Three-dimensional Inverse Design Research Articles

A quantitative three-dimensional inverse design rule based on cross-flow control of profiled end wall

Profiled end wall provides a novel and effective solution for end wall flow control in turbines and compressors. However, the application of profiled end walls in compressors still lacks quantitative design rules. This paper presents a quantitative design rule for end wall profiling based on a three-dimensional inverse method and numerically validates it on a highly loaded compressor cascade. The current inverse method can solve the corresponding end wall shape from a given end wall pressure distribution, but the determination of the end wall pressure distribution heavily relies on empirical knowledge. This study establishes a model between streamline curvature and cross-passage pressure gradient (CPG) through the circumferential equilibrium equation in the S1 stream surface, thereby providing a quantitative basis for determining the end wall pressure distribution. The quantitative design rule proposed in this paper is expressed as follows: at the axial position where the separation begins on the suction surface (SS), within the range of 0.1-0.2 pitch away from the SS, the end wall boundary layer fluid with a higher velocity than the corner region average velocity should possess the same streamline curvature as the fluid within the viscous sublayer. The inverse-designed profiled end wall using the quantitative design rule enhances the local cross-flow near the SS by imposing a stronger CPG, thus encouraging the end wall boundary layer fluid with relatively higher momentum to arrive at the SS earlier and enhancing the radial migration on the SS. Consequently, the intensified cross-flow entrains relatively higher momentum into the corner region, while the enhanced radial migration drives the low-momentum fluid away from the corner region towards the midspan. Finally, the inverse-designed profiled end wall reduces the half-span mass-flow-weighted average loss by 4.3%.

Design analysis and optimisation of an integrated motor pump-jet thruster with improved resistance to cavitation

ABSTRACT In order to meet the basic design requirements for high critical speed met, and anti-cavitation performance enhanced of Integrated Motor Pump-Jet (IMP) thrusters, a three-dimensional model of the IMP thruster using the blade parameter three-dimensional (3D) inverse design method was developed. The model utilises the shear stress transport (SST) turbulence model and the Zwart–Gerber–Belamri (Z-G-B) cavitation model. Then, based on the non-dominated ranking genetic algorithm and multi-objective parameter seeking theory to improve the IMP thruster's cavitation improvement optimization design. After optimisation, the hydrodynamic performance and anti-cavitation performance of the rotor blades were slightly improved. In order to further carry out the design of anti-cavitation performance, the oblique flow is introduced to further analyse according to the influence mechanism. The main focus was on the IMP thruster's excitation force, pulsation pressure and velocity distribution, the oblique flow angle had less impact than the cavitation number in the oblique flow field.

Multiobjective and multicondition optimization for a gas–liquid mixed-flow pump based on a three-dimensional inverse design

The mixed-flow pump performs well in transporting gas–liquid mixtures with large flow rates and high inlet gas volume fractions. However, its extensive development is still limited by the operating range and poor overall performance. In this study, a multiobjective and multicondition optimization methodology for improving the gas–liquid flow performance of a mixed-flow pump based on the inverse design is proposed. The impeller blade load is taken as the optimization variable. Moreover, the Euclidean distances of the pressure increment, efficiency, and gas volume fraction in the diffuser are adopted as optimization objectives. Results show that the numerical methodology is verified by the pressure increment and gas distribution obtained in the tests of the original pump. Optimized results demonstrate that the slope of the straight line, the stacking angle at the hub, and the intersection point of the rear parabola and the straight line significantly affect the objectives. The increased load of the first half of the impeller and the reduced load of the second half may improve the comprehensive performance of mixed-flow pumps. The blade length and wrap angle are reduced after optimization, which changes the inlet and outlet angles and deflection of the blade, thereby helping to enhance the cognition of mixed-flow pump performance optimization.

