A Fully Three-Dimensional Inverse Method for Turbomachinery Blading in Transonic Flows

1993 ◽  
Vol 115 (2) ◽  
pp. 354-361 ◽  
Author(s):  
T. Q. Dang
Keyword(s):  
High Pressure ◽  
Boundary Conditions ◽  
Centrifugal Compressor ◽  
Transonic Flow ◽  
Inverse Method ◽  
Three Dimensional ◽  
Blade Profile ◽  
Transonic Flows ◽  
Blade Passage ◽  
Highly Loaded

This paper presents a procedure to extend a recently developed fully three-dimensional inverse method for highly loaded turbomachine blades into the transonic-flow regime. In this inverse method, the required three-dimensional blade profile to produce a prescribed swirl schedule is determined iteratively using the blade boundary conditions. In the present implementation, the flow is assumed to be inviscid and the blades are assumed to be infinitely thin. The relevant equations are solved in the conservative forms and are discretized in all three directions using a finite-volume technique. Calculations are carried out for the design of high-pressure axial- and centrifugal-compressor rotors. These examples include prescribed swirl schedules corresponding to blade designs that are shock-free and blade designs that have rapid compression regions in the blade passage.

scholarly journals A Fully Three-Dimensional Inverse Method for Turbomachinery Blading in Transonic Flows

1992 ◽  
Author(s):  
T. Q. Dang
Keyword(s):  
High Pressure ◽  
Centrifugal Compressor ◽  
Transonic Flow ◽  
Inverse Method ◽  
Three Dimensional ◽  
Blade Design ◽  
Blade Profile ◽  
Transonic Flows ◽  
Blade Passage ◽  
Highly Loaded

This paper presents a procedure to extend a recently developed fully three-dimensional inverse method for highly-loaded turbomachine blades into the transonic-flow regime. In this inverse method, the required three-dimensional blade profile to produce a prescribed swirl schedule is determined iteratively using the blade boundary conditions. In the present implementation, the flow is assumed to be inviscid and the blades are assumed to be infinitely thin. The relevant equations are solved in the conservative forms and are discretized in all three directions using a finite-volume technique. Calculations are carried out for the design of high-pressure axial- and centrifugal-compressor rotors. These examples include prescribed swirl schedules that correspond to blade design that are shock-free and blade design that have rapid compression regions in the blade passage.

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.

Application of a Three-Dimensional Inverse Method to the Design of a Centrifugal Compressor Impeller

1998 ◽  
Author(s):  
Alain Demeulenaere ◽  
Olivier Léonard ◽  
René Van den Braembussche
Keyword(s):  
Centrifugal Compressor ◽  
Inverse Method ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Mean Velocity ◽  
Blade Shape ◽  
Compressor Impeller ◽  
Real Performance ◽  
The Mean

The use of a three-dimensional Euler inverse method for the design of a centrifugal impeller is demonstrated. Both the blade shape and the endwalls are iteratively designed. The meridional contour is modified in order to control the mean velocity level in the blade channel, while the blade shape is designed to achieve a prescribed loading distribution between the inlet and the outlet. The method salves the time dependent Euler equations in a numerical domain of which some boundaries (the blades or the endwalls) move and change shape during the transient part of the computation, until a prescribed pressure distribution is achieved on the blade surfaces. The method is applied to the design of a centrifugal compressor impeller, whose hub endwall and blade surfaces are modified by the inviscid inverse method. The real performance of both initial and modified geometries are compared through three-dimensional Navier-Stokes computations.

scholarly journals Semi-Inverse Method of Computation in Inviscid Transonic Flows: Application to the Design of Turbomachines Blades Profiles

1981 ◽  
Author(s):  
H. Miton
Keyword(s):  
Transonic Flow ◽  
Inverse Method ◽  
Flow Problem ◽  
Order Approximation ◽  
Suction Side ◽  
Computational Technique ◽  
Input Flow ◽  
Flow Conditions ◽  
Transonic Flows ◽  
Channel Type

The present method is based on an original computational technique of quasi two-dimensional inviscid transonic flows but which takes into account the changes of entropy due to shocks. The present approach consists in a numerical 2nd order approximation of the real transonic flow problem (hyperbolic or elliptic) by an initial values problem of hyperbolic and parabolic nature respectively. Such a method applied to the flow field between two adjacent blades profiles allows starting from a prescribed distribution of velocity along blade pressure or suction side to determine the flow details inside this domain and the profile of the opposite blade wall corresponding to input flow conditions which however should be made to satisfy the periodicity conditions as at this stage the approach is of the channel type. Examples of computation for simple cases are shown which proves the validity of the method.

