Jinju Sun

Development of an Optimization Design Method for Turbomachinery by Incorporating the Cooperative Coevolution Genetic Algorithm and Adaptive Approximate Model

An optimization design method is developed, which is motivated by the optimal design of a cryogenic liquid turbine (including an asymmetric volute, variable stager vane nozzles, shroud impeller and diffuser) for replacement of the Joule-Thompson throttling valve in the internal compression air-separation unit. The method involves mainly three elements: geometric parameterization, prediction of objective function, and mathematical optimization algorithm. Traditional parameterization approach is used for the geometry representation, while some novel work in the latter two aspects (i.e. objective function evaluation and optimization algorithm) is done to reduce the computing time and improve the optimization solution. A modified Cooperative Coevolution Genetic Algorithms (CCGA) is developed by incorporating a modified variable classification algorithm and some new self-adapted GA operators, which help to enhance the global search ability with an excessive number of optimization variables. Design of Experiment (DOE) is carried out to initialize the kriging approximation model, which is used to approximate the time-costly objective function. Then the CCGA is started, and once a potential superior individual is found, a decision will be made by the in-house code on whether or not it needs a updating. If required, the true objective function prediction based on the real model will be conducted and the obtained value of objective function will be used to update the kriging model. In such a way, the CCGA can complete its optimal searching with a limited number of real evaluations for objective function. All the above features are integrated into the optimization framework and encoded for the optimal turbine design. In addition, CFD software ANSYS CFX is used for the real objective function evaluations, and a well-organized batch code is developed by the authors for calling the CFD simulation which helps to promote this automation of the optimization process. For validation, the optimization method is used to solve some classical mathematical optimization problems and its effectiveness is demonstrated. The method is then used in the optimal design of the cryogenic liquid turbine stage, it is demonstrated that the optimal design method can help to reduce significantly the searching time for the optimal design and improve the design solution to the liquid turbine.© 2011 ASME

Blade Shape Optimization of Transonic Axial Flow Fan in Terms of Sectional Profiles and Stacking Line

Transonic axial flow fan has relatively high blade tip speed and produces higher pressure ratio than the subsonic. However, considerable losses are brought about by the shock waves close to blade tip and over part of span, leading to deteriorated overall efficiency and operating flow range. It is generally acknowledged that modifications of blade stacking line (axially sweep and tangentially lean) and sectional profiles can help to control spanwise distribution of blade loading, reduce shock loss and secondary flow, and extend the operating flow range.The present study is to maximize the comprehensive benefits of simultaneously optimizing the sectional profiles and stack line by means of a global optimization method with reduced cost. In contrast with previous studies, it is of two distinguished features. First, in blade geometry parameterization, both sectional profiles and stacking line are varied to provide more flexible blade shape variation and subsequently permit more optimization performance gains. Secondly, with simultaneous variation of sectional profiles and stacking line, number of optimization variables and nonlinearity of optimization problem will increase largely. How to obtain a global optimal solution and also reduce the computation become the major concerns. For this purpose, a global optimization method proposed by us is used. It includes an improved CCEA (Cooperative Co-Evolution Algorithm) optimizer, adaptively updated kriging surrogate model, and one-stage Expected Improvement (EI) approach that permits adaptive sampling. At initial stage, a coarse surrogate model is constructed with small number of samples. During the optimization process, some new samples are identified, evaluated, and then used to refine the model and conduct further optimal searching. In the optimization process, the accuracy of the surrogate model is improved based on its own characteristics of optimization problem and this permits the optimizer to conduct the aim-oriented optimal searches. In such a manner, the surrogate model sustains high-level of accuracy while uses fewer samples, thus the blade optimization and computations are significantly reduced.The optimization is conducted for NASA Rotor67 at design flow rate with a single workstation of DELL 7500. It is demonstrated that the optimized blade design produces significant performance gains at design condition (where the overall efficiency and pressure ratio are increased respectively by 1.27 and 6.53 points) and also at off-design conditions.Copyright