Parametric design and multi-objective optimization on blade high-pressure side of a pump-turbine

High pressure side, as the runner outlet at pump mode and runner inlet at turbine mode, playing an important role in controlling hydraulic loss and flow characteristics in vaneless region, affecting both steady characteristics and unsteady characteristics. While when it comes to three-dimensional inverse design of a pump-turbine blade, scholars are forces on the design method in runner flow channel, ignoring the geometry profile of high-pressure side. Hence, in present paper, concepts “swept”, “bowed (lean)” and “twisted” are innovatively introduced, eight new parameters are proposed to control the profile of blade high pressure side. And then a multi-objective optimization design system consisting of geometry generation, computational fluid dynamics, design of experiment, approximation model, multi-objective genetic algorithm, and self-organization map is built. Efficiency at both pump mode and turbine mode and S margin at turbine mode are selected as optimization objectives in the first optimization step. Then, the hump margin is regard as the objective in the second optimization step. Based on the two-step optimization, a runner with optimized high-pressure side is obtained and CFD results show that compared with the original runner, the efficiency at rated points and the margin of unsteady characteristics can be increased. The parametric design method on high-pressure side presented in our paper can be regard as an essential supplement to the traditional design method in hydraulic machinery.

Multi-objective optimization design of a centrifugal impeller considering both aerodynamic efficiency and structural machinability

PurposeThis study aims to complete the optimization design of a centrifugal impeller with both high aerodynamic efficiency and good structural machinability.Design/methodology/approachFirst, the design parameters were derived from the blade loading distribution and the meridional geometry in the impeller three-dimensional (3D) inverse design. The blade wrap angle at the middle span surface and the spanwise averaged blade angle at the blade leading edge obtained from inverse design were chosen as the machinability objectives. The aerodynamic efficiency obtained by computational fluid dynamics was selected as the aerodynamic performance objective. Then, using multi-objective optimization with the optimal Latin hypercube method, quadratic response surface methodology and the non-dominated sorting genetic algorithm, the trade-off optimum impellers with small blade wrap angles, large blade angles and high aerodynamic efficiency were obtained. Finally, computational fluid dynamics and computer-aided manufacturing were performed to verify the aerodynamic performance and structural machinability of the optimum impellers.FindingsProviding the fore maximum blade loading distribution at both the hub and shroud for the 3D inverse design helped to promote the structural machinability of the designed impeller. A straighter hub coupled with a more curved shroud also facilitated improvement of the impeller’s structural machinability. The preferred impeller was designed by providing both the fore maximum blade loading distribution at a relatively straight hub and a curved shroud for 3D inverse design.Originality/valueThe machining difficulties of the designed high-efficiency impeller can be reduced by reducing blade wrap angle and enlarging blade angle at the beginning of impeller design. It is of practical value in engineering by avoiding the follow-up failure for the machining of the designed impeller.

A Nonlinear Inverse Design Problem for a Pipe Type Heat Exchanger Equipped with Internal Z-Shape Lateral Fins and Ribs

A non-linear three-dimensional inverse shape design problem was investigated for a pipe type heat exchanger to estimate the design variables of continuous lateral ribs on internal Z-shape lateral fins for maximum thermal performance factor η. The design variables were considered as the positions, heights, and number of ribs while the physical properties of air were considered as a polynomial function of temperature; this makes the problem non-linear. The direct problem was solved using software package CFD-ACE+, and the Levenberg–Marquardt method (LMM) was utilized as the optimization tool because it has been proven to be a powerful algorithm for solving inverse problems. Z-shape lateral fins were found to be the best thermal performance among Z-shape, S-shape, and V-shape lateral fins. The objective of this study was to include continuous lateral ribs to Z-shape lateral fins to further improve η. Firstly, the numerical solutions of direct problem were solved using both polynomial and constant air properties and then compared with the corrected solutions to verify the necessity for using polynomial air properties. Then, four design cases, A, B, C and D, based on various design variables were conducted numerically, and the resultant η values were computed and compared. The results revealed that considering continuous lateral ribs on the surface of Z-shape lateral fins can indeed improve η value at the design working condition Re = 5000. η values of designs A, B and C were approximately 13% higher than that for Z-shape lateral fins, however, when the rib numbers were increased, i.e., design D, the value of η became only 11.5 % higher. This implies that more ribs will not guarantee higher η value.

