can be incorporated in a flow solver that uses a coordinate system attached to a moving and deforming shock surface.

Finite element simulation of mold filling using marker particles and the k- ϵ model of turbulence

An algorithm of tracking the free surface, during the filling of castings with molten metal, is developed from the Market And Cell (MAC) technique [1]. The Navier-Stokes equations, for incompressible, non-steady Newtonian flows, are solved by the finite element method. The turbulence state is defined by the k- ϵ model. A preliminary experimental study showed that a zero boundary-value of the stress vector may be applied along the free surface of the metal. The free surface can be visualized at any time of the process.