A Method for Transonic Inverse Cascade Design With a Stream Function Equation

1986 ◽  
Vol 108 (2) ◽  
pp. 200-205 ◽  
Author(s):  
Manchu Ge ◽  
Yiping Lou ◽  
Zhengti Yu
Keyword(s):  
Velocity Distribution ◽  
Stream Function ◽  
Transonic Flow ◽  
Inverse Method ◽  
Design Method ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Suction Surface ◽  
Stream Surface ◽  
Optimal Velocity

A new profile design method is developed on the basis of [1–3] for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form using calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with a local shock wave on the blade suction surface. This method consists of two parts: an inverse method with a given velocity distribution along the suction surface and a given thickness distribution; and an inverse method with given velocity distributions on suction and pressure surfaces. Using this method it is easy to obtain a blade profile with prescribed velocity and thickness distributions. The design of optimal profile may then be done with the calculated optimal velocity distribution on the blade surface. The rotational condition is satisfied when the stream function equation is adopted with the entropy term. If the compatibility condition can be fulfilled between the S1 and S2 equations, the iterative calculations of two kinds of stream surfaces in three-dimensional flow will be convergent. In this paper a unique value of density can be determined from the known stream function value. The computational program is written with this method and several transonic examples have been calculated. These results are quite good.

A Method for Transonic Inverse Cascade Design With a Stream Function Equation

1986 ◽  
Author(s):  
Ge Manchu ◽  
Lou Yiping ◽  
Yu Zhengti
Keyword(s):  
Velocity Distribution ◽  
Stream Function ◽  
Transonic Flow ◽  
Inverse Method ◽  
Design Method ◽  
Thickness Distribution ◽  
Suction Surface ◽  
Stream Surface ◽  
Optimal Velocity ◽  
Entropy Term

A new profile design method is developed on the basis of Refs.1–3 for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form of calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with local shock wave on the blade suction surface. This method consists of two parts. One is a inverse method with a given velocity distribution along the suction surface and a given thickness distribution. Another is a inverse method with given velocity distributions on suction and pressure surfaces. Using this method it is easy to get the blade profile with prescribed velocity and thickness distributions. The design of optimal profile may then be done with the calculated optimal velocity distribution on the blade surface. The rotational condition is satisfied when the stream function equation is adopted with the entropy term. If the compatibility condition can be fulfilled between the S1 and S2 equations. The iterative calculations of two kinds of stream surfaces of 3-D flow will be convergent. In this paper a unique value of density can be determined from the known stream function value. The computational programme is written with this method and several transonic examples have been calculated. These results are quite good.

scholarly journals An improved inverse method for multirow blades of turbomachinery

2020 ◽  
Vol 234 (22) ◽  
pp. 4433-4443
Author(s):  
Li Aiting ◽  
Zhu Yangli ◽  
Li Wen ◽  
Wang Xing ◽  
Qin Wei ◽  
...  
Keyword(s):  
Flow Structure ◽  
Inverse Method ◽  
Design Method ◽  
Spline Interpolation ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Internal Flow ◽  
Navier Stokes ◽  
Virtual Displacement ◽  
Blade Thickness

A three-dimensional viscous inverse design method is improved and extended to multirow blades environment. The inverse method takes load distribution as optimization objective and is implemented into the time-marching finite-volume Reynolds-averaged Navier–Stokes solver. The camber line of rotor blade is updated by virtual displacement, which is calculated by characteristic compatibility relations according to the difference between target and actual load so as to control the location and intensity of shock wave, and realize the optimization of flow structure and reduction flow separation. The inlet and outlet geometry angles of stator blade are adjusted in real time according to the inlet and outlet flow angles. Thus, it is computationally ensured that the blade row interactions are accounted and optimization process is carried out under the design condition. To preserve the robustness of calculation, the maximum virtual displacement is limited by Y+ <10 and the camber line is smoothed via cubic B-spline interpolation. The complete blade profile is then generated by adding the prescribed blade thickness distribution to the camber line. The effectiveness of the method is demonstrated in the optimization of Stage35 compressor stage. Numerical results showed that this inverse method can effectively improve the internal flow structure and optimize the matching between blade rows, and this method is robust, efficient, and flexible.

