A new two stage miniature pump: Design, experimental characterization and numerical analyses

Sensors and Actuators A 164 (2010) 74–87

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

A new two stage miniature pump: Design, experimental characterization and numerical analyses A. Rossetti ∗ , G. Pavesi, G. Ardizzon Department of Mechanical Engineering, University of Padova, via Venezia 1, 35131 Padova, Italy

a r t i c l e

i n f o

Article history: Received 27 May 2010 Received in revised form 31 August 2010 Accepted 2 September 2010 Available online 15 September 2010 Keywords: Viscous pumps Miniature pumps Two stage pumps Disk pumps

a b s t r a c t The objective of the study described here is to explore the possibilities of an innovative two-stage micro pump. The first stage was realized by a micro Rotary Shaft Pump (RSP) with an external diameter of 3 mm and a blade height of 0.4 mm. The second stage, partially integrated in the RSP, was a centrifugal viscous pump with a 4.4 mm external diameter. The numerical and experimental characteristics of two prototypes are presented. Different rotational speeds were tested up to 24,000 rpm, obtaining pressure increases up to 12 kPa and flow rates up to 150 ml/min, corresponding to a head coefficient of 0.12 and a flow coefficient of 0.4. 3D time dependent CFD simulation were also carried out and compared with experimental data. Numerical results allowed to study the flow field inside the pumps and to compute the hydraulic efficiency of the two stages, as well as, to show the distribution of losses inside the pumps. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Over the last decades, micromachining technologies were used to advance the area of micro fluidic systems. These technologies promoted the miniaturization of systems such as gas and liquid chromatography, electrophoresis, polymer chain reaction, chemical analysis systems, micro reactors and microelectronics cooling [1–9]. One of the key components in micro fluidic systems is the micro pump, which is used for the flow-controlled delivery within the system. Numerous designs are possible to meet the requirements imposed by the different applications, which may require flow rates from some ␮l/min to several dl/min. Several different micro pumps were developed based on different pump principles and using different actuation principles, which classification is not yet univocally defined. Some authors, such as Laser and Santiago [9] and Woias [10] based their classification according to the manner and the means by which the micro pump produces flow rate and pressure. By this mean, they identify two main categories: displacement pumps, which exert pressure on a finite volume of fluid by one or more moving boundaries, and dynamic pumps or “continuous flow micropumps”, which continuously add energy to the fluid, increasing either its momentum and/or its pressure. Other classifications such as the one proposed by Nguyen and Wereley [11], was based on the working principles with the two main categories being the mechanical and the nonmechanical micro pumps.

∗ Corresponding author. Tel.: +39 049 827 7474; fax: +39 049 827 6785. E-mail address: [email protected] (A. Rossetti). 0924-4247/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2010.09.003

The last category adds momentum to the fluid for pumping effect by converting another energy form into kinetic energy or directly into pressure, and is characterized by the total absence of moving elements. These pumps utilize effects which are dominant in micro-scales including: electro-Hydrodynamic (EHD) pump [12–15] which pump dielectric liquids with extremely low electric conductivity; electro-kinetic [16–19] which use the electro-osmotic and electrophoretic effects for molecular separation, magneto-hydrodynamics (MHD) [20–24], ultrasonic pumps [25,26], bubble pump and diffuser/nozzle pumps which can be used to pump any type of liquid. Mechanical pumps instead use moving elements, rotating or translating, to deliver energy from the actuator to fluid. These include membrane pumps [27–33] both without check valves [27–30] and with check valves [31–33], viscous pumps [34–39], rotary pumps [40–43], peristaltic pumps [29,44–48], centrifugal [49–53], and several other types of pumps. Non-mechanical pumps are suitable when low flow rates are requested [11], such as in biological and chemical systems [9]. Mechanical micro pumps are capable of handling a wide variety of fluids and do not require high voltage supply, as other nonmechanical micro pumps. Furthermore, mechanical micro pumps could efficiently operate over relatively high volumes of fluids, while non-mechanical pumps principles could be applied only over very small volumes of fluid. Mechanical pumps could be successfully applied when intermediate or high flow rates are involved, as in microelectronic cooling systems [11,54] even if some new applications, when low flow rates were requested, were recently presented [43,55].

