Focused Practice

I. Answer the following questions:

1. What has led to a large number of various studies?

2. What is a greater attention being devoted to?

3. Why is a reduction of the shaft length very interesting?

4. Why is the calculation of a last stage low pressure steam turbine and exhaust hood flow difficult?

5. What is a way to solve the problem?

6. What does another way consist of?

II. Analyse the grammar structures underlined in the above text.

III. Speak on: Specification of calculatingthe the above equipment.

Unit 23 Grammar: The Passive Voice. Word-building Word List:

1. convergence	сходимость, совпадение/конвергенция
2. explicit	ясный, явный, открытый
3. implicit	скрытый, неопределенный
4. turbulence	турбулентность потока
5. package	пакет, блок, узел, регулятор
6. shutdown	конец, остановка, закрытие, граница
7. local time stepping	пошаговая разбивка вычислений по ходу протекания процесса
8. phantom points	воображаемые условные точки
9. the Navier-Stakes equations	уравнения Навье–Стокса (по имени ученых в области механики жидкостей и газов)
10. numerical integration	численное интегрирование
11. conservative finite volume cell-vertex scheme	традиционный сеточный метод расчета для ограниченного объема
12. shroud (v) shroud (n)	завертывать, экранировать кожух, каркас
13. the Runge-Kutta scheme	метод Рунге–Кутта (ученые)
14. multigrid	многосеточный
15. data	данные
16. traverse	поперечина
17. medium	среда
18. hybrid scheme	гибридная схема
19. numerical methods	численные методы

Three-Stage Steam Turbine Flow Analysis

Experimental data has been available for the flow in a 1/3 scaled model of a three-stage low pressure steam turbine. The measurements have been carried out at СКTI in St. Petersburg, Russia.

The rotor blades of the first stage are shrouded whereas the strongly twisted rotor blades of the second and third stages are unshrouded but linked by coupling elements. Design tip clearances at shutdown for the second and third stages are 2.5 mm and 2.8 mm, respectively. Using five hole cone probes, traverse measurements of the flow field were performed in five planes 0, 1, 2s, 2, and 3, located at the inlet of the turbine, beyond the first stage, beyond the stator and the rotor of the second stage and at the exit of the turbine. The flow medium is hot steam at the inlet, condensing in the turbine.

The numerical method is based on the solution of the Navier-Stokes equations written in cylindrical coordinates using a conservative finite volume cell-vertex scheme. Discretization in time is performed by an explicit five-stage Runge-Kutta scheme. The artificial dissipation in the hybrid scheme used is computed at the first, third, and fifth stages whereas the diffusive terms are computed in the first stage only and frozen for the remaining stages. Convergence is accelerated by use of local time stepping, implicit residual smoothing with variable coefficients and a full-multigrid method.

A multiblock method is used to facilitate computations on structured grids for complex geometries. In this approach the tip regions of the unshrouded second and third stages are discretized by an additional grid. Numerical integration of the Navier-Stokes equations is performed in each block subsequently. Each grid block has one layer of phantom points, where the data of the neighbouring blocks is stored. In order to preserve the convergence rate of a single block scheme, the grid points in all blocks have to be on the same time level. Therefore the data transfer between the different blocks is performed after every substep of the Runge-Kutta scheme.