Figure 1.
The scanning process of the K44 turbine wheel.
Figure 1.
The scanning process of the K44 turbine wheel.
Figure 2.
(
a) The isometric view at the numerical model showing six exhaust pipes, (
b) the model cross-section, (
c) the view at the 1st stage nozzle vane and the tip clearance domain [
29].
Figure 2.
(
a) The isometric view at the numerical model showing six exhaust pipes, (
b) the model cross-section, (
c) the view at the 1st stage nozzle vane and the tip clearance domain [
29].
Figure 3.
Mesh generated on: (a) exhaust pipe, (b) 1st stage nozzle vane, (c) diffusor, (d) outlet, (e) 1st stage rotor.
Figure 3.
Mesh generated on: (a) exhaust pipe, (b) 1st stage nozzle vane, (c) diffusor, (d) outlet, (e) 1st stage rotor.
Figure 4.
(
a) The inlet mas-flow rate and pressure-outlet boundary conditions, (
b) boundary mass flow rate changes at the inlet to the exhaust pipes [
29].
Figure 4.
(
a) The inlet mas-flow rate and pressure-outlet boundary conditions, (
b) boundary mass flow rate changes at the inlet to the exhaust pipes [
29].
Figure 5.
The positions of the VTG of the 2nd stage turbine wheel: (a) blade configuration (b) α3 = 30° deg, (c) α3 = 20° deg, (d) α3 = 11° deg.
Figure 5.
The positions of the VTG of the 2nd stage turbine wheel: (a) blade configuration (b) α3 = 30° deg, (c) α3 = 20° deg, (d) α3 = 11° deg.
Figure 6.
The hexahedral mesh of the VTG domain at: (a) 30°, (b) 20°, (c) 11° opening.
Figure 6.
The hexahedral mesh of the VTG domain at: (a) 30°, (b) 20°, (c) 11° opening.
Figure 7.
The mass-average pressure changes during the single revolution of the crankshaft for different mesh density on: (
a) exhaust pipe, (
b) 1st stage rotor, (
c) VTG vanes, (
d) 2nd stage rotor [
29].
Figure 7.
The mass-average pressure changes during the single revolution of the crankshaft for different mesh density on: (
a) exhaust pipe, (
b) 1st stage rotor, (
c) VTG vanes, (
d) 2nd stage rotor [
29].
Figure 8.
The plot of the total pressure at the 1-st stage turbine inlet for the 30° VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 8.
The plot of the total pressure at the 1-st stage turbine inlet for the 30° VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 9.
The plot of the total pressure at the 1-st stage turbine inlet for the 20° deg VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 9.
The plot of the total pressure at the 1-st stage turbine inlet for the 20° deg VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 10.
The plot of the total pressure at the 1-st stage turbine inlet for the 11° VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 10.
The plot of the total pressure at the 1-st stage turbine inlet for the 11° VTG opening at: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 11.
The pressure sensors: (a) Keller M8coolHB, (b) Kistler 4049A10.
Figure 11.
The pressure sensors: (a) Keller M8coolHB, (b) Kistler 4049A10.
Figure 12.
Validation of the numerical model for (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 12.
Validation of the numerical model for (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 13.
The residuals of the numerical simulation.
Figure 13.
The residuals of the numerical simulation.
Figure 14.
The pathlines from the: (a) single exhaust pipe, (b) two opposite exhaust pipes.
Figure 14.
The pathlines from the: (a) single exhaust pipe, (b) two opposite exhaust pipes.
Figure 15.
Example of the intersection of the pressure plots monitored at the
Section 6.1 at the turbine speed of 40,000 rpm and 11° VTG opening.
Figure 15.
Example of the intersection of the pressure plots monitored at the
Section 6.1 at the turbine speed of 40,000 rpm and 11° VTG opening.
Figure 16.
The intersection of the pressure plot monitored at the
Section 6.1 for the three different VTG opening at the turbine speed: (
a) 60,000 rpm, (
b) 50,000 rpm, (
c) 40,000 rpm.
Figure 16.
The intersection of the pressure plot monitored at the
Section 6.1 for the three different VTG opening at the turbine speed: (
a) 60,000 rpm, (
b) 50,000 rpm, (
c) 40,000 rpm.
Figure 17.
The outlet total pressure variation of the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 17.
The outlet total pressure variation of the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 18.
The outlet total pressure variation of the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 18.
The outlet total pressure variation of the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 19.
The outlet total temperature variation at the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 19.
The outlet total temperature variation at the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 20.
The outlet total temperature variation at the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 20.
The outlet total temperature variation at the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 21.
The averaged total-static efficiency of the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm during the single revolution of the crankshaft.
Figure 21.
The averaged total-static efficiency of the 1st stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm during the single revolution of the crankshaft.
Figure 22.
The averaged total-static efficiency of the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 22.
The averaged total-static efficiency of the 2nd stage rotor at the three different VTG openings for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm.
Figure 23.
(
a) The measuring points A, B, and C of the mass-flow rate at
Section 6.1 of exhaust pipe 1, (
b,
c) the position of the control points at the trailing edge of the nozzle vane, (
d) the velocity triangle at the outlet from the 1st stage nozzle vane of the exhaust pipe 1.
Figure 23.
