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.

When developing counter-rotating fans for advanced new-generation aeroengines with unducted blades it is very important to provide high acoustic and aerodynamic characteristics [1]. This paper presents some results of gasdynamic and aeroacoustic optimization of unducted CRF blade profile by using 3D viscous inverse problem. Flow in unducted CRF on the basis of unsteady 3D Navier-Stokes equations is modeled at the 1st stage of designing in order to find the key tonal noise sources. Based on these results, it is found that one of the key tonal noise sources is Rotor 1 - Rotor 2 tip vortices interaction and potential rotor interaction. Then, using 3D solver of the viscous inverse problem, aerodynamic loads are redistributed along R1 and R2 blade height aiming at a decrease in tip vortex intensity and potential rotor interaction with a probable increase in the CRF thrust. To verify the aerodynamic characteristics of the modified CRF, steady flow calculations are carried out with the help of 3D Navier-Stokes equations and “mixing plane” interfaces. To verify the acoustic characteristics of the modified CRF, tonal noise modeling is carried out for original and modified CRFs using aeroacoustic CIAM’s 3DAS solver for solution of unsteady inviscid equations for disturbances. Ffowcs–Williams, Howkings approach is used for acoustic calculations in the far field. The near acoustic field and directivity diagrams in the far field are found. Using 3D inverse problem, the fan tonal noise is decreased by 4 dB for take-0ff and landing with no thrust and efficiency losses.

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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).

Flow structure and integral performances for a six-stage high pressure compressor (HPC) are found based on 3D viscous through-flow computation within RANS aided by the modified S.K. Godunov's implicit scheme, "3D-IMP-MULTI" software developed at CIAM.To increase the surge margin a decision was made to modify (R1) operates on the left branch of the characteristic line in the mode with a detached shock.To increase the surge margin a decision was made to modify R1, R3, R4 and R6 of HPC on the basis of 3D inverse problem solution by "3D-INVERSE.EXBL" software developed at CIAM. Results of HPC computations with the modified R1, R3, R4 and R6 showed an increase in the surge margin by 14.0%.Comparison of numerical and experimental data for individual stages and for the whole modified HPC are to be presented for verification of the numerical method of HPC performance computation and redesign. KEY WORDS HIGH PRESSURE COMPRESSOR, 3D INVERSE PROBLEM, EXPERIMENTAL PERFORMANCESG des , PR des , Eff des parameters in design point PS, SS profile pressure side; profile suction side OL, SL operating line, surge line MP mixing plane M Mach number SM surge margin SM = ( π SL π OL • G OL G SL − 1) • 100%  turbulent kinematic energy, (𝑢 ′2 + 𝑣 ′2 + 𝑤 ′2 )/2  specific dissipate rate 𝑢 ′ , 𝑣 ′ , 𝑤 ′ fluctuating velocity components  molecular viscosity  t turbulent viscosity Tu inlet free-stream turbulence level, 100 √2/3• 𝑈 ∞ 𝑈 ∞ inlet velocity ini; mod initial; modified