Effect of compressibility on vortex breakdown in a gas flow in a circular tube

Vortex breakdown in a steady axisymmetric viscous gas flow within a circular tube is numerically simulated. The conditions under which reverse flow regions are formed are determined over a wide range of Mach and Reynolds numbers. Data on the effect of the Mach number and inlet flow swirl on the extent and location of the recirculation zone are obtained.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–43, September–October, 1996.     

The stability of the plane Poiseuille flow of a non-Newtonian fluid

Rheologica Acta - This paper considers the flow and the stability of the flow of a fluid whose viscosity depends on the shear in the form $$\nu = {\nu _0}\left\{ {r - s{{\left( {\frac{{d\bar...     

Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid

The hydrodynamic stability of Poiseuille flow of a viscoplastic fluid is investigated. The flow is shown to be stable for infinitesimal disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–154, November–December, 1974.In conclusion the authors thank S. A. Regirer for critical remarks.     

The linear stability of plane Poiseuille flow under unsteady distortion

This paper investigates the linear stability behaviour of plane Poiseuille flow underunsteady distortion by multiscale perturbation method and discusses further the problemproposed by paper[1].The results show that in the initial period of disturbancedevelopment,the distortion profiles presented by paper[1]will make the disturbances growup,thus augmenting the possibility of instability.     

Linear stability of viscous incompressible flow in a circular viscoelastic tube

Flow stability in rigid tubes has been the subject of much research [1]. The overwhelming majority of authors of both theoretical and experimental studies now conclude that Poiseuille flow in a circular rigid tube is linearly stable. However, real tubes all possess elastic properties, the influence of which has not been investigated in such detail. For certain selected values of the parameters characterizing an elastic tube it has been shown that with respect to infinitesimal axisymmetric perturbations Poiseuille flow in the tube can be unstable [2]. In this case boundary conditions that did not take into account the fairly large velocity gradient of the undisturbed flow near the tube wall were used. The present paper reports the results of a numerical investigation of the linear stability of Poiseuille flow in a circular elastic tube with respect to three-dimensional perturbations in the form of traveling waves propagated along the system (azimuthal perturbation modes with numbers 0, 1, 2, 3, 4, and 5 are considered). It is shown that the elastic properties of the tube can have an important influence on the linear stability spectrum. In the case of axisymmetric perturbations it is possible to detect an instability which, at Reynolds numbers of more than 200, exists only for tubes whose modulus of elasticity is substantially less than that of materials in common use. The instability to perturbations of the second azimuthal mode is different in character, inasmuch as at Reynolds numbers greater than unity it occurs in stiffer tubes. Moreover, as the Reynolds number increases it can also occur in tubes of greater stiffness. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 126–134, November–December, 1986.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.     

An analytical solution for steady flow of a Quemada fluid in a circular tube

An analytical solution is obtained for steady flow of Quemada-type fluids in a circular tube driven by a constant pressure gradient. Expressions are derived for velocity distribution and for volumetric flow rate as a function of pressure gradient or wall shear stress.     

Stability of a flow in a circular tube

Many studies, both theoretical and experimental, have been dedicated to the stability of flow in a circular tube (see, for example, review [1]). In every case mathematical investigation has not succeeded in obtaining an expression for hydrodynamic instability of such a flow for disturbances of sufficiently low amplitude. (An exception is [2].) Experiment also indicates the stability of such a flow [3], with a laminar mode being extended to Reynolds numbers of the order of tens of thousands. These facts are the basis for the assumption that the flow of a viscous incompressible liquid in a circular tube is stable for small perturbations. However, there is no analytical or even numerical proof of this hypothesis. Moreover, some studies, for example [2], indicate the instability of such a flow in relation to three-dimensional nonaxiosymmetric perturbations. The analysis of hydrodynamic stability with respect to three-dimensional disturbances of flow within a circular tube conducted in this study showed the stability of the flow over a wide range of wave numbers and Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 20–24, January–February, 1973.     

