Research Papers: Internal Combustion Engines

Development and Performance Measurements of a Beta-Type Free-Piston Stirling Engine Along With Dynamic Model Predictions

[+] Author and Article Information
Kyuho Sim

Department of Mechanical System
Design Engineering,
Seoul National University of Science
and Technology,
Seoul 01811, South Korea
e-mail: khsim@seoultech.ac.kr

Dong-Jun Kim

Department of Mechanical System
Design Engineering,
Seoul National University of Science
and Technology,
Seoul 01811, South Korea
e-mail: djkim6300@gmail.com

1Corresponding author.

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received March 30, 2017; final manuscript received April 24, 2017; published online August 1, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(11), 112806 (Aug 01, 2017) (13 pages) Paper No: GTP-17-1122; doi: 10.1115/1.4036967 History: Received March 30, 2017; Revised April 24, 2017

This paper presents the development and performance measurements of a beta-type free-piston Stirling engine (FPSE) along with dynamic model predictions. The FPSE is modeled as a two degrees-of-freedom (2DOF) vibration system with the equations of motion for displacer and piston masses, which are connected to the spring and damping elements and coupled by working pressure. A test FPSE is designed from root locus analyses and developed with flexure springs and a dashpot load. The stiffness of the test springs and the damping characteristics of the dashpot are identified through experiments. An experimental test rig is developed with an electric heater and a water cooler, operating under the atmospheric air. The piston dynamic behaviors, including the operating frequency, piston stroke, and phase angle, and engine output performance are measured at various heater temperatures and external loads. The experimental results are compared to dynamic model predictions. The test FPSE is also compared to a conventional kinematic engine in terms of engine output performance and dynamic adaptation to environments. Incidentally, nonlinear dynamic behaviors are observed during the experiments and discussed in detail.

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Fig. 1

Conceptual diagram of a beta-type FPSE with an external load: (a) schematic layout of the engine and (b) free-body diagram of the pistons

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Fig. 2

Root locus trajectories with increasing spring stiffness of 100–10,000 N/m for (a) the PP damping of 50 N s/m and (b) the various PP damping of 20 N s/m, 50 N s/m, and 80 N s/m

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Fig. 3

Root locus trajectories predicted with (a) increasing heater temperatures of 600–800 °C and (b) increasing damping loads of 0–100 N s/m

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Fig. 4

Manufactured test FPSE (left) and its test rig (right)

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Fig. 5

Development process of the piston spring for the test FPSE, including the (a) design drawing, (b) structural stress analysis, (c) static load–deflection tests, and (d) measured stiffness

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Fig. 6

Free vibration tests of two pistons of (a) PP and (b) DP with 10 mm of initial condition. PP damping coefficient 22.58 N s/m, and DP damping coefficient 13.36 N s/m from logarithmic decrement.

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Fig. 7

Measured piston displacements and working pressure of the test FPSE during continuous heat-up and natural cool-down at heater temperatures of 400–800 °C under no load condition. Cooling water flow rate of 500 ml/min.

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Fig. 8

Measured piston displacements during engine start and stop, magnified from Fig. 7

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Fig. 9

Measured piston displacements, working pressure, and P–V diagram of the test FPSE at a heater temperature of 800 °C, together with curve fitting lines

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Fig. 10

Measured (a) position-velocity plots of the PP and DP and (b) the pressure–volume (P–V) diagram of the test FPSE at heater temperature of 800 °C, plotted from Fig. 9

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Fig. 11

Measured dynamic performance of the test FPSE during (a) the stepwise increases in heater temperatures of 600–800 °C by intervals of 25 °C, including the (b) piston stroke (p-p) and operating frequency, (c) pressure amplitude (p-p) and phase angle (DP–PP), and (d) P–V power and efficiency

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Fig. 12

FPSE test rig for performance measurement under external loads using a liquid (water) dashpot

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Fig. 13

Measured piston stroke (p-p), pressure amplitude (p-p), operating frequency, and phase angle of the test FPSE for increasing external loads (no disk, 28 holes–eight holes)

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Fig. 14

Measured dynamic behavior of the liquid dashpot during operation of the test FPSE for increasing loads (no disk, 28 holes–eight holes) at a heater temperature of 700 °C, including (a) measured damping force and PP velocity, (b) force–velocity diagram, and (c) estimated damping coefficients

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Fig. 15

Measured power and efficiency, P–V and shaft, of the test FPSE for increasing loads (no disk, 28 holes–eight holes) at a heater temperature of 700 °C

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Fig. 16

Measured dynamic discontinuities of the test FPSE: (a) PP stroke (p-p) at expansion space temperatures of 620–670 °C, extracted from Figs. 5(a) and 5(b) piston displacements and working pressure during steady operations near the discontinuity-occurring temperatures

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Fig. 17

Measured (a) PP and DP displacement versus time and (b) PP velocity versus displacement (phase plot) for the expansion temperature increasing from 650 °C to 660 °C



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