exploitation of active or passive valves accompanying with the conventional one, thereby giving it a simple, reliable, and low cost feature. The operational principle of the valve-less micropump is based on the flow characteristic difference between the nozzle and diffuser shown in Fig 1. The ejected velocity from nozzle is often very high and is regarded as a free jet flow; leading to a greater pressure loss with a higher loss coefficient. In the meantime, normally the loss coefficient of diffuser is less than that of nozzle, hence more fluid flow rate through the diffuser than the nozzle is expected at the same pressure drop across both elements. However, the published literature about the micro nozzle/diffuser is mainly focused on the manufacturing technology as well as its performance [8-9].
Despite its simple and robust nature, the nozzle/diffuser micropump suffers from low efficiency. In this regard, it is of crucial importance to seek some augmentation to improve the efficiency for this kind micro-pump. Unfortunately, very rate attention is made toward the improved performance using enhanced structure. Therefore it is the purpose of this study to experimentally analyze the performance of the micro diffuser/nozzle with certain enhancement structures.
Inlet Outlet Inlet Outlet
from diffuser > from nozzle from nozzle < from diffuser
Fig. 1. Operation of the diffuser-based pump: (a) Supply mode (b) Pump mode.
EXPERIMENTAL SETUP
A total of six types of micro nozzle/diffuser were made and tested. The geometries of the test micro- diffuser/nozzle structure and their detailed dimensions are tabulated in Table 1.
The test samples were fabricated using the deep reactive ion etching (DRIE). The SEM photo showing the fabricated sample is given in Fig. 2. The inlet and outlet hole are drilled using laser machining on glass wafer. Finally the silicon wafer is anodically bonded to the glass wafer.
The test sample was then placed at a test rig to examine its performance. A schematic of the test rig is shown in Fig. 3. The main objective of the experimental setup is to measure the total pressure drop across the nozzle/diffuser. The test facility is based on a one-through design, and water is used as the working fluid. A syringe is used to store water and maintain the pressure of the system. During the experiment, water flows in series to a infusion pump (KDS, Model 100, that provides flow rates from 0.1 μL/hr to 519 mL/hr), a filter and check valve, the test section, and finally into a beaker seated upon an electronic balance (AND Model GF2000, with weighing capacity up to
uncertainties of the pressure transducer, differential pressure transducer are 0.5% and 0.3%, respectively. The system temperature is measured by a resistance temperature device (RTD). The RTD was pre-calibrated by a quartz thermometer with a calibrated accuracy of 0.1 ºC. In the experiment, the derived typical uncertainty of the pressure loss coefficient is less than 5%.
Table 1. Detailed geometry of the test micro nozzle/diffuser.
No.1 Base model No.2 Fish-skin
No.3 3-fin No.4 2-fin
No.5 Obstacle I No.6 Obstacle II
(a)
Fig. 3. Schematic diagram of the experimental setup.
ANALYSIS OF THE MICRO NOZZLE/DIFFUSER
θ
L
W1 x W3
A(x) Region 2
Region 1 Region 3
W(x) Positive
direction(Diffuser) Negative
direction(Nozzle)
Fig. 4. Definitions of the different regions in the diffuser/nozzle element.
Considering the schematic of the diffuser/nozzle element shown in Fig. 4, the flow inside the diffuser/nozzle is regarded two-dimensional. The pressure drops across the nozzle/diffuser element can be divided into three parts. Namely, the pressure drop at the entrance (region 1), pressure drop within the diffuser/nozzle (region 2), and the expansion loss of the pressure drop at the exit of the nozzle/diffuser (region 3):
3
Where the subscripts of d and n denote diffuser and nozzle, respectively. For a sharp entrance of the diffuser, ξ is 0.5 whereas ξ = 0.05 [10] for a smooth round entrance. Similarly, a loss coefficient of 1 [11] is given at the exit section.
For a rectangular cross section in the diffuser or nozzle, it is essential to consider the influence of the area change. As shown in Fig. 1, the effective width of the diffuser in the x position is Where W1 is the width of the diffuser element at the
entrance section. Hence the hydraulic diameter at x is
( ) ( )
Note that H is the depth of the diffuser, A(x) and C(x) are the cross sectional area and the periphery at x location, respectively. The average velocity at x location can be obtained from the continuity equation, i.e.,
( ) ( ) A( )x
cross-sectional area and velocity at the throat position, respectively.
Therefore the Reynolds number at x position can be expressed as: ( ) ( )
The pressure drop in the region 2 can be calculated as follows: Where f(x) is the corresponding Fanning friction factor inside rectangular cross section at x position. Hartnett and Kostic [12] proposed a simplified polynomial to describe the friction factor for laminar flow through a rectangular channel that is accurate to ±0.05%:
Where α = H/W is the aspect ratio of the rectangular section. In the valve-less micropump, the nozzle/diffuser element connected to the fluid cavity volume with an oscillating diaphragm. The total pressure drop ΔP of micro nozzle/diffuser is often presented in terms of the pressure loss coefficient ξ, i.e.
