Secondary Flow Development In A Cascade Like Passage Of A Turbomachine

1983 ◽  
pp. 11-23
Author(s):  
Amer Nordin Darus
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Rotational Flow ◽  
Simultaneous Solution ◽  
Analytical Formulation ◽  
Curved Duct ◽  
Flow Development ◽  
Vorticity Equations

Makalah ini memaparkan formulasi analitik dan penyelesaian numerik aliran dimensi tiga yang rotasional di dalam sebuah saluran yang melengkung. Formulasi ini berdasarkan perhitungan halaju aliran dan komponen vortisiti selari axis saluran tersebut. Halaju sekunder ditentukan melalui penyelesaian serentak persamaan-persamaan ke terusan dan vortisiti melalui penggunaan fungsi seperti fungsi arus. Hasil-hasil numerik diberikan dan dibandingkan dengan data-data eksperimen yang ada. This article presents the analytical formulation and numerical solution of the three-dimensional rotational flow in curved duct. The formulation is based on calculating the flow - wise velocity and vorticity. components from the momentum equation. The secondary velocities are determined from the simultaneous solution of the continuity and vorticity equations through the use of a streamlike function. The results presented arc compared with the existing experimental data.

Rotational Flow Calculations in Three Dimensional Blade Passages

1982 ◽  
Author(s):  
C. Lacor ◽  
Ch. Hirsch
Keyword(s):  
Experimental Data ◽  
Solution Method ◽  
Three Dimensional ◽  
Rotational Flow ◽  
Calculation Methods ◽  
Three Dimensional Flow ◽  
Additional Function ◽  
Potential Part ◽  
Rotational Part ◽  
Element Technique

A method to calculate the three-dimensional, inviscid, rotational flow in blade passages is described. The three-dimensional flow is separated into a potential part and a rotational part. For a certain class of inlet flows, this rotational part can be described by a single additional function. The solution method can be seen as an extension of the procedure for solving the three-dimensional potential flow. The Finite Element technique is used and the method is illustrated by calculations of the flow in a rectangular elbow with 90 degrees of turning. Comparisons are made with experimental data and other calculation methods.

scholarly journals Flow Development Through Inter-Turbine Diffusers

1996 ◽  
Author(s):  
Robert G. Dominy ◽  
David A. Kirkham ◽  
Andrew D. Smith
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Flow Coefficient ◽  
Experimental Measurements ◽  
Good Prediction ◽  
Pressure Gradients ◽  
Computational Simulations ◽  
Flow Development ◽  
Inlet Swirl

Inter-turbine diffusers offer the potential advantage of reducing the flow coefficient in the following stages leading to increased efficiency. The flows associated with these ducts differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. Experimental data and numerical simulations clearly reveal the generation of significant secondary flows as the flow develops through the diffuser in the presence of cross-passage pressure gradients. The further influence of inlet swirl is also demonstrated. Data from experimental measurements with and without an upstream turbine are discussed and computational simulations are shown not only to give a good prediction of the flow development within the diffuser but also to demonstrate the importance of modelling the fully three-dimensional nature of the flow.

A Viscous Flow Study of Shock-Boundary Layer Interaction, Radial Transport, and Wake Development in a Transonic Compressor

1992 ◽  
Vol 114 (3) ◽  
pp. 538-547 ◽  
Author(s):  
C. Hah ◽  
L. Reid
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Numerical Solution ◽  
Three Dimensional ◽  
Numerical Results ◽  
Radial Transport ◽  
Layer Interaction ◽  
Transonic Compressor ◽  
Shock Boundary Layer Interaction ◽  
Boundary Layer Interaction

A numerical study based on the three-dimensional Reynolds-averaged Navier–Stokes equation has been conducted to investigate the detailed flow physics inside a transonic compressor. Three-dimensional shock structure, shock-boundary layer interaction, flow separation, radial mixing, and wake development are all investigated at design and off-design conditions. Experimental data based on laser anemometer measurements are used to assess the overall quality of the numerical solution. An additional experimental study to investigate end-wall flow with a hot film was conducted, and these results are compared with the numerical results. Detailed comparison with experimental data indicates that the overall features of the three-dimensional shock structure, the shock-boundary layer interaction, and the wake development are all calculated very well in the numerical solution. The numerical results are further analyzed to examine the radial mixing phenomena in the transonic compressor. A thin sheet of particles is injected in the numerical solution upstream of the compressor. The movement of particles is traced with a three-dimensional plotting package. This numerical survey of tracer concentration reveals the fundamental mechanisms of radial transport in this transonic compressor. Strong radially outward flow is observed inside a separated flow region and this outward flow accounts for about 80 percent of the total radial transport. The radially inward flow is mainly due to the traditional secondary flow.