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Nomenclature Symbols b width (m) D diameter (m) h pump head (Pa) l reference length (–) M torque at impeller (Nm) n shaft speed (rpm) P mechanical power consumption (W) p pressure (Pa) Q flow rate (ml/min) Red = b23 ω/ disk Reynold number (–) Re = D2 ω/ Reynold number (–) U peripheral velocity (m) z number of blades (–)  = Q (po3 − po0 )/P efficiency (–) Hy = Q (po3 − po0 )/Mω hydraulic efficiency (–) ϕ flow coefficient (–)  density (kg/m3 ) ω angular rotation speed (s−1 ) head coefficient (–) ˘ power coefficient (–) Subscripts 0 impeller inlet 1 first stage–second stage interface 1st first stage 2nd second stage 2 impeller outlet 3 pump outlet Imp impeller Vol volute Mech mechanical Superscript o total

Among the mechanical pumps, the Rotary Shaft Pumps (RSP) and the viscous drag micro pumps are attractive because they are easy to fabricate, capable of handling a wide variety of fluids, and can operate with no valves allowing them to handle particle-laden fluids. The RSPs layout provides the integration of the impeller on the driving mechanical shaft, reducing the manufacturing costs and allowing to avoid the problems related to the blade tip clearance leakage [49–53]. In Allen and Ligrani [50], centimetre scale models with different blade designs were tested in order to produce smallscale centrifugal pumps suitable as ventricular assistant devices. In Pavesi et al. [51,52], millimetre scale impellers with different blade designs, coupled with different volutes were tested to identify the optimum configuration for microelectronic cooling systems. Further optimization in the blade design was presented in Rossetti et al. [53]. The results highlighted that RSPs allow to obtain high head coefficients, but with a not acceptable unstable characteristic up to one third of the maximum flow rate [53]. Several recent investigations discuss using viscous drag as the operating principle in micromachined pumps. The feasibility of this concept in the viscosity dominated micro scale flow fields have been experimentally investigated by several researchers and this investigation was motivated by the ability of generating significant pressure heads by the simple rotation of a rigid element contiguous to the flow field [34]. A number of analytical and numerical simulations have followed on such pumps [56–58].

Fig. 1. Sketch of the RSP impeller.

Disk pumps (DPs), introduced in the early years of the twentieth century, are centrifugal bladeless viscous pumps. The impeller consists of two smooth, flat parallel disks arranged orthogonally to the driving shaft. The two disks are often joined by means of cylindrical elements of small diameter to obtain negligible interaction with the fluid. Flow enters into the core of a series of donut shaped disks, and the fluid is then directed by shearing forces and a pressure gradient into the spaces between the rotating disks. The fluid is then accelerated radially between the rotating disks by a combination of shearing and centrifugal forces. The fluid exits the periphery of the disks and is collected in a spiral volute and directed towards the exit of the housing. Typically, a shaft running through a seal maintains the disk assembly fixed within the housing. Such a pump was examined by Rice [59] and by Hasinger and Kehrt [60] in the 1960s and was deemed as an excellent pump for “exotic” fluids due to its inherently stable flow regimes. As reported by Manna and Unich [61], disk impellers could attain a good efficiency and stable characteristics. Miller et al. [62,63], proposed and studied the application of miniature disk pumps as a ventricular assistant device. The objective of this research was the integration of a RSP and a DP in a two-stage micro pump. The resulting micro pump was expected to retain the attracting features of both RSP and DP: high efficiency and head typical of RSP and the high stability of DP pumps. The paper reports the characteristics obtained with a 3 mm first stage RSP with radial blades, and a 4.4 mm disks pump used as the second stage with an overall dimension of 10 mm. Two prototypes with different second stage geometries and volutes are presented in this work. CFD analysis and experimental tests were carried out for different rotational speeds. The numerical analysis, once validated by means of experimental measures, were used to evaluate and compare the dimensional and non-dimensional characteristics of each single stage, in order to highlight the influence of the main geometrical features and of the Reynolds number. 2. Micro pump design The integration of multiple functions in the same component is one of the key concepts when miniature systems are taken into account. In the present work, the number of components of the two-stage pump was reduced to three: the shaft, the bearing and the casing. This allowed for a compact, durable design. The first stage of the machine was integrated in the shaft using the RSP layout [51,52] (Fig. 1). The external diameter of the RSP was 3.00 ± 0.01 mm. The shaft was then axially holed to obtain the suction of the impeller, which measures 1.00 ± 0.005 mm in diam-

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Fig. 2. Pump assembly: exploded view (a); section (b); particular of the inner race (c) and photograph of the impeller assembled with bearing (d).

