This paper presents the results of an entropy generation calculation made on a representative gas turbine rotor blade; in particular, the numerical study has dealt with the different flowfields which are encountered when the angle of attack is varied in a two-dimensional cascade on axial, internally cooled gas turbine rotor.

The analysis takes into consideration a two-dimensional cascade at medium Reynolds number (Rechord = 225000), sub-sonic Mach number (Main = 0.27), and steady state. The full Navier-Stokes equations of motion for a turbulent compressible viscous flow, together with the appropriate energy equation, are solved via a standard finite elements code with a k-ε closure, so that complete velocity- and temperature fields are obtained (including boundary-layer effects, via proper wall functions). These fields are then used to compute the entropy generation rates corresponding to the viscous- (v) and thermal (r) dissipation.

Several configurations have been numerically tested, the reference one being at design conditions, and the remaining being obtained from it by varying the angle of attack α (defined as the angle, measured ccw, between the relative velocity vector W1 and the tangent to the blade chord at impingement point), to simulate volume flowrate variations.

A commercial finite-element code (FIDAP, by FDI Inc.) has been modified to allow for the calculation of the local values of the entropy generation rates, the thermal- and viscous portions of which have been computed separately.

The results at design point are shown to agree well with the available cascade performance data.

The entropy generations rates are then used to compute the so-called entropy loss coefficient (a better name for which would be that of irreversibility coefficient, ζ, defined as:
where T0 is the reference ambient temperature, Δs is the total local entropy generation rate (sum of the viscous- and thermal components), and h1i and h2i are the stagnation enthalpy upstream of the rotor and the ideal exit enthalpy respectively.

The results are shown under the form of cp - and ζ graphs computed for different angles of attack α (from −4.4 to +7.6 degrees), and are representative of realistic situations which could arise in actual gas turbine rotors. The loss coefficient ζ is shown to attain a minimum value at design point.

Integral values for the entropy generation rates are also computed, and total entropy losses are thus computed for the various configurations. Maps of the viscous- and thermal entropy generation rates are shown for each angle of attack, where of interest.

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