Numerical Modeling of a Single-Disk Microscale Viscous Pump (Single-DMVP)

Numerical Modeling of a Single-Disk Microscale Viscous Pump (Single-DMVP) Hafizul Islam1,a), Nizam Manna1, Md Nur Alam Mondal1, Mir Tareque Ali1,b) 1Department of Naval Architecture and Marine Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh Corresponding author: a) [email protected] b) [email protected] Keywords: Micro pump, Disk, Viscous, Rotary, Numerical Abstract: This study presents the numerical modeling of a single-disk microscale viscous pump (Single-DMVP) for low Reynolds number where the flow is assumed laminar, steady, incompressible and two dimensional. The singledisk viscous pump (single-DMVP) is comprised of a spinning disk and a C-shaped channel with an inner and outer radius of 1.19mm and 2.38mm respectively that forms the pump chamber with a fluid inlet port and a fluid outlet ports located at opposite ends. Experimental and analytical data are obtained from a reference paper. Numerical flow rate and pressure rise are obtained for rotational speeds from 300 rpm to 5000 rpm, fluid chamber heights from 40 to 246μm, flow rates from 0 to 4920μl/min, pressure rises from 0 to 31.1 kPa and fluid viscosities from 1 to 62mPa s. The flow rate and pressure rise of the pump vary nearly linearly with rotational speed. With rotational speeds, maximum pressures (pump loads) vary inversely proportional to the square of the heights of the channel and maximum flow rates vary directly proportional to the heights of the channel. The values of the pump load for working fluid oil are about 2 orders of magnitude larger than the values obtained for working fluid water. The advantages of this micropump compared to other micropumps and viscous pumps include a wide range of possible flow rates and pressure rises, flow rate independent of fluid viscosity, well-controlled and constant flow rate, simplicity, ease of manufacture, the flow direction can be reversed by changing the disk rotational direction. Introduction Mechanical pumps like rotary pumps, peristaltic pumps, and membrane pumps have a wide variety of possible working fluids and applications. However, such mechanical micro-pumps are believed to be feasible only when they are greater than a certain size [1], due to the large viscous forces in the fluid at small pump geometries. At very small scales, the viscous forces are significant, and result in large pressure drops over small lengths for fluid flow through a channel [2]. One motivation of the present effort is to employ these large viscous forces to produce a millimeter-scale pump with an easily adjusted, constant flow rate. Many variations of macroscale viscous pumps have been proposed [3–9]. Most of these pumps have a linear relationship between flow rate and pressure rise for a range of operating parameters and pump geometries. Viscous pumps are ideal for applications where high pressure rises, and low to moderate flowrates are required [9]. Uses of different viscous pumps at microscales are described by Sen et al. [10], and Kilani et al. [11]. Sen et al. [10] presents a pump that employs a shaft whose axis is perpendicular to the flow direction, and is positioned eccentrically in a channel. The difference in viscous shear between the shaft and the two channel walls produces a net pumping effect. Numerical simulations are performed by Sharatchandra et al. [12] to determine the optimal configuration. This pump is easy to fabricate, but has limited flow rates and pressure rise capabilities. Kilani et al. [11] describes a spiral pump that uses one spinning disk rotating over a single spiral channel to produce a pumping effect. Results from a macroscale version of this pump are consistent with an analytical expression for flow rate and pressure rise [11]. A small-scale version of this pump may be complex to fabricate. A new viscous micro-pump is presented by Danny Blanchard et al.[13] called the single-disk microscale viscous pump [single-DMVP], to achieve easily controlled flow rates and pressure rises while maintaining simplicity and ease of manufacturing. The present study will represent two-dimensional numerical analysis of this Single-DMVP viscous micro pump. Experimental and analytical data were presented by Danny Blanchard et al. Nomenclature h = flow passage height of the pump i.e.,channel height ρ = fluid density [Pout−in] = static pressure rise between the fluid inlet η = pump efficiency Q and outlet ports = volumetric flow rate Ω = rotational speed of the disk [rpm] μ = dynamic viscosity Problem Specification Pump Geometry The single-disk viscous pump single-DMVP is comprised of a spinning disk, and a C-shaped channel that forms the pump chamber with a fluid inlet port and a fluid outlet ports located at opposite ends. Figure 1. (a) Front view (Without disk), (b) Isometric view (Without disk), (c) Isometric view (With disk), (d) C-shaped channel (3D), (e) C-shaped channel (2D) Boundary Conditions The flow inside the viscous micro pump was considered to be: Two dimensional flow, Incompressible flow, Laminar flow, Steady flow. Pressure