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Research Papers: Flows in Complex Systems

# Design Principles and Measured Performance of Multistage Radial Flow Microturbomachinery at Low Reynolds Numbers

[+] Author and Article Information
Changgu Lee, Selin Arslan

Department of Mechanical Engineering, Columbia University, New York, NY 10027

Luc G. Fréchette

Department of Mechanical Engineering, Columbia University, New York, NY 10027; Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada

J. Fluids Eng 130(11), 111103 (Sep 23, 2008) (11 pages) doi:10.1115/1.2979010 History: Received February 26, 2008; Revised July 14, 2008; Published September 23, 2008

## Abstract

This paper introduces and experimentally demonstrates the design concept of multistage microturbomachinery, which is fabricated using silicon microfabrication technology. The design process for multistage microscale turbomachinery based on meanline analysis is presented, along with computational fluid dynamics predictions of the key aerodynamic performance parameters required in this design process. This modeling was compared with a microturbine device with a 4 mm diameter rotor and $100 μm$ chord blades, based on microelectromechanical system technology, which was spun to 330,000 rpm and produced 0.38 W of mechanical power. Modeling suggests a turbine adiabatic efficiency of 35% and $Re=266$ at the maximum speed. The pressure distribution across the blade rows was measured and showed close agreement with the calculation results. Using the model, the microturbine is predicted to produce 3.2 W with an adiabatic efficiency of 63% at a rotor speed of $1.1×106 rpm$.

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## Figures

Figure 1

Scanning electron microscopy (SEM) image of a typical radial multistage microturbine formed by DRIE, showing the rotors (left) and stators (right) on separate chips as well as a close-up view of one blade row (upper right). The turbine is assembled by laying the stator chip over the rotor chip in order to interdigitate the concentric blade rows.

Figure 2

Velocity triangles in one turbine stage: (a) velocity triangle diagram and (b) h-s diagram

Figure 3

Stage matching for two different stage designs. Baseline flow rate of 24 mg/s; 1.5 mm diameter rotor for both. Inlet pressure of 0.6 MPa and outlet pressure varies. (a) Six stage design and (b) five stage design.

Figure 4

Typical computational grid. Upstream and downstream areas are not shown and the blade passage is repeated for illustration purposes: (a) Rotor 1 and (b) Rotor 3

Figure 5

Loss coefficient (a) and exit flow angle (b) as a function of incidence for high camber (Rotor 1) and low camber (Rotor 3) NACA A3K7 airfoils with solidity σ=2. In all cases Re=350±20 and inlet Mach number M1=0.14±0.02. The blade exit angles of Rotors 1 and 3 are 74 deg and 60 deg. (a) Loss coefficient versus incidence and (b) exit flow angle versus incidence.

Figure 6

Loss coefficient (a) and exit flow angle (b) as a function of Reynolds number for high camber (Rotor 1) and low camber (Rotor 3) NACA A3K7 airfoils with σ=2. In all cases incidence i=0 and inlet Mach number M1=0.14±0.01. (a) Loss coefficient versus Reynolds number and (b) exit flow angle versus Reynolds number.

Figure 7

Total pressure contours for NACA A3K7 turbine stage with solidity of 2 (Rotor 3), showing that low Reynolds numbers (a) lead to thick boundary layers and slightly shallower exit flow angles than higher Reynolds number flow (b). The nonuniformity of the total pressure at the entrance in (a) appears to be from the heat transfer due to acceleration of the flow. (a) Re=60 and (b) Re=665.

Figure 8

Profile of the normalized velocity magnitude (V/Vmax) across the flow passage (Rotor 3) taken at 5% chord downstream of the blade row. In x-axis, y/c=0 indicates the suction side and y/c=1 indicates the pressure side.

Figure 9

Loss coefficient and exit flow angle as a function of Reynolds number for the same airfoil (Rotor 3) but with different solidities, σ=c/s: (a) pressure loss coefficient and (b) exit flow angle

Figure 10

Configuration of the demo microturbine device. The letters (A–E) identify the five wafers.

Figure 11

Microturbine device: chip-scale view of the 15×15 mm2 device (left) and close-up infrared (IR) picture of interdigitated blade rows (right). Darker blades are rotors and brighter ones are stators.

Figure 12

Fabricated stator and rotor blade rows. Upper rows are the stator, and lower ones the rotor. After device assembly, these become interdigitated.

Figure 13

Flow rate as a function of the differential pressure across the turbine

Figure 14

Rotation rate as a function of the flow rate of pressurized air. Data are presented for two different devices showing repeatability. These data come from Ref. 14, but shown here for completeness.

Figure 15

Pressure distribution throughout the multistage microturbine. The relative radial position indicates the distance from the center of the rotor divided by the disk radius, and the pressure difference is the measured pressure subtracted by the exit pressure. The rotors and stators for each of the four stages are identified by R# and S#, respectively.

Figure 16

Estimated power production from each stage

Figure 17

Estimated pressure loss coefficient, Y, as a function of Reynolds number. The numbers are averaged values across the blade rows.

Figure 18

Estimated total adiabatic efficiency of the turbine as a function of averaged Reynolds number

Figure 19

Model prediction of the total adiabatic efficiency at extended Re range

Figure 20

Model prediction of the power production from each stage at higher differential pressure

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