Flow Of Newtonian Liquid Research Articles

Local Momentum Transfer Process in a Wall Region of an Agitated Vessel Equipped with an Eccentric Impeller

The results of the experimental studies of local momentum transfer process in the region of the cylindrical wall of an agitated vessel equipped with an eccentric axial flow impeller are presented. The data for eccentrically located impellers both, propeller and HE 3 impeller, differing in the operating liquid pumping mode were compared. In total, 5120 experimental points for both impellers were obtained on the basis of the electrochemical experiments for each of the tested impeller. Axial and angular distributions of the shear rate and friction coefficient in the agitated vessel without baffles were found within the turbulent regime of the Newtonian liquid flow. Local shear stress, dynamic velocity and energy dissipated were also identified in this region of the wall. The results of the study show that the profiles of the transport coefficients depend strongly on the eccentricity e/R, axial and angular coordinates, liquid circulation imposed by axial flow impeller, and liquid turbulence in the agitated ve...

Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity

The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we derive analytical solutions for plane, round, and annular Poiseuille flow of a Newtonian liquid, the viscosity of which increases linearly with pressure. These flows may serve as prototypes in applications involving tubes with small radius-to-length ratios. It is demonstrated that, the velocity tends from a parabolic to a triangular profile as the viscosity coefficient is increased. The pressure gradient near the exit is the same as that of the classical fully developed flow. This increases exponentially upstream and thus the pressure required to drive the flow increases dramatically.

Transport phenomena in an agitated vessel with an eccentrically located impeller

AbstractThe paper presents results of an experimental analysis of the transport phenomena at the vicinity of the wall of an unbaffled agitated vessel with an eccentrically located impeller. Distributions of the transport coefficients were experimentally studied using an electrochemical method within the turbulent regime of the Newtonian liquid flow. Measurements were carried out in an agitated vessel with the inner diameter T = 0.3 m. Liquid height in the vessel was equal to the inner diameter, H = T. The agitated vessel was equipped with a Rushton or a Smith turbine or an A 315 impeller. Eccentricity of the impeller shaft was varied from 0 to 0.53. Local values of the dimensionless shear rate, shear stress, dynamic velocity and friction coefficient were integrated numerically for the whole surface area of the cylindrical wall of the vessel. Averaged values of these quantities were correlated with the impeller eccentricity and modified Reynolds number. The proposed Eqs. (5)–(8), with the coefficients given in Table 2, have no equivalent in open literature concerning this subject. Distributions of the shear rate, γ/n, and friction coefficient, f, at the vicinity of the cylindrical wall of the unbaffled vessel equipped with eccentric Rushton or Smith turbine or A 315 impeller are very uneven and they depend significantly on the impeller eccentricity, e/R. Maximum local values of these variables are located on the wall section closest to the impeller blades. From among the tested impellers, the greatest effects of the impeller eccentricity, e/R, and the liquid turbulence (described by the modified Reynolds number Re P,M) on the averaged dimensionless shear rate (γ/n)m and friction coefficient, f m, are found for the radial-flow Rushton turbine located eccentrically in an unbaffled agitated vessel.

Gas-Newtonian and Gas-Non-Newtonian Slug Flow in Vertical Pipe, Part I: Gas Holdup Characteristics

Studies on two-phase gas-liquid co-current flow with non-Newtonian liquid system has attracted the attention of researchers over the years due to its wide-spread applications and importance in various different processes in chemical and biochemical industries, such as the process of two-phase in oil and gas wells, transportation systems of crude and refined products, and food processing in biochemical engineering and bio-reactors. This article examines the sole objective of experimental studies on gas holdup in Newtonian and non-Newtonian liquid slug flow within a range of gas and liquid flowrate of 0.5×10-4 to 1.92×10-4 m3/s and 1.6×10-4 to 6.7×10-4 m3/s, respectively. The present data was analyzed with different models. To predict gas holdup, correlations have been developed for individual system with Newtonian and non-Newtonian liquid. A general correlation was also developed to predict the gas holdup combing both the Newtonian and non-Newtonian liquid systems. The study of the gas holdup characteristics in gas-Newtonian and non-Newtonian liquid systems may give insight into a further understanding and modeling of this slug flow characteristics in industrial applications.

