The efficiency of a Carnot engine is treated for the case where the power output is limited by the rates of heat transfer to and from the working substance. It is shown that the efficiency, η, at maximum power output is given by the expression η = 1 − (T2/T1)1/2 where T1 and T2 are the respective temperatures of the heat source and heat sink. It is also shown that the efficiency of existing engines is well described by the above result.

Turbulent fluid has often been conceptualized as a transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The proposed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dimensional phase-space dynamics and, subsequently, into a thermodynamics energy problem. The Galerkin model consists of a velocity field expansion in terms of flow configuration dependent modes and of a dynamical system describing the temporal evolution of the mode coefficients. Each mode is treated as one thermodynamic degree of freedom, characterized by an energy level. The dynamical system approaches local thermal equilibrium (LTE) where each mode has the same energy if it is governed only by internal (triadic) mode interactions. However, in the generic case of unsteady flows, the full system approaches only partial LTE with unequal energy levels due to strongly mode-dependent external interactions. The first illustrated by a traveling wave governed by a 1D Burgers equation. It is then applied to two flow benchmarks: the relatively simple laminar vortex shedding, which is dominated by two eigenmodes, and the homogeneous shear turbulence, which has been modeled with 1459 modes.

A novel Pitot probe was used to measure the axial and azimuthal velocities in a vortex tube. The probe has only a single measuring port and is hence smaller than standard devices. It monitors stagnation and reference pressure sequentially as the probe is rotated around its axis. From the measured velocity field in the 25 mm diameter vortex tube the local mass flux was determined and it was observed that the return flow at the center of the tube is much larger than the cold mass flow emerging out of the cold end. Therefore, the vortex tube must have a secondary circulation imbedded into the primary vortex, which moves fluid from the back flow core to the outer regions.

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Vortex tubes are commonly used as refrigeration devices. We show that the thermal and fluid dynamics of the vortex tube bear the signature of a classic cooling cycle, and quantify its performance as a thermodynamic machine. In the process, we develop simple analytic formulas for the temperature and pressure profiles within the tube. The principal model predictions compare favorably against experimental measurements.