Development and Industrial Application of the “All-Over-Controlled Vortex Distribution Method” for Designing Radial and Mixed Flow Impellers

1992 ◽  
Author(s):  
S. J. Wang ◽  
M. J. Yuan ◽  
G. Xi ◽  
S. X. Liu ◽  
D. T. Qi ◽  
...  
Keyword(s):  
Flow Field ◽  
Centrifugal Compressor ◽  
Inverse Method ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Mixed Flow ◽  
Distribution Method ◽  
Stream Surface ◽  
Surface Theory ◽  
Performance Curves

Sixteen years ago an inverse method of designing radial, mixed flow impellers was proposed by the first author of this paper, which was based on a quasi-three-dimensional stream surface theory. The contradictions between the full controlling of the flow field in the whole impeller and the designed bables’ smooth machinability can be perfectly resolved with the above method (So it is called “all-over-controlled vortex distribution method”). This paper presents the developments and industrial applications of the above method in the last decade. Two single centrifugal compressor model stages with the 3-D impellers designed by this method are studied in detail, and several performance curves of the multistage centrifugal compressors designed by this method are also presented.

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

2019 ◽  
Vol 233 (4) ◽  
pp. 431-442 ◽  
Author(s):  
Yujie Zhu ◽  
Yaping Ju ◽  
Chuhua Zhang
Keyword(s):  
Design Optimization ◽  
Design Method ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Leading Edge ◽  
Optimization Method ◽  
Inverse Design ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Inverse Design Method

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.

Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD

2002 ◽  
Vol 124 (2) ◽  
pp. 319-328 ◽  
Author(s):  
Akira Goto ◽  
Mehrdad Zangeneh
Keyword(s):  
Design Method ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Inverse Design ◽  
Navier Stokes ◽  
Outer Diameter ◽  
Large Area ◽  
Suction Surface ◽  
Pump Stage ◽  
Inverse Design Method

A new approach to optimizing a pump diffuser is presented, based on a three-dimensional inverse design method and a Computational Fluid Dynamics (CFD) technique. The blade shape of the diffuser was designed for a specified distribution of circulation and a given meridional geometry at a low specific speed of 0.109 (non-dimensional) or 280 (m3/min, m, rpm). To optimize the three-dimensional pressure fields and the secondary flow behavior inside the flow passage, the diffuser blade was more fore-loaded at the hub side as compared with the casing side. Numerical calculations, using a stage version of Dawes three-dimensional Navier-Stokes code, showed that such a loading distribution can suppress flow separation at the corner region between the hub and the blade suction surface, which was commonly observed with conventional designs having a compact bowl size (small outer diameter). The improvements in stage efficiency were confirmed experimentally over the corresponding conventional pump stage. The application of multi-color oil-film flow visualization confirmed that the large area of the corner separation was completely eliminated in the inverse design diffuser.

Dual Point Redesign of Axial Turbines Using a Viscous Inverse Design Method

2009 ◽  
Author(s):  
Benedikt Roidl ◽  
Wahid Ghaly
Keyword(s):  
Inverse Method ◽  
Stokes Equations ◽  
Design Method ◽  
Single Point ◽  
Accurate Solution ◽  
Inverse Design ◽  
Suction Surface ◽  
Pressure Distributions ◽  
Wide Range ◽  
Inverse Design Method

A new dual-point inverse blade design method was developed and applied to the redesign of a highly loaded transonic vane, the VKI-LS89, and the first 2.5 stages of a low speed subsonic turbine, the E/TU-4 4-stage turbine that is built and tested at the university of Hannover, Germany. In this inverse method, the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces at both operating points. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and rotor regions. The dual-point inverse design method is then used to explore the effect of different choices of the pressure distributions on the suction surface of one or more rotor/stator on the blade/stage performance. The results show that single point inverse design resulted in a local performance improvement whereas the dual point design method allowed for improving the performance of both VKI-LS89 vane and E/TU-4 2.5 stage turbines over a wide range of operation.

Design Method for Turbomachine Blades With Finite Thickness by the Circulation Method

1997 ◽  
Vol 119 (3) ◽  
pp. 539-543 ◽  
Author(s):  
J. Jiang ◽  
T. Dang
Keyword(s):  
Inverse Method ◽  
Design Method ◽  
Guide Vane ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Inlet Guide Vane ◽  
Impulse Turbine ◽  
Blade Thickness ◽  
Flow Limit ◽  
Design Calculations

This paper presents a procedure to extend a recently developed three-dimensional inverse method for infinitely thin blades to handle blades with finite thickness. In this inverse method, the prescribed quantities are the blade pressure loading and the blade thickness distributions, and the calculated quantity is the blade mean camber line. The method is formulated in the fully inverse mode whereby the blade shape is determined iteratively using the flow-tangency condition along the blade surfaces. Design calculations are presented for an inlet guide vane, an impulse turbine blade, and a compressor blade in the two-dimensional inviscid- and incompressible-flow limit. Consistency checks are carried out for these design calculations using a panel analysis method and the analytical solution for the Gostelow profile.

