Cent. Eur. J. Eng. • 1(4) • 2011 • 361-368 DOI: 10.2478/s13531-011-0013-x

Central European Journal of Engineering Unsteady Flow in a Viscous Oil Transporting Centrifugal Pump Research Article Wen-Guang Li∗ Lanzhou University of Technology, 287 Langongping Road Lanzhou 730050, Gansu, China

Received 19 January 2011; accepted 04 March 2011 Abstract: Acoustic resonances are frequently fatal problems in centrifugal pump operations. Low pressure pulsation of fluid in the blade pass frequency is helpful to prevent from such problems. In addition, for a high quality centrifugal pump, a lower broadband noise level is also on demand. The acoustic resonance and broadband noise are associated with unsteadiness of flow in the pump. Even there exist extensive analyses of unsteady flow in centrifugal pumps by means of CFD so far, the effect of high viscosity of fluid pumped on the unsteadiness of flow feature remains unclear. Thus, the unsteady flow in an experimental centrifugal pump was exploited numerically when it transported the liquids with different viscosities. The velocity profiles at the impeller discharge were validated with the results of LDV measurement for water. The viscosity effect on the fluctuation of flow in the volute was clarified quantitatively. It was shown the increasing viscosity of fluid makes the fluctuation in flow variables less substantial and results into a less noticed tendency of separation of flow from the blade pressure side. Keywords: Centrifugal pump • Impeller • Volute • Performance • Unsteady flow • Fluctuation of flow • Viscosity • CFD

© Versita sp. z o.o.

1.

Introduction

Mechanical and acoustic resonances are responsible for centrifugal pump vibration problems, which are fatal to pump operations [1]. The mechanical resonance has been well treated and significantly documented for centrifugal pumps [2, 3]. The mechanical resonance frequency usually is 2 times below the pump running speed [3]. However, the acoustic resonance occurs in blade pass frequency. For a centrifugal pump with a volute having one tongue/cutwater, this frequency is the product of number of blades multiplying the pump rotating speed [4]. Reducing pressure pulsation of fluid in the blade pass fre∗

E-mail: [email protected]

quency is very helpful to prevent centrifugal pumps from acoustic resonance problem. The wake behind impeller blades is full of vortices, shows remarked fluctuation in velocity and eventually induces broadband noise [5]. For an environment-friendly centrifugal pump, a relatively low broadband noise level is essential. The propagation of acoustic wave in centrifugal pumps has been analyzed by using one-dimensional inviscid flow model, causing the equation for determining resonance frequency [6] and it was shown the exit blade angle did not seem to change the resonance frequency [7]. The acoustic field was investigated respectively in a centrifugal diffuser pump in [8] and in a centrifugal volute pump in [9] by employing two-dimensional ideal flow model and a vortex method for numerically solving the wave propagation equation. The two-dimensional point sound source in the volute of a centrifugal pump was established according to the pressure

361

Unsteady Flow in a Viscous Oil Transporting Centrifugal Pump

fluctuation measured in blade pass frequency, causing a good understanding on the acoustic noise generation in centrifugal pumps [10]. It was revealed the interaction between impeller blade and separated flow from the blade suction side contributes the noise generation mechanism in a centrifugal pump impeller [11]. In those studies, obviously, effects of high viscosity of liquid on unsteadiness of flow and subsequently acoustic field in centrifugal pumps are unavailable presently. In this paper, the unsteady, three-dimensional flow of water and viscous oil in a centrifugal pump in [12] were studied theoretically at the best efficiency and part-loading points as well as the shut-off condition. The decay feature of fluctuation in pressure and velocity head behind the impeller was quantitatively clarified. Comparisons of calculated head curves and flow velocity have been made with those measured and LDV observations. The objective of this work is to establish basic knowledge about the unsteadiness of viscous oil flow in the pump so as to develop an acoustic noise model and optimize centrifugal oil pump geometry for a low acoustic level with assistance of CFD in subsequent studies.

2.

Model Pump and Method

Figure 1.

Table 1.

Pump fluid domain (a), LDV probe positions (b), survey surfaces and observation points (c).

Primary parameters of pump, impeller, volute and working liquids.

Item

Parameter Flow rate, Q,

(m3 /h)

Head, H (m)

The single-stage, end-suction, overhung centrifugal volute pump with a specific speed of 93 in [12] for experiment serves as the computational model here. The impeller was design by using the existing mean-line one-dimensional theory in [13]. The volute was established by means of the constant velocity approach with rectangular section. Table 1 summarizes the primary parameters of the pump, impeller, volute and the working liquids in the experiments in [12]. Figure 1(a) illustrates the geometrical model of the pump generated in Gambit of Fluent.

