NUMERICAL MODELING OF THERMOACOUSTIC HEAT TRANSFER INCLUDING PRESSURE LOSSES
Heitor Herculano de Barros1; Leonardo S. de B. Alves1
1 Departamento de Engenharia Mecânica - Universidade Federal Fluminense
doi:10.20906/CPS/COB-2015-1793
Resumo
Thermodynamic and hydrodynamic models have been applied to model the behavior of thermoacoustic waves inside a one-dimensional cavity containing compressible gas or supercritical fluid in zero gravity. These thermoacoustic waves entrapped within cavity walls propagate and reflect several times inducing a rapid heating of the entire fluid, resulting in a homogeneous increase of its bulk temperature. The fast temperature relaxation phenomenon is known today as piston effect and it has been extensively studied. The original thermodynamic model developed for supercritical heat transfer under microgravity conditions is essentially the heat conduction equation with a source term proportional to the bulk temperature time derivative. This source term models the adiabatic compression mechanism responsible for the piston effect. A fully analytical solution of this thermodynamic model is obtained through a combination of the Generalized Integral Transform Technique and the Matrix Exponential Method. The hydrodynamic model utilized consists of the compressible unsteady Navier-Stokes equations solved by utilizing a flux-splitting algorithm for convection and a second order Explicit Runge-Kutta time discretization. Time scales present in this model range from acoustic (micro to miliseconds) to thermal diffusion (minutes to days), but steps are restricted to the acoustic scales. As consequence, this model has a high computational cost for long times permitting only one-dimensional modeling. In our previous works, we have modeled the pressure losses that occur when the thermoacoustic waves hit the walls by means of wall impedance. These losses were modeled through specific pressure boundary conditions in both models, where it was possible to obtain the same qualitative behavior of the experimental results. The motivation of this work is to improve the actual models to better describe the real behavior of the thermoacoustic heat transfer. For this, this study intends to improve our thermodynamic model to take in account
Palavras-chave: thermodynamic critical point; piston effect; integral transform; heat transfer; analytic solution