(
a) The measuring points A, B, and C of the mass-flow rate at
Section 6.1 of exhaust pipe 1, (
b,
c) the position of the control points at the trailing edge of the nozzle vane, (
d) the velocity triangle at the outlet from the 1st stage nozzle vane of the exhaust pipe 1.
Figure 24.
The plots of the total pressure measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 24.
The plots of the total pressure measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 25.
The plots of the total temperature measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 25.
The plots of the total temperature measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 26.
The plots of the absolute velocity C1 measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 26.
The plots of the absolute velocity C1 measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 27.
The plots of the tangential component of the absolute velocity C1u measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 27.
The plots of the tangential component of the absolute velocity C1u measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 28.
The plots of the relative velocity W1 measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 28.
The plots of the relative velocity W1 measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 29.
The plots of the tangential component of the relative velocity W1u measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 29.
The plots of the tangential component of the relative velocity W1u measured behind the 1st stage nozzle vane against the blade height for: (a–c) 60,000 rpm point A, B, C respectively, (d–f) 50,000 rpm point A, B, C respectively, (g–i) 40,000 rpm point A, B, C respectively.
Figure 30.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 60,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 30.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 60,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 31.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 50,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 31.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 50,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 32.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 40,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 32.
The plots of the absolute (α1) and relative (β1) angles measured behind the 1st stage nozzle vane against the blade height at 40,000 rpm for: (a) point A, (b) point B, (c) point C.
Figure 33.
(a) The configuration of the outlet velocity triangles at the against the height of the 1st stage nozzle vane, the comparison of the velocity triangles at the outlet of the 1st stage nozzle vane at: (b) points A, B, and C, (c) at three different turbine speeds.
Figure 33.
(a) The configuration of the outlet velocity triangles at the against the height of the 1st stage nozzle vane, the comparison of the velocity triangles at the outlet of the 1st stage nozzle vane at: (b) points A, B, and C, (c) at three different turbine speeds.
Figure 34.
(a) A diagram of a flow path from the exhaust pipe to the VTG vanes, (b) the contours of the total pressure at the 1st stage turbine wheel during the flow from the exhaust pipe no 2, (c) the velocity pathlines at the VTG vanes during the flow from the exhaust pipe no 2.
Figure 34.
(a) A diagram of a flow path from the exhaust pipe to the VTG vanes, (b) the contours of the total pressure at the 1st stage turbine wheel during the flow from the exhaust pipe no 2, (c) the velocity pathlines at the VTG vanes during the flow from the exhaust pipe no 2.
Figure 35.
The absolute and relative angle at the outlet from the 2nd stage rotor for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 35.
The absolute and relative angle at the outlet from the 2nd stage rotor for: (a) 60,000 rpm, (b) 50,000 rpm, (c) 40,000 rpm turbine speed.
Figure 36.
(a) Configuration of velocity triangles at the outlet from the 2nd stage rotor, (b) outlet velocity pathlines at 60,000 rpm, (c) outlet velocity pathlines at 50,000 rpm, (d) outlet velocity pathlines at 40,000 rpm.
Figure 36.
(a) Configuration of velocity triangles at the outlet from the 2nd stage rotor, (b) outlet velocity pathlines at 60,000 rpm, (c) outlet velocity pathlines at 50,000 rpm, (d) outlet velocity pathlines at 40,000 rpm.
Table 1.
The parameters of turbine wheel.
Table 1.
The parameters of turbine wheel.
B&W K44 Turbine Wheel |
---|
Type | Radial inflow |
Number of blades | 12 |
Inlet diameter (mm) | 120 |
Outlet diameter (mm) | 140 |
Inlet blade height (mm) | 125 |
Outlet blade height (mm) | 30 |
Table 2.
The operating parameters of the 6-cylinder, 2-stroke engine.
Table 2.
The operating parameters of the 6-cylinder, 2-stroke engine.
Engine Parameters |
---|
Number of cylinders | |
Type | 2-stroke |
Rotational speed | 1500 |
Cylinder bore (mm) | 115 |
Cylinder Stroke (mm) | 195.2 |
Displacement (cm3) | 24,000 |
Crankshaft angle step (deg) | 0.1 |
Table 3.
The parameters of the boundary conditions.
Table 3.
The parameters of the boundary conditions.
Inlet Boundary Conditions |
---|
Type | Mass-flow-inlet |
Mass flow rate (kg/s) | |
Total temperature (K) | 1100 |
Total pressure (Pa) | 240,000.0 |
Outlet Boundary Conditions |
Type | Pressure-outlet |
Outlet pressure (Pa) | 100,000 |
Outlet temperature (K) | 500 |
Table 4.
The parameters of the computer.
Table 4.
The parameters of the computer.
Computer Parameters |
---|
Number of cores | 4 |
Processor type | Inlet Core i7 |
Random-access memory (Gb) | 32 |
Graphics processor unit memory (Gb) | 0.512 |
Table 5.
The number of cells for each domain.
Table 5.
The number of cells for each domain.
Domain | Number of Elements |
---|
Exhaust pipe (×6) | 43,200 |
First-stage nozzle vane (×6) | 18,036 |
Tip clearance gap (×6) | 540 |
1st stage rotor | 1,340,000 |
Inter-stage pipes | 168,018 |
VTG vanes | 711,000 |
2nd stage rotor | 1,340,000 |
Outlet | 374,850 |