Rotating speed, n (r/min)

Pump

Specific speed, nS (r/min, m3 /s, m) p nS = 3.65n Q/H 0.75

Impeller

Volute Water

In the experiments, the water and viscous oil head-flow rate curves of the pump were measured. Subsequently, the unsteady flow velocities of water at 187 points in θ = 180°, 270°, and 360° sections shown in Fig. 1(b) were surveyed by applying LDV at the best efficiency point (QBEP =5.79L/s) and part-loading point (0.58 QBEP ). The impeller Reynolds number is Re = d2 u2 /v = 2.5×106 (water), 3.1 × 105 (oil). In the experiments, the uncertainty for pump efficiency was in a range of 0.76% ∼ 1.15% and the total uncertain of LDV measurement was 5.3% [12]. The LDV equipment is a four-beam, two-colour (blue and green), back-scattered mode and two-dimensional velocimeter produced by TSI. A shaft encoder was installed on the end of motor shaft to record the impeller rotating angle past the measuring volume so as to establish exact one to one relation between data sampled and the impeller

362

Liquid Oil

Value 25 8 1485 93

Inlet diameter, d1 (mm)

62

Outlet diameter, d2 (mm)

180

Number of blades, Z

4

Exit blade angle, β2b (o )

20

Width, B (mm)

40

Throat area, F8 (mm2 )

1440

Density, ρ(kg/m3 )

1000

Kinematic viscosity, ν (mm2 /s)

1

Density, ρ(kg/m3 )

851

Kinematic viscosity, ν (mm2 /s)

48.5

rotating angle. After the ensemble average for the data sampled was preformed by the data processing software PHASE provided by TSI, the unsteady flow velocity in the volute would be available. The LDV probe was moved by means of a three-dimensional coordinate traverser. The data sampling and processing etc can be conducted by applying the PC. The unsteady velocity measurements were taken place in θ=180°, 270° and 360° sections. The impeller rotating angle φ past each measurement point was determined automatically by the turbomachinery resolver based on its working mode selected, impulse num-

Wen-Guang Li

ber of per revolution for sampling, number of sectors and windows opened. The data files in ASCII format, which included the absolute velocity and other information of flow at each measurement point, were calculated by using PHASE. The velocity and other useful information could be extracted from the data files by means of a program developed in-house. During the numerical computations proceeding, the averaged total pressure of fluid on the survey surfaces S1, S2 and S3, the torque applied on the blades and shroud and hub by the fluid were acquired at each time step. Meanwhile, the static pressures of fluid at point P1 and P2 were monitored too. Flow parameters are uneven across the volute span, however, a maximum fluctuation in the parameters has been observed in the mid-span [14]. Therefore, the pressure and velocity just in the mid-span were recorded in terms of time. The observation points are located at 2mm, 5mm and 10mm from the impeller discharge in θ=180°, 270° and 360° sections. The computational model consists of three parts, namely inlet suction pipe, impeller and volute. Since the unsteady flow simulations in the pump is extremely time-consuming, the unstructured mesh size can not be too small. As a result of this, the numbers of tetrahedral cells are 135166, 174097 and 160550 respectively in the suction pipe, impeller and volute. Such a number of cells is comparable with that used in [14] in the analyses of unsteady flow through an end-suction and single-stage centrifugal pump. The unsteady, three-dimensional, incompressible and turbulent flow in the pump was calculated numerically by means of Fluent 6.2.16. The standard k − ε turbulence model was adopted to account for the eddy viscosity caused from turbulence. The non-equilibrium wall function was chosen to take pressure gradient effect on the shear stress along walls into account. The numerical schemesfinite volume method and SIMPLE were applied to discretize the continuity, time-averaged Navier-Stoke, k and ε equations. Two sliding meshes were prescribed respectively on the interface between the suction pipe and impeller, and that between the impeller and volute. The rotating speed of the fluid domain of impeller was 1485r/min. Initially, the type of the fluid domain of impeller was chosen to be „moving reference frame”, once the computation was converged; the type of the fluid domain was switched to ”moving mesh”. An axial inflow velocity was specified at the inlet of the suction pipe according to a known flow rate, and 1 atm was given at the volute outlet as a reference pressure, the rest boundaries were subject to the no-slip boundary condition. The roughness of the wet walls was chosen to be Ra=50µm. In unsteady computations, the time step was set to 1×10−4 s. A second-order implicit difference scheme was used for the temporal term in the

Figure 2.