Inlet: Pin = 0 (gage pressure) Pressure Outlet: Pout =0 (gage pressure that varies depend on pressure load) Channel Wall (bottom, inner & outer wall): No slip condition and Stationary wall Top surface of channel: No slip condition and Moving wall (rotational), Rotational speed, Ω=380, 800, 1200, 1800, 2500, 3200, 5000 rpm. Numerical Modeling The accuracy of numerical result largely depends on the type of mesh discretization employed; the investigation on pumping performance on viscous micropump is carried out by using structured grid Navier-Stokes method. The CFD package FLUENT 19.2 [14] is used to solve the Navier-Stokes equation numerically. It enables the use of different discretization schemes and solution algorithms, together with various type boundary conditions. A mesh generator, Gambit is used as pre-processor to draw the geometry and generate the required structured grids. Grid points are kept densed from bottom of the channel to near the top of the channel to capture flow characteristics accurately. The number of nodes and elements which led to mesh independent solution for different pump dimensions is shown in tabulated form in Table 1. Solution Method follows, Model: Laminar Model, Interpolation schemes for convection term: Power law, Solver: Pressure based )Based on FVM), Interpolation schemes for diffusion term: Least-Squares Cell-Based Solving method: SIMPLE algorithm, Interpolation Methods for Face Pressure: PRESTO! Figure 2. Mesh (3D) Table 1. Properties of different grids used and comparison of results [For h=0.117mm, Ω=1800 rpm] Mesh (3-D) Number of Cells Q (μl/s) Relative difference Mesh 1 36,000 21.7558 ------ Mesh 2 60,000 21.6959 < 0.27% Mesh 3(used) 90,000 21.6653 < 0.14% Mesh 4 1,92,000 21.6597 < 0.025% Results & Discussion As previously stated, the objectives of the present study is to develop a three-dimensional computational model of the single-disk viscous pump (single-DMVP), validate the model with available experimental & analytical results, to investigate the flow dynamical behavior of a single-disk micro-scale viscous pump, to analyze the effect of geometric configurations (i.e., channel height h). The Numerical results will be presented as contours, pressure rise & flow rate variations, effects of rotational speed of disk on pressure rise and flow rate, effects of flow passage height on the flow rate & pressure rise, effects of fluid viscosity on pressure rise and flow rate, performance of the single-DMVP relative to other microscale pumps, efficiency of the single-DMVP and streamlines. Pressure contour Fig.3(a) shows steady flow visualization (Pressure Contour at max. flowrate conditions). In region 1 of fig.3(n), near the inlet, the spinning disk draws fluid away from the inlet port, creating a low static pressure region along the wall of the channel. The resulting pressure gradient induces fluid from the inlet channel into the pump entrance. Fig.3(n) then shows that fluid is forced circumferentially through region 2 due to the viscous forces applied to the fluid by the spinning disk(s). The fluid circumferential velocity decreases as the fluid approaches the port near the outlet in region 3, where static pressure increases locally. The resulting static pressure then forces fluid toward the outlet channel, motion which is assisted by centrifugal forces at higher disk rotational speeds. Velocity contour Fig.3(b) shows steady flow visualization (Velocity Contour at max. flow conditions). The velocity is one of the most important performance parameters as it quantifies the pumping effect. Fig.3(b) illustrates the effect of the rotational speed on the velocity contour inside the micropump. Velocity is more increased at outer radius than at inner radius as rotational speed increases. Pressure Rise & Flow Rate Variations Fig.3(c) shows Variations of pressure rise with flow rate for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water. Linear relationship is between pressure rise (pump load) and flow rate for each different disk rotational speed. Slope is independent of disk rotational speed. Effects of Rotational Speed on pressure rise Fig.3(d) shows variations of pressure rise with rotational speed for the single-disk viscous pump. Working fluid is water, and Q=0. Pump load varies linearly with disk rotational speed for each constant flow passage height. These are the maximum pressure rises between inlet and outlet ports at zero net flow conditions. Effects of Rotational Speed on flow rate Fig.3(e) shows variations of maximum flow rate with rotational speed for the single-disk viscous pump. Working fluid is water (∆Pout-Pin=0). For the flow passage heights of 117μm and 246μm, numerical flow rates deviate from theoretical as the disk rotational speed increases. Because, neglecting advection terms in theoretical computations. Also numerical flow rates deviate slightly from experimental because of experimental fluid losses through the inlet and outlet tubing. Effects of Flow Passage Height on pressure rise Fig.3(f) shows variations of maximum pressure rise with flow passage height for the single-disk