Multi-Objective Optimization of a High Specific Speed Centrifugal Volute Pump Using Three-Dimensional Inverse Design Coupled With Computational Fluid Dynamics Simulations

AbstractThis paper presents three different multiobjective optimization strategies for a high specific speed centrifugal volute pump design. The objectives of the optimization consist of maximizing the efficiency and minimizing the cavitation while maintaining the Euler head. The first two optimization strategies use a three-dimensional (3D) inverse design method to parametrize the blade geometry. Both meridional shape and 3D blade geometry are changed during the optimization. In the first approach, design of experiment (DOE) method is used and the pump efficiency is obtained from computational fluid dynamics (CFD) simulations, while cavitation is evaluated by using minimum pressure on blade surface predicted by 3D inverse design method. The design matrix is then used to create a surrogate model where optimization is run to find the best tradeoff between cavitation and efficiency. This optimized geometry is manufactured and tested and is found to be 3.9% more efficient than the baseline with reduced cavitation at high flow. In the second approach, only the 3D inverse design method output is used to compute the efficiency and cavitation parameters and this leads to considerable reduction to the computational time. The resulting optimized geometry is found to be similar to the computationally more expensive solution based on 3D CFD results. In order to compare the inverse design based optimization to the conventional optimization, an equivalent optimization is carried out by parametrizing the blade angle and meridional shape.

Implementation of Three-Dimensional Inverse Design and Its Application to Improve the Compressor Performance

The implementation of a three-dimensional viscous inverse design used for an axial compressor is introduced in this paper. The derivation process of the inverse design algorithm is also described in detail. Moreover, an improved blade update method and a modified relaxation factor are included to enhance the inverse design algorithm. The inverse design is built on an in-house inverse design module coupled with commercial Computational Fluid Dynamic (CFD) software NUMECATM. In contrast to analysis design, the pressure loading and the normal thickness distribution along the blade surfaces are prescribed during the process of inverse design. The numerical methods used to solve the flow field are verified using the experimental data of the transonic fan rotor NASA Rotor 67. A recovery test for the Rotor 67 is carried out to validate the developed three-dimensional inverse design tool. To explore the potential application of the inverse design system, it is then used to improve the aerodynamic performance of a transonic fan Rotor 67 and a multi-row compressor Stage 35 at a near peak efficiency point by reorganizing the pressure loading distribution on the blade surfaces.

Suppression of secondary flows in a centrifugal impeller by optimisation design

PurposeThe purpose of this study is to suppress secondary flows and improve aerodynamic performance of a centrifugal impeller.Design/methodology/approachA multi-objective optimisation design system was described. The optimization design system was composed of a three-dimensional (3D) inverse design, multi-objective optimisation and computational fluid dynamics (CFD) analysis. First, the control parameter ΔCp for the secondary flows was derived and selected as the optimisation objective. Then, aimed at minimising ΔCp, a 3D inverse design for impellers with different blade loading distributions and blade lean angles was completed and multi-objective optimisation was conducted. Lastly, the improvement in the distribution of secondary flows and aerodynamic performance of the optimal impeller was demonstrated by CFD analysis.FindingsThe study derived the control parameter ΔCp for the secondary flows. ΔCp can indicate the distribution of secondary flows both near the blade pressure and suction surfaces. As ΔCp decreased, secondary flows decreased. The blade loading distribution with fore maximum blade loading at the shroud and aft maximum blade loading at the hub, coupled with a small negative blade lean angle, could help suppress secondary flows and improve aerodynamic efficiency.Originality/valueA direct control method on internal flow field characteristic-secondary flows by optimisation design was proposed for a centrifugal impeller. The impeller optimisation design process saves time by avoiding substantial CFD sample calculations.

