Modeling Approaches

For the low engine order analysis, it is necessary to compute the aerody­namic excitation due to a spatial stator exit flow variation, which has a larger period than the vane pitch. In the present case of the 5th EO modification, this variation has a spatial period of exactly 43/5 of the vane pitch, where 43 is the number of vane passages of the stator. If the unsteady computation is chosen to follow a linearized approach, the rotor inlet boundary condition needs to consist of an amplitude and a phase shift of this spatial flow distribution at the stator exit. The form is by definition of the linearized approach assumed to be sinusoidal. Therefore, the following modeling approaches will focus on the estimation of the LEO harmonic of the excitation, but where available, other harmonics will be included in the discussion.

Strategy 1: Viscous single passage flow assembly. The simplest method would be to compute just one single passage, and "shift" the resulting stator wakes according to the positions of the stator trailing edges. In a pre-study, it has been found that this method is not suitable to reproduce the variations be­hind the real stator. The next approximation is to only compute the minimum and maximum spacing vane passage with single passage computations, and use these to calculate the amplitude of the low engine order excitation. This approach assumes that the relation between throat area and stator exit fbw, in terms of 1st harmonic spatial distribution, is linear. For simplicity, the passages are computed with the same average exit boundary conditions. The evaluation is done by computing the absolute difference between the 1st harmonic am­plitudes of the minimum and maximum spacing results. A closer look at the differences between the two exit fbws confirmed that they are mainly in the 1st harmonic. But it should be remarked that at 90% blade height, the dif­ference in mean value was largest, which indicates that other physical effects are probably involved (see further results discussion). The computational tool VolSol, provided by Volvo Aero Corporation, Sweden, is used for the compu­tations. For the present investigation, the standard k-є turbulence model, with an extension by Kato and Launder [8], and standard wall functions were ap­plied. The numerical method [9, 10] is an explicit three stage Runge-Kutta, time marching finite volume approach. The convective flixes are calculated with a 3rd order upwind biased scheme, the viscous fhxes are computed with a 2nd order centered scheme. The code applies structured multi block H-type and O-type meshes and can be used for two – and three-dimensional computa­tions. The farfield boundary conditions are partly non-reflecting.

Strategy 2: Inviscid quasi steady linear flutter computation. The three­dimensional linearized method SliQ [11, 12] allows the computation of the unsteady ft>w due to a blade movement fbw perturbation. The method is fore­seen for blade cascade flitter analysis, and hence allows the specification of an inter-blade phase angle between the motions of adjacent blades. The present strategy sets this inter-blade phase angle between the modeled vanes of the stator to a value corresponding to the throat variation in the stator, which must be sinusoidal to allow this approach. The frequency of the blade movement is however set to zero, which is the major difference to a usual flutter computa­tion. The computation leads to a quasi-steady result of the unsteady flow to be evaluated at "a time” corresponding to the investigated stator configuration. A disadvantage of the method is that viscous effects cannot be regarded correctly.

The advantage of the strategy is that stator exit fbws due to different orders of distortion may be calculated with very quick and simple computations. This makes it suitable for design approaches, where eventually many different con­figurations need to be computed. The evaluation as follows will give some insight on the applicability of this approach.

Strategy 3: Viscous computation of a sector of several vane passages.

The number of NGVs (43) is not an integer multiple of the engine order under consideration. For an exact CFD analysis of this configuration, the whole an­nulus would have to be modeled. To reduce the computational effort, a sector of the stator is modeled, which violates the real geometry with an assumption of periodicity. Two approaches are presented:

A modified configuration with a scaled stator is modeled, where the throat width pattern repeats after an integer number of vanes. The NGVs are scaled so that the pitch/chord ratio and hence the vane loading re­mains identical to the original configuration. In the present case, this implies that the stator is scaled from 43 to 45 vanes on the circumfer­ence, each vane reduced in size by a factor 43/45. A sector of 9 passages is modeled to represent a periodic domain for the 5th engine order ex­citation, resulting in a mesh of approximately 1.9 million points. The inlet total pressure, total temperature, and flow angle distribution was taken from traverse measurements taken from an earlier measurement campaign. These were scaled to the correct mean total pressure and to­tal temperature levels. The exit boundary condition used here sets the mid-span circumferentially averaged pressure, thus allowing radial vari­ations, according to the radial equilibrium condition, and circumferential variations due to the re-distribution of the flow according to the varying stator spacing. The computations are performed with the TRACE code, developed in cooperation between the DLR Institute of Propulsion Tech­nology and MTU Aero Engines [13]. The block-structured code uses a cell-centered explicit finite-volume to solve the Reynolds-averaged Navier-Stokes equations formulated in relative Cartesian coordinates. It employs a time-marching Runge-Kutta scheme along with matrix dissi­pation to minimize corruption of solutions by numerical smoothing. For the current analysis, a k-w turbulence model was employed in combina­tion with wall functions on the blade, hub and tip surfaces.

The stator is not scaled, but the nearest number of passages represent­ing a periodic sector are modeled. In the present case, 9 passages are modeled, which results in a domain that is slightly larger than the 5th engine order domain of 43/5 passages. Without scaling of the vanes, this represents the exact geometry of the 9 passages measured in the experi­mental program. The modeling error is introduced by assuming a peri­odic continuation of the domain, i. e. that passages 10 to 18 are identical to the modeled passages 1 to 9. The computations are performed with VolSol with similar computational parameters as for the single passage approach described in the previous strategy (Strategy 1).