https://ntrs.nasa.gov/api/citations/20010018414/downloads/20010018414.pdf

Reduced-order modeling: new approaches for computational physics

A harmonic balance technique for modeling unsteady nonlinear e ows in turbomachinery is presented. The analysis exploits the fact that many unsteady e ows of interest in turbomachinery are periodic in time. Thus, the unsteady e ow conservation variables may be represented by a Fourier series in time with spatially varying coefe cients. This assumption leads to a harmonic balance form of the Euler or Navier ‐Stokes equations, which, in turn, can be solved efe ciently as a steady problem using conventional computational e uid dynamic (CFD) methods, including pseudotime time marching with local time stepping and multigrid acceleration. Thus, the method is computationally efe cient, at least one to two orders of magnitude faster than conventional nonlinear time-domain CFD simulations. Computational results for unsteady, transonic, viscous e ow in the front stage rotor of a high-pressure compressor demonstrate that even strongly nonlinear e ows can be modeled to engineering accuracy with a small number of terms retained in the Fourier series representation of the e ow. Furthermore, in some cases, e uid nonlinearities are found to be important for surprisingly small blade vibrations.

/pdf/computation-of-unsteady-nonlinear-flows-in-cascades-using-a-7z3pen2wz8.pdf

Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique

Work on rotating stall and its related disturbances has been in progress since the Second World War. During this period, certain ‘hot topics’ have come to the fore — mostly in response to pressing problems associated with new engine designs. This paper will take a semi-historical look at some of these fields of study (stall, surge, active control, rotating instabilities etc.) and will examine the ideas which underpin each topic. Good progress can be reported, but the paper will not be an unrestricted celebration of our successes because, after 75 years of research, we are still unable to predict the stalling behaviour of a new compressor or to contribute much to the design a more stall resistant machine. Looking forward from where we are today, it is clear that future developments will come from CFD in the form of better performance predictions, better flow modelling and improved interpretation of experimental results. It is also clear that future experimental work will be most effective when focussed on real compressors with real problems — such as stage matching, large tip clearances, eccentricity and service life degradation. Today’s topics of interest are mostly associated with compressible effects and so further research will require more high speed testing.Copyright © 2015 by ASME

Stall, Surge, and 75 Years of Research

A nonlinear harmonic methodology has been developed to calculate unsteady viscous flows through turbomachinery blades. Flow variables are decomposed into time-averaged variables and unsteady perturbations, resulting in the time-averaged equations with extra nonlinear stress terms depending on the unsteady perturbations. An efficient evaluation of an unsteady flowfield is obtained by solving the first-order harmonic equations. The nonlinear interactions between the time-averaged flowfield and the unsteady perturbations were included by a strong coupling approach. The basic computational methodology was applied to the two-dimensional Navier-Stokes equations, and the method was validated against several test cases. Computational results show that this method is much more efficient than the nonlinear time-marching methods while still modeling dominant nonlinear effects

Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines

CFD is now an essential tool for the design of all types of turbomachinery. However, as engineers are exposed more and more to the results of CFD and less and less to experimental data there is a danger that they may not realise the limitations of CFD and so will view its predictions as more reliable than they really are and not question them sufficiently. This is particularly dangerous when CFD is use as part of an optimisation procedure. The objective of this paper is to try to expose some of the limitations of CFD as used for routine turbomachinery design. CFD is not an exact science. Errors can arise from the following sources: • Numerical errors due to finite difference approximations. • Modeling errors, where the true physics is not known or is too complex to model — e.g. turbulence modeling. • Unknown boundary conditions, such as inlet pressure or temperature profiles. • Unknown geometry such as tip clearances or leading edge shapes. • Assumption of steady flow. Each of these sources of error is discussed and examples of the differences they can cause in the predictions are shown. Despite these limitations CFD remains an extremely valuable tool for turbomachinery design but it should be used on a comparative basis and not trusted to give quantitative predictions of performance.Copyright © 2010 by ASME

Some Limitations of Turbomachinery CFD

A time-marching Euler calculation for 2-D and quasi-3-D unsteady flows in oscillating blade rows is presented, based on a finite volume scheme with cell-vertex discretization in space and 2-step Runge-Kutta integration in time. Calculated results for unsteady flows in an oscillating flat plate cascade are in good agreement with those from two well-established linear methods, LINSUB and FINEL. The unsteady pressure distribution and aerodynamic damping calculated by the present method for a turbine blade test case (Aeroelasticity Workshop Standard Configuration No. 4 cascade) agree well with the corresponding experimental data

An Euler Solution for Unsteady Flows Around Oscillating Blades

Fourier methods for turbomachinery applications

Rotating-stall inception in axial-e ow compressors has been studied computationally using a quasi-threedimensional time-marching Navier ‐ Stokes method with a mixing-length turbulence model. Of particular interest was the effect of external circumferential disturbances corresponding to inlet stagnation pressure distortions and rotor/stator blade interactions. The present results show that rotating stall onset patterns in terms of number of stall cells and rotating speeds were ine uenced by small external circumferential stationary or rotational disturbances. First mode circumferential disturbances had the most destabilizing effect, resulting in a single-cell pattern rotating in the absolute frame at about 50% rotor speed, as is observed in most experiments. Short-scale multiple-cell patterns rotating at a higher absolute speed could also be excited by a disturbance with the same circumferential length scale. Short-scale multiple-cell patterns tended to be more persistent in an isolated blade row than in a stage. In the latter case, a shortscale pattern initiated by a rotor ‐ stator interaction would quickly change into a long-scale single-cell pattern, associated with a distinct change of the rotating speed.

Computational Study of Rotating-Stall Inception in Axial Compressors

A quasi-three-dimensional time-linearized Euler method has been developed to compute unsteady flows around oscillating blades. In the baseline method, unsteady flow is decomposed into a steady flow plus a linear harmonically varying unsteady flow. Both the steady flow equations and the unsteady perturbation equations are solved using a pseudo-time-marching method. Based upon this method, a novel nonlinear harmonic Euler method has been developed. Due to the nonlinearity of the aerodynamic governing equations, time-averaging generates extra unsteady stress terms. These nonlinear effects are included by a strongly coupled approach between the perturbation equations and the time-averaged equations. Numerical results demonstrate that nonlinear effects are very effectively modeled by the nonlinear harmonic method.

Li He

Papers

Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines

An Euler Solution for Unsteady Flows Around Oscillating Blades

Fourier methods for turbomachinery applications

Computational Study of Rotating-Stall Inception in Axial Compressors

Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods