UNSTEADY FLOW ANALYSIS AND EXPERIMENTAL INVESTIGATION OF AXIAL-FLOW PUMP.*

ZHANG De-sheng, SHI Wei-dong, CHEN Bin, GUAN Xing-fan

Technical and Research Center of Fluid Machinery Engineering, Jiangsu University, Zhenjiang 212013, China, E-mail:desheng1982@163.com

(Received April 2, 2009, Revised August 2, 2009)

UNSTEADY FLOW ANALYSIS AND EXPERIMENTAL INVESTIGATION OF AXIAL-FLOW PUMP.*

ZHANG De-sheng, SHI Wei-dong, CHEN Bin, GUAN Xing-fan

Technical and Research Center of Fluid Machinery Engineering, Jiangsu University, Zhenjiang 212013, China, E-mail:desheng1982@163.com

(Received April 2, 2009, Revised August 2, 2009)

The three-dimensional unsteady turbulent flow in axial-flow pumps was simulated based on Navier-Stoke solver embedded with k-ε RNG turbulence model and SIMPLEC algorithm. Numerical results show that the unsteady prediction results are more accurate than the steady results, and the maximal error of unsteady prediction is only 4.54%. The time-domain spectrums show that the static pressure fluctuation curves at the inlet and outlet of the rotor and the outlet of the stator are periodic, and all have four peaks and four valleys. The pressure fluctuation amplitude increases from the hub to the tip at the inlet and outlet of the rotor, but decreases at the outlet of the stator. The pressure fluctuation amplitude is the greatest at the inlet of the rotor, and the average amplitude decreases sharply from the inlet to the outlet. The frequency spectrums obtained by Fast Fourier Transform (FFT) show that the dominant frequency is approximately equal to the blade passing frequency. The static pressure on the pressure side of hydrofoil on different stream surfaces remains almost consistent, and increases gradually from the blade inlet to the exit on the suction side at different time steps. The axial velocity distribution is periodic and is affected by the stator blade number at the rotor exit. The experimental results show that the flow is almost axial and the pre-rotation is very small at the rotor inlet under the conditions of 0.8QN-1.2QN. Due to the clearance leakage, the pressure, circulation and meridional velocity at the rotor outlet all decrease near the hub leakage and tip clearance regions.

axial-flow pump, unsteady flow, pressure fluctuation, high efficiency, flow field measurement

1. Introduction

The low head axial-flow pump is widely applied in large hydraulic engineering, drainage and irrigation. With the construction of the South-to-North Water Diversion Projects and large pumping station renovation projects, the study on the axial-flow pump becomes a hot research topic, especially in China. The flow in an axial-flow pump is greatly influenced by turbulence and viscosity. The hub leakage and the tip clearance lead to the tip cavitation and non-uniform flow. The rotor-stator interaction induces unsteady flow and pressure fluctuation, as one of the main causes of vibration, noise, fissures, blade cracking and guide vanes bearing failures. The physical phenomenas involved in this complex flow field take a lot of studies to understand. Alpan[1]analyzed the suction reverse flow in an axial flow pump by experiments. Zierke[2,3]proposed an experiment technology and discussed the flow characteristics of high Reynolds number pump and tip clearance flow. Dupont et al.[4]investigated the unsteady effects associated with rotor stator interactions in a vaned-diffuser radial-flow pump. Li[5]and Wang[6,7]investigated the performance of an axial-flow pump with inducer and a large-bore axial-flow pump with half-elbow suction sump by a steady numerical simulation, and discussed the pressure fluctuation of unsteady flow in the axial-flow pump. Zierke[8]investigated the flow through an axial-flow pump. The flow field in the axial-flow pump was simulated and measured in many studies in recent years[9-14]. In this article, in order to analyze the flow characteristics of the adjustable axial-flow pump model, a model with high efficiency was simulated by Fluent code under various conditions, a five-hole probe was used to measure the flow field at the inlet and blade exit, and finally, some meaningful conclusions were drawn.

