An analytic solution to the coupled pressure–temperature equations for modeling of photoacoustic trace gas sensors

Kaderli, Jordan; Zweck, J.; Safin, Artur; Minkoff, Susan E.

doi:10.1007/s10665-016-9867-5

Cited by 8 publications

(15 citation statements)

References 26 publications

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“…Hence, the derivativation begins by linearizing the incompressible Navier-Stokes equations around zero and including acoustic and thermal effects. For a derivation and particular physical assumptions, we refer the reader to [1,12]. We will also assume a periodic forcing function S to reduce to a time-harmonic system of equations.…”

Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

“…However, the temperature appears in this equation both with a moderate 0-order term as well as with (small parameter) times the Laplacian. This situation can be favorably altered following [12]. We can subtract iγ Λ M times the first equation from the second to eliminate the temperature Laplacian.…”

Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

“…In [12], this reformulation enabled an analytical solution in the case of cylindrical symmetry with Gaussian forcing, but we give a finite element analysis amenable to less-idealized configurations. In particular, we find that this reformulated system also leads to more efficient preconditioners than we considered for the original system.…”

Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

“…This included error estimates and the introduction and analysis of block preconditioners. Kaderli et al derived an analytical solution for the coupled system in idealized geometry in [12]. Their technique involves reformulating the system studied in [11] by an algebraic simplification that eliminates the temperature Laplacian from the pressure equation.…”

Section: Introductionmentioning

confidence: 99%

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Optimal-order preconditioners for the Morse–Ingard equations

Kirby

Coogan

2020

Computers & Mathematics with Applications

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The Morse-Ingard equations of thermoacoustics [1] are a system of coupled time-harmonic equations for the temperature and pressure of an excited gas. They form a critical aspect of modeling trace gas sensors. In this paper, we analyze a reformulation of the system that has a weaker coupling between the equations than the original form. We give a Gårding-type inequality for the system that leads to optimal-order asymptotic finite element error estimates. We also develop preconditioners for the coupled system. These are derived by writing the system as a 2 × 2 block system with pressure and temperature unknowns segregated into separate blocks and then using either the block diagonal or block lower triangular part of this matrix as a preconditioner. Consequently, the preconditioner requires inverting smaller, Helmholtz-like systems individually for the pressure and temperature. Rigorous eigenvalue bounds are given for the preconditioned system, and these are supported by numerical experiments.

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Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

Section: The Morse-ingard Equations and Finite Element Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal-order preconditioners for the Morse–Ingard equations

Kirby

Coogan

2020

Computers & Mathematics with Applications

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“…A possible indirect solution for the junction temperature evaluation would be to identify it from the measurement results and establish a link with the ambient temperature. With regard to solar radiation, the hardware solution of placing multiple solar radiation sensors would obviously increase the cost of installation [10][11][12][13]. The purpose of this section is to show the possibility of identifying the values of solar radiation and temperature from an experimental point of view.…”

Section: Estimation Of Solar Radiation and Temperaturementioning

confidence: 99%

Estimation of Climatic Parameters of a PV System Based on Gradient Method

2019

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The behavior of a photovoltaic generator is generally described by its current-voltage characteristic whose appearance depends on the climatic conditions (temperature and solar radiation). The aim of this work is to show the possibility of identifying the values of these two parameters from an experimental curve Ipv (Vpv) using numerical method. Subsequently, we will also estimate the series and shunt resistors of the equivalent scheme of a PVG. This estimate is certainly beneficial to properly evaluate its energy balance. The integration of these resistances allows us to obtain a new model. In this work, we will propose a mathematical calculation strategy to ensure the estimation of all the parameters.

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A one-way coupled model for the vibration of tuning fork-based trace gas sensors driven by a thermoacoustic wave

2020

Self Cite

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We present a single computational model for both quartz-enhanced photoacoustic spectroscopy and resonant optothermoacoustic detection trace gas sensors. These sensors employ a quartz tuning fork to detect the acoustic pressure and thermal waves generated when a laser excites a trace gas. The model is based on a coupled system of equations developed by Morse and Ingard for pressure and temperature in a fluid. The pressure and temperature solutions drive the resonant vibration of the tuning fork, which is modeled using the equations of linear elasticity. At high ambient pressure, excellent agreement is obtained with laboratory experiments. This result provides the first quantitative match between a fully computational simulation and experiments for a QEPAS sensor. Such a model could ultimately facilitate sensor design optimization. At low ambient pressure (less than 60 Torr), quantitative agreement is obtained after re-weighting the contributions from the pressure and thermal components of the signal. While this result is a substantial improvement over previous results in which a scaling factor was required to obtain agreement at any ambient pressure, at low pressures it appears that a more accurate physical model may be required to match experimental data.

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An analytic solution to the coupled pressure–temperature equations for modeling of photoacoustic trace gas sensors

Cited by 8 publications

References 26 publications

Optimal-order preconditioners for the Morse–Ingard equations

Optimal-order preconditioners for the Morse–Ingard equations

Estimation of Climatic Parameters of a PV System Based on Gradient Method

A one-way coupled model for the vibration of tuning fork-based trace gas sensors driven by a thermoacoustic wave

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