Comparison of CFD predicted pump head curve with measurement.

governing equations of flow. The convergence criterion (RMS) was kept to be 1×10−4 for all flow parameters.

3.

Flow Model Validations

3.1.

Head Curves

Figure 2 illustrates a comparison of pump head curves between CFD computation and measurement at the best efficiency point, low flow rate and shut-off conditions, respectively. In the figure, the head curves in [15] is involved as well, which are based on the steady flow model. The slope of the head curves of steady flow model differs from that of measured head curves. At low flow rates, the heads of viscous oil show very good agreement with experimental values for unsteady flow model. For water, the estimated heads indicate slightly large error compared to the test results at the best efficiency point and part-loading point. At the shut-off condition, the predicted head by means of the unsteady flow model is consistent very well with the observations. In general, a very good agreement has been achieved in the heads between estimation and measurement by the unsteady flow model. Such an observation is identical to [16]. At ν = 1mm2 /s, the estimated heads are 5%∼10% higher than the tests. At ν = 48mm2 /s, however, the -1%∼5% error is found in head between computation and measurement.

363

Unsteady Flow in a Viscous Oil Transporting Centrifugal Pump

Figure 3.

3.2.

Figure 4.

Comparison of CFD estimated unsteady circumferential and radial velocity components of water at point 2mm behind impeller with those observed by LDV at part-loading point.

Figure 5.

Torque on impeller in terms of its rotating angle at both best efficiency and part-loading points.

Comparison of CFD estimated unsteady circumferential and radial velocity components of water at point 2mm behind impeller with those observed by LDV at best efficiency point.

Comparison with LDV Measurements

Figure 3 and 4 present the estimated and LDV measured circumferential and radial components of water velocity in terms of impeller rotating angle φ at the points 2mm far from the impeller discharge in θ =180°, 270° and 360° sections of the volute at the best efficiency and part-loading points. The LDV survey was made in [17] for the same pump. At these three stationary points in the volute, since the fluid flow variables vary periodically with the impeller rotating angle, we just need to show the fluid velocity profile in one circle of the rotation. It can be seen that the circumferential velocity of CFD prediction agrees well with the LDV measurement, but a slightly large error is identified for the radial velocity. Further, such an error is enlarged at the low flow rate. Compared to the best efficiency point, at the low flow rate the CFD prediction tends to produce less regular fluid velocity pattern in terms of impeller rotating angle. Generally speaking, the CFD estimated fluid velocities are consistent with the LDV observations. According to above comparisons, it is confirm that the unsteady flow model seems reasonable and applicable to characterize the unsteady flow in the pump.

364

4.

Results and Discussion

4.1.

Torque and Total Pressure Fluctuation

Figure 5 indicates the predicted total torque applying on the four blades, shroud and hub as a function of impeller rotating angle at the best efficiency and part-loading points for water and the viscous oil. It is clear that the torque shows a periodic pattern against the rotating an-

Wen-Guang Li

Figure 6.

Total and static pressures at entrance and exit to impeller as well as pump outlet as a function impeller rotating angle at both beast efficiency and part-loading points.

gle; moreover, the fluctuation (amplitude) in the torque of viscous oil is less than that of water. Figure 6 gives the estimated average total pressure in terms of impeller rotating angle at the survey plane S1 near the impeller entrance, and the cylindrical surface S2 close to the impeller outlet as well as at the outlet of the volute under the best efficiency and part-loading conditions for water and the viscous oil. The nearest distance is 30mm between the survey plane S1 and the blade leading edge, whereas the cylindrical survey surface S2 is behind the impeller outlet with 1.25mm. In the figures, the total pressure represents a relative value since a reference pressure (1 atmospheric pressure) has been subtracted from it. If a total pressure is negative, the pressure will be less than the reference pressure. Nevertheless, a relative value plus the reference pressure can contribute to the absolute total pressure. It is obvious that the fluctuation in the inlet total pressure is comparable to that in the outlet total pressure. At the inlet to impeller, when the flow rate is lowered to 0.58 QBEP from QBEP , the fluctuation of total pressure is reduced by half. At the outlet to impeller, the fluctuation in total pressure is irrelevant to the change in flow rate. For the viscous oil, the fluctuation of total pressure is reduced by 30%∼40% compared with water. The reduction in total pressure implies that the intensity of hydrodynamic noise generated by the impeller is damped, causing a sound released with a lower level. It was found that the pump was less noisy during the performance tests when the viscous oil was a working liquid. Simultaneously, the random movement of the pointers of vacuum and pressure gauges was substantially reduced. Those effects suggest the fluctuation of total pressure does have been suppressed by the

Figure 7.