2. Unsteady simulations

2.1 Governing equations

The governing equations for the turbulent incompressible flow are the three-dimensional unsteady Reynolds-average Navier-Stokes equations for the conservation of mass and momentum, given as

wheretμ is the turbulent viscosity and k the turbulent kinetic energy. For two-equation turbulence models, such as the k-ε variants, the turbulent viscosity is computed through the solution of two additional transport equations for the turbulent kinetic energy k and the turbulence dissipation rate ε.

2.2 Turbulence model

The RNG k-ε turbulence model is used in this article, which provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately. A more comprehensive description of the RNG theory and its applications to turbulence computation can be found in Ref.[15].

The turbulence kinetic energy k and its rate of dissipationε are obtained from the following transport equation.

The production term in Eq.(4) is given by

where S is the modulus of the mean strain rate tensor, defined by

The effective viscosity is calculated by

The model constants are,

2.3 Numerical method

The whole hydraulic passage of the axial-flow pump is taken as the computational domain. A hybrid meshing scheme is used, with relatively fine grids near the hub, shroud, and blade surfaces, as well as near the leading, trailing edges and tip clearance. The mesh in the whole computational zones has 3 522 986 grids. Two interfaces between the rotor and the stator are formed, as shown in Fig.1. A sliding interface technology is used to simulate the rotor-stator interaction. Standard wall functions are used to simulate the boundary layers. The second order implicit scheme is adopted for the turbulent simulation. Governing equations are discretized in both space and time domains. The spatial discretization is used to integrate the differential equations on each control volume. SIMPLEC algorithm is used to solve the pressure and velocity coupling at each time step. A uniform axial velocity based on the mass-flow rate is specified at the inlet for each computation run, and at the outflow boundary, a fully developed flow is assumed, which means that the velocity distribution is fixed along the flow direction. All physical surfaces of the pump are set as no-slip walls.

Fig.1 Computational grids and interfaces

In this article, one time step corresponds to 3oof the rotor rotation, so 120 time steps should be calculated in one cycle of the rotor. Steady simulation results serve as the initial conditions for the unsteady calculations. When the convergence of the variables is reached, the time step is advanced and the rotor mesh rotates an assigned degree to start a new step of calculation.

2.4 Numerical results

2.4.1 Performance prediction

The simulated model is an adjustable axial-flow pump with the specific speed nsof 700, nsis defined below:

The rotor has 4 blades and the stator has 7 blades. The rotating speed n is 1450 r/min, with flow rate Q of 372.10 l/s, head H of 7.15 m and efficiencyη of 85.60% at blade angle Φ=0o. The performance of the axial-flow model was evaluated by the unsteady and steady simulations, respectively, and compared to the test results. The head and efficiency of the unsteady simulation under different conditions are the average values of 120 time steps. The prediction data agree with the experimental head and efficiency, as shown in Tables 1 and 2. From the predicted results, it is seen that the unsteady results are more accurate than the steady results. The maximal error is 17.5% in the steady prediction, but only 4.54% in the unsteady simulation.

2.4.2 Pressure fluctuation

The measuring points are distributed in the flow passages to monitor the pressure fluctuation and its developing trend. Three groups of points can be seen in Fig.2.

Fig.2 Pressure monitoring points

Figures 3-7 show the pressure fluctuation curves in the time domain at the measuring points at the inlet of the rotor, the outlet and the outlet of the rotor. The fluctuating features at these points are almost the same, all with four peaks and four valleys, in accordance with the blade number.

