Temperature gradient integration in thermoacoustic stacks

Different approaches to numerical modeling of thermoacoustic effects are being investigated as a step towards developing a model for inert gas–vapor mixtures in thermoacoustics. This paper describes these approaches to numerical calculations, which differ primarily in the way that the temperature profile is computed for the stack. Different aspects of the constant property of the thermodynamic enthalpy in the stack are used by each approach: one maintains a constant value for the enthalpy while calculating the temperature and the other keeps the spatial derivative of the enthalpy equal to zero. The runtime and accuracy of the two approaches are compared by applying them to both a thermoacoustic refrigerator and engine model, and it is found that the second method’s introduction of an additional integration variable leads to more error than the first method’s use of large numbers in the calculation.