A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1992 ◽  
Vol 114 (3) ◽  
pp. 548-552 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three-dimensional aerothermodynamic design problem with some type of Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachine, the three-dimensional coordinates of the blade are attained through stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem, the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

scholarly journals A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1991 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three–dimensional aerothermodynamic design problem with some type of the Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachinery the three–dimensional coordinates of the blade is attained through the stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-driving System

2000 ◽  
Vol 122 (2) ◽  
pp. 213-218 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained. [S1050-0472(00)01102-8]

A Three-Dimensional Numerical Method for Turbomachinery Blading

1992 ◽  
Author(s):  
C. W. Gu ◽  
J. Z. Xu ◽  
J. Y. Du
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Stream Function ◽  
Three Dimensional ◽  
Computational Results ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Stream Functions ◽  
Derivatives Of ◽  
Convergent Solution

By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-Driving System

2000 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

Abstract This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained.

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.

Calculation of Cascade Profiles From the Velocity Distribution

1974 ◽  
Vol 96 (4) ◽  
pp. 407-412 ◽  
Author(s):  
C. Lecomte
Keyword(s):  
Mach Number ◽  
Velocity Distribution ◽  
Subsonic Flow ◽  
A Priori ◽  
External Flow ◽  
Analytical Function ◽  
Graphic Display ◽  
Analytical Functions ◽  
Number Distribution ◽  
Mach Number Distribution

The method using the properties of analytical functions is applied to a plane, steady, inviscid, everywhere subsonic flow. From data fixed a priori concerning the external flow and some details of the profile, the hodograph is obtained as an analytical function whose real part is known on a contour. The set of imposed conditions being in general superabundant, the proposed Mach number distribution is corrected by means of a function whose form is fixed a priori, or rejected altogether. The problem is treated on a graphic display console connected with a computer, which provides also the profile corresponding to the calculated hodograph.

A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils

1993 ◽  
Vol 254 ◽  
pp. 151-181 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Neal E. Fine
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Present Method ◽  
Cavity Length ◽  
Three Dimensional ◽  
Cavitation Number ◽  
Cavity Surface ◽  
Cavity Shape ◽  
Dynamic Boundary

The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result.The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT's cavitation tunnel.

Process Modeling: Lost-Foam Pattern Filling

2004 ◽  
Author(s):  
Peter J. Blaser ◽  
Dale M. Snider ◽  
Ken A. Williams ◽  
Alan E. Cook ◽  
Mark Hoover
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Phase Particle ◽  
Three Dimensional ◽  
Video Data ◽  
Particle In Cell ◽  
Polystyrene Beads ◽  
Multi Phase ◽  
Foam Pattern ◽  
Lost Foam

A transient, three-dimensional, multi-phase particle-in-cell approach is used to solve for the flow of polystyrene beads in complex three dimensional geometries which represent patterns used for lost-foam casting. The numerical method solves the gas conservation equations on an Eulerian grid and the motion of polystyrene beads is calculated in a Lagrangian frame of reference. The true particle size distribution is modeled, and the particle flow ranges from dilute to close-pack. Predicted fill behavior is compared to experimentally blown patterns using colored beads and to the measured transient filling of a pattern. The colored beads show a complex fill pattern which is calculated well by the numerical method. The transient calculation compares very well with measured video data, and the particle motion has unique particle behavior unlike a fluid. Because of uncertainties in boundary conditions in production lost-foam tooling, the sensitivity of lost-foam pattern filling to boundary conditions is examined.

An Iterative Boundary Integral Numerical Solution for General Steady Heat Conduction Problems

1981 ◽  
Vol 103 (1) ◽  
pp. 26-31 ◽  
Author(s):  
M. S. Khader ◽  
M. C. Hanna
Keyword(s):  
Boundary Conditions ◽  
Present Method ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Boundary Integral ◽  
Temperature Dependent ◽  
Convective Boundary ◽  
Arbitrary Boundary ◽  
Steady Heat Conduction ◽  
Steady Heat

An iterative boundary integral numerical method for solving the steady conduction of heat is developed. The method is general for two- and three-dimensional regions with arbitrary boundary shapes. The development is generalized to include the first, second, and third kind of boundary conditions and also radiative boundary and temperature-space dependent convective coefficient cases. With Kirchhoff’s transformation, cases of temperature-dependent thermal conductivity with general boundary conditions are also accounted for by the present method. A variety of problems are analyzed with this method and their solutions are compared to those obtained analytically. A comparison between the present method and the finite difference predictions is also investigated for a case of mixed temperature and convective boundary conditions. Moreover, two-dimensional regions with three kinds of boundary conditions and irregular-shaped boundaries are used to illustrate the versatility of the technique as a computational procedure.

Sign in / Sign up

Export Citation Format

Share Document