Flows In Cylindrical Channels Research Articles

AN ENGINEERING APPROACH TO THE STUDY OF THE PROCESSES OF DOUGH FLOW IN THE PRODUCTION OF PASTA AT AGRO-INDUSTRIAL ENTERPRISES

Background. In modern conditions, the provision of domestic pasta produced from durum wheat varieties on modern technological equipment is becoming important. At the same time, the quality of the finished pasta is also determined by the rheological properties of the pasta dough when passing through the pasta press matrix, which determined the purpose of the study to develop a method of computational evaluation for calculating the relationship between the speed parameters of the flow of pasta dough in the cylindrical sections of the channels of the molding matrix with pressure drops to overcome viscous resistance, the dimensions of the structural elements of the channel, as well as with indicators of the rheological properties of pasta dough. Materials and methods. To study the flow of pasta dough, baking flour of the highest grade M-54 28 was chosen as a raw material in stepped cylindrical channels. The applied rheological model is described and a technique for mathematical modeling of the flow parameters of pasta dough in cylindrical channels is given. Due to the small contribution of the pasta dough shear strength to the total pressure loss, a rheological model of a nonlinear-viscous medium is used, which is described by a power equation containing physically determined constants. Neglecting the elastic deformations of the dough due to their smallness, we assumed the condition of constancy of the volumetric productivity for each cross section of the channel. Results. Analytical dependencies are presented that relate the change in velocity over the channel cross section to the pressure developed necessary to overcome the viscous resistance, as well as to the radii and length of the channel, and to the rheological properties of the pasta dough. These dependences formed the theoretical basis of the method for calculating the parameters of pasta dough flow in cylindrical channels. Conclusion. On the example of an industrial matrix of a pasta press, made in the form of a system of cylindrical channels of a stepped-variable diameter in the preforming zone, calculations were made to determine the average and maximum flow rates of pasta dough in each section of the channel and the developed pressure. The results of the research can be used in engineering practice when designing new matrices for forming pasta dough and in the production processes of enterprises to calculate their production capacities.

Proračun sile trenja i toplotnog uticaja mlaza mlaznog motora na unutrašnju površinu lansirne cevi

Introduction/purpose: To study the dynamics of launchers with sources of high-energy gas jets, it is relevant to calculate shear forces from the action of a high-temperature supersonic jet on the inner surface of a cylindrical channel and the temperature of the channel walls. The aim of this work is to develop a comprehensive method for calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket. Methods/results: The research method is based on the theory of supersonic gas flows in cylindrical channels and the theory of the boundary layer. The gas jet is considered continuous, stationary and axisymmetric. The system of differential equations of motion of the projectile in the guide integrates numerically over time. The flow parameters in the pipe sections are found according to the dependences of the theory of supersonic gas flows, taking into account friction losses. To calculate shear stress on the guide wall, we use the relations of the asymptotic theory of the turbulent boundary layer, the theory of turbulent spots of Emmons of the transition boundary layer, and data on the Reynolds numbers of the beginning of the laminar-turbulent transition in wind tunnels. At the same time, the differential equation for heating the thin wall of the guide in the range of contact between the surface of the guide and the jet is numerically integrated. The calculations of the distribution of flow parameters, friction force and the temperature of the wall of the tubular guide during the movement of the projectile inside the jet from the moment the engine is started to the moment the shell exits completely from the guide are performed and graphically presented. Conclusions: This method of calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket due to a high temperature supersonic gas jet - taking into account the effects of nonisothermality, compressibility and laminar-turbulent transition in the boundary layer - can be used to study the dynamics of the launch of rockets from launchers equipped with tubular guides.

The phenomenon of bicyclones a high-frequency induction discharge and the related questions of flows in channels with the presence of zones of heating, bounded along the longitudinal coordinate

The phenomenon of a bicyclones in a high-frequency induction discharge is explained. It is shown that this phenomenon should be characteristic of a wider range of objects having an internal heat source, limited by the longitudinal coordinate. In the present work, this phenomenon is considered as peculiar to fairly wide class of flows in cylindrical channels if there are one or several heating zones (internal or external) inside these channels, limited by the longitudinal coordinate.

