Present paper contains a method of solution of inverse problem for Navier-Stokes equations for 3D flows without any simplification of the problem statement and applied to design of turbomachinery bladed rows. In the developed method blade surface is impermeable and no-slip or any other boundary condition compatible with Navier-Stokes equations is applied on the blade surface. Solution of inverse problem is determined using moving grid, which is re-generated at each step of time-marching procedure (variation of flow-rate, impulse and energy fluxes due to movement of grid nodes is taken into account). Normal speed of face of grid cell adjacent to blade surface is determined using given static pressure (inverse mode) with the aid of relationships which are the elements of Godunov scheme applied for integration of flow equations.

Widening of surge margin of a transonic compressor stage is the main objective of the paper. This stage is a typical middle stage of a modern high pressure compressor (HPC) with decreased number of stages. Hot tip clearance of the stage being integrated into a six-stage HPC providing total pressure ratio π* HPC ≥ 12 and mass flow-rate < 16 kg/sec is estimated at 2.5 – 3% of blade height and is classified as a large tip clearance. In this paper experimental and 3D viscous numerical performances of the stage are obtained for two values of rotor tip clearance — equal to 0.76% (small size) and 2.66% (large size) of blade height. In doing so, tip clearance enlargement from 0.76% to 2.66% has been made by increase of casing (shroud) radius. This increase is manufactured as a circumferential trench (recess) with axial width 30% larger than rotor axial chord. Below this tip clearance is called “recessed” tip clearance. A distinguishing feature of leakage flow in case of large tip clearance is a formation of reversed flow near rotor casing. This backflow being intensified by throttling causes increase of incidence at the rotor leading edge and development of rotor stall. Casing treatments are intended to inhibit and delay the process. Among them circumferential grooves is the simplest casing treatment. Investigated in this paper casing circumferential grooves cover 82% of rotor axial chord. Numerical visualization of the near-casing streamlines demonstrates that tip leakage flow drains into the casing grooves giving rise to extended domains of positive axial velocity. Calculated mass flow-rate through groove’s cross-section demonstrates maximum over the rotor blade tip (flow into the groove) and minimum at mid-pitch (flow out of the groove). Amplitude of this variation depends on the groove location and stage throttling.

Present paper is devoted to numerical investigation of unsteadiness caused by impeller-diffuser interaction in a 8:1 total pressure ratio centrifugal compressor. The compressor designed by CIAM [7], and manufactured and tested by Customer gave satisfactory performances even under the first test. Further development requires new insights and advanced numerical tools. In this context, this paper presents Navier-Stokes computations of 3D viscous unsteady flow field within the impeller-diffuser configuration. Steady and unsteady computations indicated spacious zone of low velocity / reverse flow on pressure surface of the diffuser vane. To suppress this reverse flow, new vaned diffuser has been tailored through application of 3D inverse design procedure for Navier-Stokes equations [8]. Subsequent steady and unsteady N-S calculations performed for compressor with the new diffuser demonstrated depression of reverse flow within diffuser and different unsteady loading of the diffuser vane.

Present paper contains application of inverse problem for 3D Navier-Stokes equations to design turbomachinery bladed rows. In-house software package used to solve 3D inverse problem is named 3D-INVERSE.EXBL. Inverse problem is based on desired static pressure distribution on suction side of blade, given blade thickness and pressure difference (named loading) in corresponding points of suction and pressure sides of blade. Inlet and outlet gas-dynamic parameters (pressure, density and flow velocity vector) are taken from direct solution of flow within multistage compressor and remains unchanged during inverse problem solution. Solution of inverse problem is determined using moving grid. Normal speed of face of grid cell adjacent to blade surface is determined using given static pressure (inverse mode) with the aid of relationships which are the elements of Godunov scheme applied for integration of flow equations. In the paper inverse solution provides effectiveness and operability of first rotor of multistage low pressure compressor (LPC) for a wide range of rpm (70 ± 100%) in case of absence of inlet guide vane (IGV).

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