Periodic flows through curved tubes: the effect of the frequency parameter

1990 ◽  
Vol 210 ◽  
pp. 353-370 ◽  
Author(s):  
Costas C. Hamakiotes ◽  
Stanley A. Berger
Keyword(s):  
Flow Field ◽  
Flow Rate ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Frequency Parameter ◽  
Dean Number ◽  
Single Vortex ◽  
Curved Pipe ◽  
Periodic Flows ◽  
Axial Pressure Gradient

In a previous paper we reported on the effect of Dean number, κm, on the fully developed region of periodic flows through curved tubes. In this paper we again consider a sinusoldally varying volumetric flow rate in a curved pipe of arbitrary curvature ratio, δ, and investigate the effect of frequency parameter α, and Reynolds number Rem on the flow. Specifically, we report on the flow-field development for the range 7.5 [les ] α [les ] 25, and 50 [les ] Rem [les ] 450. The results, obtained by numerical integration of the full Navier–Stokes equations, reveal a number of characteristics of the flow previously unreported. For low values of Rem the secondary flow consists of a single vortex (Dean-type motion) in the half-cross-section at all times and for all values of α studied. For higher Rem we observe inward ‘centrifuging’ (Lyne-type motion) at the centre. This motion always occurs during the accelerating period of the volumetric flow rate. It appears at lower α for higher Rem and, for the given Rem at which it appears, it occurs at earlier times in the cycle for lower a. A striking feature is observed for α = 15 for the range 315 [les ] Rem [les ] 400: period tripling. The flow field varies periodically with time for the duration of three volumetric-flow-rate cycles then repeats for the subsequent three cycles, and so on. The computed axial pressure gradient also varies periodically with time but with the same period as the volumetric flow rate.

Effects of Fe3O4/Water Nanofluid on the Efficiency of a Curved Pipe

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Milad Kelidari ◽  
Ali Jabari Moghadam
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Volume Concentration ◽  
Volume Fraction ◽  
Working Fluid ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Curved Pipe ◽  
Overall Efficiency

Different-radius of curvature pipes are experimentally investigated using distilled water and Fe3O4–water nanofluid with two different values of the nanoparticle volume fraction as the working fluids. The mass flow rate is approximately varied from 0.2 to 0.7 kg/min (in the range of laminar flow); the wall heat flux is nearly kept constant. The experimental results reveal that utilizing the nanofluid increases the convection heat transfer coefficient and Nusselt number in comparison to water; these outcomes are also observed when the radius of curvature is decreased and/or the mass flow rate is increased (equivalently, a rise in Dean number). The resultant pressure gradient is, however, intensified by an increase in the volume concentration of nanoparticles and/or by a rise in Dean number. For any particular working fluid, there is an optimum mass flow rate, which maximizes the system efficiency. The overall efficiency can be introduced to include hydrodynamic as well as thermal characteristics of nanofluids in various geometrical conditions. For each radius of curvature, the same overall efficiency may be achieved for two magnitudes of nanofluid volume concentration.

The Effect of Slip on the Discharge From Partially Filled Circular and Fully Filled Lens and Figure 8 Shaped Pipes

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Samuel Irvine ◽  
Luke Fullard
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Flow Rate ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Symmetry Plane ◽  
Volumetric Flow Rate ◽  
Wall Slip ◽  
Circular Pipe ◽  
Gravity Driven Flow

In this work, we examine the effect of wall slip for a gravity-driven flow of a Newtonian fluid in a partially filled circular pipe. An analytical solution is available for the no-slip case, while a numerical method is used for the case of flow with wall slip. We note that the partially filled circular pipe flow contains a free surface. The solution to the Navier–Stokes equations in such a case is a symmetry of a pipe flow (with no free surface) with the free surface as the symmetry plane. Therefore, we note that the analytical solution for the partially filled case is also the exact solution for fully filled lens and figure 8 shaped pipes, depending on the fill level. We find that the presence of wall slip increases the optimal fill height for maximum volumetric flow rate, brings the “velocity dip” closer to the free surface, and increases the overall flow rate for any fill. The applications of the work are twofold; the analytical solution may be used to verify numerical schemes for flows with a free surface in partially filled circular pipes, or for pipe flows in lens and figure 8 shaped pipes. Second, the work suggests that flows in pipes, particularly shallow filled pipes, can be greatly enhanced in the presence of wall slip, and optimal fill levels must account for the slip phenomenon when present.

scholarly journals Flow-Field Characteristics of High-Temperature Annular Buoyant Jets and Their Development Laws Influenced by Ventilation System

