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Start-up and damping of a standing wave thermoacoustic engine: model development and experimental evaluation

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Abstract

This paper puts forward a transient numerical model for thermoacoustic energy convertors using Rott’s equations combined with electrical circuit analogy. To enhance the accuracy of model outcomes, the lumped element values are updated at each time step as a function of temperature. Accordingly, a nonlinear temperature distribution is obtained along the hot core. The developed numerical approach is in line with the experimental results of a standing wave thermoacoustic engine. Based on this method, the temperature variations along the stack and the impact of stack material on start-up time and onset temperature are numerically investigated. Additionally, the onset temperature profiles are calculated and presented comparatively for the numerical and experimental results. The start-up time of spontaneous oscillations is calculated for the standing wave system. Consequently, the best geometry that quickly reaches sustained oscillations can be selected using this model. Examining the temperature profile during the start-up and damping process highlights a temperature difference between these two processes. This is calculated as 35 K in the numerical solution and measured as 38 K in the experiment for a standing wave engine. Observations show that using a material with lower thermal conductivity in the stack section can reduce the onset-damping temperature difference. The novel approach described here shows potential in capturing the onset-damping behavior of thermoacoustic systems efficiently.

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Abbreviations

A :

Area, m2

Cp :

Specific isobaric heat capacity, J/K.mol

E :

Acoustic power, W

F(x) :

Energy flow, W

f :

Spatially averaged thermoviscous function

G(x) :

Thermoacoustic pumping effect, W

g :

Controlled source coefficient

Im[] :

Imagine part of parameter

k :

Thermal conductivity coefficient, W/m2K

p :

Amplitude of oscillating pressure, Pa

P :

Mean pressure, Pa

Q :

Heat power, W

R :

Universal gas constant, J/K.mol

Re[] :

Real part of parameter

T :

Temperature, K

U :

Amplitude of oscillating volume flow rate, m3/s

V :

Volume, m3

DR:

Drive ratio

γ :

Ratio of specific heat

ρ :

Average density of gas, kg/m3

δ :

Viscous penetration depth, m

σ :

Prandtl number

ω :

Rotational frequency, rad

μ :

Dynamic viscosity, kg. s/m

a :

Ambient

in :

Input

i :

Spatial discretization node numerator

out :

Output

v :

Viscous

κ :

Thermal

p :

Isobaric

gas :

Related to the gas

solid :

Related to the solid media

m :

Mean

norm:

Normalized parameter

o :

Onset period

d :

Damping period

e :

Error

~:

Complex conjugate

n :

Time step

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Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Faculty of Engineering, Tarbiat Modares University (TMU), Tehran, Iran

    Alireza Moradi, Mohsen Bahrami & Fathollah Ommi

  2. Khayyam Research Institute, Tehran, Iran

    Zoheir Saboohi

Authors
  1. Alireza Moradi
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  2. Mohsen Bahrami
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  3. Fathollah Ommi
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  4. Zoheir Saboohi
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Alireza Moradi and Mohsen Bahrami under the supervision of Fathollah Ommi and Zoheir Saboohi.

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Correspondence to Fathollah Ommi.

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Alireza Moradi and Mohsen Bahrami contributed equally to this work and should be considered co-first author.

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Moradi, A., Bahrami, M., Ommi, F. et al. Start-up and damping of a standing wave thermoacoustic engine: model development and experimental evaluation. Heat Mass Transfer 58, 2175–2193 (2022). https://doi.org/10.1007/s00231-022-03235-w

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  • DOI: https://doi.org/10.1007/s00231-022-03235-w

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