Comment on “Coating flow of viscous Newtonian liquids on a rotating vertical disk” [Phys. Fluids 21, 103102 (2009)

First Page

Coating flow of viscous Newtonian liquids on a rotating vertical disk

We study a Newtonian viscous liquid coating a vertical rotating disk in the creeping flow regime. Experiments were performed at varying disk rotation speeds and liquid volumes, and the thickness profile at steady state was measured. While the maximum liquid supported by the rotating disk varied with rotation rate and liquid viscosity, the numerical value of a dimensionless number signifying the ratio of gravity to viscous forces was the same in all the cases, γ=0.30. A lubrication analysis for the time evolution of the film thickness that accounted for gravity, surface tension, and viscous forces was solved numerically to steady state. The predicted thickness profiles are in quantitative agreement with those obtained experimentally. The lubrication equation at steady state was solved analytically in the absence of surface tension to obtain constant height contours that were circular and symmetric about the horizontal axis. However to obtain a complete solution, knowledge of the height variation across the contours is required, and this is controlled by the surface tension. On including this effect, we derived an asymptotic solution to predict thickness profiles that agree well with measurements for large values of viscosity or rotation rates.

Flow of Newtonian and power law liquids in tube bundles

AbstractIn this work, the annular (tangential) flow of Newtonian and non‐Newtonian fluids in tube bundles has been studied experimentally. Extensive pressure drop data has been obtained embracing wide ranges of the Reynolds number (13–6600) and for two test modules of different geometrical arrangements, but of similar overall void fraction. Preliminary experiments suggest that the pressure drop is mainly determined by the overall void fraction of the bundle and is relatively insensitive to the detailed geometrical configuration of the bundle. A simple predictive correlation has been developed which reconciles the present results for Newtonian and power law fluids with acceptable levels of reliability.

Micro-flow metering and viscosity measurement of low viscosity Newtonian fluids using a fibreoptical spatial filter technique

The paper describes an experimental method that is capable of measuring liquid flows of the order of millilitres per hour. Volume flow of laminar flows of Newtonian liquids in pipes or channels can be determined by measurement of the centreline velocity and application of the equation of Hagen-Poiseuille. Micro-flow meters with double fibre-array sensor were developed for the measurements of liquid volume flow in capillaries and micro-channels. The main units of the micro-flow meters are a laser-diode system, a double fibre-array sensor and different transparent capillaries or micro-channels. The accuracy of the measured water volume flow was tested with a balance and a syringe pump with given volume flow. Furthermore, the influence of the size of tracer particles on the volume flow results was also determined. This method of flow metering of Newtonian liquids needs no calibration and the results are not influenced by changes in temperature, pressure or nature of Newtonian liquid. An additional measuring result is the determination of the viscosity function by the application of a stripe model of the two-dimensional micro-channel flow. Possible applications of the fibreoptical micro-flow meter lie in micro- volume flow measurements of different Newtonian liquids and in viscosity measurements of Newtonian and non-Newtonian liquids.

Distribution of local heat transfer coefficient values in the wall region of an agitated vessel

AbstractExperimentally found local heat transfer coefficients are analyzed as a function of the measuring point on the heat transfer surface area of the agitated vessel wall and of the impeller eccentricity. Eccentric Rushton turbine and A 315 impeller are considered. Local heat transfer coefficients were measured by means of the computer-aided electrochemical method. The measurements were performed in an agitated vessel with inner diameter 0.3 m, filled with liquid up to the height equal to the vessel diameter. The experiments were carried out within the turbulent regime of the Newtonian liquid flow in the agitated vessel. The results were compared with the data obtained for the agitated vessel equipped with an eccentrically located axial flow propeller or an HE 3 impeller. Experimental studies show that the distributions of the heat transfer coefficient values depend on the impeller eccentricity, impeller type and the direction of the liquid circulation in the agitated vessel.

Measurement of tack of Newtonian liquids on porous substrates

Probe-tack experiments of Tirumkudulu et al. [Phys. Fluids 15, 1588 (2003)] have shown that squeeze flow of Newtonian liquids on flat, impermeable substrates can be successfully modeled using the lubrication approximation. Here, we present a model for squeeze flow of Newtonian liquids on porous substrates where the flow in the gap is coupled to the fluid flow in the porous media. The competition of spreading and imbibition of liquid on a partially saturated porous substrate determines the force versus gap profile in both the squeeze (compression) and pull-off (tension) modes. The finite difference method was used to discretize the lubrication equation in the gap while boundary element method was employed to solve for flow in the porous substrate. The model predicts a lower magnitude of force for porous substrates in both compression and tension modes compared to that for impermeable substrates. Experiments on porous alumina substrates with Newtonian liquids show close agreement with the model predictions in both compression and tension modes when the gap is corrected for the obliqueness of the confining surfaces. Cavitation is predicted for some cases in the tension mode when the pressure in the gap reduced below the vapor pressure of liquid.