Stability of plane Poiseuille flow of a slightly viscoelastic fluid

Consideration is given to the stability of planePoiseuille flow of a slightly viscoelastic fluid which has a constant viscosity and normal stress differences varying nearly with the shear rate. It is shown that the presence of elasticity lowers the criticalReynolds number at which instability occurs.     

Effect of a longitudinal magnetic field on the flow of an electrically conducting fluid in a circular tube with a sharp narrowing at the entrance

The procedure described in [1] is used to study the effect of entry conditions to the test section on the nature of the flow of an electrically conducting fluid in a circular tube in a longitudinal magnetic field.

     

Poiseuille flow and thermal creep in a capillary tube on the basis of the kinetic R-model

Flow of a diatomic rarefied gas in a capillary tube of infinite length and an arbitrary cross-section under a given small pressure gradient (Poiseuille flow) or a small temperature gradient (thermal creep) is studied on the basis of a kinetic model that takes account for the rotational degrees of freedom of molecules (R-model). Numerical investigation is carried out for flows between parallel flat plates and in a circular capillary tube at the gas parameters corresponding to nitrogen. The main calculated quantity is the gas flow rate through a tube cross-section. The results are compared with the corresponding data obtained on the basis of the S-model.     

Effect of curvature on dual solutions of flow through a curved circular tube

Dual solutions, i.e., two-vortex and four-vortex solutions, of the flow through a curved circular tube are numerically obtained by the spectral method for 0 ⩽ δ ⩽ 0.8 and 500 ⩽ Dn ⩽ 10000, where δ is the non-dimensional curvature of the tube and Dn the Dean number. It is found that the critical Dean number above which the four-vortex solution exists takes the lowest value 956 at δ = 0 and increases with δ. In terms of the Reynolds number of the flow, however, the critical Reynolds number decreases from infinity as δ increases from zero, takes the minimum value of about 250 at δ ≈ 0.52, and then increases again.     

Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria

We present new results on the nonlinear stability of Bingham fluid Poiseuille flows in pipes and plane channels. These results show that the critical Reynolds number for transition, Re_c, increases with Bingham number, B, at least as fast as Re_cB^1/2 as B→∞. Estimates for the rate of increase are also provided. We compare these bounds and existing linear stability bounds with predictions from a series of phenomenological criteria for transition, as B→∞, concluding that only Hanks [AIChE J. 9 (1963) 306; 15 (1) (1963) 25] criteria can possibly be compatible with the theoretical criteria as B→∞. In the more practical range of application, 0≤B≤50, we show that there exists a large disparity between the different phenomenological criteria that have been proposed.     

Perturbation solution of the compressible annular Poiseuille flow of a viscous fluid

The isothermal annular Poiseuille flow of a weakly compressible Newtonian liquid with constant shear and bulk viscosities is considered. A linear equation of state is assumed and a perturbation analysis in terms of the primary flow variables is performed up to the first order using the isothermal compressibility as the perturbation parameter. The effects of compressibility, the bulk viscosity, the radii ratio, the aspect ratio, and the Reynolds number on the velocity and pressure fields are studied.     

MHD of a fractional viscoelastic fluid in a circular tube

We investigate the effect of a transverse magnetic field on the unsteady flow of a generalized second grade fluid through a porous medium in a circular tube. Using fractional partial differential equations, we are able to describe the velocity and stress fields of the flow. We also obtain exact analytic solutions of these differential equations in terms of the Fox’s H-function.     

Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid

The isothermal, planar Poiseuille flow of a weakly compressible Oldroyd-B fluid is considered under the assumption that the density of the fluid obeys a linear equation of state. A perturbation analysis for all the primary flow variables is carried out with the isothermal compressibility serving as the perturbation parameter. The sequence of partial differential equations which results from the perturbation procedure is solved analytically up to second order. The effects of the compressibility parameter, the aspect ratio, and the Weissenberg number are discussed. In particular, it is demonstrated that compressibility has a significant effect on the transverse velocity and the first normal stress difference.     

