Vortex Pump as Turbine for Energy Recovery in Viscous Fluid Flows with Reynolds Number Effect

2021 ◽  
Author(s):  
Wen-Guang LI
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Flow Rate ◽  
Power Efficiency ◽  
Stokes Equations ◽  
Entropy Generation Rate ◽  
Hydraulic Loss ◽  
Centrifugal Pumps ◽  
Vortex Pump ◽  
Turbine Mode

Abstract A vortex pump with a specific speed of 76 was studied in its turbine mode by using Fluent 6.3 based on the steady, three-dimensional, incompressible, Reynolds time-averaged Navier-Stokes equations, standard k-? turbulence model and non-equilibrium wall function in multiple reference system. The performance and flow structure of six liquids with different densities and viscosities were characterized, and the hydraulic, volumetric, and mechanical losses were discomposed. The correction factors of flow rate, head, shaft-power, efficiency, and disc friction power in turbine mode were correlated with impeller Reynolds number at three operational points. The conversion factors of flow rate, head, efficiency from the pump mode to the turbine mode were expressed with Reynolds number and compared with the counterparts of centrifugal pumps in the literature. It was indicated that the vortex pump can produce power as a turbine but becomes inefficient with increasing viscosity or decreasing impeller Reynolds number, especially as the number is smaller than 104 due to increased hydraulic, volumetric, and mechanical power losses. A vortex structure with radial, axial, and meridian vortices occurs in the impeller at different flow rates and viscosities. The incidence at blade leading edge and deviation angle at blade trailing edge depend largely on flow rate and viscosity. The impeller should be modified to improve its hydraulic performance under highly viscous fluid flow conditions. The entropy generation rate method cannot demonstrate the change in hydraulic loss with viscosity when the Reynolds number is below 104.

Velocity characteristics in a multiphase pump under different tip clearances

2020 ◽  
pp. 095765092094653
Author(s):  
Guangtai Shi ◽  
Zongku Liu ◽  
Yexiang Xiao ◽  
Helin Li ◽  
Xiaobing Liu
Keyword(s):  
Velocity Distribution ◽  
Flow Rate ◽  
High Speed ◽  
Stokes Equations ◽  
Design Flow ◽  
Tip Clearance ◽  
High Speed Photography ◽  
Hydraulic Loss ◽  
Impeller Blade ◽  
Multiphase Pump

To investigate the effect of tip clearance on the velocity distribution in a multiphase pump, the internal flow and velocity distribution characteristics in pump under different tip clearances are studied using experimental and numerical methods. Simulations based on the Reynolds-Averaged Navier-Stokes equations (RANS) and the standard k-ε turbulence model are carried out using ANSYS CFX. Under conditions of inlet gas void fraction (IGVF) is 5% at the flow rate of 0.6Q, 0.7Q and 0.8Q (Q is the design flow rate), the accuracy of the numerical method is verified by comparing with the experimental data using high-speed photography. Results show that the leakage flow interacts with the main flow and evolves into the tip leakage vortex (TLV). Due to the TLV, the pressure, velocity, turbulent kinetic energy (TKE), vorticity and streamlines on the S2 stream surface in the impeller and diffuser are changed greatly under different tip clearances. The velocities at the impeller outlet and diffuser inlet along the radial direction are also changed. The axial velocity distribution is similar to the meridional velocity distribution at the impeller blade outlet. While the relative velocity and absolute velocity distribution show the opposite trends. In addition, the vorticity is larger near the tip separated vortex and the hydraulic loss in pump is also increased due to the TLV.

scholarly journals Inter-Blade Vortex and Vortex Rope Characteristics of a Pump-Turbine in Turbine Mode under Low Flow Rate Conditions

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2554 ◽  
Author(s):  
Seung-Jun Kim ◽  
Jun-Won Suh ◽  
Young-Seok Choi ◽  
Jungwan Park ◽  
No-Hyun Park ◽  
...  
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Low Flow ◽  
Renewable Energy Resources ◽  
Two Phase ◽  
Constant Frequency ◽  
Pump Turbine ◽  
Vortex Rope ◽  
Turbine Mode ◽  
Low Flow Rate

