This paper concerns the study of self–sustained combustion instabilities that occur in a test rig characterized by a single longitudinal combustion chamber equipped with a full scale industrial burner and a longitudinal plenum. The length of both plenum and combustion chamber can be continuously varied. During tests, at a fixed value of the length of the combustion chamber, a sensibility of the amplitude of pressure oscillations to the length of the plenum has been registered, while the frequency remained constant. To investigate this behavior, a linear stability analysis has been performed evaluating the influence of the length of the plenum on the frequency and growth rate of the registered unstable mode. The analysis has been performed by means of a finite element method (FEM) code with a three–dimensional distribution of the n-τ Flame Transfer Function (FTF) computed by means of computational fluid dynamics (CFD) simulations. According to the Rayleigh criterion, the distribution of the local Rayleigh index has been computed in order to evaluate the acoustic energy production, while the scattering matrix of the entire system has been used to evaluate the acoustic energy losses. Numerical results show that the reduction of the plenum length induces an increase of acoustic energy losses while the energy production remains almost constant. This result is in agreement with the reduction of the pressure oscillations amplitude observed during tests.

In this paper we consider a class of obstacle problems of the typewhere ψ is the obstacle, K ψ (Ω) = {v ∈ u0 + W 1,p 0 (Ω, R) : v ≥ ψ a.e. in Ω}, with u0 ∈ W 1,p (Ω) a fixed boundary datum, the class of the admissible functions and the integrand f (x, Dv) satisfies non standard (p, q)-growth conditions. We prove higher differentiability results for bounded solutions of the obstacle problem under dimension-free conditions on the gap between the growth and the ellipticity exponents. Moreover, also the Sobolev assumption on the partial map x → A(x, ξ) is independent of the dimension n and this, in some cases, allows us to manage coefficients in a Sobolev class below the critical one W 1,n .

No abstract

No abstract

We establish an a priori estimate for the second derivatives of local minimizers of integral functionals of the formwith convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.