Three-Dimensional Inverse Design Method for Hydraulic Machinery

Hydraulic machinery with high performance is of great significance for energy saving. Its design is a very challenging job for designers, and the inverse design method is a competitive way to do the job. The three-dimensional inverse design method and its applications to hydraulic machinery are herein reviewed. The flow is calculated based on potential flow theory, and the blade shape is calculated based on flow-tangency condition according to the calculated flow velocity. We also explain flow control theory by suppression of secondary flow and cavitation based on careful tailoring of the blade loading distribution and stacking condition in the inverse design of hydraulic machinery. Suggestions about the main challenge and future prospective of the inverse design method are given.

Effect of lean mode of blade trailing edge on hydraulic performance for double-suction centrifugal pump

For three-dimensional inverse design of water pump, both blade-loading distribution and stacking condition of high-pressure side are important factors affecting the quality of design. For example, inclined trailing edge of blade can suppress the pressure fluctuation and reduce the sound pressure level and sound power of noise for single-suction centrifugal pump. And the lean mode of blade trailing edge can influence hydraulic performance of pump-turbine in pump mode. However, there is no clear view on the effect of lean mode of blade trailing edge on hydraulic performance for double-suction centrifugal pump. Therefore, three different linear lean modes, namely positive lean(+20°), zero lean(0°) and negative lean(-20°), are adopted to simulate the transient flow field respectively for a middle specific speed double-suction centrifugal pump. Concretely, results show that different lean modes of blade trailing edge have little effect on the external characteristics of the pump, and all three schemes can meet the requirements of basic performance. And in operating range of 0.6Q0∼1.2Q0, positive blade lean can suppress the jet-wake structure better. In the vicinity of rated condition, both positive blade lean and negative blade lean can suppress the pressure fluctuation to a certain degree. But with the changes of flow rate, the effect of positive blade lean on pressure fluctuation is unstable. In addition, when pumping sediment-laden water, both positive blade lean and zero blade lean are not conducive to improving the anti-erosion performance of the blade, and especially for the positive blade lean. In summary, in order to improve the integrated performance of low and middle specific speed double-suction centrifugal pump, under the condition of guaranteeing good blade-loading distributions firstly, negative lean mode of blade trailing edge is suggested.

An experience-independent inverse design optimization method of compressor cascade airfoil

Most of the inverse design methods of turbomachinery experience the shortcoming where the target aerodynamic parameters need to be manually specified depending on the designers’ experience and insight, making the design result aleatory and even deviated from the real optimal solution. To tackle this problem, an experience-independent inverse design optimization method is proposed and applied to the redesign of a compressor cascade airfoil in this study. The experience-independent inverse design optimization method can automatically obtain the target pressure distribution along the cascade airfoil through the genetic algorithm, rather than through the manual specification approach. The shape of cascade airfoil is then solved by the adjoint method. The effectiveness of the experience-independent inverse design optimization method is demonstrated by two inverse design cases of the compressor cascade airfoil, i.e. the inverse design of only the suction surface and the inverse design of both the suction and pressure surfaces. The results show that the proposed inverse design method is capable of significantly improving the aerodynamic performance of the compressor cascade. At the examined flow condition, a thin airfoil profile is beneficial to flow accelerations near the leading edge and flow separation avoidance near the trailing edge. The proposed inverse design method is quite generic and can be extended to the three-dimensional inverse design of advanced compressor blades.

Three-Dimensional Inverse Design of Low Specific Speed Turbine for Energy Recovery in Cooling Tower System

A three-dimensional inverse design of a low specific speed turbine is studied, and a set of design criteria for low specific speed turbine runner is proposed, including blade loading distributions and blade lean angles. The characteristics of the loading parameters for low specific speed turbine runner are summarized by analyzing the suction performance of different loading positions, loading slopes and blade lean angles based on the orthogonal experiment design and range analysis. It is found that the blade loading distribution at the band plays a more important role than it does at the crown and it should be fore loaded for both band and crown. The blade lean angle at the blade leading edge should be negative. Then, the blade is optimized through the inverse method by fixing blade lean angle, based on the response surface method. After seeking the optimal value of the response surface function, the optimal result of the design parameters is obtained, which is in conformity with the design criteria and verifies the rationality of the established design criteria for low specific speed turbine.