Stability of gravity-driven free-surface flow past a deformable solid at zero and finite Reynolds number

The linear stability of Newtonian liquid flow down an inclined plane lined with a deformable elastic solid layer is analyzed at zero and finite Reynolds number. There are two qualitatively different interfacial modes in this composite system: the free-surface or gas-liquid (“GL”) mode which becomes unstable at low wave numbers and nonzero Reynolds number in flow down a rigid plane, and the liquid-solid (“LS”) mode which could become unstable even in the absence of inertia at finite wave numbers when the solid layer is deformable. The objectives of this work are to examine the effect of solid layer deformability on the GL and LS modes at zero and finite inertia, and to critically assess prior predictions concerning GL mode instability suppression at finite inertia obtained using the linear elastic model by comparison with the more rigorous neo-Hookean model for the solid. In the creeping-flow limit where the GL mode instability is absent in a rigid incline, we show that for both solid models, the GL and LS modes become unstable at finite wavelengths when the solid layer becomes sufficiently soft. At finite wavelengths, the labeling of the two interfacial modes as GL and LS becomes arbitrary because these two modes get “switched” when the solid layer becomes sufficiently deformable. The critical strain required for instability becomes independent of the solid thickness (at high enough values of thickness) for both GL and LS modes in the linear elastic solid, while it decreases with the thickness of the neo-Hookean solid. At finite Reynolds number, it is shown for both the solid models that the free-surface instability in flow down a rigid plane can be suppressed at all wavelengths by the deformability of the solid layer. The neutral curves associated with this instability suppression are identical for both linear elastic and neo-Hookean models. When the solid becomes even more deformable, both the GL and LS modes become unstable for finite wave numbers at nonzero inertia, but the corresponding neutral curves obtained from the two solid models differ significantly in detail. At finite inertia, for both the solid models, there is a significant window in the shear modulus of the solid for moderate values of solid thickness where both the GL and LS modes are stable at all wave numbers. Thus, using the neo-Hookean model, the present study reaffirms the prediction that soft elastomeric coatings offer a passive route to suppress and control interfacial instabilities.

Measuring the velocity field in film‐splitting flows of Newtonian liquids

AbstractRigorous mathematical analysis of viscous free surface flows and comprehensive experimental analysis have been used to develop coating technology in the last 30 years. Theoretical analysis usually require advanced numerical methods to solve the mass and momentum‐conservation equations coupled with the appropriate boundary conditions for flows with liquid‐gas interfaces. Experimental analysis usually requires pilot plant trials and bench‐top flow visualization experiments to reveal details of the flow inside the coating bead. The first attempts to visualize a coating flow were limited to displaying the free‐surface configuration as a function of the operating parameters. Later, careful experiments were used to visualize streamlines with vortices inside a coating bead for different coating processes. Streamline visualization were crucial on enhancing the fundamental understanding of different coating flows. However, the application of quantitative methods capable of providing instantaneous measurements of the velocity field inside a coating bead is still rare. Velocity measurements in coating flows are extremely challenging because of the small scale, and the presence of liquid‐air interfaces. In this work, the particle‐image velocimetry (PIV) technique was used to study the flow between a rotating roll and a stationary plate, a prototype forward roll coating flow. Theoretical predictions of the same flow were obtained by solving the Navier‐Stokes equations with the appropriate boundary conditions for free‐surface flows. The velocity and the rate of deformation at each point were measured at different operating parameters. Some of the results were compared with the theoretical predictions. © 2006 American Institute of Chemical Engineers AIChE J, 2007.

Numerical Simulations of Non-Isothermal Flow in Off-Axis Rotation of a Can Containing a Headspace Bubble

This paper describes numerical simulations of the non-isothermal, laminar flow of Newtonian and non-Newtonian liquids inside rotating cylindrical cans containing a headspace air bubble. Two modes of rotation are considered: axial rotation about a horizontal axis and end-over-end rotation. The rotational speed is held constant so that once initial transients have decayed the flow field in both cases is periodic. The aim of the numerical simulations, carried out using the ANSYS CFX computational fluid dynamics software, is to compare liquid heating times for different flow conditions. To reduce computational run times the calculations are carried out for a liquid with an artificially high value of thermal diffusivity. For axial rotation the simulations have been carried out using 2D and 3D models and it is shown that a 2D model can identify trends in heating times. In both end-over-end and axial modes, rotational speeds and radii of rotation are identified which minimize the heating time. The conditions are shown to correspond closely to those which maximize a measure of mixing in previous studies of isothermal flow.