Thermal acceleration of gas mixture flows in channels with a constant or variable section area

Many important properties of gas flows in cylindrical channels and in channels with a variable section area, with heat supply through the wall, can be obtained from one-dimensional applied gas dynamics equations [1]. These equations describe the flows under the assumption that the gas parameters depend on the unique coordinate x directed along the channel axis, and have equal values at all points of any cross section. Such a model is a first approximation to the true flow pattern.However, simplicity of the mathematical description and agreement between many resulting corollaries and experimental results make it possible to apply it for analyzing important properties of real flows.

Inertial and surfactant effects on the steady droplet flow in cylindrical channels

The flow of neutrally buoyant droplets in circular channels at finite Reynolds numbers (0.1 ≤ Re ≤ 400) and moderate capillary numbers (0.005 ≤ Ca ≤ 0.1) is studied numerically using a front tracking method. The drops are either clean or contain surfactants which are modeled to behave according to the Langmuir equation of state. The numerical results agree well with previous studies in the Stokes flow regime for small, undeformed drops, as well as very large drops. Increasing the Reynolds number causes a non-monotonic trend in both the relative velocity of the drop and the extra pressure loss required to maintain a constant flow rate. The trends are attributed to changes in drop shape caused by increasing inertial effects. For moderate-sized drops with radii 0.5 to 0.9 times the tube radius, the velocity first decreases and then increases with Reynolds number. For larger drops with radii 1.2 to 1.5 times the tube radius, the effect of inertia is to further elongate the drop and a non-monotonic trend in velocity is not observed. At large Reynolds numbers, stable, oscillatory flows with shape changes confined to the rear of the drop are observed. For long viscous drops, the film thickness increases monotonically with the Reynolds number for all capillary and Reynolds numbers studied. In the presence of inertia, surfactant-laden drops show a maximum in the drop velocity (and a minimum in extra pressure loss) at an intermediate Biot number. In general, at large Reynolds numbers, the effects of surfactants tend to diminish as compared to previous Stokes flow simulations.

Thermal acceleration of subsonic gas flows in cylindrical channels

Subsonic motion of heated ideal gas in a cylindrical channel with constant heat flux through the wall is considered. It is shown that consideration of friction forces on the wall results in that the position of gas temperature maximum caused by thermodynamic cooling at expansion depends on the heat flux, the friction coefficient, and the Mach number value at the inlet channel section. The condition under which there is no temperature maximum in the channel is found.

Free-Molecular Gas Flow in a Narrow (Nanosize) Channel

We have analyzed a free-molecular gas flow in cylindrical channels (capillaries) with impermeable walls for various schemes of the scattering of molecules by channel walls, taking account of the surface diffusion of adsorbed molecules, and a gas flow in such channels with allowance for phase transformations on their walls. A substantial influence of surface diffusion on the mass transfer in gaseous mixtures in the indicated channels has been revealed. The modification of the phenomenological relations of the nonequilibrium thermodynamics of discontinuous systems is considered. The problem of uniform deposition of thin films on the inner surface of a cylindrical channel is discussed.

On gas-dynamics and heat exchange of flows in cylindrical channels in the presence of heat sources bounded along a longitudinal coordinate

The analysis of energy balance equation for viscous laminar flow of fluid or gas in the cylindrical channel in the area (zone) of warm-up bounded along the longitudinal coordinate is made. It was found that at laminar flow of fluid or gas in a round pipe, in each warm-up area bounded along the longitudinal coordinate there are the areas of direct and reverse flows separated by a plane that is a locus of points where temperature is maximal for each fixed value of radial coordinate r.

Regularities pertinent to dispersed-film concurrent motion of steam-liquid flow

We present the results of experimental investigations into the dynamics of concurrent dispersed-film two-phase flow in cylindrical channels as applied to design of distillation installations.

Stability of foam flows in cylindrical channels: formation of a wall liquid layer during slow foam motion

The results of theoretical and experimental investigations into the stability of foam flows in cylindrical channels are presented. Expressions relating the stable foam flow to the structural and rheologic parameters of the foam are derived. The mechanism of the formation of a wall liquid layer in a cylindrical channel is considered.

Energy losses in cocurrent annular-mist gas-liquid flow

The results of the integrated experimental study of the energy losses in upward cocurrent annularmist gas-liquid flow in cylindrical channels are presented.

Flow in a Transverse Section of Athabasca Glacier, Alberta, Canada

Measurements of ice deformation at the surface and at depth in the Athabasca Glacier, Canada, reveal for the first time the pattern of flow in a nearly complete cross-section of a valley glacier, and make it possible to test the applicability of experimental and theoretical concepts in the analysis of glacier flow. Tilting in nine bore holes (eight holes essentially to the bottom at depth about 300 m) was measured with a newly developed electrical inclinometer. The new instrument permitted bore-hole configurations to be determined with greater speed and accuracy than possible with earlier methods. The measurements define the distribution of the velocity vector and the strain-rate tensor over about 70% of the area of the glacier cross-section.The main longitudinal component of flow has the following general features: (1) basal sliding velocity which exceeds 70% of the surface velocity over half of the width of the glacier, (2) marginal sliding velocity (not more than a few meters per year) much less than basal sliding velocity at the center-line (about 40 m a-1), (3) marginal shear strain-rate near the valley walls two to three times larger than the basal shear strain-rate near the center-line (0.1 a-1).The observed longitudinal flow is significantly different from that expected from theoretical analysis of flow in cylindrical channels (Nye, 1965). The relative strength of marginal and basal shear strain-rate is opposite to that expected from theory. In addition, the longitudinal flow velocity averaged over the glacier cross-section (which determines the flux of ice transported) is larger by 12% than the average flow velocity seen at the glacier surface, whereas it would be essentially the same if the theoretical prediction were correct. These differences are caused to a large extent by the contrast between the actual distribution of sliding velocity and the constant sliding velocity for which the theoretical analysis holds. The observed relation between marginal and basal sliding velocity is probably a general flow feature in valley glaciers, and may be caused by lateral variation of water pressure at the ice-rock contact. The observed pattern of longitudinal velocity over the section also shows in detail certain additional features incompatible with the theoretical treatment, even after the difference in boundary conditions (distribution of sliding velocity) is taken into account.Longitudinal strain-rate (a compression of about 0.02 a-1at the surface) decreases with depth, becoming nearly o at the bed in the center of the glacier, which confirms a prediction by Savage and Paterson (1963). The depth variation cannot be explained completely by overall bending of the ice mass as a result of a longitudinal gradient in the curvature of the bed, and is at variance with existing theories, which require the longitudinal strain-rate to be constant with depth.Motion transverse to the longitudinal flow occurs in a roughly symmetric pattern of diverging margin-ward flow, with most of the lateral transport occurring at depth in a fashion reminiscent of extrusion flow. The observed lateral velocities averaged over depth (up to 1.9 m a-1) are compatible with the lateral flux required to maintain equilibrium of the marginal portions of the glacier surface under ablation (about 3.7 m of ice per year) and are driven by the convex lateral profile of the ice surface.