The Influence of Blade Tip Loading Distribution on the Performance of a High Loading Centrifugal Impeller

It has been proved that different blade loading distributions between tip and hub has a significant effect on centrifugal impeller performance, but the effect of loading difference at different location along the stream has not been fully understood. In this paper, several blades were modelled by a three-dimensional inverse design method, in which the impellers are defined by the blade loading distribution at its tip and hub and the flows are computed numerically by a commercial CFD code. Firstly, two impellers were modelled using the same distribution at the hub but giving different distributions at tip. The results show that the impeller with a smoother tip loading distribution performs better. At design flow rate, the total pressure ratio is found to be 1.8% higher and the efficiency rises 1.36% as well. Then a further research about the effect of increasing tip load at different parts along the flow path was carried out. Further analysis indicates that adding the load at the fore part of tip could increase the efficiency at design flow rate and brings more uniform impeller exit flow. However, the surge margin was narrowed by such change. Besides, adding the vur at the aft part of tip will promote the pressure ratio, with no adverse effect on the stable operation range.

Optimization of a Centrifugal Impeller with the Constraint on Efficiency at the Stall Point

An optimization strategy is presented concerning the aerodynamic performance of an impeller at the design point with a constraint of efficiency at the stall point, on the basis of the combination of three-dimensional inverse design method and the response surface methodology (RSM). A specific inlet angular momentum is given in the prescribed blade loading to facilitate the change of the blade inlet angle at either the hub or shroud of the impeller. Three variables, the inlet angular momentums at both the hub and shroud as well as a coefficient relation with blade loading, were chosen as the optimization variables after a sensitivity analysis, which is conducted by means of the orthogonal design experiment. The candidate impellers were generated by different angular momentum distributions determined by the Box-Behnken design, and the performances of corresponding compressors were simulated. The response surface models of the performances of the compressors were obtained at the design and stall points. Thus the optimal impeller was obtained and the compressor’s performance at the design flow rate could be predicted under the constraint of a specified efficiency at the stall flow rate. A comparison between the computational results of the original and optimized impeller indicates that a considerable improvement of the efficiency of the compressor over the whole working range is obtained, which confirms the validity of the optimization strategy.

Redesign of a Compressor Stage for a High-Performance Electric Supercharger in a Heavily Downsized Engine

Engine downsizing is a modern solution for the reduction of CO2 emissions from internal combustion engines. This technology has been gaining increasing attention from industry. In order to enable a downsized engine to operate properly at low speed conditions, it is essential to have a compressor stage with very good surge margin. The ported shroud, also known as the casing treatment, is a conventional way used in turbochargers to widen the working range. However, the ported shroud works effectively only at pressure ratios higher than 3:1. At lower pressure ratio, its advantages for surge margin enhancements are very limited. The variable inlet guide vanes are also a solution to this problem. By adjusting the setting angles of variable inlet guide vanes, it is possible to shift the compressor map toward the smaller flow rates. However, this would also undermine the stage efficiency, require extra space for installing the inlet guide vanes, and add costs. The best solution is therefore to improve the design of impeller blade itself to attain high aerodynamic performances and wide operating ranges. This paper reports a recent study of using inverse design method for the redesign of a centrifugal compressor stage used in an electric supercharger, including the impeller blade and volute. The main requirements were to substantially increase the stable operating range of the compressor in order to meet the demands of the downsized engine. The three-dimensional (3D) inverse design method was used to optimize the impeller geometry and achieve higher efficiency and stable operating range. The predicted performance map shows great advantages when compared with the existing design. To validate the computational fluid dynamics (CFD) results, this new compressor stage has also been prototyped and tested. It will be shown that the CFD predictions have very good agreement with experiments and the redesigned compressor stage has improved the pressure ratio, aerodynamic efficiency, choke, and surge margins considerably.