scholarly journals Design Method for Turbomachine Blades With Finite Thickness by the Circulation Method

1994 ◽  
Author(s):  
Jun Jiang ◽  
Thong Dang
Keyword(s):  
Inverse Method ◽  
Incompressible Flows ◽  
Design Method ◽  
Guide Vane ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Inlet Guide Vane ◽  
Impulse Turbine ◽  
Blade Thickness ◽  
Design Calculations

This paper presents a procedure to extend a well-developed fully three-dimensional inverse method for infinitely-thin blades to handle blades with finite thickness. In this inverse method, the prescribed quantities are the blade pressure loading and the blade thickness distributions, and the calculated quantity is the blade geometry. The method is formulated in the fully inverse mode whereby the blade shape is determined iteratively using the flow-tangency condition along the blade surfaces. This technique is demonstrated here in the first instance for the design of cascaded blades in inviscid and incompressible flows. Design calculations are presented for an inlet guide vane, an impulse turbine blade, and a compressor blade. Consistency checks are carried out for these design calculations using a panel analysis method and the analytical solution for the Gostelow profile.

Improving Aerodynamic Matching of Axial Compressor Blading Using a Three-Dimensional Multistage Inverse Design Method

2005 ◽  
Vol 129 (1) ◽  
pp. 108-118 ◽  
Author(s):  
M. P. C. van Rooij ◽  
T. Q. Dang ◽  
L. M. Larosiliere
Keyword(s):  
Inverse Method ◽  
Design Method ◽  
Three Dimensional ◽  
Computational Time ◽  
Design Calculation ◽  
Pressure Loading ◽  
Design Intent ◽  
Design Point ◽  
Analysis And Design ◽  
Blade Row

Current turbomachinery design systems increasingly rely on multistage CFD as a means to diagnose designs and assess performance potential. However, design weaknesses attributed to improper stage matching are addressed using often ineffective strategies involving a costly iterative loop between blading modification, revision of design intent, and further evaluation of aerodynamic performance. A scheme is proposed herein which greatly simplifies the design point blade row matching process. It is based on a three-dimensional viscous inverse method that has been extended to allow blading analysis and design in a multi-blade row environment. For computational expediency, blade row coupling is achieved through an averaging-plane approximation. To limit computational time, the inverse method was parallelized. The proposed method allows improvement of design point blade row matching by direct regulation of the circulation capacity of the blading within a multistage environment. During the design calculation, blade shapes are adjusted to account for inflow and outflow conditions while producing a prescribed pressure loading. Thus, it is computationally ensured that the intended pressure-loading distribution is consistent with the derived blading geometry operating in a multiblade row environment that accounts for certain blade row interactions. The viability of the method is demonstrated in design exercises involving the rotors of a 2.5 stage, highly loaded compressor. Individually redesigned rotors display mismatching when run in the 2.5 stage, evident as a deviation from design intent. However, simultaneous redesign of the rotors in their multistage environment produces the design intent, indicating that aerodynamic matching has been achieved.

Optimization of Microturbine Aerodynamics Using CFD, Inverse Design and FEM Structural Analysis: 2nd Report — Turbine Design

2004 ◽  
Author(s):  
Hiroyoshi Watanabe ◽  
Hidenobu Okamoto ◽  
Shijie Guo ◽  
Akira Goto ◽  
Mehrdad Zangeneh
Keyword(s):  
Structural Reliability ◽  
Design Method ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Inverse Design ◽  
Blade Profile ◽  
Performance Improvements ◽  
Radial Turbine ◽  
Blade Thickness ◽  
Inverse Design Method

In this second report, a new aerodynamic design is presented for a radial turbine stage of a microturbine engine. To optimize three-dimensional (3-D) flows, an inverse design method, in which 3-D blade geometry is numerically obtained for specified blade loading distribution, has been applied together with numerical assessment using CFD (Computational Fluid Dynamics) and FEM (Finite Element Method). The runner blade profile along the hub surface was modified to attain nearly radially arranged blade elements especially at the exducer part of the radial turbine in order to achieve required structural strength. Also the blade thickness distribution was optimized to avoid vibration resonance and to meet creep strength requirements. The blade profile along the shroud surface was optimized via 3-D inverse design and CFD. CFD predicted aerodynamic performance of the modified turbine runner was confirmed to be similar to that of the fully 3-D blade shape, while maintaining structural reliability. The turbine nozzle also has been re-designed by using the inverse design method, with stage performance improvements confirmed by stage calculations using CFD.

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