Hydro-Gas-Dynamic Processes Modeling in the GTE Cooled Blades Channels with Account for a Priori Estimation of the Computational Grid Cell Size

Аuthors

Osipov S. K.^*, Bryzgunov P. A.^**, Rogalev N. D.^***, Sokolov V. P.^****, Milyukov I. A.^*****

National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya str., Moscow, 111250 Russia

*e-mail: OsipovSK@mpei.ru
**e-mail: BryzgunovPA@mpei.ru
***e-mail: RogalevND@mpei.ru
****e-mail: SokolovVPet@mpei.ru
*****e-mail: MiliukovIA@mpei.ru

Abstract

At present, the vast majority of gas turbine engines are being accomplished with cooled turbine blades, which is stipulated by the high temperatures of the working fluid at the turbine inlet (over 1500-1700 K). The internal cooling channels geometry of the cooled blades is complex as a rule, due to the necessity to ensure various heat removal degree at the different parts of the blade, as well as the necessity of maximum heat exchange intensification at minimum hydraulic resistance of the circuit to minimize the coolant consumption and energy losses for its pumping.
With the reverse engineering approach, numerical simulation application of fluid dynamics and heat and mass transfer processes may significantly reduce the amount of physical testing of blade prototypes and, as a result, reduce the cost of product development. Nevertheless, the taking certain design decisions requires validation of computational models by physical experiments, which reduces the modeling introduction economic effect. It seems thereupon worthwhile to develop the techniques for models anticipatory verification, allowing transfer from typical geometries with well-known characteristics to the complex composite channels formed from the typical ones.
On the other hand, the computational grid quality is known as one of the basic parameters, determining the modeling accuracy. Practically, there are no generalized recommendations at present for a priori estimation of the grid cells sizes in the main flow region. The presented article suggests application of the earlier developed technique for the anticipatory verification of the numerical modeling results. The technique is based on the decomposition principle and searching for the transition points to the grid convergence ensuring exact solution with an error less than 10%, and compiling correlations associating optimal non-dimensional size of the element (the earlier introduced Ko parameter) with mode and geometric parameters. The article considered models of typical channels frequently occurring in the blades cooling system, such as the channels with sudden expansion, narrowing, as well as diffusor channels. A k–ω turbulence model is applied for modeling.
Variants computations with the search of the grid convergence points were performed for these channels at various geometrical parameters in the Reynolds number range of 20,000–100,000. Statistically significant correlations, associating the Reynolds number, hydraulic diameter of the channel with the non-dimensional cell height in the main flow zone were obtained by the results of the variant computations processing. Pearson criterion at the 95% probability level was employed for the static significance checking. 
An overall statistically significant correlation was obtained as well for all considered channels. The correlation coefficient for the channel with a sudden expansion was 0.75, while it was 0.95 and 0.63, respectively for the channel with a sudden narrowing, and a diffuser. Correlation coefficient of the overall dependence is 0.76.

Keywords:

hydro-gas-dynamic processes modeling in the cooled channels of gas turbine engine blades, advanced verification of hydraulic channels models, typical channels of gas turbine engine turbine cooled blades, reverse engineering of gas turbine engines cooled turbine blades

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