Momentum transfer in an agitated vessel with off-centred impellers

AbstractMomentum transfer was investigated in an unbaffled agitated vessel of inner diameter 0.3 m equipped with different off-centred impellers. The distribution of the shear rate on the tank wall as a function of the impeller type and Reynolds number was studied in the turbulent regime of the Newtonian liquid flow. The dependences of the averaged dimensionless shear rate, friction coefficient, and dissipated energy on the Reynolds number and eccentricity ratio were approximated using four-parameter equations.

Taylor-Couette Instabilities in Flows of Newtonian and Power-Law Liquids in the Presence of Partial Annulus Obstruction

The flow inside a horizontal annulus due to the inner cylinder rotation is studied. The bottom of the annular space is partially blocked by a plate parallel to the axis of rotation, thereby destroying the circumferential symmetry of the annular space geometry. This flow configuration is encountered in the drilling process of horizontal petroleum wells, where a bed of cuttings is deposited at the bottom part of the annulus. The velocity field for this flow was obtained both numerically and experimentally. In the numerical work, the equations which govern the three-dimensional, laminar flow of both Newtonian and power-law liquids were solved via a finite-volume technique. In the experimental research, the instantaneous and time-averaged flow fields over two-dimensional meridional sections of the annular space were measured employing the particle image velocimetry (PIV) technique, also both for Newtonian and power-law liquids. Attention was focused on the determination of the onset of secondary flow in the form of distorted Taylor vortices. The results showed that the critical rotational Reynolds number is directly influenced by the degree of obstruction of the flow. The influence of the obstruction is more perceptible for Newtonian than for non-Newtonian liquids. The more severe is the obstruction, the larger is the critical Taylor number. The height of the obstruction also controls the width of the vortices. The calculated steady-state axial velocity profiles agreed well with the corresponding measurements. Transition values of the rotational Reynolds number are also well predicted by the computations. However, the measured and predicted values for the vortex size do not agree as well. Transverse flow maps revealed a complex interaction between the Taylor vortices and the zones of recirculating flow, for moderate to high degrees of flow obstruction.

Dynamics of magma flow inside volcanic conduits with bubble overpressure buildup and gas loss through permeable magma

Many volcanic eruptions show transitions between extrusive and explosive behaviour. We develop a new generic model that considers concurrence between pressure buildup in the bubbles due to the viscous resistance to their growth and gas escape through the bubble network as they become interconnected. When the pressure difference between bubbles and magma reaches the strength of the material fragmentation occurs. The effect of grain size distribution on the flow in gas-particle dispersion is modelled by two populations of particles which strongly influence the velocity of sound in the mixture. Solutions to the steady-state boundary value problem show non-uniqueness. There are at least two regimes for the fixed parameters in the magma chamber. In the low discharge rate regime, fragmentation does not occur and magma rises with partial gas escape. This regime corresponds to extrusive activity. The upper regime corresponds to explosive activity. The simulations using the parameters defined at the workshop produced the following results for a rhyolitic magma composition: discharge rate 5.5×10 7 kg/s; fragmentation at depth of 2585 m with magma vesicularity of 0.74; exit gas velocity varies from 200 to 450 m/s depending on the mass fraction of small particles in the fragmented mixture; exit pressure is in the range 1.5 to 3 MPa. Variation of conduit diameter d in the range 40 to 70 m gives a mass flow rate Q which depends on the diameter as d 2.8, less strongly than for the case of viscous flow of Newtonian liquid in a cylindrical pipe where Q∼ d 4. With the increase in conduit diameter, fragmentation happens later in the flow and conduit resistance remains high. Changes in magma temperature from 700 to 950 °C lead to increase in discharge rate only by a factor of 4 whereas viscosity decreases by more then 8000 times.

Stirring of a liquid in a stirred tank with an eccentrically located impeller

The results of an experimental analysis of the stirring of a liquid in a tank equipped with an eccentrically located propeller or HE 3 impeller are presented in the paper. Mixing time, power consumption and the distributions of the momentum and heat transfer coefficients on the tank wall as a function of the impeller eccentricity e / R were studied within the turbulent regime of the Newtonian liquid flow. The effects of the liquid pumping mode of the stirrer (up- or downwards) and the position of the measuring point at the plane r, ϕ of the tank cross section on the dimensionless mixing time Θ were found. Axial and angular distributions of the dimensionless shear rate γ • / n , friction coefficient f and heat transfer coefficient α l were identified on the cylindrical wall of the stirred tank (at the plane z, ϕ ). The profiles of the γ • / n , f and α l depend strongly on the eccentricity e / R , angular co-ordinate ϕ and liquid circulation imposed by the axial flow impeller. The results of the experimental studies were approximated mathematically (Eqs. (6)–(10)).