Pump-turbines are often used to provide a stable power supply with a constant frequency in response to intermittent renewable energy resources. However, existing pumped-storage power stations often operate under off-design conditions because of the increasing amounts of inconsistent renewable resources that have been added to the grid. Under off-design low flow rate conditions, inter-blade vortex and vortex rope phenomena usually develop in the runner and draft tube passages, respectively, in turbine mode. These vortices cause complicated flow patterns and pressure fluctuations that destabilize the operation of the pump-turbine system. Therefore, this study investigates the influence of correlation between the inter-blade vortex and vortex rope phenomena under low flow rate conditions. Three-dimensional steady- and unsteady-state Reynolds-averaged Navier–Stokes equations were calculated with a two-phase flow analysis using a shear stress transport as the turbulence model. The inter-blade vortices in the runner passages were captured well at the low flow rate conditions, and the vortex rope was found to develop within a specific range of low flow rates. These vortex regions showed a blockage effect and complicated flow characteristics with backflow in the passages. Moreover, higher unsteady pressure characteristics occurred at locations where the vortices were especially pronounced.

Modeling and Optimal Control of a Variable-Speed Centrifugal Pump With a Pipeline

2016 ◽  
Author(s):  
Cristian F. Jaimes Saavedra ◽  
Sebastian Roa Prada ◽  
Jessica G. Maradey Lázaro
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Flow Control ◽  
Flow Rate ◽  
Power Efficiency ◽  
Control Valve ◽  
Operating Point ◽  
Variable Frequency ◽  
Centrifugal Pumps ◽  
Variable Frequency Drive

Pumping processes often require different operating conditions for the same pipeline. The conditions downstream in the pipeline can change in such a way that the pressure at the discharge of the pump may vary, which automatically introduces changes in the flow supplied by the pump into the pipeline due to the head vs flow characteristic curve of the pump. Even under varying pipeline pressure conditions, it may be necessary to keep the flow discharge of the pump constant. The two most commonly used control strategies for flow control with centrifugal pumps are by means of a fixed-speed pump and a control valve at the outlet of the pump, or by means of a variable frequency drive which avoids the need for the control valve. It has been demonstrated that the approach with the fixed-speed pump and the control valve provides poor power efficiency results, so a variable frequency drive is normally the solution of choice in industry applications. The use of a variable frequency drive allows reaching the flow required by the system without changing the physical characteristic of the pump or pipeline, i.e., it is not necessary to shut the system down to replace the impeller of the pump. However, affinity laws of centrifugal pumps dictate that a change in the rotational speed of the impeller shifts the characteristic curves of the pump, not only the flow vs head curve, but also the efficiency curves, among others. Besides, searching for a different operating point by changing the speed of the pump does not necessarily guarantees optimal operating power efficiency. This paper proposes an optimization approach where a compromise is made between flow control and power efficiency by minimizing the error in the flow rate while at the same time maximizing the power efficiency. To accomplish this goal, this paper presents the modeling of the pump and pipeline, and the design of a linear quadratic regulator control for the fluid flow passing through a given pipeline. The fluid under consideration is water. The mathematical model of the overall system is derived by considering the model of an AC motor, the pump and the hydraulic circuit. Then, with the help of the software MATLAB, the controller was designed and implemented with the linearized mathematical model. The actuator of the control system is the variable frequency drive that changes the speed of the impeller to adjust the flow rate to the required operating point under different loading conditions. The results show the behavior of the compensated system with the optimal controller. In practice, the control system must take into account the constraints of the control effort, which means, the frequency of the pump must be kept within safe values to achieve proper functioning of the pumping system.

