Method of 1D calculation was developed. It is applicable to various ideal gases and their mixtures with regard to variability of their physical properties within wide temperature range.
Four checking cross-sections were set for each vane/blade row: at the row inlet, in the row throat, at the row outlet, and downstream the row at the distance of the inter-row gap.
Relations for the calculation of the flow outlet angle and maximum outlet velocity when the velocity in the throat reaches sonic values were a basis for a mathematical model. These relations considered the row geometry, tapering of a meridional streamline, a compressibility of gas, and losses variable along a channel. They made it possible to determine a gas mass flow at various flow outlet velocities.
The row loss coefficient was determined from numerous test results. Losses in uncooled row were composed of a friction, edge, wave (due to incidence), and tip losses. A cascade density, the row height, the edge thickness, the airfoil surface roughness, inlet and outlet angles, Re, and the flow turbulence were also considered.
Semi-empirical relations, describing an impact of a cooling air blow-off through a perforation in the airfoil and tip shrouds, trailing edge slot, at the shroud mating area, and in the gap downstream the row, were applied for the cooled turbine calculation. The influence of the blade cooling air pre-swirl on its temperature and turbine power was taken into account as well.
Axial flows and the impact of a circumferential flow were defined when the radial gap flow for shroudless blades was calculated. For shrouded blades flows through linear and step labyrinths calculated. Influence of the rotation direction on the flow and gas heating in the labyrinth were also taken into account.
Disk-gas losses are also calculated.
Inputs were geometry of each row, a rotation velocity, a pressure, a temperature, a flow inlet angle, cooling air mass flow, temperature and pressure. Outputs could be any operation parameter of a turbine or a stage and flow parameters at checking cross-sections. Calculation covered whole range of turbine operation modes, including stage operation modes with energy consumption.
A high-performance code was written on a basis of this method. It was verified against test results of some model turbines. A comparison showed quite good correspondence to tests both for turbine integral parameters and flow parameters at the checking cross-sections.
Hot Streaks and Phantom Cooling in a Turbine Rotor Passage: Part 2 — Combined Effects and Analytical Modelling