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Next: Three-Dimensional Results Up: UNSTEADY TWO- AND THREE-DIMENSIONAL Previous: Parallel Processing across a

Two-Dimensional Results

The STAGE codes have been validated and calibrated using an extensive experimental database for a 2.5 stage compressor configuration generated by Dring and Joslyn [6] and Stauter, et al. [7] of United Technologies Research Center. The 2.5 stage compressor is a large-scale, low-speed rig which has design features that are convenient for CFD code validation. The compressor has 44 airfoils in each of the IGV, rotor and stator rows. An equal airfoil count in every row allows the flow to be computed with only a single passage in each row of the compressor. A periodicity condition can be used to model the flow in the other passages thus reducing the computational cost. In addition, constant hub and tip radii simplify grid generation procedures for three-dimensional computations of the flow through the compressor. The midspan radius is 27 inches and each airfoil has a 4 inch chord and a 6 inch span. The rotor airfoils are driven at 650 RPM which results in low subsonic flow within the compressor. At design conditions, the flow coefficient is tex2html_wrap_inline178 , the inlet Mach number is tex2html_wrap_inline180 and the inlet Reynolds number is Re = 100,000 per inch.

The two-dimensional calculation models the mid-span geometry and flow conditions of the 2.5 stage compressor. Several approximations have been made which can affect the comparison between the computational results and the experimental data. The most significant of these approximations is use of a two-dimensional code to compute an inherently three-dimensional flow field. Hub-corner stall, tip leakage flow and end-wall boundary layer growth all contribute to the three-dimensionality within the experimental compressor. Stream-tube contraction terms have now been implemented in STAGE-2 to partially account for these flow features, but were not yet implemented in this code at the time the 2.5 stage compressor computation was completed.

For a fair comparison between computational results and experiment, the operating condition in the compressor calculation has been allowed to differ slightly from that of the experiment. The effective stream-tube contraction inherent in the experiment caused the midspan axial velocity to increase by 10% from the inlet to the exit of the 2.5 stage compressor. However, the axial velocity in the computation is nearly constant along the axis of the compressor because stream-tube contraction terms were not yet implemented in the code for this computation. If the flow coefficient were forced to equal the experimental value, the axial velocity would differ from the experimental axial velocity by 10% at the exit of the compressor. This would reduce the quality of the agreement between the calculation and the experiment in the second stage of the compressor, where the experimental data exist. Instead, the operating point has been set by imposing the experimental pressure rise across the compressor on the computation. The flow coefficient is allowed to vary until it accommodates the operating point specified by the pressure rise. For the results presented here, the flow coefficient in the calculation adjusted itself to a value of tex2html_wrap_inline184 while the experimental value is tex2html_wrap_inline178 .

For this computation, the compressor flowfield was discretized using grids similar to those shown in Figure 1. The grids were refined in the second stage of the compressor because the experimental data exist only in the second stage of the compressor. Approximately 100,000 points were used in the 12 grid system in order to fully discretize the 2.5 stage compressor. A comparison between computed results and experimental data for time-averaged surface pressure coefficients is shown in Figure 2. The time-averaged pressure coefficient is computed by averaging the static pressure over a cycle, where a cycle is defined as the time it takes a rotor to move circumferentially from its position relative to one stator to the same position relative to the next stator. The pressure is then nondimensionalized and plotted versus axial distance down the compressor. The computed results are plotted as solid lines and experimental data are plotted as symbols in Figure 2. The comparison between computed results and experimental data is good, with both the shape and level of the pressure curves being well predicted.

Time-averaged wake profiles for 4 different axial stations downstream of the second-stage rotor are shown in Figure 3. Total velocities relative to the rotor frame of reference are averaged over a cycle, nondimensionalized by wheel speed and plotted versus nondimensional distance across the pitch of the compressor. Zero percent pitch represents the position of the rotor trailing edge. The solid lines represent the computed results and the symbols show the experimental data. The axial stations shown are 1.9%, 8.5%, 15.1% and 25.9% of the rotor axial chord behind the second-stage rotor trailing edge. For reference, the second-stage stator is located approximately 50% of the rotor axial chord behind the second-stage rotor trailing edge. The computed wake depths and widths are in good agreement with experimental data for each of the axial stations. The computational velocities also generally compare well with the experimental velocities in the passages between the wakes. In addition, the circumferential convection rate of the wake relative to the rotor trailing edge is well predicted.

