We have investigated supercritical-p (p > 1192 psi (8.22 MPa)) methanol at pressures up to 1645 psi (11.3 MPa) flowing through a heated tube at flow rates of 4-7 lb/hr (1.8-3.2 kg/hr). Tube heated lengths have been varied from 4 to 6 in (10 to 15 cm), internal diameters from 0.027 to 0.069 in (0.069 to 0.175 cm), and heat inputs between zero and 800 W. Fluid temperature at the tube inlet remained subcritical; outlet temperatures were transcritical or supercritical. Two phenomena were observed: system-wide bulk-mode oscillations and localized acoustic modes. In the present study, predictive efforts are undertaken to characterize system-wide bulk-mode oscillations. The parameter space has been nondimensionalized, yielding four dimensionless variables. Stability criteria based on these dimensionless groups have been established for two separate test articles and fluids; both criteria suggest that the heat required for the onset of oscillations is proportional to the mass flow rate times the mean pressure and inversely proportional to the fuel density
We have investigated one-dimensional compression waves, produced by heat addition in quiescent and uniform initial conditions, in six different supercritical fluids, each taken in four states ranging from compressible pseudo-liquid fluid to ideal gas. Navier-Stokes simulations of a canonical semi-infinite domain flow problem, spanning five orders of magnitude of heating rate, are also carried out to support the theoretical analysis. Depending on the intensity of the Gaussian-shaped energy source, linear waves or shock waves due to nonlinear wave steepening are observed. A new reference heating rate parameter allows to collapse in the linear regime the whole dataset, together with existing experimental data, thanks to its absorption of real-fluid effects. Moreover, the scaling strategy illustrates a clear separation between linear and nonlinear regimes for all fluids and conditions, offering motivation for the derivation of a unified fully predictive model for shock intensity. The latter is performed by extending the validity of previously obtained theoretical results in the nonlinear regime to supercritical fluids. Finally, thermal-to-mechanical power conversion efficiencies are shown to be proportional, in the linear regime, to the fluid's Gr\"uneisen parameter, which is the highest for compressible pseudo-liquid fluids, and maximum in the nonlinear regime for ideal gases.
We have performed high-order compressible Navier-Stokes simulations of a thermoacoustically unstable resonator employing CO2 in transcritical conditions. The parameter space spans the range of base pressures p_0=1.01-1.5 p_cr and temperature differences Delta T=T_hot-T_cold up to 200 K, with thermodynamic and transport properties obtained from the Peng-Robinson equation of state and Chung's model. The setup is a classic standing wave thermoacoustic resonator, which has been optimized resulting in a minimum temperature difference of 23 at p_0=1.01 p_cr required to sustain the instability. Strong real-fluid effects in the thermoacoustic response in the linear regime are observed: (i) the thermoviscous functions need to depend on the complex eigenvalue (and not just the angular frequency) for linear theory to accurately predict the growth rate observed in the Navier-Stokes simulations, due to a high growth-rate-to-frequency ratio; (ii) the growth rate and frequency vary in a non-monotonic fashion with respect to p_0 and Delta T; (iii) the pressure eigenmode amplitude tends to flatten out, and the pressure-velocity phase difference smoothly transitions from pi/2 to -\pi/2 at the average pressure node location; (iv) the sharp change in base acoustic impedance at transcritical conditions introduces a discontinuity in the eigenmodes' spatial derivative. The energy budgets illustrate, for a given Delta T, the increase of the acoustic power produced, but also of the heat input required, for thermodynamic conditions approaching the critical point. Finally, intense mass transport events at transcritical conditions are shown to entail thermodynamic and convective nonlinearities, which do not, however, govern the limit cycle physics, dominated instead by nonlinear minor losses.
We have carried out turbulent channel flow simulations at supercritical pressure in transcritical thermal conditions where the top and bottom walls are kept at the supercritical temperature and subcritical temperature condition, respectively, bracketing the pseudo-boiling temperature of the working fluid, R-134a. A high-order numerical scheme for the solution to the fully compressible Navier-Stokes equations in conservative form is coupled with the Peng-Robinsion equation of state and the Chung's method to model real fluid effects. The simulations are carried out at a bulk pressure of 44.649 bar equal to 1.1 times the critical pressure, a bulk velocity of 36 m/s, and top-to-bottom temperature differences of 5 K and 10 K. Viscosity has been increased by a factor of 60 to allow for adequate direct numerical resolution to be achieved at physically relevant channel sizes. The average location of the pseudo-phase change is y/h = -0.25 and 0.66 for 5 K and 10 K of temperature difference, respectively where h is the channel half-height and y is the wall-normal distance from the centerline. The average density on the bottom wall at 10 K temperature difference equals approximately twice that on the top wall density. Instantaneous visualizations reveal strong ejections of dense fluid from the pseudo-liquid viscous sublayer into the channel core creating a third RMS peak in the thermodynamic quantities near the channel centerline and such events are correlated with streamwise elongated streaks in the temperature gradients at the wall.