Secondary Flows in Centrifugal Pump Impellers: PIV Measurements and CFD Computations

2009 ◽  
Author(s):  
R. W. Westra ◽  
L. Broersma ◽  
K. van Andel ◽  
N. P. Kruyt
Keyword(s):  
Reynolds Number ◽  
Centrifugal Pump ◽  
Flow Rate ◽  
Stokes Equations ◽  
Suction Side ◽  
Velocity Profiles ◽  
Secondary Flows ◽  
Design Flow ◽  
Low Velocity ◽  
Flow Rates

Two-dimensional Particle Image Velocimetry measurements and three-dimensional Computational Fluid Dynamics (CFD) analyses have been performed of the flow field inside the impeller of a low specific-speed centrifugal pump operating with a vaneless diffuser. Flow rates ranging from 80% to 120% of the design flow rate are considered in detail. It is observed from the velocity measurements that secondary flows occur. These flows result in the formation of regions of low velocity near the intersection of blade suction side and shroud. The extent of this jet-wake structure decreases with increasing flow rate. Velocity profiles have also been computed from Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model, using a commercial CFD-code. For the considered flow rates the qualitative agreement between measured and computed velocity profiles is very good. Overall, the average relative difference between these velocity profiles is around 7%. Additional CFD computations have been performed to assess the influence of Reynolds number and shape of the inlet velocity profile on the computed velocity profiles. It is found that the influence of Reynolds number is mild. The shape of the inlet profile only has a weak effect at the shroud.

Effects of Blade Inlet Width on Performance of Centrifugal Pump as Turbine With Special Impeller Using in Turbine Mode

2016 ◽  
Author(s):  
Tao Wang ◽  
Xiaobing Liu ◽  
Xide Lai ◽  
Qiuqin Gou
Keyword(s):  
Centrifugal Pump ◽  
Flow Rate ◽  
High Efficiency ◽  
Cost Effective ◽  
Pressure Head ◽  
Design Flow ◽  
Hydraulic Loss ◽  
Obvious Effect ◽  
Velocity Moment ◽  
Turbine Mode

A reverse running centrifugal pump is one of the attractive choices in micro-hydropower development and industrial pressure energy recovery. One of the main problems in utilizing pump as turbine (PAT) is that the performance of PAT is usually not ideal due to the impeller with the routine backward curved blades which do not match well with turbine running condition. A cost effective suitable way for solving this problem is to redesign impeller with forward curved blades from turbine working condition while the other components do not undergo any modifications. Blade inlet width is one of the main factors in impeller design. Therefore, research on the influence of blade inlet width on PAT performance is useful. In this paper, based on the constant velocity moment theory, the velocity moment at impeller inlet is acquired, firstly. Next, a relationship expression between blade inlet angle and the design flow rate is deduced. To perform research on blade inlet width influencing PAT’s performance with special impeller, three impellers which inlet widths are 13 mm, 16 mm and 19 mm, respectively, are designed by using ANSYS Bladegen software. Numerical simulation and analysis of the three PATs are performed using a verified computational fluid dynamics (CFD) technique. Comparison of three PATs’ performance curves obtained by CFD, we can find that the blade inlet width has obvious effect on the performance of PAT. The flow rate, required pressure head, generated shaft power, and efficiency at best efficiency point (BEP) increase with the increase of blade inlet width. The flow rates of three PATs at BEP are about 90 m3/h, 100 m3/h and 105 m3/h, respectively, when impeller inlet width varies from 13 mm to 16 mm and 19 mm. The BEP of three PATs shifts towards higher discharge and its high efficiency range becomes wider with the increase of blade inlet width. At above 100 m3/h discharge, the PAT efficiency increases in accordance with the increase of blade inlet width. And the hydraulic loss and turbulence kinetic energy loss within impeller decrease with the increase of blade inlet width. In order to improve efficiency, it is helpful to choose a relatively larger blade inlet width in the design of special impeller using in turbine mode of PAT.

