Real fluid effects on thermoacoustic standing-wave resonance in supercritical CO2

We have investigated real fluid effects in a canonical thermoacoustically unstable duct filled with supercritical CO2 at a base pressure of p0 = 1.1pcr, where pcr = 7.3773 MPa is the critical pressure of CO2. Thermodynamic and transport properties of CO2 are obtained from the Peng-Robinson equation of state and Chung’s model. A toy thermoacoustically unstable resonator is investigated, composed of an inviscid hot cavity filled with pseudo-gas (Thot > Tcr), a thermoacoustic stack with an imposed axial wall-temperature gradient via isothermal boundary conditions, and an inviscid resonator (Tcold < Tcr) filled with pseudo-liquid. The parameter Tcold/Tcr is varied from 0.65 to 0.9 such that total 6 computational cases considered retain the pseudo-boiling conditions inside the stack. The acoustic energy budgets are derived theoretically, showing that the thermoacoustic production is proportional to Θ = d ln ρ0-1/dx in the standing wave configuration, where ρ0 is the base state density. Due to real fluid effects, Θ spikes at spatial location of PB thus rendering thermoacoustic instability sensitive to PB. Maximum growth rates are achieved corresponding to a location of the pseudo-interface at approximately the center of the stack. Moreover, at the pseudo-interface, the spatial derivative of the base acoustic impedance spikes causing discontinuities in the spatial derivatives of the eigenmodes. Moreover, changes in the Prandtl number (Pr) result in increased thermoacoustic production of energy density due to traveling wave component for small h/2δν. Ongoing work includes high-order fully compressible numerical simulations of the proposed setup.