Fig.3 Pressure fluctuation at the rotor inlet

Table 1 Experimental and predicted results of head

Table 2 Experimental and predicted results of efficiency

Fig.4 Pressure fluctuation at the rotor outlet

Fig.5 Pressure fluctuation at the stator outlet

The peak-to-peak values of the pressure fluctuation at the rotor inlet and outlet as shown in Fig.6 increase with the increase of the radius. The fluctuation amplitude near the tip is 1.47 times as that near the hub at the rotor inlet, and 1.22 times at the rotor outlet. The pressure fluctuation amplitude at the stator outlet decreases from the hub to the tip, and the amplitude near the hub is 2.29 times as that near the tip. It is obvious that the trend of amplitude change from the hub to the tip at the stator outlet is opposite to those at the rotor inlet and outlet. The results agree with those reported in the reference[7]. The average pressure fluctuation amplitude at the rotor inlet is 7.85 times as that at the rotor outlet, which is the greatest amplitude in the axial-flow pump as shown in Fig.6, and it is different from the traditional understanding. At the stator outlet, the amplitude becomes smaller owing to the role played by the diffuser.

Fig.6 Pressure fluctuation magnitudes

Fig.7 Frequency spectrum of P19

Fig.8 Frequency spectrum of P25

Fast Fourier Transform (FFT) is applied to show the unsteady pressure features in frequency domain. Figs.7, 8 and 9 show the frequency spectrums of P19, P25 and P35, respectively.

Fig.9 Frequency spectrum of P35

It is found that the dominant frequency at monitoring points of the three groups all takes the same value of 96.3 Hz,which is approximately equal to the Blade Passing Frequency (BPF), and other main frequencies are 193.3 Hz and 290.1 Hz, as some multiples of BPF.

Fig.10 Static pressure distributions

2.4.3 Static pressure distribution

The static pressure on the pressure side of blades increases slightly at the circumferential direction, as shown in Fig.10, and keeps almost constant at a same radial direction, while increases gradually from the blade inlet to the exit on the suction side. It is found that the static pressure on the pressure side of airfoils at different stream surfaces remains almost constant at different time steps. At the leading edges of the blades, the pressure increases due to the local impact.

2.4.4 Axial velocity distribution

The blades of the impeller are usually designed based on a uniform pattern of the meridional velocity vm. However, this distribution has not been established in numerical simulations. Figure 11 shows the axial velocity component at the rotor outlet plane at four time steps t =0.0310s , t =0.0345s, t =0.0380s and t =0.0414s. It can be seen that the axial velocity changes periodically along the circumferential direction, with a frequency the same as the stator blade number, and the distributions, which are affected by the downstream flow, keep the same trend at different time steps. In general, the axial velocity increases from the hub to the tip, and is affected by the tip clearance and hub leakage, which would result in a sharp velocity decrease.

Fig.11 Axial velocity distribution at blade outlet (m/s)

3. Experimental investigations

3.1 Experiment design

The experiment was carried out in the fluid machinery laboratory of Jiangsu University. Three components of velocity at the rotor inlet and outlet under different conditions were measured by calibrated five-hole pressure probes, and the static pressure and the total pressure at the same locations were measured at the same time. Figure 10 shows the measurement locations.

Treaster and Offtinge[16]listed sources of errors in conventional probe measurements of flow in turbine machinery. They also estimated the magnitude of these errors, and it is indicated that the wall proximity effects could be neglected if the distance between the measurement position and the wall is more than twice of the probe diameter. The first and last of the measurement locations shown here satisfy that condition. The presence of the probe may perturb the flow but the size of the probe is less than tenth of the width of the blade passage, therefore, the effects of the probe blockage can be neglected.

3.2 Experimental results

3.2.1 Rotor inlet flow

The loacation factor is calculated by

where r is radius, t is tip, h is hub.

Due to the size of the probe and the vicinity of the hub, the first measurement is located atr?=0.08 and the last one at r?=0.92, as shown in Fig.12.

Fig.12 Probe measurement locations

The data were collected using a field point measurement method. In this procedure, the measurement volume remains stationary, and the flow in the pump was assumed to be in a steady state. The measurement results were compared to the simulated results at time t =0.0310s. The five-hole probe is used to identify the three components of velocity at the blade inlet. Figure 13(a) shows that the absolute flow angle α takes almost a value of zero at various flow rates, as expected, which means the inlet flow is almost axial and the pre-rotation at the blade inlet is very small. The meridional velocityvmas shown in Fig.13(b), all increases slightly from the tip to the hub under 0.8QN, 1.0QNand 1.2QNconditions, as maybe relevant to the shape of the front hub. The distribution of the static pressure at the inlet is almost consistent with the design condition, which is the expression of a steady flow field. Under off–design conditions, the unsteady flow in the rotor induces the static pressure change at different radial locations, but to a small extent, as can be observed in Fig.13(c).