Laminar Inward Flow of an Incompressible Fluid Between Rotating Disks, With Full Peripheral Admission

1968 ◽  
Vol 35 (2) ◽  
pp. 229-237 ◽  
Author(s):  
K. E. Boyd ◽  
W. Rice
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Stokes Equations ◽  
Complete Solution ◽  
Applied Pressure ◽  
Tangential Velocity ◽  
Tangential Component ◽  
Rotating Disks ◽  
Outer Periphery ◽  
Inlet Conditions

The laminar flow of an incompressible Newtonian fluid, radially inward between parallel co-rotating disks is considered. The through-flow is supported by an externally applied pressure difference between the outer periphery and a circular fluid exhaust hole at an inner radius. The fluid supplied at the outer periphery is considered with arbitrary velocity components, such that the tangential component may be greater or less than the disk peripheral velocity. A sufficiently complete problem statement is formulated from the Navier-Stokes’ equations. The problem has three parameters: a Reynolds number, a flow-rate parameter, and a peripheral tangential velocity component parameter. A numerical method of solution is detailed and typical numerical results are given illustrating the phenomena that occur in the inlet region for various inlet conditions. It is shown that the solution becomes the asymptotic solution given by previous investigators at interior radii following the inlet. Correspondence between the complete solution given herein and the earlier asymptotic solutions is established as dependent on corresponding values of Reynolds number and flow rate only. The results are discussed from the point of view of application of the solution in the development of multiple-disk turbines.

Affinity laws for impellers trimmed in two partial emission pumps with very low specific speed

2020 ◽  
pp. 095440622093631
Author(s):  
Wen-Guang Li
Keyword(s):  
Flow Rate ◽  
Substantial Reduction ◽  
Flow Coefficient ◽  
Energy Utilization ◽  
Utilization Efficiency ◽  
Hydraulic Loss ◽  
Centrifugal Pumps ◽  
Recirculation Flow ◽  
Low Specific Speed ◽  
Specific Speed

Partial emission pumps or open impeller pumps or tangent pumps with very low specific speed at either fast or conventional speed have found extensive applications in aircraft, liquid rockets, cryogenic fluid systems, chemical and petroleum-chemical industries, energy and food processing systems, etc. Usually, impeller trimming of rotodynamic pumps serves as an effective tool to meet required hydraulic performance of a liquid transport system and also to improve the entire system energy utilization efficiency. However, the affinity laws for the impeller trimming in a partial emission pump have been unavailable so far. In the paper, such affinity laws in terms of constant and variable exponents were established for flow rate, head, efficiency, flow coefficient and head coefficient based on the existing experimental data of two partial emission pumps at best efficiency points. It was shown that the affinity laws differ from the counterparts for centrifugal pumps, especially the exponent of around 2 for flow rate and the exponent of approximately 1.5 for head in comparison with nearly 1.5 for flow rate and about 2 for head in centrifugal pumps. The underlying mechanism for this effect was disclosed in terms of the ratios of the hydraulic, volumetric and mechanical efficiencies after trimming to the efficiencies before trimming analytically. The hydraulic loss, leakage flow rate and recirculation flow rate in two pumps were estimated according to the elements of fluid mechanics. It was identified that the hydraulic loss in the volute is more dominant than in the impeller and responsible for the rise of hydraulic efficiency with the trimming in progress. Moreover, the significant increase of recirculation flow rate between the volute tongue and the impeller outlet contributes to the substantial reduction in flow rate after impeller trimming.

scholarly journals Effect of Lower Surface Roughness on Nonlinear Hydraulic Properties of Fractures

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinglong Li ◽  
Xianghui Li ◽  
Bo Zhang ◽  
Bin Sui ◽  
Pengcheng Wang ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Regimes ◽  
Lower Surface ◽  
Nonlinear Flow ◽  
Hydraulic Pressure

