Fully three-dimensional and viscous inverse method for turbomachine blade design

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Thong Q. Dang

Second Advisor

J. A. Lagraff


Blade, Turbomachine, Three-dimensional, Viscous inverse method

Subject Categories

Aerospace Engineering | Mechanical Engineering


The flow in turbomachine blade passages is three-dimensional (3D), viscous and unsteady. Each of these effects strongly influences its performance. Thus there is a need to develop a design tool (inverse methods) that accounts for all of these effects and gives the designer control over some flowfield and structural characteristics. The current inverse methods employed by industry are limited because they are two-dimensional, axisymmetric and/or quasi-three-dimensional (quasi-3D), with modelling of 3D effects through empirical correlations. Three-dimensional inverse methods presently available are limited by the inviscid-flow assumption, hence still in research phase. The proposed fully three-dimensional and viscous inverse method is developed to overcome these limitations.

To test the proposed viscous inverse concept, a quasi-3D method, directly extendable to 3D, is first developed. Here, one can prescribe either the mass-averaged swirl schedule $(r\bar V\sb{\theta})$ or the blade pressure loading (i.e. pressure difference across the blade, $\Delta p$) and a blade tangential thickness distribution. The blade camber surface sought after is made permeable during flow calculations and are modified by imposing the flow-tangency conditions. This method is formulated in a cell centered finite-volume scheme that uses a robust shock-capturing algorithm to solve the Navier-Stokes equations. Wall-functions are used along with a simple eddy viscosity model to retain a relatively large 'slip' velocity at the blade surface to aid the inverse calculations. The code is evaluated by comparing solutions with Liu's Navier-Stokes code. The inverse mode is validated by recovering a given blade geometry.

A 3D viscous inverse method is developed along the same lines as the quasi-3D inverse method, with a prescription of stacking line as an additional boundary condition. The method is validated for a transonic rotor in an industrial compressor. The solutions compare well with a standard Navier-Stokes analysis solver employed by industry.

Finally, the practical utility of this 3D inverse viscous method is demonstrated by carrying out a design modification of a first-stage rotor in an industrial compressor. By employing a simple modification to the blade pressure loading distribution, the new blade geometry is predicted to perform better than the original design over a wide range of operating points, including an improvement in choke margin.


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