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yi Wang ◽  
Yanqiu Huang ◽  
Jiaping Liu ◽  
Hai Wang ◽  
Qiuhan Liu
Keyword(s):  
High Temperature ◽  
Flow Field ◽  
Cross Section ◽  
Flow Rate ◽  
Ventilation System ◽  
Volumetric Flow Rate ◽  
Outer Diameter ◽  
Exhaust Hood ◽  
Buoyant Jets ◽  
Flow Field Characteristics

The flow-field characteristics of high-temperature annular buoyant jets as well as the development laws influenced by ventilation system were studied using numerical methods to eliminate the pollutants effectively in this paper. The development laws of high-temperature annular buoyant jets were analyzed and compared with previous studies, including radial velocity distribution, axial velocity and temperature decay, reattachment position, cross-section diameter, volumetric flow rate, and velocity field characteristics with different pressures at the exhaust hood inlet. The results showed that when the ratio of outer diameter to inner diameter of the annulus was smaller than 5/2, the flow-field characteristics had significant difference compared to circular buoyant jets with the same outer diameter. For similar diameter ratios, reattachment in this paper occurred further downstream in contrast to previous study. Besides, the development laws of volumetric flow rate and cross-section diameter were given with different initial parameters. In addition, through analyzing air distribution characteristics under the coupling effect of high-temperature annular buoyant jets and ventilation system, it could be found that the position where maximum axial velocity occurred was changing gradually when the pressure at the exhaust hood inlet changed from 0 Pa to −5 Pa.

Pressure drop and power dissipation in oscillatory wavy-walled-tube flows

1988 ◽  
Vol 187 ◽  
pp. 573-588 ◽  
Author(s):  
M. E. Ralph
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Power Dissipation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Frequency Parameter ◽  
Mean Power ◽  
Pressure Drops ◽  
The Mean

Pressure drops occurring in oscillatory viscous flows in wavy-walled tubes have been studied experimentally, for Reynolds numbers up to 1500 and Strouhal numbers in the range 0.005 to 0.02, and by numerical solution of the Navier-Stokes equations, for Reynolds numbers up to 200 and Strouhal numbers between 0.005 and 0.1. Agreement was good for values of the mean modulus of the pressure drop at lower Strouhal numbers and for values of the mean power dissipation at all Strouhal numbers.Numerical solutions have shown that the pressure drop may vary non-sinusoidally, even though the imposed variation in flow rate is sinusoidal. This cannot be explained by the nonlinearity of the steady pressure drop-flow rate relationship, and arises because the velocity field is not quasi-steady. In particular energy may be stored in strong vortices formed during the acceleration phase of the flow cycle, and partially returned to the main flow later. The peak pressure drops in such flows, which are associated with the formation of these vortices, can be almost twice as large as values predicted by adding the appropriate quasi-steady and unsteady inertial contributions. This finding is important in the wider context of unsteady conduit flow.The dependences of the mean modulus of the pressure drop and the mean power dissipation on the Strouhal number and frequency parameter were investigated in detail numerically for two geometries. It was not possible to reduce either dependence to a function of a single parameter. The ‘equivalent’ straight-walled tube for power dissipation was found to have a smaller bore than that for pressure drop, leading to smaller ‘phase angles’ than might have been expected at large values of the frequency parameter. This is because as the pressure drop becomes increasingly dominated by unsteady inertia, there remain relatively large recirculations in which energy is dissipated.

Deviations Due to Non-Newtonian Influences Within a Miniature Viscous Disk Pump

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Phil Ligrani ◽  
Hui Jiang ◽  
Benjamin Lund ◽  
Jae Sik Jin
Keyword(s):  
Newtonian Fluid ◽  
Flow Rate ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Sucrose Concentration ◽  
Pure Water ◽  
Pressure Rise ◽  
Volumetric Flow Rate ◽  
Newtonian Flow ◽  
Newtonian Behavior

A miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid deviations due to non-Newtonian influences relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding different concentrations of sucrose to purified water, with increasing non-Newtonian characteristics as sucrose concentration increases from 0% (pure water) to 10% by mass. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm, and 2.38 mm, respectively, and a channel depth of 200 μm. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Within the present study, experimental data are given for rotational speeds of 1200–2500 rpm, fluid viscosities of 0.001–0.00134 Pa s, pressure rises of 0–220 Pa, and flow rates up to approximately 0.00000005 m3/s. The theory of Flumerfelt is modified and adapted for application to the present VDP environment. Included is a new development of expressions for dimensionless volumetric flow rate, and normalized local circumferential velocity for Newtonian and non-Newtonian fluid flows. To quantify deviations due to the magnitude non-Newtonian flow influences, a new pressure rise parameter is employed, which represents the dimensional pressure rise change at a particular flow rate and sucrose concentration, as the flow changes from Newtonian to non-Newtonian behavior. For 5% and 10% sucrose solutions at rotational speeds of 1200–2500 rpm, this parameter increases as the disk dimensional rotational speed increases and as the volumetric flow rate decreases. Associated magnitudes of the pressure difference parameter show that the fluid with the larger sucrose concentration (by mass) produces significantly larger differences between Newtonian and non-Newtonian fluid flow, for each value of dimensional volumetric flow rate. For each disc rotational speed, compared to Newtonian data, dimensional pressure rise variations with dimensional volumetric flow rate, which are associated with the non-Newtonian data, are generally lower when compared at a particular volumetric flow rate. Agreement with analytic results, for any given flow rate, rotational speed, and flow passage height, validates the shear stress model employed to represent non-Newtonian behavior, as well as the analytic equations and tools (based upon the Navier–Stokes equations) which are employed to predict measured behavior over the investigated range of experimental conditions.

Laminar entrance flow in a curved pipe

1984 ◽  
Vol 148 ◽  
pp. 109-135 ◽  
Author(s):  
W. Y. Soh ◽  
S. A. Berger
Keyword(s):  
Secondary Flow ◽  
Flow Separation ◽  
Axial Velocity ◽  
Stokes Equations ◽  
Velocity Profiles ◽  
Dean Number ◽  
Curvature Ratio ◽  
Curved Pipe ◽  
Flow Vortex ◽  
Entrance Flow

The full elliptic Navier–Stokes equations have been solved for entrance flow into a curved pipe using the artificial compressibility technique developed by Chorin (1967). The problem is formulated for arbitrary values of the curvature ratio and the Dean number. Calculations are carried out for two curvature ratios, a/R = 1/7 and 1/20, and for Dean number ranging from 108.2 to 680.3, in a computational mesh extending from the inlet immediately adjacent to the reservoir to the fully developed downstream region.Secondary flow separation near the inner wall is observed in the developing region of the curved pipe. The separation and the magnitude of the secondary flow are found to be greatly influenced by the curvature ratio. As observed in the experiments of Agrawal, Talbot & Gong (1978) we find: (i) two-step plateau-like axial-velocity profiles for high Dean number, due to the secondary flow separation, and (ii) doubly peaked axial-velocity profiles along the lines parallel to the plane of symmetry, due to the highly distorted secondary-flow vortex structure.

scholarly journals Differential Throttling and Fluidic Thrust Vectoring in a Linear Aerospike

2021 ◽  
Vol 6 (2) ◽  
pp. 8
Author(s):  
Michele Ferlauto ◽  
Andrea Ferrero ◽  
Matteo Marsicovetere ◽  
Roberto Marsilio
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Combustion Chambers ◽  
Thrust Vectoring ◽  
Fluidic Thrust Vectoring

Aerospike nozzles represent an interesting solution for Single-Stage-To-Orbit or clustered launchers owing to their self-adapting capability, which can lead to better performance compared to classical nozzles. Furthermore, they can provide thrust vectoring in several ways. A simple solution consists of applying differential throttling when multiple combustion chambers are used. An alternative solution is represented by fluidic thrust vectoring, which requires the injection of a secondary flow from a slot. In this work, the flow field in a linear aerospike nozzle was investigated numerically and both differential throttling and fluidic thrust vectoring were studied. The flow field was predicted by solving the Reynolds-averaged Navier–Stokes equations. The thrust vectoring performance was evaluated in terms of side force generation and axial force reduction. The effectiveness of fluidic thrust vectoring was investigated by changing the mass flow rate of secondary flow and injection location. The results show that the response of the system can be non-monotone with respect to the mass flow rate of the secondary injection. In contrast, differential throttling provides a linear behaviour but it can only be applied to configurations with multiple combustion chambers. Finally, the effects of different plug truncation levels are discussed.

