Interaction of Turbomachinery Components in Large-scale Unsteady Computations of Jet Engines

The objective of the Stanford ASC project is to develop a framework able to perform multi-disciplinary, integrated simulations on massively parallel platforms. 4 This paper focuses on the turbomachinery computation and, in particular, on the physics of interaction of different turbomachinery components in the engine. Typical flow features such as tip and horse-shoe vortices as well as blade wakes will be discussed for these multi-component turbomachinery simulations. The compressor and turbine of a modern turbofan engine, Figure 1, typically have two counter-rotating concentric shafts to allow for different rotational speeds of their components as well as a reduction of net torque. The low-pressure parts rotate at a lower rate than the high-pressure components. Typical rotation rates are 5,000 to 7,000 RPM for the former and 15,000 to 20,000 RPM for the latter. The compressor and turbine themselves consist of a series of rotors and stators for which the blade counts are normally chosen such that no sector periodicity occurs. Combined with the inherently unsteady nature of turbomachinery flows due to the motion of the rotors, the full wheel geometry needs to be considered in a time accurate numerical simulation of the flow. The computational requirements for such a simulation are severe. The high-pressure compressor (HPC) alone consists of 5 stages (rotor/stator combinations) and 50 to 200 blade passages per stage. Since approximately a million nodes are required per blade passage to obtain a grid-converged Reynolds-Averaged Navier-Stokes (RANS) solution, the computational mesh for a full wheel HPC simulation contains 500 million to 1 billion nodes. The turbine consists of less stages due to the the favorable pressure gradient. However, a full wheel simulation still requires 150 million to 300 million nodes. The spatial mesh is to be integrated in time for 2,000 to 10,000 time steps, based on the estimate that 50 to 100 time steps are needed to resolve a blade passing, to remove the transient effects. Alone the full wheel unsteady HPC simulation will require 20 to 40 million CPU hours on today’s fastest computers. Adding the low-pressure compressor (LPC), fan as well as highand low-pressure turbine (HPT and LPT, respectively), the computational requirements are far beyond what is currently affordable for practical applications and therefore approximations are used to reduce the computational costs. The most widely-used industrial practice for solving turbomachinery problems is the mixing plane assumption. A circumferential averaging of the flow variables is applied at the interface between rotor and stator. These average quantities are then imposed as upstream and downstream values for the following and preceding blade rows respectively and a steady-state computation can be performed for both the rotor and the stator. Due to this averaging and the periodicity assumption only one blade passage needs to be simulated per blade row, independently of the blade counts. Although this assumption models the mean effect of the rotor/stator interaction, all the unsteady information is lost due to the averaging. An alternative approach used to perform an unsteady simulation is to chose a periodic sector of, for example 20o, where the blade counts are changed such that the full wheel can be split into 18 sections and periodicity conditions can be used. The pitch and chord of the blades then need to be adjusted to preserve the flow blockage. Because of these changes it is clear that only approximate information can be obtained