Multi-point Optimization Method Research Articles

Multipoint Design Optimization of a Radial-Outflow Turbine for Kalina Cycle System Considering Flexible Operating Conditions and Variable Ammonia-Water Mass Fraction

The radial-outflow turbine has advantages due to its liquid-rich gas adaptability when applied in the Kalina ammonia-water cycle system. However, the operational conditions of the turbine often deviate from its design values due to changes of the heat source or the cooling conditions, and such deviates may deteriorate the flow behavior and degrade the turbine performance. To enhance the turbine efficiency at complex conditions for flexible running of the Kalina cycle system, a multipoint design optimization method is developed: the flexible operating has been defined by three critical, dimensionless parameters, which cover a wide range in a 3D operating space; the representative off-design points are identified to define the objective function; and adaptive optimization methods are integrated to permit optimization searching using limited CFD callings. The developed multipoint design method is adopted to improve the turbine performance under complex operating conditions. The obtained results demonstrate that the application of the developed multipoint optimization method effectively eliminates the flow separation at various operating conditions; thus, the turbine off-design performance has been comprehensively improved.

Effective strategy of non-axisymmetric endwall contouring in a linear compressor cascade

The corner separation and the related secondary flow have great impact on the compressor performance, and non-axisymmetric endwall contouring is proved effective in improving compressor efficiency. The aim of the study is to improve the compressor performance by two local endwall contouring strategies at the design and off-design conditions. The endwall is parameterized and the Bezier curve is used to loft the endwall surface. The design of the contoured endwall is based on a multi-point optimization method to minimize the aerodynamic pressure loss. In order to identify the influence of the contoured endwall, a detailed flow analysis is conducted on four effective contoured endwall designs. The selected endwall geometries exhibit great control ability on the corner separation and significantly reduce the pressure loss at the two operating conditions. The directional concave near the leading edge can induce strong streamwise pressure gradient and accelerate the endwall flow, greatly reducing the cross-passage pressure gradient. The convex structures near the concave edge and at the outlet can block the cross-flow and prevent the interaction between the cross-flow and the suction corner flow. The benefit of the contoured endwall is mainly due to the re-distributed endwall static pressure and blocking of the cross-flow movement. In terms of the control effect, the shape of the concave also matters and better control effect is observed on the deep and wide concave. The flow will be guided by the concave, and the best suppression on corner separation is observed on the concave which follows the suction side. The results also indicate that the relief of the hub corner separation slightly increases the shroud pressure loss.

Aerodynamic design of a multi-stage industrial axial compressor

Axial compressors are widely used in industrial applications; high efficiencies and large operating ranges are main performance requirements for their aerodynamic designs. In this study, an aerodynamic design method for multi-stage axial compressors is proposed. The design of the first stage is based on the S1/S2 stream surface theory, and a repeated stage design method is proposed for subsequent stage designs. And in the first stage design, a multi-point optimization design is used to design the rotor and stator blade profiles for both high efficiencies and large operating ranges. A five repeated stage axial compressor with a large mass flow rate has been designed by this design method. Analysis results of the rotor and stator three-dimensional flow fields indicate that the flow is primarily limited to the S1 stream surface and the two-dimensional design method is applicable; the flow in subsequent stages possesses similar characteristics as the flow in first stage. In addition, the designed five-stage axial compressor has a total pressure ratio that approaches the design goal and a stability margin that exceeds the design goal. The novelty of this study includes two parts, one is the usage of multi-point optimization method for rotor and stator blade design, and the other is the repeated stage design method.

Performance Improvement of a Supercritical Airfoil by a Multi-point Optimized Shock Control Channel

A shock control channel (SCC) is a flow control method introduced here to control the shock wave/boundarylayer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. An SCC transfers an appropriate amount of mass and momentum from downstream of the shock wave location to its upstream to decrease the pressure gradient across the shock wave and as a result the shock-wave strength is reduced. Here, a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of the SCC. This flow control method is implemented on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of the SCC. The solver is validated against experimental works studying effect of cavities in transonic airfoils. It is shown that the application of an SCC improves the average aerodynamic efficiency in a range of off-design conditions by 13.2% in comparison with the original airfoil. The SCC is shown to be an effective tool also for higher angle of attack at transonic flows. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.