An inverse study to design the optimal shape and position for delta winglet vortex generators of pin-fin heat sinks

A three-dimensional inverse design problem is examined in this study using a general purpose commercial code CFD-ACE+ and the Levenberg-Marquardt Method (LMM) to estimate the optimal position and shape for delta winglet vortex generators of pin-fin heat sinks for best cooling performance. The algorithm is based on the minimization of the average temperature on the base plate of heat sinks and then try to obtain the optimal design variables for vortex generators of pin-fin heat sinks. The delta winglet vortex generators are utilized on a pin-fin heat sink to estimate the optimal design when the inlet velocities of air al to Re = 10,000, 15,000 and 20,000, respectively. Finally, the heat sink and vortex generator modules are carried on the experimental verification. The results indicate that with the designed optimal vortex generators the cooling performance is indeed better than that with the original design vortex generators and the temperature distributions on the base plate are very similar between the experimental and numerical data.

Three-dimensional inverse design of nanopatterns with block copolymers and homopolymers.

We propose a facile inverse design strategy to generate three-dimensional (3D) nanopatterns by using either block copolymers or a binary homopolymer blend via dissipative particle dynamics simulations. We find that the composition window of block copolymers to form a specific 3D morphology can be expanded when the self-assembly of block copolymers is directed by templates. We also find that a binary homopolymer blend can serve as a better candidate in the inverse templating design, since they have similar performances on recovering the target pattern, with much lower cost. This strategy is proved efficient for fabricating templates with desired topographical configuration, and the inverse design idea sheds lights on better control and design of materials with complex nanopatterns.

Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm

In order to maintain a uniform distribution of pareto-front solutions, a modified NSGA-II algorithm coupled with a dynamic crowding distance (DCD) method is proposed for the multi-objective optimization of a mixed-flow pump impeller. With the pump meridional section fixed, ten variables along the shroud and hub are selected to control the blade load by using a three-dimensional inverse design method. Hydraulic efficiency, along with impeller head, is applied as an optimization objective; and a radial basis neural network (RBNN) is adopted to approximate the objective function with 82 training samples. Local sensitivity analysis shows that decision variables have different impacts on the optimization objectives. Instead of randomly selecting one solution to implement, a technique for ordering preferences by similarity to ideal solution (TOPSIS) is introduced to select the best compromise solution (BCS) from pareto-front sets. The proposed method is applied to optimize the baseline model, i.e. a mixed- flow waterjet pump whose specific speed is 508 min-1·m3s-1·m. The performance of the waterjet pump was experimentally tested. Compared with the baseline model, the optimized impeller has a better hydraulic efficiency of 92% as well as a higher impeller head at the design operation point. Furthermore, the off-design performance is improved with a wider high- efficiency operation range. After optimization, velocity gradients on the suction surface are smoother and flow separations are eliminated at the blade inlet part. Thus, the authors believe the proposed method is helpful for optimizing the mixed-flow pumps.

The design of optimum perforation diameters for pin fin array for heat transfer enhancement

A three-dimensional inverse design problem is examined in this work using a general purpose commercial code CFD-ACE+ and the Levenberg–Marquardt Method (LMM) to estimate the optimal perforation diameters of perforated pin fin array based on the desired temperature difference between base plate averaged temperature and ambient temperature (ΔT) and system pressure drop (ΔP). The analysis consists of three cases. In design #1, five design variables are used to estimate the optimal perforation diameters and the objective is to minimize ΔT and ΔP of the pin fin array. In design #2, four design variables are considered to determine the optimal perforation diameters based on the minimization of ΔT and ΔP. In design #3, all the perforation diameters are assumed identical and use only one parameter to determine the optimal perforation diameter based on the minimization of ΔT and ΔP. The numerical design results show that, for all six designs considered here, the designed optimum heat sinks always have the lowest average base plate temperature, it can decrease from 6.3% to 7.3% when compared with the solid pin fin array. Finally, experimental verifications are performed on these heat sink modules and the results indicate that there are good agreements between the experimental and numerical temperature distributions on those heat sinks.