eter. A countersink with an angle of 45 ± 0.2◦ , was also made at the inlet using a drill to reduce the entrance losses. Eight radial holes of 400 ± 5 ␮m were then evenly machined on the bottom of the suction hole to define the passages of the RSP impeller. The metal slots between two subsequent passages act as impeller blades, increasing the fluid moment of momentum. Two ball bearings supporting the RSP impeller were positioned symmetrically to the passages’ holes (Fig. 2a–c). The bearings’ posi-

tioning in front and at the rear of the holes allowed to use the bearings’ surfaces to define both the second stage and the pump volute. Consistently, the disk pump (DP) was defined by the profile of the inner race of the bearings, which rotate with the RSP impeller. The stationary parts of bearing sides defined instead the volute profile. The external diameter of the disk stage was 4.40 ± 0.01 mm, while the external diameter of the bearings was equal to the maximum diameter of the volute and measured 10.00 ± 0.01 mm.

Fig. 3. Sketch of the test facility.

A. Rossetti et al. / Sensors and Actuators A 164 (2010) 74–87 Table 1 RSP impeller principal dimensions.

Internal diameter External diameter Passages width Blade number

Symbol

Value

D1 D2 b2 z

1.00 ± 0.005 mm 3.00 ± 0.010 mm 400 ± 5 ␮m 8

The advantages of this design included the reduced number of components and the simplicity of building. The bearings were first fixed to the shaft, obtaining the requested volute and DP width, and then the assembled shaft was fixed to the frame. Furthermore, because the volute was defined by the bearings, which were fixed to the shaft, no misalignments between the components occurred in the duration of the pump’s life. 3. Test facility

Table 2 DP impellers principal dimensions.

Internal diameter External diameter Passages width

Symbol

Value

D2 D3 b3

3.00 ± 0.010 mm 4.40 ± 0.005 mm 200 ± 5 ␮m, 400 ± 5 ␮m

The experimental characterizations of the tested micro pumps were acquired using the open rig schematized in Fig. 3. The micro pumps were fixed inside the test frame (labelled with number 2 in Fig. 3). The test frame inflow was connected to a water tank (1), which level was maintained constant by an external pump (6).

Table 3 Volute principal dimensions.

Internal diameter External diameter Passages width

77

symbol

Value

D3 DVol bVol

4.40 ± 0.005 mm 10.0 ± 0.010 mm 200 ± 5 ␮m, 400 ± 5 ␮m

Prior researchers [64–66] stated that optimal performances for DP are related to the distances between the disks b3 , the rotational speed of the impeller ω and the fluid kinematic viscosity . These parameters could be correlated by the Reynolds number, defined as: ReDP = ωb23 /. The optimal performances appear to be obtainable when the disk Reynolds number is slightly less than 10. Assuming the rotational speed of the pump to be on the order of 20,000 rpm [51] and water as the working fluid, a disk stage width on the order of 60 ␮m should be used to obtain the best performance. A DP stage with 60 ␮m of width would interact poorly with the RSP outlet channel of 400 ␮m, causing a choking in the first stage, a sudden radial velocity increase at the RSP outlet and a dramatic increase of the losses at the DP inlet. Therefore, two larger axial distances between the bearings were analyzed, varying the volute width and the gap between the disks of the viscous stage. Configurations with b3 = bVol = 200 ± 5 ␮m and b3 = bVol = 400 ± 5 ␮m were considered, corresponding to ReDP of about 95 and 380 respectively, at the reference speed of 20,000 rpm. These models were referred to in the paper as configurations DSP200 and DSP-400. To avoid the blockage of the first stage, when the disks gap was reduced, the internal edge of the inner race was rounded with radius of about 100 ␮m. The geometrical features of the two stages and of the volute are reported on Tables 1–3. The discharges of the pumps were obtained by drilling a 3.00 ± 0.01 mm hole, tangential to the maximum diameter of the volute and with the axis lying on the volute mean span plane. The exploded view and the section of the pump are presented in Fig. 2a–c, while in Fig. 2d is reported the photograph of the RSP assembled with the bearings. Sealed bearings were used to minimize the leakage and avoid the insertion of dedicated sealing components. All components were obtained using a high precision Computer Numeric Control (CNC) machining centre, using special carbide tools combined with high rotational speeds and low feed rates. A multi-sensor coordinate measuring machine with mechanical and non-contact probing systems, image processing and an integrated Focault TTL laser (resolution of 0.1 ␮m) was used to measure the pumps and to check the accuracy of the fabrication process. Aluminium alloy 7075 was used for both the RSP impeller and the test frame. The bearings were made of stainless steel, with acrylonitrile-butadiene rubber (NBR) contact seals.