scholarly journals On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

2021 ◽  
pp. 1-46
Author(s):  
Shangkun Weng ◽  
Zhouping Xin ◽  
Hongwei Yuan
Keyword(s):  
Angular Velocity ◽  
Boundary Conditions ◽  
Transonic Flow ◽  
Existence And Uniqueness ◽  
Outer Cylinder ◽  
Euler System ◽  
Energy Estimates ◽  
Concentric Cylinder ◽  
Transonic Flows ◽  
Cylindrically Symmetric

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli’s function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.

Numerical Simulation of Impeller–Volute Interaction in Centrifugal Compressors

1999 ◽  
Vol 121 (3) ◽  
pp. 603-608 ◽  
Author(s):  
K. Hillewaert ◽  
R. A. Van den Braembussche
Keyword(s):  
Numerical Simulation ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Flow Calculation ◽  
Total Temperature ◽  
Temperature And Pressure ◽  
Good Agreement

A numerical procedure to predict the impeller–volute interaction in a single-stage centrifugal compressor is presented. The method couples a three-dimensional unsteady flow calculation in the impeller with a three-dimensional time-averaged flow calculation in the volute through an iterative updating of the boundary conditions on the interface of both calculation domains. The method has been used to calculate the flow in a compressor with an external volute at off-design operation. Computed circumferential variations of flow angles, total temperature, and pressure are shown and compared with measurements. The good agreement between the predictions and measurements confirms the validity of the approach.

scholarly journals Design of Multi-Stage Turbomachinery Blading by the Circulation Method: Actuator Duct Limit

1992 ◽  
Author(s):  
T. Q. Dang ◽  
T. Wang
Keyword(s):  
Centrifugal Compressor ◽  
Infinite Number ◽  
Iterative Procedure ◽  
Inverse Method ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Circulation Method ◽  
Industrial Processing ◽  
Multi Stage ◽  
Blade Row

This paper presents an extension of a recently developed three-dimensional inverse method for turbomachine blades to handle multi-stage machines in the limit of an infinite number of blades in each blade row. The axisymmetric flowfield is assumed to be inviscid, compressible, and rotational. The use of blockage and entropy-increase terms are included in the theory to model losses. An iterative procedure is presented for the calculations of the blade profiles which produce prescribed swirl schedules in the bladed regions. The numerical technique employed to solve the relevant equations is based on a finite-volume formulation. The method is applied to the design of a low-pressure multi-stage centrifugal compressor used in industrial processing.

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.

scholarly journals Design of Aspirated Compressor Blades Using Three-Dimensional Inverse Method

2003 ◽  
Author(s):  
T. Q. Dang ◽  
M. P. C. van Rooij ◽  
L. M. Larosiliere
Keyword(s):  
Boundary Conditions ◽  
Performance Improvement ◽  
Inverse Method ◽  
Three Dimensional ◽  
Optimum Combination ◽  
Pressure Loading ◽  
Compressor Blades ◽  
Outflow Boundary Conditions ◽  
Full Interaction ◽  
Outflow Boundary

A three-dimensional viscous inverse method is extended to allow blading design with full interaction between the prescribed pressure-loading distribution and a specified transpiration scheme. Transpiration on blade surfaces and endwalls is implemented as inflow/outflow boundary conditions, and the basic modifications to the method are outlined. This paper focuses on a discussion concerning an application of the method to the design and analysis of a supersonic rotor with aspiration. Results show that an optimum combination of pressure-loading tailoring with surface aspiration can lead to a minimization of the amount of sucked flow required for a net performance improvement at design and off-design operations.

Design of Turbomachinery Blading in Transonic Flows by the Circulation Method

1992 ◽  
Vol 114 (1) ◽  
pp. 141-146
Author(s):  
T. Q. Dang
Keyword(s):  
Fourier Series ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Fourier Series Expansion ◽  
Main Task ◽  
Design Technique ◽  
Transonic Flows ◽  
Circulation Method ◽  
Expansion Technique ◽  
Volume Method

The newly developed three-dimensional design technique for turbomachinery blading based on the circulation method has been successfully extended into the transonic flow regime. The main task involves replacing the classical Fourier series expansion technique by a finite-volume method. Calculations were carried out for the design of infinitely thin cascaded blades in transonic flows, including shocked and shock-free cascaded blades.

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