Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity

1981 ◽  
Vol 76 (2) ◽  
pp. 97-133 ◽  
Author(s):  
M. Slemrod
Keyword(s):  
Asymptotic Stability ◽  
Global Existence ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Non Linear ◽  
Linear Thermoelasticity

Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity

1990 ◽  
Vol 115 (3-4) ◽  
pp. 257-274 ◽  
Author(s):  
Song Jiang
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Nonlinear Thermoelasticity ◽  
Initial Boundary Value ◽  
Smooth Data

SynopsisWe consider the initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity in ℝ+; and prove a global existence-uniqueness theorem for small smooth data. The asymptotic behaviour is simultaneously obtained.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

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