Fig.13 Hydrodynamic flow field at inlet at various locations at different flow rates

3.2.2 Rotor outlet flow

The hydrodynamic flow field at the blade exit is shown in Fig.14. Under the design condition, the distribution of meridional velocity component vm2is almost uniform. It means that the flow at the blade outlet is steady without radial flows. When the flow rate is reduced, significant changes occur in the flow field, with a new feature that a reverse flow develops in this region, where vm2increases sharply from the hub to the mid-radius, and then decreases, but increases again near the tip. Hub leakage, which can be seen in Fig.14(a), is a factor responsible tovm2decrease near the hub. This phenomenon can be explained as follows: the reverse flow from the pressure side to the suction side reduces vm2associated with the drop of p0, p and vu2near the hub leakage.

14(a) Velocity component vm2distribution

Figure 14(b) shows the distributions of vu2. It can be noted that vu2decreases gradually from the hub to the tip under 1.0QNand 1.2QNconditions in accordance with the consistent Γ distributions. Under small flow rate conditions, the distribution of vu2is similar to vm2, which is also influenced by the reverse flow.

14(b) Velocity component vu2distribution

The decrease of the total pressure p0and the static pressure p at the tip and hub regions in Figs.14(c), 14(d) indicates large energy losses in these regions owing to the leakage , where we should pay more attention during the axial-flow design process. vm2also decreases slightly near the tip, due to the small tip clearance of 0.15 mm.

14(c) Static pressure distribution

14(d) Total pressure distribution

The blade exit circulation is shown in Fig.14(e). The distribution of circulation Γ at places downstream of the rotor blades is the most important factor related to efficiency. Under the design condition and large flow rate conditions, the circulation Γ is almost constant but with a small decrease near the hub due to the hub leakage. This phenomenon may be further effective for the circulation distribution at the hub and tip regions in the design to make the circulation consistent along the radial locations in practice. Under small flow rate conditions, Γ decreases sharply from the tip to the hub, as an expression of recirculation near the hub.

Fig.14 Hydrodynamic flow field at blade outlet at various locations at different flow rates

4. Conclusions

The unsteady turbulent flow in the adjustable axial-flow pump was simulated based on software Fluent, and the pressure fluctuation, static pressure distributions and axial velocity at the rotor outlet at different time steps were discussed. Through experimental investigations, the following conclusions can be drawn.

(1) Compared to the test results, the unsteady results are more accurate than the steady results, and the maximal error of unsteady prediction is only 4.54%.

(2) The time-domain spectrums show that the static pressure fluctuation curves at the rotor inlet, the outlet and the stator outlet are periodic, and the pressure fluctuation amplitude increases from the hub to the tip at the rotor inlet and outlet, but decreases at the stator outlet. The pressure fluctuation amplitude is the greatest at the rotor inlet, and the average amplitude decreases sharply from the inlet to the outlet. The frequency spectrums show that the dominant frequency is approximately equal to the BPF, and other frequencies are multiples of BPF.

(3) The simulation results agree with the experimental results, and the results show that the inlet flow is almost axial and the pre-rotation at the inlet is very small under the conditions of 0.8QN-1.2QN. The pressure circulation and meridional velocity at the rotor outlet all decrease near the hub leakage and blade tip regions.

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10.1016/S1001-6058(09)60025-1

* Project supported by the National High Technology Research and Development Program of China (863 Program, Grant No. 2007AA05Z207), the Graduate Student Innovation Foundation of Jiangsu Province (Grant No. CX08B_064Z) and the National Science and Technology Support Program (Grant No. 2008BAF34B15).

Biography: ZHANG De-sheng (1982-), Male, Ph. D.