Fig. 4. Computational domains (a) and impeller course mesh (b).

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A fibre filter was placed between the recirculation pump (6) and the water reservoir (1) to assure the absence of particles in the working fluid. The discharge port of the test frame was connected to a silicone tube fixed to the shuttle of a vertical slide. The operating conditions of the tested pumps were controlled by changing the height of the shuttle in respect of the water reservoir level. The pump was driven by an external brushless DC motor (3) with a maximum speed of 50,000 rpm. The speed was measured by the Hall effect sensors integrated in the motor, and maintained constant during the tests and accurate within 1 rpm by a PID controller implemented on a PC. The maximum testing speed was limited to 24,000 rpm. The torque delivered to the pump by the brushless motor was obtained by multiplying the measured current with the torque constant of the motor. The pump power consumption was then obtained as the product of the torque and the measured rotational speed. The test frame was mounted on a two axis micro positioner (9) monitored by a PC to allow a precise control of the relative alignment between the pump shaft and the brushless motor.

Fig. 5. Head versus flow rate; prototype DSP-400 (a); prototype DSP-200 (b).

Two pressure ports were machined on the test frame 10 mm before the pump inlet and after the volute discharge. The pressure ports were connected to a DP15 differential Validyne pressure sensor (7). Two pressure sensor diaphragms were used in the transducers with a full range of 2.2 kPa and 14.0 kPa respectively, with an accuracy of ±0.25% FS and sensitivity 0.01 kPa. A carrier demodulator processed the output signals from the pressure sensors. The unit provided a Vdc output, suitable for processing and recording by a National Instrument device with a dynamic range of 12-bit. The flow rate was measured collecting the flow at the discharge channel into a plastic glass (4) in a given period of time. A balance with a sensitivity of 0.1 g was used to measure the water collected while the time was measured using a digital chronometer with a sensitivity of 0.1 s. To reduce the uncertainly, due to the measuring instruments and the operator reaction time, the liquid measure period was greater than 60 s and the water mass collected more than 10 g.

Fig. 6. Head coefficient versus flow rate coefficient; prototype DSP-400 (a); prototype DSP-200 (b).

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Fig. 7. Power input for DSP-400 pump.

Fig. 9. Comparison between experimental and numerical nondimensional characteristic; prototype DSP-400 (a); prototype DSP-200 (b).

Due to the pump layout and dimension, only the leakage on the rear side (shaft side) was monitored during the experimental tests. The sealed bearing and the couplings of the internal and external ring with the shaft and the frame proved to guarantee zero leakage. Despite no direct measurement were possible on the front side of the pump, the symmetry of the system allowed to reasonably assume the front leakage to be negligible. All experiments were performed at room temperature and carried out a minimum of four times, using clean water as the working fluid. The data in this paper represents the mean values obtained. A first-order uncertainty analysis is performed using a constant odds combination method, based on a 95% confidence level. The resulting uncertainty magnitudes associated with experimentally measured pressure rise, flow rate, and rotational speed are shown in Table 4. Table 4 Uncertainties associated with experimental data. Variable

Fig. 8. Efficiency versus flow rate; prototype DSP-400 (a); prototype DSP-200 (b).

Uncertainty poout

−

po1

Head

h=

Flow rate Rotational speed Power

Q (ml/min) n (rpm) P (W)

(Pa)

±5.5 (Pa); h < 2.2 (Pa) ±35 (Pa); h > 2.2 (Pa) ±0.35 (ml/min) ±1 (rpm) ±0.2 (W)

