Research Papers: Flows in Complex Systems

Numerical Modeling of a Wave Turbine and Estimation of Shaft Work

[+] Author and Article Information
Ravichandra R. Jagannath

School of Aeronautics and Astronautics,
Purdue University,
701 W. Stadium Avenue,
West Lafayette, IN 47907
e-mail: rjagann@purdue.edu

Sally P. M. Bane

School of Aeronautics and Astronautics,
Purdue University,
701 W. Stadium Avenue,
West Lafayette, IN 47907
e-mail: sbane@purdue.edu

M. Razi Nalim

Department of Mechanical Engineering,
Indiana University—Purdue University,
723 W. Michigan St.,
Indianapolis, IN 46202-5160
e-mail: mnalim@iupui.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 16, 2017; final manuscript received April 10, 2018; published online May 18, 2018. Assoc. Editor: Wayne Strasser.

J. Fluids Eng 140(10), 101106 (May 18, 2018) (13 pages) Paper No: FE-17-1279; doi: 10.1115/1.4040015 History: Received May 16, 2017; Revised April 10, 2018

Wave rotors are periodic-flow devices that provide dynamic pressure exchange and efficient energy transfer through internal pressure waves generated due to fast opening and closing of ports. Wave turbines are wave rotors with curved channels that can produce shaft work through change of angular momentum from inlet to exit. In the present work, conservation equations with averaging in the transverse directions are derived for wave turbines, and quasi-one-dimensional model for axial-channel non-steady flow is extended to account for blade curvature effects. The importance of inlet incidence is explained and the duct angle is optimized to minimize incidence loss for a particular boundary condition. Two different techniques are presented for estimating the work transfer between the gas and rotor due to flow turning, based on conservation of angular momentum and of energy. The use of two different methods to estimate the shaft work provides confidence in reporting of work output and confirms internal consistency of the model while it awaits experimental data for validation. The extended wave turbine model is used to simulate the flow in a three-port wave rotor. The work output is calculated for blades with varying curvature, including the straight axial channel as a reference case. The dimensional shaft work is reported for the idealized situation where all loss-generating mechanisms except flow incidence are absent, thus excluding leakage, heat transfer, friction, port opening time, and windage losses. The model developed in the current work can be used to determine the optimal wave turbine designs for experimental investment.

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Fig. 1

Experimental measurements and computational predictions of pressure ratio for a four-port wave rotor [13]

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Fig. 2

Unwrapped view of the three-port wave rotor with internal waves and velocity diagrams [14]

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Fig. 3

Schematic of a slanted or “staggered” straight wave rotor channel

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Fig. 4

Schematic of a “nonstaggered” symmetrically curved wave rotor channel

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Fig. 5

Schematic illustrating the relative frame inflow angle of the flow at the wave rotor inlet [11]

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Fig. 6

Control volume used for estimating work output for the wave rotor and the channel geometry

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Fig. 7

Velocity triangles for (a) positive and (b) negative blade angle

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Fig. 8

Mean channel pressure as a function of angular position of channel for different grid densities

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Fig. 9

Pressure at middle of the channel as a function of angular position of channel at different grid densities

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Fig. 10

Velocity at inlet for three computational time steps. Zoomed-in view shows the shock wave timing at 108 deg and expansion wave profile at 159–162 deg.

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Fig. 11

Velocity at the outlet for three computational time steps

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Fig. 12

Shaft power due to incidence mismatch for an axial channel

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Fig. 13

Relative frame inflow angle as a function of angular position of the channel for an axial channel three port wave rotor

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Fig. 14

Axial velocity, temperature, and logarithm of pressure for an axial-channel three-port wave rotor with optimal duct angle

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Fig. 15

Relative frame inflow angle with respect to channel inlet angle for +30 deg to −30 deg symmetric blade wave turbine

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Fig. 16

Axial velocity, temperature, and log of pressure (all nondimensional) for three-port wave turbine with +30 deg to −30 deg symmetric parabolic blade and optimal duct angle

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Fig. 17

Shaft power due to flow turning in a wave turbine with symmetric blades




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