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We investigate the stability of streaks in the buffer layer of turbulent channel flows with temperature-dependent density and viscosity by means of linear theory. The adopted framework consists of an extended set of the Orr-Sommerfeld-Squire equations that accounts for density and viscosity nonuniformity in the direction normal to the walls. The base flow profiles for density, viscosity, and velocity are averaged from direct numerical simulations (DNSs) of fully developed turbulent channel flows. We find that the inner scaling based on semilocal quantities provides an effective parametrization of the effect of variable properties on the linearized flow. The spanwise spacing of optimal buffer layer streaks scales to λz,opt≈90 for all cases considered and the maximum energy amplification decreases, compared to the one for a flow with constant properties, if the semilocal Reynolds number Reτ increases away from the walls, consistently with less energetic streaks observed in DNSs of turbulent channels. A secondary stability analysis of the two-dimensional velocity profile formed by the mean turbulent velocity and the nonlinearly saturated optimal streaks predicts a streamwise instability mode with wavelength λx,cr≈230 in semilocal units, regardless of the fluid property distribution across the channel. The threshold for the onset of the secondary instability is reduced, compared to a constant property flow, if Reτ increases away from the walls, which explains the more intense ejection events reported in DNSs. The opposite behavior is predicted by the linear theory for decreasing Reτ, in accord with DNS observations. We finally show that the phase velocity of the critical mode of secondary instability agrees well with the convection velocity calculated by DNSs in the near-wall region for both constant and variable viscosity flows.
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We investigate the stability of streaks in the buffer layer of turbulent channel flows with temperature-dependent density and viscosity by means of linear theory. The adopted framework consists of an extended set of the Orr-Sommerfeld-Squire equations that accounts for density and viscosity nonuniformity in the direction normal to the walls. The base flow profiles for density, viscosity, and velocity are averaged from direct numerical simulations (DNSs) of fully developed turbulent channel flows. We find that the inner scaling based on semilocal quantities provides an effective parametrization of the effect of variable properties on the linearized flow. The spanwise spacing of optimal buffer layer streaks scales to λz,opt≈90 for all cases considered and the maximum energy amplification decreases, compared to the one for a flow with constant properties, if the semilocal Reynolds number Reτ increases away from the walls, consistently with less energetic streaks observed in DNSs of turbulent channels. A secondary stability analysis of the two-dimensional velocity profile formed by the mean turbulent velocity and the nonlinearly saturated optimal streaks predicts a streamwise instability mode with wavelength λx,cr≈230 in semilocal units, regardless of the fluid property distribution across the channel. The threshold for the onset of the secondary instability is reduced, compared to a constant property flow, if Reτ increases away from the walls, which explains the more intense ejection events reported in DNSs. The opposite behavior is predicted by the linear theory for decreasing Reτ, in accord with DNS observations. We finally show that the phase velocity of the critical mode of secondary instability agrees well with the convection velocity calculated by DNSs in the near-wall region for both constant and variable viscosity flows.
Organic Rankine cycle (ORC) turbogenerators are the most viable option to convert sustainable energy sources in the low-to-medium power output range (from tens of kWe to several MWe). The design of efficient ORC turbines is particularly challenging due to their inherent unsteady nature (high expansion ratios and low speed of sound of organic compounds) and to the fact that the expansion encompasses thermodynamic states in the dense vapor region, where the ideal gas assumption does not hold. This work investigates the unsteady nonideal fluid dynamics and performance of a high expansion ratio ORC turbine by means of detailed Reynolds-averaged Navier-Stokes (RANS) simulations. The complex shock interactions resulting from the supersonic flow (M≈2.8 at the vanes exit) are related to the blade loading, which can fluctuate up to 60% of the time-averaged value. A detailed loss analysis shows that shock-induced boundary layer separation on the suction side of the rotor blades is responsible for most of the losses in the rotor, and that further significant contributions are given by the boundary layer in the diverging part of the stator and by trailing edge losses. Efficiency loss due to unsteady interactions is quantified in 1.4% in absolute percentage points at design rotational speed. Thermophysical properties are found to feature large variations due to temperature even after the strong expansion in the nozzle vanes, thus supporting the use of accurate fluid models in the whole turbine stage.
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Organic Rankine cycle (ORC) turbogenerators are the most viable option to convert sustainable energy sources in the low-to-medium power output range (from tens of kWe to several MWe). The design of efficient ORC turbines is particularly challenging due to their inherent unsteady nature (high expansion ratios and low speed of sound of organic compounds) and to the fact that the expansion encompasses thermodynamic states in the dense vapor region, where the ideal gas assumption does not hold. This work investigates the unsteady nonideal fluid dynamics and performance of a high expansion ratio ORC turbine by means of detailed Reynolds-averaged Navier-Stokes (RANS) simulations. The complex shock interactions resulting from the supersonic flow (M≈2.8 at the vanes exit) are related to the blade loading, which can fluctuate up to 60% of the time-averaged value. A detailed loss analysis shows that shock-induced boundary layer separation on the suction side of the rotor blades is responsible for most of the losses in the rotor, and that further significant contributions are given by the boundary layer in the diverging part of the stator and by trailing edge losses. Efficiency loss due to unsteady interactions is quantified in 1.4% in absolute percentage points at design rotational speed. Thermophysical properties are found to feature large variations due to temperature even after the strong expansion in the nozzle vanes, thus supporting the use of accurate fluid models in the whole turbine stage.
