Convergent laminar fluid flow between two rotating disks

A stationary flow from the periphery to the center in a hollow between two coaxial, closely located rotating disks is studied by the iterative method of solving a system of equations of the dynamics of a viscous incompressible fluid. The existence and uniqueness of the approximate solution are shown. Moscow State University of the Food Industry, Moscow 125080. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 77–83, March–April, 2000.     

Pulsating laminar flow of a viscous fluid in a capillary

The possibility of using the hypothesis of quasistationarity for a pulsating laminar flow of viscous fluid in a capillary has been tested experimentally. It is shown that for the given parameters the use of this hypothesis leads to a satisfactory agreement between theory and experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–176, May–June, 1982.     

Velocity distributions in Taylor vortex flow with imposed laminar axial flow and isothermal surface heat transfer

Fully-developed flow in a concentric annulus formed by a stationary outer cylinder, which may be heated isothermally, and a rotatable inner cylinder has been studied experimentally by means of hot-wire anemometry techniques. Velocity profiles for the axial, tangential, and radial directions of flow have been obtained for adiabatic conditions and for wide and narrow annular gaps.It has been shown that the onset of Taylor vortex flow has a pronounced effect on the velocity profiles for all three directions. However, while the profiles for the axial and tangential directions are explicable, those for the radial direction are not so, at present. Also, it was found that heat transfer through the outer annular surface had a greater effect on the radial velocity profile than on the axial or tangential, but in the narrow gap case only.     

Oscillating laminar fluid flow in a cylindrical elastic pipe of annular cross-section

The coupled elastohydrodynamic problem based on the dynamic equations for a viscous incompressible fluid and for two closed finite-length cylindrical elastic shells, inner and outer, described using the Kirchhoff-Love hypotheses is formulated and solved with the corresponding boundary conditions for harmonic variation of the pressure at the inlet and outlet of an elastic annular pipe. From the solution of this problem the flow parameters and the elastic shell displacements are found. The amplitude and phase frequency characteristics and resonant frequencies of the shells are found. The cases of shells simply supported and with fixed ends are considered. The effect of the support mode and the fluid characteristics on the resonant frequencies and the amplitude frequency characteristics of the shells is investigated.     

Velocity profiles for the laminar flow of structurally viscous fluips between parallel planes

In [1], a rheological equation for structurally viscous fluids was proposed and the expediency of distinguishing a special subclass of fluids with a linear flow law was demonstrated.The present paper compares the theoretical and experimental velocity profiles of structurally viscous fluids.     

An asymptotic theory for laminar pipe flow of a non-Newtonian fluid

For a generalized Newtonian fluid the viscosity * varies with the shear rate . Instead of assuming a certain dependence like rheological models do, the viscosity is expanded in a Taylor serie with respect to . Based on this expansion a perturbation approach to laminar pipe flow withq _w = const. and viscous heating included is formulated. The basic flow (zero order solution) is that of a Newtonian fluid. Higher order terms successively account for the influence of a non-Newtonian fluid. — The asymptotic results compare reasonably well with those of specific rheological models like power law or Ellis model. — The influence of temperature dependent properties (including the viscosity) can be accounted for by the same kind of asymptotic approach. The influence of shear rate as well as temperature dependence thus can be combined in general results valid for all generalized Newtonian fluids.Für ein verallgemeinertes Newtonsches Fluid ist die Viskosität * von der Scherrate abhängig. Statt nun eine bestimmte Abhängigkeit anzunehmen, wie dies für rheologische Modelle geschieht, wird die Viskosität als Taylor-Reihe in Bezug auf entwickelt. Ausgehend von dieser Entwicklung wird eine reguläre Störungsrechnung durchgeführt. Dies schließt den Effekt der Reibungswärme ein. Die Grundströmung ist die Strömung eines Newtonschen Fluides. Terme höherer Ordnung berücksichtigen den Einfluß des nicht-Newtonschen Fluidverhaltens. — Die asymptotischen Ergebnisse stimmen gut mit denen spezifischer rheologischer Modelle (power law, Ellis) überein. — Mit der gleichen asymptotischen Methode kann auch der Einfluß der Temperaturabhängigkeit der Stoffwerte erfaßt werden. Damit kann dann der Einfluß sowohl der Scherraten- als auch der Temperaturabhängigkeit auf eine allgemeine Weise für verallgemeinerte Newtonsche Fluide formuliert werden.     

Calculation of laminar flow of a viscous fluid between rotating disks

The results are given of a numerical investigation of the laminar flow of a viscous incompressible fluid with heat transfer from the periphery to the center between two rotating disks. The system is a simplified model of one of the elements of the cooling circuit of a gas turbine. The complete Navier—Stokes equations in the vortlcity—flow function variables were solved by an explicit conservative scheme with appoximation of the convective terms of divergence type by directed differences. The calculations were made in a wide range of variation of the dimensionless determining parameters of the problem. The results agree well with the known experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–81, January–February, 1982.We thank V. M. Kapinos for discussion and helpful comments.     