Multi-point Optimization of Lean and Sweep Angles for Stator and Rotor Blades of an Axial Turbine

In this research, numerical optimization of the rear part of a gas turbine, consisting of a single-stage axial turbine, is carried out. Automated aerodynamic shape optimization is performed by coupling a CFD flow simulation code with the genetic algorithm. An effective multi-point optimization method to improve efficiency and/or pressure ratio of the axial turbine is performed. Some variations of optimization parameters such as lean and sweep angels of stator and rotor blades are accomplished. Furthermore, during the optimization process, three-dimensional and turbulent flow field is numerically investigated using a compressible Navier–Stokes solver. The gas turbine experimental investigations are used for choosing optimization points, specifying the boundary conditions and validation of the simulations. Two operating speeds of the gas turbine are selected for the optimization. Using verified numerical simulation models and the genetic algorithm, the effects of stator and rotor lean and sweep angles on the turbine performance are studied. The present optimization method successfully obtains a result that improves 1.31 and 1.17 % in the turbine stage total-to-total efficiency in its design and off-design speeds, respectively. The modified turbine mass parameter at choke condition increases 2.40 %.

Application of the adjoint multi-point and the robust optimization of shock control bump for transonic aerofoils and wings

A shock control bump (SCB) is a flow control method which uses a local small deformation in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, both equally and variably weighted multi-point optimization and a robust adjoint optimization scheme are used to optimize the SCB. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for two benchmark aerofoils. A multi-point optimization method under a constant-lift-coefficient constraint is implemented to find the optimum design of a two-dimensional (2D) SCB and it is observed that the general results are similar to other optimization algorithms. To show that these results are extendable to real three-dimensional (3D) cases, a 3D bump model with 11 parameters is introduced, and it is optimized using both single- and multi-point optimization procedures. Although the 3D flow structure involves much more complexity, the overall results are shown to be similar to the 2D case.

The Multi-point Optimization of Shock Control Bump with Constant-Lift Constraint Enhanced with Suction and Blowing for a Supercritical Airfoil

Both shock control bump (SCB) and suction and blowing are flow control methods used to control the shock wave/boundary layer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. A SCB uses a small local surface deformation to reduce the shock-wave strength, while suction decreases the boundary-layer thickness and blowing delays the flow separation. Here a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of SCB and suction and blowing. These flow control methods are used separately or together on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of all devices. It is shown that the simultaneous application of blowing and SCB (hybrid blowing/SCB) improves the average aerodynamic efficiency at off-design conditions by 18.2 % in comparison with the clean airfoil, while this increase is only 16.9 % for the hybrid suction/SCB. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.

Multi-point design optimization of hydrofoil for marine current turbine

The comprehensive performance of the marine current turbine is an important issue in the ocean energy development. Its key is the performance of the hydrofoil, which is used to form the turbine blade. A multi-point optimization method of the hydrofoil is proposed in this paper. In this method, the Bezier curve is used to parameterize the hydrofoil. The geometrical parameters are used as variables while the lift-drag ratio and the cavitation performance of the hydrofoil are used as the objective functions. The NSGA-II algorithm is chosen as the optimization algorithm. In order to resolve the difficulty of this high-dimensional multi-objective optimi- zation problem, the conception of the distance metric in the metric space is introduced to unify the lift-drag ratio and the cavitation performance under different working conditions. And then, the above optimization method is applied in the NACA63-815 hydro- foil's optimal design under three typical conditions. Finally, the results from the performance comparison of the original and optimi- zed hydrofoils obtained by using the CFD simulation are analyzed in detail. It is indicated that the optimized hydrofoils enjoy a better hydrodynamic performance than the original ones under the three conditions. The feasibility and the theoretical validity of this optimization method are confirmed by the results.

Modelling phase transition kinetics of chenodeoxycholic acid with the Runge–Kutta method

The phase transition kinetics of two chenodeoxycholic acid polymorphic modifications— form I (stable at high temperature), form III (stable at low temperature) and the amorphous phase has been examined under various conditions of temperature and relative humidity. Form III conversion to form I was examined at high temperature conditions and was found to be non-spontaneous, requiring seed crystals for initiation. The formation kinetic model of form I was created incorporating the three-dimensional seed crystal growth, the phase transition rate proportion to the surface area of form I crystals, and the influence of the amorphous phase surface area changes with an empirical stage pointer q that contained the incomplete transition of the amorphous phase to form I with a residue ω A ∞ . The extent of transition and the phase transition rate constant depended on form I seed crystal amount in the raw mixture, and on the sample preparation. To describe phase transition kinetic curves, we employed the Runge–Kutta differential equation numeric solving method. By combining the Runge–Kutta method with the multi-point optimization method, the average quadratic deviation of the experimental results from one calculated series was under 2%.

Robust airfoil optimization to achieve drag reduction over a range of Mach numbers

An airfoil shape optimization method that reduces drag over a range of free stream Mach numbers is sought. We show that one acceptable choice is a weighted multipoint optimization method using more design points than there are free-design variables. Alternate methods that use far fewer design points are explored. A new method called profile optimization is developed and analyzed. This method has three main advantages: (a) it prevents severe degradation at the off-design points by using a smart descent direction, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it is not sensitive to the number of design points. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.