The wakes generated by the airfoils convect several chords downstream to interact with other wakes as well as downstream airfoils. This behavior is seen in the entropy contours shown in Figure 4. Magenta denotes the highest levels of entropy and blue denotes the freestream entropy. In this orientation, the flow enters the IGV row at the left of the picture, and progresses to the right through the first stage rotor, first stage stator, second stage rotor and second stage stator. The rotors are moving in the downward direction in the figure. The viscous flowfield can be quite complicated in a multistage turbomachine, in particular in the latter stages as the convected wakes accumulate and interact with each other. For instance, the second-stage stator leading edge interacts with a system of three wakes. In Ref. 1, it was shown that interactions between groups of wakes can substantially change the unsteady forces on an airfoil. In particular, relative phase differences between convected wakes may have a substantial effect on unsteady forces in the later stages of a multistage turbomachine.

The flow through a single-stage turbine configuration known as the generic gas generator (GGG) has also been computed with STAGE-2. The GGG turbine was designed with 38 stator airfoils and 52 rotors airfoils and a simulation of the full 90 airfoil system represented an unacceptable computational expense, even in two dimensions. It was therefore necessary to reduce the computational expense of the simulation. The approach used was to modify the number of airfoils in each row of the stage. The number of stator vanes was increased from 38 to 39, thus changing the ratio of stators to rotors to 3:4. The stators were then decreased in size by a factor of 38/39 in order to maintain the same blockage. This approach reduces the simulation to a 7 airfoil calculation and uses 21 grids to fully discretize the geometry.

The grid system for the GGG turbine is shown in Figure 5. While the flow field is not periodic within the 3 stator/4 rotor system, the geometry itself is periodic from airfoil to airfoil, thus the grids for only one airfoil passage are shown here. In this figure, the flow enters the stators from the left and exits the rotors to the right. Note that the circumferential extent of the outer stator grids is larger than that of the outer rotor grids by a factor of 4:3 so that a 3 stator/4 rotor system spans the same circumferential extent. The 21 grid system uses approximately 87,000 grid points.

The GGG turbine operates at an inlet Mach number of tex2html_wrap_inline188 , an inlet Reynolds number of Re = 490,000 per inch, and an exit pressure coefficient of tex2html_wrap_inline192 . Estimates of the normalized stream-tube height were originally provided by the GGG turbine design team. Instantaneous static pressures for the GGG turbine are shown in Figure 6. The range in color from white to blue indicates a decrease in the static pressure field. While the flow is almost incompressible at the inlet to the turbine, the flow becomes supersonic near the stator trailing edge. Shock waves periodically form and decay in the gap region as the rotor airfoils pass the stator airfoils for this small axial gap case. Rangwalla, et al. tex2html_wrap_inline194 showed that these shock waves do not exist for larger axial gap cases and that the presence of the unsteady shock waves changes the time-averaged pressure in the turbine.

Experimental data are not available for the GGG turbine. However, time-averaged surface pressures from STAGE-2 (solid lines) are compared with results from Rangwalla, et al. tex2html_wrap_inline194 (dashed lines) for the stator in Figure 7. and for the rotor in Figure 8. For the stator, the time-averaged static pressure is normalized by the inlet absolute total pressure while the rotor time-averaged static pressure is normalized by the relative total pressure at the inlet to the rotor. The comparison between the two sets of computational results is good for both the rotor and stator airfoils. Small differences between the computational results are probably caused by the different grid density used in the two computations. For clarity, the unsteady pressure envelope has not been plotted in Figures 7 and 8. However, the unsteady pressure field strongly affects the time-averaged pressures for this small axial gap case, because of the periodic formation of the shock wave. Therefore, it is expected that the unsteady pressure fields also compare well.


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Next: Three-Dimensional Results Up: UNSTEADY TWO- AND THREE-DIMENSIONAL Previous: Parallel Processing across a

Karen L. Gundy-Burlet
Wed Apr 9 13:50:35 PDT 1997