Flow in a Transverse Section of Athabasca Glacier, Alberta, Canada

AbstractMeasurements of ice deformation at the surface and at depth in the Athabasca Glacier, Canada, reveal for the first time the pattern of flow in a nearly complete cross-section of a valley glacier, and make it possible to test the applicability of experimental and theoretical concepts in the analysis of glacier flow. Tilting in nine bore holes (eight holes essentially to the bottom at depth about 300 m) was measured with a newly developed electrical inclinometer. The new instrument permitted bore-hole configurations to be determined with greater speed and accuracy than possible with earlier methods. The measurements define the distribution of the velocity vector and the strain-rate tensor over about 70% of the area of the glacier cross-section.The main longitudinal component of flow has the following general features: (1) basal sliding velocity which exceeds 70% of the surface velocity over half of the width of the glacier, (2) marginal sliding velocity (not more than a few meters per year) much less than basal sliding velocity at the center-line (about 40 m a-1), (3) marginal shear strain-rate near the valley walls two to three times larger than the basal shear strain-rate near the center-line (0.1 a-1).The observed longitudinal flow is significantly different from that expected from theoretical analysis of flow in cylindrical channels (Nye, 1965). The relative strength of marginal and basal shear strain-rate is opposite to that expected from theory. In addition, the longitudinal flow velocity averaged over the glacier cross-section (which determines the flux of ice transported) is larger by 12% than the average flow velocity seen at the glacier surface, whereas it would be essentially the same if the theoretical prediction were correct. These differences are caused to a large extent by the contrast between the actual distribution of sliding velocity and the constant sliding velocity for which the theoretical analysis holds. The observed relation between marginal and basal sliding velocity is probably a general flow feature in valley glaciers, and may be caused by lateral variation of water pressure at the ice-rock contact. The observed pattern of longitudinal velocity over the section also shows in detail certain additional features incompatible with the theoretical treatment, even after the difference in boundary conditions (distribution of sliding velocity) is taken into account.Longitudinal strain-rate (a compression of about 0.02 a-1at the surface) decreases with depth, becoming nearly o at the bed in the center of the glacier, which confirms a prediction by Savage and Paterson (1963). The depth variation cannot be explained completely by overall bending of the ice mass as a result of a longitudinal gradient in the curvature of the bed, and is at variance with existing theories, which require the longitudinal strain-rate to be constant with depth.Motion transverse to the longitudinal flow occurs in a roughly symmetric pattern of diverging margin-ward flow, with most of the lateral transport occurring at depth in a fashion reminiscent of extrusion flow. The observed lateral velocities averaged over depth (up to 1.9 m a-1) are compatible with the lateral flux required to maintain equilibrium of the marginal portions of the glacier surface under ablation (about 3.7 m of ice per year) and are driven by the convex lateral profile of the ice surface.

Polymer flow in cylindrical channels

The author examines the problem of flow of a polymer melt in a cylindrical channel of arbitrary cross section. It is assumed that the polymer is an isotropic viscoelastic medium. All the coefficients of the equation of state obtained for the flow in question are functions of the second invariant of the strain rate tensor only and can be determined experimentally in simple types of flow. A perturbation method is proposed for the solution of specific problems, the Dirichlet problem for Poisson's equation being solved in each perturbation step.

Flow of gases through channels with reference to porous materials

Knowledge of the gas flow in pumping lines, in internal channels, and in porous materials undergoing vacuum processes is basic to the design and operation of a vacuum system. The gas flow equations for viscous and molecular flow in cylindrical channels are ideally simple, in slip flow they are not so easy, but in porous materials in all the flow regions they are more complicated. The permeability of a porous material has been obtained directly by measuring with a flowmeter the amount of gas flowing through it under an absolute pressure gradient, and the same has been done with model materials. Correlation of the permeability and mean absolute pressure provides basic information on structural factors of the material such as porosity, tortuosity factor, and equivalent pore diameter which could, for example, be applied to vacuum and freeze-drying processes.

Heat transfer by laminar flow in a cylindrical tube

In a recent paper1) a method for determining the discrete set of eigenvalues and the associated eigenfunctions of a certain Sturm-Liouville differential system has been developed and it has been pointed out that by this method the problem of heat transfer by laminar flow in cylindrical channels can be worked out withaxial heat conduction, viscous dissipation and any prescribedheat generation included. In the present paper an exact solution of this problem for a circular channel is presented and the first four eigenvalues and the corresponding eigenfunctions are found for Peclet numbers 100 and 1000 (hitherto worked out by assuming thatδ2T/δx2 ≪δ2T/δr2 + (1/r)δT/δr, and also neglecting the viscous dissipation). It is found that the effect of axial heat-conduction is almost negligible for higher Peclet numbers (Pe>100), and hence it can be definitely stated that the approximate solution is good enough under the usual experimental conditions. The heat transfer problem for plug flow is also solved exactly, and it is concluded that the effect of axial heat conduction is negligible forPe>100. The mean mixed temperature and the Nusselt numbers are tabulated and plotted against the Graetz number.