The influence of vibration on Poiseuille flow of a non-Newtonian fluid. II

Summary An incompressible, isotropic, non-Newtonian fluid undergoes plane Poiseuille flow between two parallel plates, or through a pipe of circular cross-section, as a result of a uniform time-independent pressure gradient. The effect is studied of superposed vibrations of the boundaries, which are not necessarily purely sinusoidal, on the mean rate of discharge of the fluid. The calculations are carried out in detail for a particular constitutive equation of the Rivlin-Ericksen type, with the assumption that the fluid is slightly non-Newtonian. It is seen that in addition to a change in the mean rate of discharge which arises as an interaction of the vibration with the pressure gradient, there may also occur a change in the mean rate of discharge which arises from the interaction of the harmonic components of the vibration and may be independent of the pressure gradient.

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Zusammenfassung Gegenstand der Untersuchung ist eine inkompressible, isotrope, nicht-newtonsche Flüssigkeit entweder in einer ebenen Poiseuille-Strömung zwischen zwei parallelen Platten oder einer solchen durch ein kreiszylindrisches Rohr unter dem Einfluß eines zeitunabhängigen Druckgradienten. Es wird der Einfluß von überlagerten Vibrationen der Wände, die nicht rein sinusförmig zu sein brauchen, auf den mittleren Flüssigkeitsdurchsatz untersucht. Die Rechnungen werden im einzelnen für eine spezielle Stoffgleichung vom Rivlin-Ericksen-Typ durchgeführt, wobei die Flüssigkeit als nur schwach nicht-newtonisch angenommen wird. Man findet, daß außer der Änderung des mittleren Durchsatzes als Folge der Wechselwirkung von Vibration und Druckgradient eine solche Änderung auch als Folge der Wechselwirkung der harmonischen Komponenten der Vibration auftreten kann, die u. U. vom Druckgradienten unabhängig ist.

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On the dispersion of a solute in Poiseuille flow of a third-grade fluid in a channel

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls are extended to the flow of non-Newtonian viscoelastic fluid (known as third-grade fluid) using a generalized dispersion model which is valid for all times after the solute injection. The exact expression is obtained for longitudinal convective coefficient K₁(Γ), which shows the effect of the added viscosity coefficient Γ on the convective coefficient. It is seen that the value of the K₁(Γ) for Γ≠0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K₂(t,Γ) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C_m of the solute over the channel cross-section is determined at a fixed instant after the solute injection for several values of the added viscosity coefficient.     

The influence of vibration on Poiseuille flow of a non-Newtonian fluid,I.

Summary The effect is calculated of a superposed sinusoidal vibration on the rate of discharge of an incompressible, isotropic, non-Newtonian fluid, which is in plane Poiseuille flow, under a constant pressure gradient, between two parallel plates. The calculations are made both when the vibration is longitudinal and when it is transverse. Calculations are also made in the case of Poiseuille flow through a straight pipe of circular cross-section, when a sinusoidal vibration, either longitudinal ar rotational, about the axis of the pipe is superposed.

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Zusammenfassung Es wird die Wirkung einer überlagerten Sinusschwingung auf den Durchsatz einer inkompressiblen, isotropen, nicht-newtonschen Flüssigkeit berechnet, die in einer ebenen Poiseuille-Strömung zwischen zwei parallelen Platten unter der Wirkung eines konstanten Druckgefälles ausfließt. Dabei werden sowohl Longitudinal- als auch Transversal-Schwingungen betrachtet. Anschließend werden analoge Rechnungen für eine Poiseuille-Strömung in einem geraden zylindrischen Rohr durchgeführt, wobei eine in bezug auf die Rohrachse entweder longitudinale oder rotatorische Sinusschwingung überlagert wird.

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