Prediction of Axial Thrust Load Acting on a Cryogenic Liquid Turbine Impeller

A single stage cryogenic liquid turbine is developed for replacing the Joule-Thompson valve and recovering energy from the liquefied air during throttling process in the large-scale internal compression air-separation unit, and evaluation of the impeller axial thrust at different conditions is essential for a reliable bearing design and stable operation. To predict the axial thrust load, a numerical model is established to simulate the turbine flow in a turbine stage environment, which includes the main flow domain (an asymmetrical volute, variable geometry nozzle, impeller, and diffuser), impeller front and back side gaps, and shaft seal leakage. Numerical simulation of flow is conducted by using the ANSYS-CFX. Flow characteristics in both main flow domain and impeller side gaps of the turbine stage are captured and analyzed. The axial thrust is then calculated based on the obtained pressure data in the impeller and its front and side gaps by using a direct integration approach. Flow behaviour in both main flow domain and impeller side gaps has been well exhibited by the numerical results. At the impeller back side gap inlet, the back flow is encountered even for design condition and it returns the impeller main flow stream; the impeller side gap flow has much influence on the axial thrust. To investigate influence of turbine operation condition on axial thrust, flow simulation is conducted at different mass flow rates and inlet pressure for the turbine stage, based on which the axial thrust is calculated. It is demonstrated from the obtained numerical results that the axial thrust increases as the inlet pressure increases and decreases as turbine flow rate increases. Geometry parametric study is conducted for the shaft seal clearances, which has demonstrated that the axial thrust is influenced largely by the clearance size and it decreases as the clearance grows. For the purpose of comparison, the empirical method is also used to predict the axial thrust load. The obtained results are compared to the numerical ones and evident deviation of the empirical from the numerical exists and the reason is that axial force components caused by the impeller main flow stream and its side gap flow are approximated very roughly in the empirical method.© 2011 ASME

Axial flow compressor blade optimization through flexible shape tuning by means of cooperative co-evolution algorithm and adaptive surrogate model

The present study is to explore potential benefits of axial flow compressor blade optimization through a flexible tuning. Modifications of blade sectional profiles and their stacking line can control spanwise blade loading distribution, reduce shock losses, and extend operating flow range. Most previous studies focused on tuning either sectional profiles or stacking line, but little work was conducted by collaboratively varying both, which may be due to abrupt rise of optimization variables and complexity. An efficient optimization method is developed to handle highly nonlinear high-dimension blade optimization problem with simultaneous variation of both sectional profiles and stacking line. It incorporates an improved cooperative co-evolution algorithm optimizer and one-stage expected improvement based adaptive surrogate model. The former decomposes the high-dimension problem into low-dimension subproblems and they can be readily solved; the latter enables the optimizer to jump out of the local minima and conduct the aim-oriented optimal search toward global optimum. A coarse surrogate model is firstly constructed with some DOE samples but it is refined during optimization process with newly identified and evaluated samples. The model prediction accuracy is gradually improved, thus it captures the distinct features (especially global optimum) of optimization problem. Both blade sectional profiles and their spatial positions are simultaneously varied. Four sectional profiles of hub, 33% span, 67% span, and shroud are parameterized, and each is defined by a mean camber line and thickness distribution. Both of them are represented, respectively, by a third-order B-Spline curve. Spatial position of each profile varies in term of sweep and lean. Blade design optimization is conducted for Rotor67 at design flow on a single workstation of Dell 7500. Performance gains are significant: at design flow, overall efficiency and pressure ratio are increased, respectively, by 1.44 and 7.24%; off-design performances are also improved over the entire flow range.

