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A coupled computational model of nonlinear thermoacoustics of standing wave heat engines

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Abstract

Thermoacoustic engines have been recently regarded and developed as reliable, long-life, and environment-friendly engines by using experiments or mathematical models. Thermoacoustic mathematical models can be divided into two categories of linear and nonlinear. This paper introduces a coupled 1D-2D computational nonlinear model of heat and flow fields inside loaded standing-wave thermoacoustic engines. On the one hand, the computational cost of the present model is much lower than that of full CFD models whose computational domain contains the entire engine. On the other hand, it does not have the limitation of uniform global cross section as the simplified numerical models do. In addition to the coupled nonlinear model, another simulation based on linear thermoacoustic theory (LTA) has been performed. The model has been well validated using previous experimental data and compared with the results of LTA. Subsequently, the temperature and pressure distributions, the mean acoustic power, and heat transfer and volume flow rate distributions have been presented and discussed. This model is extendable to many other systems whose some parts have negligible multidimensional effects and the other parts have considerable ones.

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Abbreviations

A :

Cross sectional area of gas flow (m2)

a :

Coefficient of nodal point variable (**)

a1,a2,a3 :

Coefficients of time derivative scheme

b :

Constant of discretized equation (**)

C :

Specific heat (J.kg−1.K−1)

C P :

Isobaric specific heat (J.kg−1.K−1)

C v :

Isochoric specific heat (J.kg−1.K−1)

f D :

Darcy friction factor

f k :

Rott’s thermal function

f v :

Rott’s viscous function

h :

Heat transfer coefficient (W.m−2.K−1)

i :

Imaginary unit

Im :

Imaginary part of complex number

k :

Thermal conductivity (W.m−1.K−1)

l :

Half of plate thickness (m)

\( \dot{m} \) :

Mass flow rate (kg.s−1)

n :

Normal vector of control surface

P :

Pressure (Pa)

P r :

Prandtl number

q ′ ′ ′ :

Heat source per unit volume (W.m−3)

R :

Gas constant (J.kg−1.K−1)

Re :

Real part of complex number

Re δ :

Reynold number

R u :

Residual of x-momentum (kg.m.s−2)

T :

Temperature (K)

t :

Time (s)

U :

Volume flow rate (m3.s-1)

u :

Gas velocity in x-direction (m.s−1)

V :

Volume (m3).

v :

Gas velocity in y-direction (m.s−1)

x :

Longitudinal coordinate (m)

y :

Transverse coordinate (m)

y 0 :

Half of plate spacing (m)

α :

Relaxation factor

γ :

Specific heat ratio

Δx :

Grid size in x-direction (m)

Δy :

Grid size in y-direction (m)

Δt :

Time step (s)

μ :

Dynamic viscosity (Pa.s)

ρ :

Density (kg.m−3)

τ :

Stress tensor (Pa)

Φ :

Viscous dissipation function (Pa.s−1)

ω :

Oscillating frequency (rad.s−1)

amb :

Ambient

CS :

Control surface

CV :

Control volume

L :

Lateral surface

nb :

Neighboring

sol :

Solid

0 :

Mean value

1 :

Acoustic value

*:

Complex conjugate

.(dot):

Time derivative

k :

Time level

**:

The dimension depends on the equation (momentum or energy) in which the parameter is used

References

  1. Rott N (1969) Damped and thermally driven acoustic oscillations in wide and narrow tubes. Z Angew Math Phys 20:230–243

    Article  Google Scholar 

  2. Swift GW (1988) Thermoacoustic engines. J Acoust Soc Am 84:1145–1180

    Article  Google Scholar 

  3. Karpov S, Prosperetti A (2002) A nonlinear model of thermoacoustic devices. J. Acoust Soc Am 112(4):1431–1444

    Article  Google Scholar 

  4. P. in’t Panhuis (2009) Mathematical aspects of thermoacoustics, PhD Dissertation, Eindhoven University of Technology

  5. Nowak I, Rulik S, Wroblewski W, Nowak G, Szwedowicz J (2014) Analytical and numerical approach in the simple modelling of thermoacoustic engines. Int J Heat Mass Transfer 77:369–376

    Article  Google Scholar 

  6. Selimefendigil F, Öztop HF (2014) POD-based reduced order model of a thermoacoustic heat engine. Eur J Mech B/Fluids 48:135–142

    Article  MathSciNet  Google Scholar 

  7. Namdar A, Kianifar A, Roohi E (2015) Numerical investigation of thermoacoustic refrigerator at weak and large amplitudes considering cooling effect. Cryogenics 67:36–44

    Article  Google Scholar 

  8. Skaria M, Abdul Rasheed KK, Shafi KA, Kasthurirengan S, Behera U (2015) Simulation studies on the performance of thermoacoustic prime movers and refrigerator. Comput Fluids 111:127–136

    Article  Google Scholar 

  9. Maiwand Sharify E, Takahashi S, Hasegawa S (2016) Development of a CFD model for simulation of a traveling-wave thermoacoustic engine using an impedance matching boundary condition. Appl Therm Eng 107:1026–1035

    Article  Google Scholar 

  10. Abd El-Rahman AI, Abdelfattah WA, Fouad MA (2017) A 3D investigation of thermoacoustic fields in a square stack. Int J Heat Mass Transf 108:292–300

    Article  Google Scholar 

  11. Kuzuu K, Hasegawa S (2017) Effect of non-linear flow behavior on heat transfer in a thermoacoustic engine core. Int J Heat Mass Transf 108:1591–1601

    Article  Google Scholar 

  12. Piccolo A, Pistone G (2007) Computation of the time-averaged temperature fields and energy fluxes in a thermally isolated thermoacoustic stack at low acoustic Mach numbers. Int J Ther Sci 46:235–244

    Article  Google Scholar 

  13. Rogozinski K, Nowak I, Nowak G (2017) Modeling the operation of a thermoacoustic engine. Energy 138:249–256

    Article  Google Scholar 

  14. Boroujerdi AA, Ziabasharhagh M (2014) Investigation of a high frequency pulse tube cryocooler driven by a standing wave thermoacoustic engine. Energy Convers Manag 86:194–203

    Article  Google Scholar 

  15. Yu G, Wang X, Dai W, Luo E (2013) Study on energy conversion characteristics of a high frequency standing-wave thermoacoustic heat engine. Appl Energy 111:1147–1151

    Article  Google Scholar 

  16. Brereton GJ, Mankbadi RR (1995) Review of recent advances in the study of unsteady turbulent internal flows. Appl Mech Rev 48(4):189–212

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, 19919-43344, Iran

    A. A. Boroujerdi & M. Ziabasharhagh

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  1. A. A. Boroujerdi
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  2. M. Ziabasharhagh
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Correspondence to M. Ziabasharhagh.

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Boroujerdi, A.A., Ziabasharhagh, M. A coupled computational model of nonlinear thermoacoustics of standing wave heat engines. Heat Mass Transfer 55, 3223–3241 (2019). https://doi.org/10.1007/s00231-019-02635-9

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  • DOI: https://doi.org/10.1007/s00231-019-02635-9

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