Flow Patterns and Electrokinetic Mixing Performance in Heterogeneous Microchannels

2011 ◽  
Author(s):  
Jafar Jamaati ◽  
Hamid Niazmand ◽  
Metin Renksizbulut
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Concentration Field ◽  
Velocity Slip ◽  
Experimental Investigations ◽  
Mixing Efficiency ◽  
Surface Charges ◽  
Complex Flow ◽  
Single Vortex ◽  
Mixing Performance

Due to the recent advances in microfabrication techniques, it is possible to produce microchannels with positive, negative, or even neutral surface charges. According to several numerical and experimental investigations, such a combination of charge patterns on the microchannel walls results in complex flow fields with circulation zones that are highly desirable for fluid mixing requirements as in lab-on-a-chip devices. In this paper, the mixing efficiency associated with electro-osmotic flows in heterogeneous microchannels is investigated. The Navier-Stokes equations are solved for the flow field along with species transport equations to obtain the concentration field. The effects of the Electric Double Layer (EDL) on the flow field are considered using the Helmholtz-Smoluchowski model in which the EDL effects on the fluid adjacent to the walls are replaced by velocity slip at walls. Different configurations and profiles for the wall charges can be applied to the microchannel walls. In the present study, heterogeneous patterns consisting of different patches with constant zeta-potentials are considered. The flow pattern of a single patch consists of a single vortex attached to the channel wall, which significantly increases the mixing performance. It is expected that a combination of several patches would increase the mixing performance considerably. Therefore, the effects of the size, number, and locations of multiple patches on the mixing performance are investigated in detail. The results for a single patch indicate that the mixing efficiency increases with the size of the patch and its proximity to the microchannel inlet. It is expected that with a suitable combination of patches, an optimized configuration can be found in which the mixing efficiency is maximized and the length of the mixing section is minimized. The results can be applied to the design of micro-mixers to minimize their size while achieving the desired mixing requirements.

Flow Field Numerical Simulation and Performance Analysis of Progressing Cavity Pump

2021 ◽  
pp. 1-16
Author(s):  
Wu Liu ◽  
Mingcai Shu ◽  
Yongyao Sun ◽  
Yuanbo Fan
Keyword(s):  
Flow Field ◽  
Void Fraction ◽  
Working Conditions ◽  
Flow Rate ◽  
Rotation Speed ◽  
Volumetric Flow Rate ◽  
Differential Pressure ◽  
System Efficiency ◽  
Performance Parameters ◽  
Oil Viscosity

Summary Progressing cavity pump (PCP) is the essential booster equipment in oil–gas mixing delivery. Changes in relevant parameters in PCP operations directly affect the working performance and service life of the pump. On the basis of computational fluid dynamics (CFD) in this study, we apply dynamic grid technology to establish a 3D flow field numerical calculation model for the CQ11-2.4J PCP, which is used in the field of the Hounan Operation Area in Changqing oil field, China. The effects of several operating parameters, such as oil viscosity, pump rotation speed, differential pump pressure, and void fraction of oil, on the pressure and the velocity distribution of the PCP flow field are examined. Various performance parameters in the transport of the oil–gastwo-phase mixture are used in the analysis, including volumetric flow rate, slippage, shaft power, volumetric efficiency, and system efficiency. The results show that the pressure and speed distribution in the pump chamber of the PCP is relatively homogenous under different working conditions, whereas the pressure and speed exhibited sharp changes at the stator and rotor sealing line and adjacent areas in the pump chamber. Increasing the viscosity of the oil and the speed of the rotor can effectively improve the flow characteristics of the PCP, but extremely high pump rotation speed would cause a decline in system efficiency. Increasing the differential pressure and the void fraction of oil would result in a decrease in the volumetric flow rate and efficiency of the PCP. Considering the variation law of the PCP's performance parameters, the optimal interval for each operating parameter of the PCP is as follows: Oil viscosity at 50–100 mPa·s, pump rotation speed at 200–300 rev/min, differential pressure at 0.2–0.3 MPa, and the void fraction of oil not more than 50%. This research can provide technical support for the optimization of the working conditions of the PCP on site.

Steady entry flow in a curved pipe

1987 ◽  
Vol 177 ◽  
pp. 233-246 ◽  
Author(s):  
P. H. M. Bovendeerd ◽  
A. A. Van Steenhoven ◽  
F. N. Van De Vosse ◽  
G. Vossers
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Circular Cross Section ◽  
Axial Flow ◽  
Doppler Velocity ◽  
Velocity Measurements ◽  
Dean Number ◽  
Curved Pipe ◽  
Entry Velocity ◽  
Secondary Velocity

Laser-Doppler velocity measurements were performed on the entry flow in a 90° bend of circular cross-section with a curvature ratio a/R = 1/6. The steady entry velocity profile was parabolic, having a Reynolds number Re = 700, with a corresponding Dean number κ = 286. Both axial and secondary velocities were measured, enabling a detailed description of the complete flow field. The secondary flow at the entrance of the bend was measured to be directed completely towards the inner bend. Significant disturbance of the axial velocity field was not measured until a downstream distance (aR)½. Maximum secondary velocities were measured at 1.7 (aR)½ downstream from the inlet. The development of the axial flow field can be quite well explained from the secondary velocity field.

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