Improvement of Transonic Low Pressure Steam Turbine using High Performance Computation

Steam turbines hold the largest share of electricity production worldwide. In order to meet growing energy demands, steam turbine designers strive for increased power output, improved efficiency, and longer operational lifespan. Modern steam turbine designs employ large exit annulus area with long blades of up to 60 inches in the last stage of a low-pressure steam turbine in order to achieve these objectives. Increase in last stage blade height introduces supersonic flows in the tip span of the last stage rotor inlet. Such flows are subject to high unsteadiness induced by shock waves. In addition, condensation, droplet formation and unsteady blade loads in the rotor transonic tip region introduce a very complicated flow for numerical computations. Therefore, optimization of blade stacking in the last stage of a transonic low-pressure steam turbine is one of the most delicate and time-consuming parts of the design process. This requires design modifications including blade sweep, lean or twist. The experiments for scaled geometries are nevertheless very expensive and designers have to rely on time accurate computational fluid dynamics. The accuracy of computations is extremely critical in order to guide optimization algorithms and designers to the most viable design. The time-accurate computations are an order of magnitude more expensive than steady state. During design optimization, detailed geometrical features are excluded in order to achieve realistic computational runtime at the cost of accuracy. The geometrical features mostly excluded are hub-tip cavities, seals, part span snubbers, full span shroud, blade count modification or exclusion of upstream or downstream stages. Full-scale multi-stage model with all-inclusive geometrical features results in very large meshes of up to one billion mesh nodes. The proposed meshes must have matching block interfaces throughout the mesh in order to keep a second-order accuracy in space and time posing additional requirements of a very fine mesh in order to resolve high blade twist, shroud connections, and cavities-seals in the flow path. In the case of low-pressure steam turbines, the steam transition from superheated to condense in penultimate and last stages. This necessitates the inclusion of steam modeling at the least for the prediction of wetness as well as numerical accuracy. This results in additional computational resource requirements posing a very challenging computing problem. The recent widespread use of modern general-purpose graphics processing units (GPUs) for scientific computing provides a possibility to scale time-accurate computational fluid dynamic solvers for such challenging problems. A steady decline in graphics processing unit costs and at the same time improvements in throughput and onboard memory gradually allow hybrid high performance computing cluster as a viable option for the design engineering process. The key objective of this work is to improve the aerodynamic efficiency of a modern low-pressure steam turbine, using carefully tailored stator stacking, numerically on a cluster of GPUs and explain underlying time-resolved flow mechanisms. For this purpose, in-house Unsteady Reynolds Averaged Navier-Stokes (URANS) solver MULTI3 is developed for multi-GPU supercomputing clusters with additional equilibrium steam modeling, able to handle full-scale model. In this work, the typical scale of about 386 million mesh nodes for a full annular four-stage model running on 114 Pascal P100 GPUs with time-resolved equilibrium steam modeling is reported with a convergence run-time of less than a week. For design optimization, a typical scale of 57 million mesh nodes including tip-cavities and seals for the last two stages is achieved within a week of run-time on 17 GPUs. Last two-stage computational model of 16.9 million mesh nodes excluding tip cavities converge within 21 hours of reported runtime on two GPUs. Further, a key understanding is developed on computational accuracy versus cost with each geometrical or modeling approximation and guidelines are proposed for a suitable compromise of numerical approximation in a low-pressure steam turbine design optimization process. The results show the transonic tip region as the main source of entropy loss in the last stage of the transonic low-pressure steam turbine. The proposed stator stacking with an increase in tip axial gap (forward curved sweep) and throat-to-pitch ratio variation designs show aerodynamic total-to-total efficiency improvements of up to 1.3% and 1.1% respectively. The key improvements are seen in supersonic flow expansion in the last stage rotor tip driven by a reduction of relative inlet Mach. The flow unsteadiness in the transonic stator-rotor tip gap is primarily driven by leading edge bow shock, however as found in this work, also depends on the axial gap. Despite an increase in unsteadiness by the closing throat (stator twist design) in the last stage stator tip, a decrease in relative Mach improves efficiency by improvements in the flow expansion in the supersonic rotor tip airfoils. The control of throat-to-pitch ratio is found to be the most effective way to control reaction variation and mass flow redistribution in both the stator and rotor. The analysis shows that at least penultimate stage is compulsory in the computational model along with tip cavities and seals for the last stage optimization as any change in throat area as a result of stacking modification introduce a change in stage pressure ratio, workload, and reaction for both stages