The inlet Mach number to the first-stage stator was 0.07 and the inlet flow was assumed to be axial. The rotor rotational speed was 410 rpm. The free stream Reynolds number was 39,370/cm. The midspan pressure coefficient 14% of chord aft of the second-stage stator trailing edge of (used to set the exit boundary condition) was determined from the inlet total pressure and the static pressure measured in the second-stage stator trailing-edge plane. In this investigation is defined as
The airfoil surfaces were assumed to be at 267 degrees Kelvin while the free stream temperature was 295 degrees Kelvin. The surface temperature was chosen to simulate the surface temperature to freestream temperature ratios encountered in engine operation. A hot-streak was introduced at the inlet which was directly in line with the first-stage stator (see Dorney and Gundy-Burlet, 1996, for the importance of the relative position between the hot streak and first-stage stator, and the effects on rotor heating). A hot streak temperature of 1.2 times that of the surrounding inlet flow was chosen for this investigation. Actual hot streak temperatures 1.1 to 1.6 of free stream are typical of engine operating environments (Takahashi, 1996).
The numerical simulations were run at 2000 time steps (with 2 Newton sub-iterations at each time step) per cycle on the Cray C90 supercomputer at NASA Ames Research Center. A cycle corresponds to the rotor blade rotating through an angle of where n is the number of stator blades (i.e., n=1) used in the simulation and N is the number of stator airfoils in the modeled machine ( i.e., N=28). The code operates at -secs/it./grid point and 384 Mflops on the Cray C90.
Figure 2, figure 3, and figure 4 show the time-averaged pressure coefficient and pressure coefficient amplitude distributions for the midspan of the first-stage stator, first-stage rotor and second-stage stator, respectively. The pressures are time-averaged and the minimum and maximum pressures are determined over one rotor-passing cycle. The time-averaged results from the numerical analysis are represented as a solid line, while the experimental suction side results are shown as squares and the pressure side results are indicated by circles. The comparison between the time-averaged computational results and the experimental data (Dring et al. 1986a,1986b) is good. Neither the hot streak nor the constant surface temperature significantly affect the pressure field.
Figures 5-13 illustrate the surface heat flux within the turbine. In these figures, the time-averaged heat flux on the suction surface is a solid line and the suction-surface unsteady heat flux envelope is denoted by dashed lines. The chain-dot line is the time-averaged pressure-surface heat flux while the dotted lines show the pressure-surface unsteady heat flux envelope. Figure 5, figure 6, and and figure 7 present the surface heat of the first-stage stator at the 12.5%, 50.0% and 87.5% span locations, respectively. The influence of the hot steak can be seen in the heat transfer. The midspan heat transfer is generally high with a peak at the leading edge where the hot streak impacts the first-stage stator. The radial migration of the hot streak combined with slow pressure-side convection rates results in high heat transfer on the pressure surface near the hub trailing edge. There is uniform unsteadiness over the majority of the blade span because of the equal blade count ratios modeled in the simulation.
Figure 8 figure 9 and and figure 10 contain the surface heat flux of the first-stage rotor at the 12.5%, 50.0% and 87.5% span locations, respectively. The peak unsteadiness in the heat flux occurs on the suction surface near midspan and is caused by the rotor sweeping through a hot streak entrained in the shedding first-stage stator wake. The imprint of the rotor passage vortices can be seen at approximately the 10 cm axial position on both the 12.5% and 87.5% span stations. The passage vortex causes a distinct increase in heat transfer aft of this point. On the pressure side, time-averaged heat transfer increases near the trailing edge as the hot streak moves radially toward the tip. At the midspan station, the heat transfer is greater on the suction surface than on the pressure surface until approximately 90% of the axial chord. Dorney and Gundy-Burlet (1996) showed that the rotor pressure and suction surface temperatures were approximately equal for an adiabatic computation with the hot streak fully impinging on the first-stage stator. However, when the hot streak was aligned with the mid-passage of the first-stage stator, the temperature on the rotor pressure surface was substantially higher than that of the suction surface. It is surmised that if the mid-passage hot streak case were recomputed with heat-transfer effects at the surface, the pressure surface would show substantially more heat transfer than in the current full-impingement calculation.
Figure 11, figure 12, and figure 13 show the surface heat flux of the second-stage stator at the 12.5%, 50.0% and 87.5% span locations. The figures show generally higher levels of heat transfer and unsteadiness on the suction surface of the second-stage stator. The imprint of the passage vortex at the hub can be seen at approximately mid-chord at the 12.5% span station. Because of the full impingement of the hot streak on the first-stage stator, the hot streak has largely mixed out by the time it reaches the second-stage stator. Heat transfer effects on the second-stage stator are minimized in this case.
Figure 14 shows time-averaged heat-transfer contours over each of the pressure and suction surfaces in the turbine. In this figure, blue indicates low heat flux, red indicates high heat flux and the color scale is the same for all of the surfaces. The flow is from left to right for each of the surfaces. The path of the hot streak over the surface of the first-stage stator is readily apparent. The highest levels of heat flux are at the leading edge suction surface where the hot streak expands over the stator and at the trailing edge pressure surface. The imprints of the passage vortices on the suction surfaces of each airfoil are accentuated by the higher heat flux in those regions. The rotor shows the highest heat flux near the midspan leading edge although the hub passage vortex and the tip leakage flows induce significant heat transfer. The radial movement of the hot streak toward the tip of the pressure side of the rotor is also apparent.