Pertubation solution of non-newtonian fluid axial laminar flow through eccentric annuli

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity ε is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.     

A finite element formulation for laminar flow of a fluid with microstructure

A finite element formulation for the steady laminar flow of an incompressible fluid with microstructure has been developed. The particular fluids considered are commonly known as micropolar fluids, in which case suspended particulate microstructures are modelled by an ‘extended’ continuum formulation. The particle microspin is a new kinematic variable which is independent of the classical vorticity vector and thereby allows relative rotation between particles and the surrounding fluid. This formulation also gives rise to couple stresses in addition to classical force or traction stresses. The finite element formulation utilizes a variational approach and imposes conservation of mass through a penalty function. A general boundary condition for microspin has been incorporated whereby microspin at a solid boundary is constrained to be proportional to the fluid vorticity. The proportionality constant in this case can vary from zero to unity. Sample solutions are presented for fully developed flow through a straight tube and compared with an analytical solution. Results are also generated for flow through a constricted tube and compared with a Newtonian fluid solution.     

Entropy generation in developing laminar fluid flow through a circular pipe with variable properties

Entropy generation in a circular pipe is analyzed numerically. A two-dimensional solution for the velocity ant temperature profiles is obtained considering temperature dependent thenmophysical properties. Uniform wall heat flux case is considered as the thermal boundary condition. The distribution of the entropy generation rate is investigated throughout the volume of the fluid as it flows through the pipe. Engine oil is selected as the working fluid. In addition, ethylene glycol and air are used in a parametric study. The total entropy generation rate is calculated by integration over the various cross-sections as well as over the entire volume. The results are compared with those obtained for the constant viscosity case. A considerable discrepancy is found between the two cases since the viscosity of these fluids is highly sensitive to the temperature variation.     

Numerical study of laminar fluid flow in a curved elliptic duct with internal fins

The fully developed laminar incompressible flow inside a curved duct of elliptical cross-section with four thin, internal longitudinal fins is studied using the improved CVP method. We present numerical results for the friction factor and an investigation of the effect of the fin height and the Dean number on the flow. It is found that the friction factor increases for large fins and for high Dean numbers and that in some cases, it has a strong dependence on the cross-sectional aspect ratio. The thermal results show that the heat transfer rate is enhanced by the internal fins and that it depends on the aspect ratio.     

Studies on the law of laminar helical flow of power-law fluid in eccentric annuli

According to the principle of fluid mechanics,the law of laminar,helical flow of power-law fluid in eccentric annuli is studied extensively in this paper.The apparent viscosity,velocities distribution of laminar helical flow of power-law fluid are discussed and calculating methods of flow rate and pressure loss are presented.The factors influencing flow are also analysed.On the basis of theoretical studies some new results of the present paper are compared with the theories of the helical flow of the power-law fluid in concentric annuli.The test verified that theoretical formulas in this article are proper and general.They can be used for calculating hydraulic parameters in drilling engineering.     

Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder

The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60≤Re≤160 and 0.5≤n≤2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n=0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudo-periodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.     

Effect of blowing on the resistance of a sphere in laminar flow of viscous fluid

Using the method of matching asymptotic expansions [1–3], a stationary field of velocities is obtained in the vicinity of a sphere for Reynolds numbers R and R computed from the blowing velocity and the fluid flow, respectively; they satisfy the relations R² 1 and R 1. It is also shown that for intensive blowing (R 1), the resistive force is considerably smaller than that found by using the Stokes formula. For weak blowing the results are in good agreement with the solution of Oseen.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskai Fiziki, No. 3, pp. 110–114, May–June, 1972.     

Numerical solution of Navier-stokes equations for laminar fluid flow in rows of plates in staggered arrangement

Laminar fluid flow in rows of plate elements with staggered arrangement has been investigated by solving the complete Navier-Stokes equations using numerical methods. The results have been compared with those obtained on the basis of boundary-layer simplifications. The theoretical pressure-drop values compare well with available numerical and experimental data     

Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by

as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.     

A comparative assessment of fluid flow and heat transfer parameters in laminar flow around a circular cylinder and a sphere

Theoretical studies have been carried out for a comparative assessment of hydrodynamic boundary layer thickness, displacement thickness and shear stress at the wall for laminar flow around a circular cylinder and a sphere with the help of the approximate method due to Karman and Pohlhausen for two dimensional flow and the method as applied to bodies of revolution based on the work of F. W. Scholkemeier, respectively. Thermal boundary layer thickness and Nusselt number have been evaluated around the surface of the solids. Comparison is made with available solutions. The graphical presentation of the results depicts a concise and relative assessment of fluid flow and heat-transfer parameters for flow around cylinder and sphere.