Design and Numerical Flow Analysis of a LNG Power Recovery Turbine

The liquefaction process of natural gas often operates at high pressure level, thus the LNG product is of very high pressure and must be reduced to satisfy the technical requirement for storage and transportation. Traditionally, the high-pressure LNG is expanded isenthalpically by means of J-T valves but this introduces an unexpected temperature rise, leading to vaporization of LNG product and subsequently a reduced delivery. An efficient alternative is using the LNG expanders to replace the J-T valves and achieve a near-isentropic expansion and subsequently suppress the cavitation. In the present study, a single stage LNG turbine expander is developed as a replacement of J-T valve for the purpose of cavitation suppression. The cavitating flow behavior is investigated by using a multiphase cavitation model. The effect of impeller geometric parameters on the turbine flow and performance has been identified through sensitivity studies. The following are demonstrated: (1) The predicted turbine overall efficiency is 91.34%, shaft power delivery is 81.16kW, temperature drop is 0.84 K; and the overall vaporization rate is less than a percentage. (2) Cavitation is encountered in the impeller leading edge region and half stream-wise region, resulting respectively from the viscous dissipation and flow separation. (3) At larger than design flow rates, the predicted turbine overall efficiency decreases nonlinearly with the flow rate due to cavitation zone growth in the leading edge region; at lower than design flow rates, the overall efficiency increases with the flow rate, due to cavitation zone decrease in the half streamwise region. (4) Cavitating flow behavior is sensitive to impeller geometry tuning. Variation of the impeller inducer twist angle reduces the trialing edge cavitation and subsequently improves the turbine overall performance. (5) Cavitation flow behavior is also sensitive to the radial gap size of the nozzle and impeller.Copyright

Investigation of Impeller Strength for a Cryogenic Liquid Turbine

A single stage cryogenic liquid turbine is designed for a large-scale internal compression air-separation unit to replace the Joule-Thompson valve and recover energy from the liquefied air during throttling process. It includes a 3-dimensional impeller, variable geometry nozzle, and asymmetrical volute. Strength evaluation of such a liquid turbine is both essential and complicated, which involves a proper evaluation of stress acting on the components and mechanical property of the chosen materials at low temperature. For metals under low temperatures, brittle fracture of the metal may occur prior to fatigue damage. A comprehensive consideration of low-temperature mechanical properties of materials and mechanical loads (due to hydrodynamic force and centrifugal force) acting on the components is of particular importance. Aluminum alloy 2031 is used for the turbine impeller and its mechanical properties under low temperatures are analyzed. To evaluate the stress acting on the components, numerical investigation using 3-D incompressible Navier-Stokes Equation together with k-epsilon turbulence model and mixing plane approach at rotator-stator interface are carried out at design and off-design flow with different nozzle-vane settings. The obtained pressure force is transformed into hydrodynamic load acting on the solid surface by means of fluid-solid interaction technology, and then used in the FEM (Finite Element Method) structure analysis together with the centrifugal force. Stress distribution of the component is obtained and deformation of the component analyzed. Evaluation of impeller strength is conducted for the cryogenic liquid turbine by combining the foregoing two aspects, and a use of alloy 2031 for the turbine expander is validated.Copyright

Swirling and cavitating flow suppression in a cryogenic liquid turbine expander through geometric optimization

A single-stage cryogenic liquid turbine expander is developed as a replacement of Joule–Thompson valve in the internal compression air separation unit for energy-saving purpose. Flow analysis and optimization is conducted for the turbine expander. With the original geometry, static pressure drops gradually from the nozzle to impeller together with a 2.7 K temperature drop, which exhibits simultaneously a smooth throttling characteristic and cryogenic refrigeration effect. However, similar to the conventional hydraulic turbine, a vortex-rope is apparently formed around the draft tube centerline. It leads to considerable mechanical energy dissipation and, subsequently, a local pressure drop and temperature rise, which have made the turbine expander vulnerable to cavitation. The draft tube vortex swirling flow has been found to be sensitive to exit geometric shape of rotating impeller. To suppress the swirling flow and cavitation, design optimization of impeller geometric shape is further conducted with an efficient global optimization method developed by the authors, where in particular, an innovative optimization objective function and a simultaneous tuning of both impeller meridian profile and blade shape are incorporated. The former is a linear combination of the draft tube loss factor and normalized impeller exit static pressure. It depicts the draft tube swirling flow behavior and also captures somehow the cavitation flow physics. The latter permits a very flexible variation of the impeller geometry. Such a highly nonlinear problem is solved by the global optimization algorithm, in which the Kriging surrogate model is used but updated through adaptive sampling. It is demonstrated that with the optimized geometry, the vortex-rope like characteristics has diminished apparently and both scale and intensity of swirling region are reduced significantly. As a result, the low static pressure region has shrunk and the local temperature rise is reduced and, subsequently, the cavitation is effectively suppressed.