2
2 1 u P=ξ× ρ
Δ (9)
The most common modeling and evaluation of micropump performance used efficiency ratio of the nozzle/diffuser element can be expressed as
diff nozzle
ξ
η=ξ (10)
Another evaluation of micropump performance is termed the static rectification efficiency. It is equivalent to the “pump stroke efficiency” [13]. The static rectification efficiency ε is given as
Where Q is the flow rate of the nozzle/diffuser at a pressure P, the flow into the converging diffuser flow is regarded as positive (+) while in the diverging one is negative (-).
RESULTS AND DISCUSSION
Test results of pressure drops vs. Reynolds number for all the test samples are plotted in Fig. 5. As expected, the pressure drop increases with the rise of Reynolds number. For the pressure drop among the test samples, it can be found that the pressure drops increase considerably when the obstacle and fin structure are added. However, it should be pointed out that the pressure drops are quite sensitive to the surface structure. For instance, the pressure drops for sample #2, the so called fish skin surface, reveals a much lower pressure drop than the base model. Apparently, with the fish skin outward wavy surface, some of the liquid is trapped within this structure, yet it gives rise to lower friction at the interface of this trapped liquid and of the liquid flow in/out of the nozzle/diffuser. Accordingly, one can see a much lower pressure drop of this sample in comparison with other samples. Conversely, the structure employing a fin like design like samples #3~#6, possesses a higher pressure drop than the base model. This is somehow expected due to the presence of additional fin surface which provides more flow resistance.
100
Fig. 5. Pressure drops vs. Reynolds number for micro nozzle/diffuser.
As shown in Fig. 6, the pressure drop coefficient and efficiency ratio as a function of Reynolds number are plotted for further comparison against the theoretical analysis and measured data of conventional micro nozzle/diffuser. The results show that the measured pressure loss coefficients are higher than calculated results, the phenomenon is especially
and 2 [11]. In summary of these two effects, one can see the difference amid the measured data and the calculation. Notice that the forgoing effects prevail in both nozzle and diffuser;
therefore the efficiency ratio is good agreement between measured data and calculated results as shown in Fig. 6.
1
Fig. 6. Pressure loss coefficient and efficiency ratio vs.
Reynolds number for conventional micro nozzle/diffuser.
Fig 7. The resistance coefficient of (a) uniform (b) parabolic outlet velocity distribution.
For further comparison of the performance for the test samples, the pressure drops are then in terms of dimensionless efficiency ratio vs. the Reynolds number. The Reynolds numbers are based on throat width of the test samples without enhancement. Test results are shown in Fig. 8, the ordinate of the figure is η/ηno1.A value above unity indicates that the efficiency ratio for enhancement design exceeds that of conventional nozzle/diffuser at the same Reynolds number. The results shown in this figure suggest that the micro nozzle/diffuser with adding fins such as No. 3 and No. 4 shows considerable improvement in performance. The maximum efficiency ratio improvement is about 16 % for an added 3-fin operated at low Reynolds number around 70. Upon this situation, the static rectification efficiency of No. 3 is increased
encountered at the very low Reynolds number region. On the other hand, the improvement of micro nozzle/diffuser with enhancement decreases with the rise when the Reynolds number above than 70. It is due to the efficiency ratio of conventional micro nozzle/diffuser significantly increases with the Reynolds number. In conventional micro nozzle/diffuser, the loss coefficient for the nozzle at the exit is higher due to free jet flow accompanied with some additional pressure recovery for diffuser, leading to a higher efficiency at the higher Reynolds number region [8]. Accordingly in higher flow velocity region, the added enhancements reduce the influence of the above-mentioned two factors, thereby resulting in a lower efficiency.
Fig. 8. The efficiency ratio between conventional micro nozzle/diffuser vs. Reynolds number.
CONCLUSIONS
In this study, we have fabricated and measured the pressure drop characteristic of micro diffusers/nozzles with six types of enhancement structures, and its performance is analyzed. The pressure drops across the designed micro nozzles/diffusers are found to be increased considerably when the obstacle and fin structure are added. Further, the micro nozzle/diffuser having circular area gives rise to a lower pressure drop, owing to the hydraulic diameter is increased by circular area and lower interface friction. The tested results show that the measured pressure loss coefficients are higher than the calculated results, the phenomenon is especially pronounced for higher Reynolds number region. The departure of prediction and measurement is because the model is fully developed base yet the velocity distribution of outlet condition provides some additional pressure drop of the water flow at high Reynolds number region.
The maximum improvement of the proposed structures is about 16 % for an added 3-fin structure operated at a Reynolds number around 70. Upon this situation, the static rectification efficiency improves over 4.43 times than the conventional
nozzle/diffuser. Experimental results indicate that the improvement of micro nozzle/diffuser with enhancement peaks at a Reynolds number of 70, and a detectable decline is encountered when the Reynolds number is further decreased. It is due to the efficiency ratio of conventional micro nozzle/diffuser significant increases with the Reynolds number.
ACKNOWLEDGMENTS
The authors are indebted to the financial support from the Bureau of Energy and Department of Industrial Technology, the Ministry of Economic Affairs, Taiwan and National Science Council of the Republic of China (Taiwan) under contact NSC 98 - 2218 - E - 151 - 001.
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