This study investigates the effect of fracture lower surface roughness on the nonlinear flow behaviors of fluids through fractures when the aperture fields are fixed. The flow is modeled with hydraulic pressure drop = 10 − 4 ~ 10 5   Pa / m by solving the Navier-Stokes equations based on rough fracture models with lower surface roughness varying from JRC = 1 to JRC = 19 . Here, JRC represents joint roughness coefficient. The results show that the proposed numerical method is valid by comparisons between numerically calculated results with theoretical values of three parallel-plate models. With the increment of hydraulic pressure drop from 10-4 to 105 Pa/m spanning ten orders of magnitude, the flow rate increases with an increasing rate. The nonlinear relationships between flow rate and hydraulic pressure drop follow Forchheimer’s law. With increasing the JRC of lower surfaces from 1 to 19, the linear Forchheimer coefficient decreases, whereas the nonlinear Forchheimer coefficient increases, both following exponential functions. However, the nonlinear Forchheimer coefficient is approximately three orders of magnitude larger than the linear Forchheimer coefficient. With the increase in Reynolds number, the normalized transmissivity changes from constant values to decreasing values, indicating that fluid flow transits from linear flow regimes to nonlinear flow regimes. The critical Reynolds number that quantifies the onset of nonlinear fluid flow ranges from 21.79 to 185.19.

The slow translation of a sphere in a rotating viscous fluid

1982 ◽  
Vol 117 ◽  
pp. 251-267 ◽  
Author(s):  
S. C. R. Dennis ◽  
D. B. Ingham ◽  
S. N. Singh
Keyword(s):  
Reynolds Number ◽  
Partial Differential Equations ◽  
Numerical Methods ◽  
Angular Velocity ◽  
Finite Difference ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Partial Differential

The motion of a sphere along the axis of rotation of an incompressible viscous fluid that is rotating as a solid mass is investigated by means of numerical methods for small values of the Reynolds and Taylor numbers. The Navier–Stokes equations governing the steady axisymmetric flow can be written as three coupled, nonlinear, elliptic partial differential equations for the stream function, vorticity and rotational velocity component. Two numerical methods are employed to solve these equations. The first is the method of series truncation in which the dependent variables are expressed as series of orthogonal Gegenbauer functions and the equations of motion are then reduced to three coupled sets of ordinary differential equations, which are integrated numerically subject to their boundary conditions. In the second method, specialized finite–difference techniques of solution are applied to the two-dimensional partial differential equations. These techniques employ finite-difference equations with coefficients that depend upon the exponential function; a particularly suitable form of approximation for use in calculating numerical solutions is obtained by expanding the exponential coefficients in powers of their exponents.Calculated results obtained by the two methods are in good agreement with each other. The calculations have been carried out according to theoretical assumptions that simulate the experiments of Maxworthy (1965) in which the sphere experiences no resultant torque exerted by the surrounding fluid and is free to rotate with constant angular velocity. Numerical estimates of this angular velocity and of the drag exerted by the fluid on the sphere are found to agree well with the experimental results for Reynolds and Taylor numbers in the range from zero to unity. The results for small values of the Reynolds number are also consistent with theoretical work of Childress (1963, 1964) which is valid as the Reynolds number tends to zero.

scholarly journals Optimized Blade Design of Counter-Rotating-Type Pump-Turbine Unit Operating in Pump and Turbine Modes

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Jin-Woo Kim ◽  
Jun-Won Suh ◽  
Young-Seok Choi ◽  
Kyoung-Yong Lee ◽  
Toshiaki Kanemoto ◽  
...  
Keyword(s):  
Flow Rate ◽  
Turbine Unit ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Latin Hypercube Sampling ◽  
Low Flow ◽  
Pump Turbine ◽  
Design Variables ◽  
Turbine Mode

In this study, a counter-rotating-type pump-turbine unit was optimized to improve the pump and turbine mode efficiencies simultaneously. Numerical analysis was carried out by solving three-dimensional Reynolds-averaged Navier–Stokes equations using the shear stress turbulence model. The hub and tip blade angles of the rear impeller (in the pump mode) were selected as the design variables by conducting a sensitivity test. An optimization process based on steady flow analysis was conducted using a radial basis neural network surrogate model with Latin hypercube sampling. The pump and turbine mode efficiencies of the unit were selected as the objective functions and they combined into a single specific objective function with the weighting factors. Consequently, the pump and turbine mode efficiencies of the optimum design increased simultaneously at overall range of flow rate, except for low flow rate of turbine mode, compared to the reference design.

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