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4. Numerical procedure The proposed micro pumps were modelled and analyzed by means of the commercial CFD code Ansys CFX 11.0. The computational domain was extended to all the fluid volume inside the test frame. The first parts of the pressure ports ducts were also modelled to allow a better comparison with the experimental data. An unstructured tetrahedral mesh was used for all the domains of the model. The overall size of the mesh was obtained as results of a preliminary study of influence. The independent solution was ensured by increasing simultaneously the nodes density near the walls, in the small geometrical feature of the model and the number of edge grid points until the distribution of the pressure and of the tangential and radial velocity components on a circumferential plane at the impeller outlet, varied by less than 0.1% between two consecutive mesh refinements. Also considered was the change of the pressure losses in the volute, the greater variation admitted was equal to 0.1%. A grid independent solution, in terms of head, efficiency, and velocity field was observed using 5.3 × 106 elements, with y+ values below 3 in the whole computational region and a wall normal expansion ratio of 1. The domains and the computational grid are shown in Fig. 4. The flow was assumed incompressible and isothermal with a temperature of 25 ◦ C equal to the temperature of the working fluid measured in the tank. The turbulence model was chosen on the basis of the expected Reynolds number Re = lω2 /. The length orders varied in the pumps, from 4 × 103 ␮m in DSP-400 and 2 × 103 ␮m in DSP-200, to 4 × 102 ␮m, with rotational speeds from 10,000 to 24,000 rpm. Accordingly, the Reynolds number ranged from 47.6 to 38,000 depending on the geometry and the operational conditions (Table 5), while some parts of the pumps were expected to work in laminar condition, others were presumed to be in transition or in a fully turbulent state. The Shear-Stress-Transport (SST) turbulence model with the transition to laminar based on two transport equations, one for the intermittency and one for the transition onset

Fig. 11. Nondimensional characteristic curves head coefficient versus flow coefficient of the second stages (a) and volute (b).

criteria in terms of momentum thickness Reynolds number, was preferred for the micro pump simulations [67,68]. Mass flow rates were prescribed at the inlet boundary with stochastic fluctuations of the velocities with 5% free-stream turbulence intensity, while average static pressure was imposed at outflow.

Table 5 Pump Reynolds number.

Fig. 10. Nondimensional characteristic curves head coefficient versus flow coefficient of the first stages.

n = 10k rpm n = 20k rpm

l = b3 = 2 × 102 ␮m

l = b3 = 4 × 102 ␮m

l = D3 = 4 × 103 ␮m

Re = 4.76 × 10 Re = 9.51 × 101

Re = 1.904 × 10 Re = 3.807 × 102

Re = 1.904 × 104 Re = 3.807 × 104

1

2

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Table 6 Nondimensional coefficient for the different parts of the pumps. Flow coefficient First stage

1st =

Q/D2 b2 U2

Second stage

2nd =

Q/D3 b3 U3

Volute

Vol = 2nd

Head coefficient 1st

=

2nd

=

Vol

=

Reynolds number

po2 − po1

Re1st =

U22 po3 − po2

b2 U2 

Re2nd = ReDP =

U32 |poout − po3 | U32

ReVol = ReDP =

Power coefficient ˘1st =

b23 ω 

˘2nd =

P1st D25 ω3 P2nd D35 ω3

b23 ω 

Fig. 12. Hydraulic efficiency and power coefficient versus flow coefficient of the tested pumps.

Unsteady model was used for all the calculations. The time discretization scheme adopted was a second order implicit time stepping, to reduce the computational time without reducing the accuracy of the solution. Time step corresponding to 20◦ of impeller rotation was used for the first 2.0 revolutions. The time step was then gradually reduced between 2.0 and 2.5 revolutions to an impeller rotation of 3◦ , ensuing a mean Courant number of approximately CFL = 1.29. A maximum number of ten iterations were fixed for each time step, resulting in a mass residue of 10−6 , momentum residues of 10−5 , and turbulence kinetic energy and energy dissipation residues of 10−5 . The standard transient sliding interface was applied for the rotor stator interface. To allow the comparison of the unsteady simulation with the experimental data, the numerical results were acquired and averaged out over the 6.0 and 6.5 impeller revolutions.

5. Experimental results Fig. 5 shows the experimental characteristic of head versus flow rate of the two tested pumps, for different rotational speeds between 10,000 and 24,000 rpm. The tested pumps exhibit very different characteristics. The DSP-400 shows higher maximum flow rate, while the DSP-200 pump is characterized by the highest maximum head. The reduced width of the pump DSP-200 second stage increases the energy exchange due to the viscous tangential forces, increasing the head at low flow rate. Alternatively, the reduced width of the DSP-200 increased the distributed losses at high flow rate, reducing the head and limiting the maximum flow rate. To compare experimental results obtained at different rotational speeds, the flow and the head coefficients were computed

according to: = =

Q/D3 b3 U3 (poout − po1 ) U32

(1)

