The performance of fluid pumps based on Wankel-type geometry, taking the shape of a double-lobed limaçon, is characterized. To the authors’ knowledge, this is the first time such an attempt has been made. To this end, numerous simulations for three different pump sizes were carried out and the results were understood in terms of the usual scaling coefficients. The results show that such pumps operate as low efficiency (<30%) valveless positive displacements pumps, with pump flow-rate noticeably falling at the onset of internal leakage. Also, for such pumps, the mechanical efficiency varies linearly with the head coefficient, and, within the onset of internal leakage, the capacity coefficient holds steady even across pump efficiency. Simulation of the flow field reveals a structure rich in three-dimensional vortices even in the laminar regime, including Taylor-like counterrotating vortex pairs, pointing towards the utility of these pumps in microfluidic applications. Given the planar geometry of such pumps, their applications as microreactors and micromixers are recommended.

The present study is part of a larger effort aimed at exploring applications of fluid pumps based on Wankel-type geometry and is focused on the performance characterization of the simplest of such pumps.

Such Wankel-type pumps are essentially rotary positive displacement pumps, which operate by having an inner rotor orbit inside a chamber. The rotor path, determined by the chamber profile, creates a trapped fluid volume which is displaced through the chamber. In contrast to rotodynamic pumps, the trapped fluid is continually compressed to a high pressure without being imparted high kinetic energies. As a positive displacement pump, it has characteristics similar to the reciprocating positive displacement pump and, hence, would generate the same flow at a given speed (RPM) regardless of the discharge pressure, that is, a flat H-Q curve. However, a rotary pump is more susceptible to internal flow leakages especially at high pump heads, leading to a significant reduction in efficiency. The advantages of rotary pumps are that, as well as being able to deliver a flow that is less pulsatile compared with reciprocating piston pumps, they are more compact in design and capable of valveless operation.

There are a number of rotary pump types that have been well established and have found industrial application, such as the Gear Pump, Lobe Pump, Sliding-Vane Pump, Screw Pump, and Progressive-Cavity Pump [

Mathematically, the perimeter of Wankel-type geometry is an epitrochoid, the parametric form of which is given by

In the case of the blood pump mentioned above and in the pumps examined in the present study, the pump chamber geometry is obtained by setting

Estimated geometry of blood pump used in the calibration simulation.

In the present study, numerous computer simulations for three different pump sizes were carried out using commercially available computational fluid dynamics (CFD) codes (after calibrating a typical setup against experimental data). To the authors’ knowledge, it appears that, to date, there has been no such previous attempt for these Wankel-type pumps, although there are numerous studies incorporating computational fluid dynamics (CFD) analyses, reported in the open literature, on particular and general aspects of various other pump types, including both rotodynamic and positive displacement pump types.

We list but several recent references, in the case of positive displacement type pumps, as follows. For gear pumps, see Riemslagh et al. [

In the case of rotodynamic pump types, for centrifugal pumps, see Gao et al. [

Numerical results generated in the present study were expressed in terms of the usual scaling coefficients. To conclude, we present details of the flow structure within the chamber for a pump sized for microfluidic applications.

The simulations were carried out in a proprietary finite volume CFD code, ANSYS CFX v 15, using the immersed solid method to model the motion of the rotor.

To solve for the flow field, the shear-stress transport (SST) turbulence model of Menter [

The immersed solid technique, implemented within the finite volume code of CFX [

The simulation setup for the pump performance characterization work was calibrated against the experimental data from [

Direct comparison was not possible as the exact dimensions of the blood pump and fluid properties were not reported. By trial and error and by examination of the information available, the parameters of

A mesh grid sensitivity study was carried out by comparing instantaneous pump flow-rates obtained for different grid cell sizes. As shown in Figure

Instantaneous flow-rates obtained for various grid cell sizes in grid sensitivity study.

Predicted instantaneous flow-rate (blue curve) overlaid on experimental flow-rate (black line) from [

The uncertainty of the numerical results could not be assessed as Monties et al. [^{3} [

Mesh grid for the (a) rotor and (b) pump cavity.

For the scaling studies, pumps of three different sizes of

Collected data were analyzed with the aid of the following dimensional groups: capacity coefficient,

Time averaged values of flow-rate and reactive torque (over one cycle) were used in calculating the dimensional groups’ values.

From the plots of capacity coefficient,

Plots of capacity coefficient,

Variation of head coefficient,

It appears therefore that the capacity coefficient,

Linear scaling of pump flow-rate,

While the results of the above scaling studies are useful for a preliminary assessment of a suitable pump size for a particular application, detailed examination of the flow field in the pump chamber would be necessary to see if such pumps could be exploited for certain biomedical, microfluidic, or microreactor applications.

Hence, in this section, we report on a 3D simulation of pump scales to

By plotting surface streamlines on a horizontal plane bisecting the thickness of the pump chamber as well as on a vertical plane along the axis of symmetry of the pump chamber for various rotor positions, as shown in Figure

(a) Surface streamlines taken on a plane bisecting the thickness of the pump chamber for various rotor positions; (b) surface streamlines on a plane along the axis of symmetry of the pump chamber.

Delving deeper, surface streamlines at various vertical planes across the pressure side of the pump chamber, for a particular rotor position, were then plotted. As shown in Figure

Two views of 2D streamlines on various cut-planes in the pressure side of the pump chamber, showing Taylor-like vortices being stretched as they traverse to the pump discharge.

Velocity vectors plotted on one of the cut-planes in Figure

Velocity vectors plotted for one of the rotor positions in Figure

Thus as the flow transits from the suction to the pressure sides, it is being continuously stretched from a pattern characterized by a dominant, horizontal lateral vortex to one characterized by pairs of vertical, lateral Taylor-like counterrotating vortices that are continuously deformed as the flow is being evacuated.

The resulting complex flow pattern, rich in three-dimensional vortices, suggests that pumps based on Wankel geometries have a good potential for mixing applications.

We conclude this technical brief with the following salient points.

A fluid pump based on the simplest Wankel geometry (double-lobed limaçon) operates as a positive displacement pump, without requiring the use of valves.

As with positive displacement pumps in general, the capacity coefficient,

For a particular set of dimensionless groups, pump efficiency,

Within the onset of internal leakage, the capacity coefficient,

Maximum pump efficiency is in the region of 30%.

Even in the laminar flow regime, flow structure within the pump chamber is complex and very rich in three-dimensional vortices.

Detailed examination of the flow structure reveals a transition from a structure dominated by a backward facing step type recirculation zone to one characterized by Taylor-like counterrotating vortex pairs that are continuously stretched, as the trapped fluid traverses from the suction side to the pressure side of the pump chamber.

It appears that a fluid pump based on the simplest Wankel geometry is best suited for applications in which pump efficiency is not an overriding issue; valveless operation is an advantage and complex flow patterns in the pump chamber are exploited to serve a particular function. Given the planar geometry of such pumps, their application as microreactors and micromixers is recommended.

Epitrochoid eccentricity

Acceleration due to gravity

Turbulent kinetic energy

Epitrochoid shape parameter

Pump head coefficient

Pump capacity coefficient

Pump head

Shaft speed

Pump flow-rate

Rotor tip-to-centroid distance

Device Reynolds number

Momentum source term

Reactive torque

Ratio of rotor tip clearance to rotor tip-to-centroid distance

Pump mechanical efficiency

Molecular viscosity

Eddy viscosity

Fluid density

Turbulent energy specific dissipation rate

Rotor tip clearance.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to acknowledge the support provided by “Down-Hole Multiphase Flow Equipment Design & Analysis”-SERC TSRP Programme of Agency for Science, Technology and Research (A