The Efficient Computation of Transient Flow in Turbine Blade Rows Using Transformation Methods

Abstract

Computational predictions of the transient flow in turbine blade rows are considered. Adjacent blade rows typically contain unequal numbers of blades and vanes, requiring a computation over multiple passages per row to permit application of simple periodic boundary conditions. For typical geometries, use of conventional solution methods requires computation over all or a significant portion of the wheel to ensure a time accurate solution. The computational load is significantly reduced by methods which enable a one or two-passage solution to accurately model the full wheel (or part wheel, if applicable) solution. In this work, three methods are used: Profile Transformation, Fourier Transformation and Time Transformation. This paper will concentrate on the evaluation of these methods on two turbine geometries. The first test case is a frozen gust analysis for a high pressure transonic turbine; the geometry includes hub and casing cavities together with a complex tip. The second test case is a low pressure turbine stage run over a range of operating points. Comparisons between the various methods and the equivalent part wheel periodic solution are made to demonstrate the accuracy and computational efficiency of the transformation methods.

Applications of Eddy Resolving Methods

“…Hence, the simulations demonstrated that LES could now be used in house, for this type of flow. Connell et al (2012) apply the SAS hybrid RANS-LES approach. The key aspect of this work is that it proposes time-inclining (see Chap.…”

An Efficient Approach for Predicting Resonant Response with the Utilization of the Time Transformation Method and the Harmonic Forced Response Method

“…For the time-integration methods, they consist of the time-shifted methods and the scaling methods. The former is mainly the Fourier transformation (FT) method, which is based on the time shift and phase shift [10], and it is improved by introducing the Fourier series decomposition at the rotor/stator and periodic interfaces [11,12]. This makes the significant data compression and efficiency improvement with two blade passages modeled per row, but it usually needs more calculation periods to reach convergence [13].…”

“…The TT method was validated on several test cases [12,[18][19][20]. However, the discussion of this method in the open literature was more concerned about the total performance parameters (mass flow, efficiency, and total pressure ratio) and time-averaged variables.…”

Experimental and Numerical Studies of a High-Head Francis Turbine: A Review of the Francis-99 Test Case

“…Periodic boundary conditions are implemented using a simple phase shift of the complex amplitudes, which are solved for the frequencies of the perturbations coming from adjacent computational domains with different rotational speeds. Detailed explanation of this technique is available in the literature [25][26][27][28][29].…”

“…A method called a Fourier transformation is used in this technique [25][26][27]. Two research groups modeled the Francis turbine using this technique and presented the results during the workshop [6,16].…”