(2)

where Q is the flow rate, D3 , b3 and U3 are the diameter, the width and the peripheral velocity at the second stage outlet respectively po the total pressure and  is the water density. Fig. 6 shows the head coefficient versus the flow coefficient for the two configurations. The DSP-200 model shows the highest flow coefficient and the highest head coefficient. Although the DSP-400 attains the highest flow rate, the DSP-200 achieves a flow coefficient up to 1.5 times the maximum flow coefficient of the wider model. Furthermore, the adimensional characteristic of DSP-200 shows a lower mean slope. The distinctive high maximum head coefficient and hyperbolic trend curve with a very flat curve for the high flow rate of the bladeless stage appears to dominate the characteristics of the two stage machine whenever the distance between the disks was reduced. The small data dispersion, visible in Fig. 6, suggests the applicability of the affinity laws for the higher velocity. At low velocity, the systematic divergence of the curves appears to be due to the laminar–turbulent transition inside the pumps. The effect is more pronounced on the DSP-200 model in which the lowest Reynolds numbers take place (Table 5). The rotational speed reduction implies an increase of the non-dimensional head and the reduction of the maximum flow coefficient consistent with the change between fully turbulent flow into laminar–turbulent transition flow and the corresponding change of the friction factor. Nonetheless, the transition effects on the experimental data appear

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Table 7 Efficiency definition. Element

Efficiency definition

Pump

Hy =

Impeller

Hy

Imp

First stage

Hy

1st

Second stage

Hy

2nd

=

Volute

Hy

Vol

=

Q (poout − po1 ) = =

P Q (po3 − po1 ) P Q (po2 − po1 ) P1st Q (po3 − po2 ) P2nd po4 − po1 po3 − po1

to be limited by two opposing effects. The first is the presence of the roughness, particularly on the RSP passages due to the small passages width. The relative high roughness accelerates the transition to turbulent flow and reduces the effect of the Reynolds number on the friction factor for turbulent flow. The second is the presence of high-localized losses at the pump inflow and outflow, and depending mainly on the kinematic affinity, reduces the dispersion caused by the incomplete affinity of distributed losses. Power variations were observed at constant speed and different operation points, but the overall input power was influenced mainly by the rotational speed. Most of the power appears to be dissipated by the bearing and the seals. Therefore, specific tests were conducted to evidence the pump’s physical life, the power absorbed and the efficiencies. Fig. 7 reposts the mechanical power consumption for different rotational speeds of the pump DSP-400 with new bearings, and after about 40 h of exercise. After a rapid increase of the mechanical power consumption in the first hour, no further changes were observed up to and after 40 h, assuring the attainment of standard performances. Because no decrease in the maximum flow rate or in the maximum head was observed, the volumetric efficiency was considered unaffected by wear. Assuming the hydraulic efficiency to be time independent, the increase of the power consumption of the pump was related to the increase of the mechanical losses of the systems. Using the standard condition for the power consumption the efficiency of the pumps was computed as: =

Q (poout − po1 ) P

(3)

Fig. 8 shows the efficiency for the two pumps for different rotational speeds. For both of the models, the efficiency increased with the rotational speed due to the contemporary increase of the mechanical and hydraulic efficiencies. While the hydraulic power transmitted to the fluid increases with the third power of the rotational speed, according to the affinity laws, the overall power consumption, ruled mainly by the mechanical losses, increases almost linearly (Fig. 7). The highest efficiency was then obtained for the higher rotational speed. The effect of the rotational speed over the hydraulic efficiency will be discussed in the next session backed by the numerical results. 6. Numerical results Numerical investigations were carried out to analyze the mutual influence of the two-stage configurations and to allow the characterization of each single stage and of the volutes. Two different rotational speeds (10,000 rpm and 20,000 rpm) were simulated to highlight the effect of the Reynolds number on the performance. The head coefficients versus flow rate characteristic obtained by numerical simulations are compared with the experimental curves in Fig. 9 for the two stages of the DSP-400 and the DSP-200 models. The numerical results agree with the experimental results for

Fig. 13. Power coefficients curves versus flow coefficient of the fist (a) and the second stage (b).

both the models and the rotational speeds. The change in the curve slope is correctly predicted by the numerical analyses for both the models demonstrating a good capability to describe the effects of the Reynolds number (see Table 5). The single stage head and the volute losses were disaggregated for the two stages DSP-400 and DSP-200 models and rearranged by the non-dimensional coefficients of Table 6, to compare the data at different speeds. Fig. 10 illustrates the results for the RSP first stage of the two pumps. The data show a quite coincident characteristic at the same rotational speed for both the pump configurations. Therefore, the second stage geometry appears to have a negligible influence on the first stage performance. On the contrary, a remarkable Reynolds number influence could be observed. Both the first stages show a decrease of the curve slope as the Reynolds number increase and a contextual increase of the maximum head at shut off condition (Fig. 10). The influence of the Reynolds number on the characteristics of the second stage and of the volute is shown in Fig. 11. The head and flow rate coefficients increase as the Reynolds number decreases (Fig. 11a). Contextually, the reduction of the Reynolds number origins a rapid increase of the losses in the stator (Fig. 11b). Both outcomes are ruled by the viscous forces, which promote the energy

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Fig. 14. Hydraulic efficiency versus flow coefficient of the impeller (a) and volute (b).

exchange in the disk stage and dissipate the energy inside the stator. According to these opposite effects, the head increase, obtained inside the disk stage, was mostly lost in the volute. As a result, the Reynolds number impact on the overall characteristics is reduced, concurring to the small dispersion showed in Fig. 6. Fig. 11a highlights the non-linear characteristic of the disk pump, particularly at low flow rate and high rotational speed, while the radial RSP stage has a monotonic decreasing flat characteristic (Fig. 10). Consistently, the experimental characteristic of DSP-200 prototype shows a slope increased for high rotational speed (22k rpm and 24k rpm in Fig. 5b) with an improvement in the stability of the head characteristic if compared with the solution of a RSP couple with a volute [53]. The DSP-400 configuration does not highlight the same propensity due to the lower relative contribution of the disk pump head (Fig. 11a), on the overall characteristics of the pump. Hydraulic efficiencies of the two pumps, and of the different stages, were computed by the numerical analyses according to the definitions reported in Table 7. Fig. 12a shows the hydraulic efficiency of the tested geometries for two rotational speeds. The DSP-400 obtained higher efficiency compared to DSP-200 configuration according to the experimental data (Fig. 8). The smaller DSP-200 volute width caused almost twice

Fig. 15. Hydraulic efficiency versus flow coefficient of the first stages (a) and second stage (b).

the loss in the volute (Fig. 11b) than in the DSP-400 model, justifying the appreciable overall efficiency reduction. The rotational speed exerted a notable role on the hydraulic efficiency. The increase of the rotational speed from 10,000 rpm to 20,000 rpm increased the maximum efficiency of about ten points. This result appears to be ascribed to the different trends of the head and of the power versus impeller speed. While the affinity law appears to be applied quite well to the head curves (Figs. 6 and 9), a systematic difference of the power coefficient (Fig. 12b) ˘=

P D35 ω3

=

P1st + P2nd D35 ω3

at low and high velocity data could be appreciated.

(4)

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Fig. 16. Head and typical size for various micro pumps.

The data show the applicability of the affinity law to the power coefficient for both RSP first stage of the two pumps (Fig. 13). Otherwise a remarkable velocity influence could be observed on the second stage. The DSP-200 appears to work within laminar flow (Table 5) and the DSP-400 model seems to work across the critical and transition zones (Table 5) where the friction factor is highly affected by the Reynolds number. The reduction of the friction factor, as results of the Reynolds number increase, appears to justify the noticeable reduction in the specific power consumption for high rotational speeds and to cause the affinity utter flop in accordance with the experimental data (Fig. 8).

To highlight the roles of the rotor and the stator on the global effectiveness, the hydraulic efficiency was split into the product of the impeller and the volute components. Hy =

Q (po3 − po1 ) P

=

Q (po2 − po1 ) P

·

po3 − po1 po2 − po1

= Hy Imp · Hy Vol

(5)

The higher impeller efficiency, attained by the DSP-200 (Fig. 14a), is heavily counterbalanced and worsened by inefficiency of the volute due to the small hydraulic diameter of the stator (Fig. 14b). To investigate more in depth the loss distribution, the hydraulic efficiency was calculated for each stage, computing the total energy increase in each stage and the corresponding mechanical torque

Fig. 17. Volumetric flow rate and typical size for various micro pumps.