viscous pump. Working fluid is water, and Q=0. Good agreements between numerical and analytical values. For Q=0, ∆Pout-Pin ∝ 1 , which is consistent with analytical equation. ℎ2 Effects of Flow Passage Height on flow rate Fig.3(g) shows variations of maximum flow rate with flow passage height for the single-disk viscous pump. Working fluid is water. Decrease of flow rates due to fluid losses are significant for heights above 100μm. For ∆Pout-Pin=0, Q ∝ h, which is consistent with flow rate scaling in couette flow between parallel plates with one translating plate. Effects of Fluid Viscosity on pressure rise Fig.3(h) shows variations of pressure rise with rotational speed variation for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water and 5W-30 motor motor oil. The values of pump load for working fluid oil are about 2 orders of magnitude larger than the values obtained for working fluid water. Effects of Fluid Viscosity on flow rate Fig.3(i) shows variations of maximum flow rate with rotational speed variation for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water. The variations of flow rate with rotational speed is linear and independent of fluid viscosity Performance of the Single-DMVP Relative to other Microscale Pumps Fig.3(j) shows the variations of pressure rise and flow rate for various micro pumps. The data (except SingleDMVP) corresponds to the maximum flow rate and maximum pressure. Motor oil is used for Single-DMVP at rotational speed 2500rpm. The Single-DMVP provides higher pump loads than many other reported micropumps for same flow rates. Efficiency of the Single-DMVP Efficiency, η = ∆𝑃×𝑄 , here,∆𝑃= static pressure rise (Pa) = 80 pa,𝑄 = flow rate (m3/s),𝑇 = pump torque (Nm),𝑤 = 𝑇×𝑤 rotational speed of disk (rad/s). Graph values does not account for any type of motor losses. Fig.3(k) shows, for h=.246mm, Ω=800 rpm η=.0337 or 3.37% because for ∆P=80pa, flow rate is comparatively very low (for ∆P=87pa, Q=0) for this height of the model. Efficiency is decreasing for a specific height with increasing speed, because of increasing pump torque rather than flow rate. Efficiency vs Pump load Fig.3(l) shows a typical efficiency of the present device for a rotational speed of 800 rpm , pump chamber height of 117μm , pump load 150 Pa and water as the working fluid is 0.24 or 24%. Stream lines The streamline is a good qualitative picture of the flow patterns which gives a clear idea about the characteristics of the operation of the pump. Fig.3(m) shows no vortices effect are found throughout the channel. However, the flow patterns are quite same in all cases. Fig.3(a) shows steady flow visualization (Pressure Contour at max. flowrate conditions). Fig.3(b) shows steady flow visualization (Velocity Contour at max. flow conditions). Fig.3(c) shows Variations of pressure rise with flow rate for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water. Fig.3(e) shows variations of maximum flow rate with rotational speed for the single-disk viscous pump. Working fluid is water (∆Pout-Pin=0). Fig.3(g) shows variations of maximum flow rate with flow passage height for the single-disk viscous pump. Working fluid is water. Fig.3(d) shows variations of pressure rise with rotational speed for the single-disk viscous pump. Working fluid is water, and Q=0. Fig.3(f) shows variations of maximum pressure rise with flow passage height for the single-disk viscous pump. Working fluid is water, and Q=0. Fig.3(h) shows variations of pressure rise with rotational speed variation for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water and 5W-30 motor motor oil. Fig.3(i) shows variations of maximum flow rate with rotational speed variation for the single-disk viscous pump with a flow passage height of 117 micro-meter. Working fluid is water. Fig.3(k) shows, for h=.246mm, Ω=800 rpm, η=.0337 or 3.37% because for ∆P=80pa, flow rate is comparatively very low (for ∆P=87pa, Q=0) for this height of the model. Fig.3(m) shows no vortices effect are found throughout the channel. Fig.3(j) shows the variations of pressure rise and flow rate for various micro pumps. Working fluid is motor oil. Fig.3(l) shows a typical efficiency of the present device for a rotational speed of 800 rpm , pump chamber height of 117μm , pump load 150 Pa and water as the working fluid is 0.24 or 24%. Fig. (n) 3 significant regions of the channel Conclusions The goal of the present study was to investigate the effect of micro-pump geometry and the disk rotational speed on the flow behavior of the Newtonian fluid inside the micro pump and the pump performance at different pressure load. Numerical results of the flow through the micro pump were calculated by simulating Navier-Stokes equations. The validation of the present numerical results is done by comparing with available experimental results. It was found that with rotational speeds, maximum pressures (pump loads) vary inversely proportional to the square of the heights of channel and maximum flow rates vary directly proportional to the heights of channel. 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