Heat transfer in temperature-dependent non-Newtonian flow

Flow and thermal convection in heat exchangers can be affected by variations in viscosity. In circular pipes the significance of this effect was expressed by Sieder and Tate’s empirical formula. Similar correction can be derived for other heat transfer problems. Exact solutions for heat transfer during the non-isoviscous laminar flow of Newtonian and non-Newtonian liquids in circular and flat ducts under conditions of constant wall temperature or constant wall heat flux are analyzed. Simple generalized procedures for heat transfer coefficient and friction estimate are recommended.

Numerical Simulation and Experimental Visualization of the Isothermal Flow of Liquid Containing a Headspace Bubble Inside a Closed Cylinder During off-Axis Rotation

Numerical simulations and visualization of the isothermal flow of Newtonian and non-Newtonian liquids inside a rotating cylindrical Perspex ‘can’, which includes a headspace air bubble, are presented. The can has a diameter of 76 mm and is 66 mm long and, in the experiments, rotational speeds up to 40 rpm are considered. The Newtonian liquid is Corena Oil 27, which has a viscosity of 0.09 P as at 20 °C, and the non-Newtonian liquid is Keltrol, which is a shear-thinning liquid with a zero shear viscosity of 349 P as at 20 °C and a viscosity of 0.07 P as at a shear rate of 120s–1, which is typical of the largest shear rates that occur in this study. The work forms part of a broader study of the in-container convective processing of foods. The centroid of the can rotates around a circle in a vertical plane and the axis of symmetry of the can may be normal to the plane of rotation (termed ’axial’ rotation) or lie in the plane of rotation (termed ‘end-over-end’ rotation). The numerical simulations are (spatially) two- or three-dimensional and time-dependent, use a rotating co-ordinate system and determine the air–liquid interface (i.e. the headspace bubble position), for Newtonian and non-Newtonian liquids, using a homogeneous two-phase flow model. These complex simulations are carried out with the aid of the CFX software. A specially constructed rig is used for the experiments. Numerically predicted headspace bubble positions are in very good agreement with the experimental flow visualizations. It is shown that for a certain combination of off-axis position of the can and rotational speed the headspace bubble will move through the liquid. Such behaviour significantly enhances mixing and so is of great interest to companies who use this method of food processing. The circumferentially averaged median shear rate is used to quantify the effect of varying the off-axis position and rotational speed and, for both Newtonian and non-Newtonian liquids, conditions are identified under which this parameter is maximized. Two examples illustrating how the validated numerical simulations can be used to carry out parametric studies are then given.

Viscoelastic effects on the stability of wall-bounded shear flows

The dissolution of high molecular weight polymers and surfactants to wall-bounded shear flows of Newtonian liquids significantly modifies their stability characteristics. The critical Reynolds number Rec first decreases with increasing flow elasticity E until a critical value E=E* is reached and increases back again for E>E*. We explore the mechanisms that cause this behavior in the viscoelastic plane Poiseuille flow of an Oldroyd-B liquid. The minimum in the Rec−E curve arises from two competing contributions to the perturbation vorticity transport: The contribution from the viscoelastic shear stress perturbations that becomes more dissipative with increasing E and that from the viscoelastic normal stress perturbations that becomes more destabilizing with increasing E. Similar behavior is also exhibited by the contributions of the normal and the shear stress perturbations to the kinetic-energy budget. When a Deborah number based on the time scale of the critical disturbance becomes O(1) (≈1.6±0.1, irrespective of the solvent to total viscosity ratio), the dissipative influence of the shear stress perturbations becomes dominant. The elasticity value EC at which this occurs is approximately equal to E*. Moreover, both E* and EC exhibit similar asymptotic dependence on the solvent to total viscosity ratio. Furthermore, E* and EC are of the same order of magnitude as the elasticity values for which the onset of polymer-induced drag reduction is predicted by direct numerical simulations. Finally, we show that the perturbation velocity vector aligns progressively closer with the base flow velocity as E is increased for E<E*, contributing to the initial destabilization.