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Fig. 18. Head versus flow rate for various micro pumps.

consumption (Table 7). The efficiencies of the RSP first stage and of the second stage are plotted in Fig. 15a and b respectively. The RSP stages work with maximum efficiency value at very low flow coefficients and a quite linear decrease of it with the flow rate. The increase of the rotational speed improves the efficiency at high flow coefficients but it does not change substantially the maximum values. For all the rotational speeds, the DSP-400 RSP stage obtains higher efficiency than the DSP-200 RSP stage. The unequal behaviour could be explained considering the two stages’ interaction. The constant width of the DSP-400 model involved a very low interaction between the two stages. The reduction of the second stage width in the DSP-200 model causes instead the reduction of the RSP efficiency due to the blockage effect at the interface between the two stages. The efficiency of the disk pumps stage appears to be strongly affected by both the rotational speed and the flow field coming out the first stage. Whereas, the single disk pumps reach the maximum efficiency with disk Reynolds number Red less than 10, the considered two stage micro pumps reach the optimum value inside the range 47–94 as highlighted in Fig. 15b. The increase of the optimum Red value appears to be related to the interaction of the disk stage with the first stage. The excessive reduction of the second stage width causes the reduction of the first stage efficiency and the development of a sudden acceleration of the flow inside the disk stage affecting then the second stage efficiency. Moreover, the jet and wake structure at RSP discharge [53] persists inside the disk stage, due to the small volume between the disks, and further reduces the disk stage efficiency. 7. Comparison with other mechanical pumps The tested two stage miniature pumps were compared with mechanical pumps of comparable sizes. The typical size was defined as the principal dimension of the element delivering energy to the fluid, such as the diameter of the moving element for rotating pumps, the length or the width for rectangular vibrating elements. The DSP produces a higher head than many other reported micro pumps of similar size and/or one order of magnitude greater, as

shown in Fig. 16. Fig. 17 instead compares the maximum flow rate for the same micro pumps. The DSP layout is able to assure both the highest flow rate and head when models smaller than 1 cm are considered. The presence of the second stage improves both the maximum flow rate and the maximum head in respect of the simple RSP and assures a stable characteristics over a wide range of flow rates as shown in Fig. 18. Only the spiral pumps appear to have some advantage, but with a characteristic size ten times greater.

8. Conclusions The experimental and numerical analyses of two miniature two stage pumps with an overall dimension of 10 mm were presented. The innovative design integrated a bladed first stage with a bladeless second stage. The Rotary Shaft Pump design, which integrates the impeller in the shaft, was used as first stage. The second stage was designed as bladeless centrifugal disk pump. The application of disk pumps in a millimetre scale pump is original and attractive because of the high importance of viscous forces in small scale. The noteworthy and positive impact on the head increase and on the stability of the head curve was proved. The influence of the disk stage width was also discussed comparing the results between two different prototypes. Flow rate and pressure rise up to 150 ml/min ( = 0.12) and 12 kPa ( = 0.4), respectively, were obtained with pure water as working fluid. Relative high overall efficiency was attained, up to a maximum of 0.3% due to a proper design, directed to reduce mechanical looses and leakage flow rate. CFD analyses obtained very good agreement with experimental data and allowed the efficiency of each stage to be calculated. The importance of the volute losses and the effects of the Reynolds number over the efficiency of each element of the pump were estimated. The two-stage prototypes performance was also compared with other mechanical miniature pumps demonstrating the two-stage design can be considered a good compromise between size, maximum flow rate and maximum head for pumps smaller than ten millimetres.

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Biographies Antonio Rossetti graduated from the University of Padua in Mechanical Engineering in 2005 and received a PhD in mechanical engineering in 2008 from University of Padua with a thesis titled: “Development and optimization of micro pumps”. Current research areas include theoretical, numerical and experimental analysis of millimetre scale centrifugal and viscous pumps, design and optimization of hydraulic turbines and power-split hydrostatic drivelines.

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Giorgio Pavesi is currently Associate Professor of Energy Conversion Systems and Machines, at the University of Padova, vice president of Energetic Engineering and member of the organizing Committee of Engineering of the Energy, member of the Energetic, member of the School of Doctorate in Industrial Engineering. Current research areas include theoretical and experimental analysis of flow field in turbomachines, stator/rotor interaction in turbomachinery, acoustical analysis of turbomachines aimed at increasing the machine performance and at respecting the European Regulations in terms of noise emissions, design and optimization of hydraulic machines and small wind turbine. He is member of the IEC (International Electrotechnical Commission) for Pump and Small Hydraulic Turbines. He is currently member dell’ International Editorial Board of the “International Journal of Rotating Machinery”. Guido Ardizzon is currently Full Professor of Energy Conversion Systems and Machines, Head of the Department of Mechanical Engineering at the University of Padova and Member of the School of Doctorate in Industrial Engineering. Current research areas include theoretical and experimental analysis of flow field in turbomachines, design and optimization of hydraulic machines and small wind turbine.