A solution for the quasi-one-dimensional linearised Euler equations with heat transfer

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and...

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Bibliographic Details
Published in:Journal of fluid mechanics 2022-04, Vol.936, Article R3
Main Authors: Yeddula, Saikumar R., Guzmán-Iñigo, Juan, Morgans, Aimee S.
Format: Article
Language:English
Subjects:
Acoustics
Differential equations
Entropy
Euler-Lagrange equation
Eulers equations
Heat transfer
JFM Rapids
Linearization
Noise
Nozzles
Numerical prediction
Parameters
Perturbation
Rapid flow
Stagnation temperature
Supercritical flow
Transfer functions
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Summary:The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging–diverging nozzle with constant heat transfer for both subcritical and supercritical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2022.101