2.3. Determination of diametrical sizes on the entry of the compressor turbine and number of its stages.

In GTPP with two-spool compressor LPC rotates due to low pressure turbine (LPТ), аnd HPC – due to high pressure turbine (HPТ).

Geometrical sizes on the entry to the HPT (section 3) and on the entry to the LPT (section 3H) are determined the same as for one-spool engine. For determination geometrical sizes between HPT and LPT, at first, their works L_HPT і L_LPT are calculated by the formulas:

L_HPT = L_HPC/[(1 +g_fuel)(1 – g_cooling – g_exchange)] = 242150.53 / [(1 +

+ 0.0213)(1 – 0.08 – 0)] = 257717,711 (J/kg) ,

L_LPT = L_t – L_HPT = 451591.652 – 257717.711 = 193873.941 (J/kg)

Temperature Т^*_3H and pressure р^*_3H after HPT are defined as:

(K) (Pa)

HPT efficiency value ^*_CH is taken greater than value^*_t (chosen on thermodynamic calculation) on 0,01–0,02.

Let’s consider the section before HPT.

Cross sectional area at the entry of the HPT is defined by the formula:

(m²)

Mean diameter on the entry of the HPT is equal to:

D_3m = D_2t (1.1 ÷1.2) = 1.15 ∙ 0.482 = 0.5543 (m)

h₃ = F₃/(3,14D_3m) = 0.0507 / (3.14 ∙ 0.5543) = 0.0291 (m),

D_3t = D_3m + h₃ = 0.5543 + 0.0291 = 0.5834 (m),

D_3H = D_3m – h₃ = 0.5543 – 0.0291 = 0.5252 (m).

Further let’s consider section after HPT (3Н-3Н).

Cross sectional area at the exit from the HPT is defined by the formula:

(m²)

where G_t = G_air(1 + g_fuel)(1– g_cooling – g_exchange) = 27.724∙(1 + +0.0213)(1-0.08) = 26.049 – gas expenses in turbine; _cc = 0,97...0,99 (taken in thermodynamic calculation); _n = 0,985...0,995 – coefficient of total pressure losses in the nozzle; m₃ = 0,0396; q(λ₃) = 1 (because in turbine first stage always there is supercritical pressure difference λ₃ = 1) – flux density function, α₁ = 15–20 ° hence sin α₁ = 0.309 .

Choosing a type of turbine we can find mean diameter, vane height, tip and hub diameters.

At D_3Hm = const = D_3m = 0.5543 m,

h_3H = F_3H/(3,14D_3Hm) = 0.0979 / (3.14∙0.5543) = 0.0562 (m),

D_3Ht = D_3m + h_3H = 0.5543 + 0.0562 = 0.6105 (m),

D_3HH = D_3m – h_3H = 0.5543 – 0.0562 = 0.4981 (m).

After determination the value of angular velocity on the mean diameter of compressor turbine u_tcm= u_HPC ∙ D_3Hm / D_1t = 411.25 ∙ 0.5543/ 0.522 = 436.697 (m/s) and choosing the loading coefficient у^*= 0,45–0,6 (assume as y* = 0.525), let’s determine approximate number of compressor turbine stages z_t.k. by the formula:

z_t.k = . By approximation we have 3 stages of compressor turbine. Values L_t та ^*_c are taken from thermodynamic calculation.

2.4. Determination of diametrical sizes at the entry to the power turbine and at the exit from it, number of power turbine stages

Cross sectional area F₄ at the entry to the power turbine is defined by the formula:

(m²)

where G_t = G_air(1 + g_fuel)(1– g_exchange) =27.724∙(1+0.0213) = 28.315 – gas expenses through the power turbine; Т^*₄, р^*₄ – gas temperature and pressure before power turbine that is taken fro thermodynamic calculation; т₄ = 0,0309; ₁ = 20–25(assume as ₁ = 23, sin ₁ = 0.3907) ; _l = 0,98–0,99 – coefficient of pressure losses between turbines. If there is supercritical pressure difference in the power turbine nozzle q(₄) = 1.

Assume that compressor turbine has shape with constant mean diameter.

At D_4m = const = D_3Hm = 0.5543 m,

h₄ = F₄/(3,14D_4m) = 0.195 / (3.14∙0.5543) = 0.112 (m),

D_4t = D_4m + h₄ = 0.5543 + 0.112 = 0.6663 (m),

D_4H = D_4m – h₄ = 0.5543 – 0.112 = 0.4423 (m).

Cross sectional area F₅ at the exit from the power turbine is defined by the formula:

(m²),

where value ₅ in the range 0,5–0,7 (assume that ₅ = 0.6), let’s determine value q(₅) = 1,527₅(1 – 0,143₅²)^3,02 = 1.527 ∙ 0.6 ∙ (1-– 0.143 ∙ 0.6²)^3.02 = 0.781. Values Т^*_т, р^*_т are taken from thermodynamic calculations.

Let’s determine diametrical sizes at the exit from the power turbine: tip diameter d_5t, mean d_5m and hub d_5H diameters and vane height h_5.

At D_5H = const = D_4H = 0.4423 m,

(m),

h₅ = (D_5t – D_5H) / 2 = (0.7713 – 0.4423) / 2 = 0.1645 (m),

D_5m = D_5H + h₅ = 0.4423 + 0.1645 = 0.6068 (m).

Moreover, for providing the enough strength of turbine last stage vane, it is necessary to fulfill the inequality D_5m/h₅ > 4.

Let’s check this condition D_5m/h₅ = 0.6068 / 0.1645 = 3.7 (m). Condition is satisfied.

At first, angular velocity on mean diameter at the entry to the power turbine is chosen (for non-coolant turbine value u_ptm is taken in the range 220–280 m/s, assume that u_ptm = 250 m/s) and power turbine stage number is found according to the formula:

z_pt = 2у^*2L_pt/(^*_ptu^*2_ptm) = 2 ∙ 0.525² ∙ 306026.710 / (0.9 ∙ 250²) = 3.0

Value у^* for power turbine is chosen in the same range as for compressor turbine (assume as y* = 0.525).