Pressure and velocity heads in terms of impeller rotating angle at best efficiency point when delivering water (a)-(c) and viscous oil (d)-(f).

viscous oil. The qualitative agreement with the observations was achieved with the unsteady flow model. At the survey plane S3 of the pump outlet, the total pressure is basically independent of the impeller rotational angle and keeps to be a constant. The variation in flow variables has been suppressed effectively in the volute nozzle.

4.2.

Pressure and Velocity Head Fluctuation

Figure 7 illustrates the static pressure and velocity head of water and the viscous oil against the impeller rotating angle at the two points behind the impeller discharge by 2mm and 10mm in the θ=180°, 270° and 360° sections at the best efficiency point. At ∆r=2mm point, the averaged velocity head is around 33% of the mean static pressure head. The pressure and velocity heads get a more uniform pattern with increasing distance measured from the impeller outlet. Particularly, the larger distance, the smaller velocity head, but a slightly rising pressure is observed with the increasing distance. Compared to the velocity head, the profile of pressure head against the impeller rotating angle is flat except at the blade trailing edges where a sharp drop in the pressure head is found. A wake behind the blade trailing edges manifests itself with

365

Unsteady Flow in a Viscous Oil Transporting Centrifugal Pump

a higher velocity head. For the viscous oil, the fluctuation in pressure head is slightly high, but the pulsation in velocity head is considerably suppressed. Such a fluctuation becomes even more uniform with increasing distance to the impeller.

4.3. Pressure and Velocity Head Decay in Volute Commonly, there exist two methods for quantitatively describing the fluctuation in a flow parameter at present. One is to estimate the amplitude or RMS fluctuation in blade pass frequency [18]. One is to calculate the amplitude of fluctuation in every harmonic frequency [19]. In the second approach, the pressure and velocity head curves in terms of time have to be best fitted by using a Fourier series to obtain the amplitude of fluctuation of every harmonic frequency. It was shown that there were remarked errors in such curve fitting processes with the Fourier series. As a result of this, the fitting curves showed an unrealistic departure from the pressure and velocity head curves given by CFD. Consequently, the second method has to be abandoned and the first approach was adopted instead. In this case, we simply estimate the amplitudes (peak-to-peak) of pressure and velocity heads, Ap and Av from their time history curves. Figure 8 presents the amplitudes of static pressure and velocity heads of water and the viscous oil versus the distance from the impeller outlet at the best efficiency and part-loading points. It is shown that the amplitudes of these flow parameters are declined substantially in a distance of 0mm∼10mm from the impeller; beyond 10mm, little variation happens in the amplitudes. It suggests the wake behind the impeller is decayed significantly in this distance. Such a phenomenon is consistent with the LDV measurements in [12], where the flow velocity becomes more uniform as the fluid is further from the impeller outlet. At the part-loading point, the amplitudes of pressure and velocity heads are larger by one-fold than those at the best efficiency point, especially for the velocity head. Such an observation is much similar to the measurements in [12] as well. At the same working condition and at the same point in the volute, the velocity head fluctuation amplitude of the viscous oil is just around half of water, particularly in the region more nearby the impeller discharge. At the best efficiency point, the amplitude of pressure pulsation appears to be unaffected by viscosity of the liquids. It is the significant decay in the velocity head that may be responsible for the low level noise generated in the viscous oil performance test of the pump. Compared to θ=180°, 270° sections, the amplitude of ve-

366

Figure 8.

Amplitude decay of pressure and velocity heads of water and viscous oil behind impeller at best efficiency (a)-(c) and part-loading (e)-(f) points, Ap and AV are peak-to-peak amplitudes of static pressure and velocity head.

locity head of water shows a relative considerable increase in vicinity of the impeller outlet at θ=360° section. However, the amplitude of pressure head is comparable in these three sections. The amplitude of pressure head of the viscous oil doesn’t seem to demonstrate a noticed difference from that of water in the three sections. The decay of fluctuation in a plane wake or in a wake behind an aerofoil conforms a power law in theory [20, 21]. Likewise, it is assumed that the amplitude Ap and Av yield such a low as follows: Ap ∝ (2∆r/d2 )−mp and Av ∝ (2∆ r/d2 )−mv . Those powers can be estimated through the data obtained with CFD. The corresponding results are tabulated Table 2. The last column in the table presents the mean value of the powers at the best efficiency and part-loading points. Two powers are dependent of fluid viscosity, pump working condition. The power for Ap is approximate half smaller than the power for Av . According to the mean values of power, it seems to indicate increased viscosity results into greater power in θ = 270°, 360°sections. The decay power of pressure is in the 0.31∼0.68 range compared to 0.77 suggested in [18], whereas the decay power of velocity head is in the

Wen-Guang Li

Table 2.

