Direct boundary value solution of wave rotor flow fields

A computational method to analyze the flow in wave rotors and their adjoining ducts has been formulated and implemented. The method solves the flow within the rotor in the absolute frame of reference. The approach rigorously treats of the duct-rotor interface, allowing for the blade-induced work due to an initial non-uniform angle of attack. Several cases were simulated, showing that for off-design conditions the port flows are significantly non-uniform, contrary to conventional models. The calculations also predict a significant region of recirculation in the high pressure duct. The new computational approach shows promise for further development. Introduct ion to Wave Rotors Wave rotors are devices which utilize unsteady wave processes to effect work exchange between two fluid streams, a process thermodynamically equivalent to that of a turbocompressor. As in a turbocompressor, the expanding and the compressing fluid streams enter and leave the device via ducts in which the flow is substantially steady. Unsteady processes within the wave rotor cause the expanding stream to perform work on the secondary stream. These unsteady processes are generated in a series of cells arranged longitudinally around the periphery of a rotor, reminiscent of a Gatling gun. The rotor is rotated to cause valving action, exposing the cell ends to the fluid ports or blank wall. The timing is such that the moving compression and expansion waves generated by these time-dependent boundary conditions produce the desired pressure changes for each stream. The process in each cell is cyclic, since the boundary conditions are periodic as the rotor makes a revolution. This means 1) each time the cell is at a particular angular position, it must have the same distribution of gas properties along its length, and 2) every cell must go through the same cycle, with only aphase difference from its neighbors. The consequence is that the wave pattern, although unsteady in the frame of reference of the cell, is almost steady as viewed by a stationary observer. The small unsteadiness is “jitter” as the cell walls pass. In the limit of infinitesimal cell widths Copyright 0 1 9 9 3 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. d’ ‘d’ (infinite blading), the wave rotor flow is steady. The present paper is a description of a method of exploiting that fact to create a powerful wave rotor analysis technique. Wave rotors are not new, having been successfully used since the late 1950s in scientific and commercial applications (the only commercially-produced wave rotor is the Comprex supercharger for automotive and truck engines’). The Wave Superheater built in the late 1950s by Cornell Aeronautical Laboratories was a type of wave rotor; it remains today the only steady-flow uncontaminated-air hypersonic test facility ever built, capable of generating air at 5000 K and 100atm2. Current interest in wave rotors centers on aerospace applications, primarily their use as topping units for gas turbine engines3. In this application, the compressing stream would be air (from the conventional compressor), and the expanding stream would be hot gas from the combustor. The compressing stream leaves the wave rotor and enters the combustor; the expanding stream exit supplies the conventional turbine. Experimental and analytical studies are currently under way at the NASA Lewis Research Center aimed at establishing a reliable methodology for wave rotor design. The chief advantage to using a wave rotor as a topping unit is increased maximum cycle temperature. The rotating element of a wave rotor is alternately exposed to the hot gas and the full flow of cooler air. Thus, the rotor material temperature establishes an intermediate level (analogous to the cylinder head temperature in an automobile engine). This 100% cooling air effect is expected to allow burner exit temperatures hundreds of degrees higher than current gas turbine engines, even using existing materials. Current and envisioned calculational methods for wave rotors fall into two categories: 1) design codes, which solve the I-D Euler equation for time-dependent flow4, and 2) 2-D time-dependent CFD codes. The second approach is numerically intensive and would not be cost-effective for design. However, the design codes now in use solve the hyperbolic PDE in a single tube,