Decay power of amplitude of pressure and velocity heads in two sections of volute.

Best efficient Part-loading

Item

θ=270°

mv

section

θ=360° section

mp

mp mv

Mean value

point

point

Water

0.3497

0.3086

0.3292

Oil

0.3518

0.4872

0.4915

Water

0.7339

0.8108

0.7724

Oil

1.0656

0.9298

0.9977

Water

0.4975

0.4549

0.4762

Oil

0.6844

0.6075

0.6460

Water

0.8813

0.9124

0.8969

Oil

1.0656

0.8156

0.9406

0.63∼1.07. Such a variation range of power of velocity head corresponds to the 0.32∼0.54 range for the decay power of velocity compared with 0.5 behind an airfoil in [21] and 0.51∼0.58 behind a two-dimensional airfoil cascade in [22]. In above three sections, the pulsations in flow parameters behind the impeller have been made clear, but a survey of flow patterns in the impeller and volute is ignored. In the following, the effect of viscosity on the flow patterns will be paid attention.

4.4.

Figure 9.

Water and viscous oil flow pathlines in impeller and volute at best efficiency and part-loading points, (a) QBEP , ν=1mm2 /s, (b) 0.58QBEP , ν=1mm2/s, (c) QBEP , ν=48mm2 /s, (d) 0.58QBEP , ν=48mm2 /s.

Discussion

Figure 9 illustrates the pathlines of water and the viscous oil flows in the impeller and volute at the best efficiency and part-loading points at a time instance that a blade is passing the tongue of volute. Obviously, the water flow has been separated from the pressure side of the blade approaching the tongue of volute at the best efficiency point. Surprisingly, for the viscous oil, such a separation doesn’t appear to exist. At the part-loading point, for water, a dominated separated flow is observed on the pressure side of that blade; for the viscous oil, however, the size of the reverse flow seems to be smaller. It suggests that a tongue can induce a separated flow on the pressure side of a blade whenever coming near the tongue. According to above results, it is clear that the tendency of separation of a viscous oil flow from the blade pressure side in the impeller is in decline. Such an effect has been observed through viscous oil flow visualizations in the impellers of centrifugal pump in [23]. Figure 10 presents the pathlines of water and the viscous oil at the shut-off point when a blade is approaching the tongue. In the volute, the fluid is in spiral motion. The impeller accommodates full of vortices, further, a vortex obstructs the

Figure 10.

Water and viscous oil flow pathlines in impeller and volute at shut-off condition, (a) ν=1mm2 /s, (b) ν=48mm2 /s.

discharge of every flow passage. At the impeller entrance, the flow is in spiral and a recirculation is established. This recirculation flow pattern quite resembles that in [24]. Note that the extent of the recirculation of water flow is around 50% longer than that of the viscous oil. This indicates that the extensive rotation of flow has been suppressed by an increased viscosity of fluid at the impeller entrance.

5.

Conclusions

The unsteady turbulent flows of water and viscous oil in an experimental centrifugal pump have been analyzed numerically by means of CFD code Fluent®. The influences of viscosity of fluid on the fluctuations in torque and head have been clarified. The relationship between the pulsa-

367

Unsteady Flow in a Viscous Oil Transporting Centrifugal Pump

tion amplitude of static pressure and velocity heads of fluid flow behind the impeller at different working conditions and viscosities of fluid have been established. The major findings are as follows: (1) the unsteady flow model can achieve a more precise estimation of pump head; (2) the amplitude of fluctuation in flow parameters is comparable at impeller entrance and outlet; (3) the increased viscosity of liquid can suppress the pulsation in velocity of fluid behind the impeller; (4) the decay power of pressure and velocity behind impeller depends on viscosity and working condition, specially the power for pressure decay is in the 0.31∼0.68 range, but for velocity it is in 0.32∼0.54. Further investigations consist of acoustic model for highly viscous oil flow and pump geometrical optimization for a low radiated noise level.

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