Flow Development Through Interturbine Diffusers

1998 ◽  
Vol 120 (2) ◽  
pp. 298-304 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham ◽  
A. D. Smith
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Flow Coefficient ◽  
Experimental Measurements ◽  
Good Prediction ◽  
Pressure Gradients ◽  
Computational Simulations ◽  
Flow Development ◽  
Inlet Swirl

Interturbine diffusers offer the potential advantage of reducing the flow coefficient in the following stages, leading to increased efficiency. The flows associated with these ducts differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. Experimental data and numerical simulations clearly reveal the generation of significant secondary flows as the flow develops through the diffuser in the presence of cross-passage pressure gradients. The further influence of inlet swirl is also demonstrated. Data from experimental measurements with and without an upstream turbine are discussed and computational simulations are shown not only to give a good prediction of the flow development within the diffuser but also to demonstrate the importance of modeling the fully three-dimensional nature of the flow.

Three-Dimensional Dynamic Simulation of Helical Compression Springs

1989 ◽  
Author(s):  
Y. Lin ◽  
A. P. Pisano
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Numerical Algorithm ◽  
High Speed ◽  
Moving Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Physical Reality ◽  
Dynamic Equations ◽  
Helical Springs

Abstract The dynamic equations for general helical springs are solved and classified according to the number of energy terms used to formulate them. Solutions of several sets of dynamic equations, each with a different number of energy terms, are compared with experimental data. It is found that at higher compression speeds the numerical solution with a traditional, fixed boundary represents a physically impossible situation. A moving boundary technique is applied to improve the numerical solution and bring it into agreement with physical reality. Since a convergence proof for a numerical algorithm for nonlinear partial differential equations with a moving boundary is not available, a grid study has been performed to demonstrate convergence. The agreement between the solutions of different grid sizes and the experimental data is taken to show that the numerical algorithm was convergent. This three dimensional spring simulation model can be used in the simulation of high-speed mechanical machinery utilizing helical springs, and in particular, for design optimization of automotive valve springs.

Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines

1990 ◽  
Vol 112 (3) ◽  
pp. 391-398
Author(s):  
S. Abdallah ◽  
C. F. Smith
Keyword(s):  
Experimental Data ◽  
Poisson Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Type Equation ◽  
Neumann Boundary ◽  
Momentum Equation ◽  
Rotor Blades ◽  
Pressure Poisson Equation

A primitive variable formulation is used for the solution of the incompressible Euler equation. In particular, the pressure Poisson equation approach using a nonstaggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a nonstaggered grid. Numerical solutions of the momentum equations are obtained using the second-order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive overrelaxation method. Three turbo-machinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.

The Numerical Prediction of Developing Turbulent Flow in Rectangular Ducts

1981 ◽  
Vol 103 (3) ◽  
pp. 445-453 ◽  
Author(s):  
F. B. Gessner ◽  
A. F. Emery
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Momentum Equation ◽  
Scale Model ◽  
Length Scale ◽  
Basic Technique ◽  
Numerical Predictions ◽  
Iterative Procedures

Comparisons are made between experimental data and numerical predictions based on a three-dimensional length-scale model applicable to developing turbulent flow in rectangular ducts of arbitrary aspect ratio. The numerical method utilizes an explicit (Dufort-Frankel) differencing scheme for the axial momentum equation and involves no iterative procedures. Although the basic technique has been applied previously to another class of three-dimensional flows, it has not been applied until now to slender shear flows dominated by secondary flow of the second kind. The merits of the length-scale model and the computational procedure are assessed by means of comparisons with results referred to both k–ε and full Reynolds stress closure models which have been applied in recent years.

Three-Dimensional Dynamic Simulation of Helical Compression Springs

1990 ◽  
Vol 112 (4) ◽  
pp. 529-537 ◽  
Author(s):  
Y. Y. Lin ◽  
A. P. Pisano
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Numerical Algorithm ◽  
High Speed ◽  
Moving Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Physical Reality ◽  
Dynamic Equations ◽  
Helical Springs

The dynamic equations for general helical springs are solved and classified according to the number of energy terms used to formulate them. Solutions of several sets of dynamic equations, each with a different number of energy terms, are compared with experimental data. It is found that at higher compression speeds the numerical solution with a traditional, fixed boundary represents a physically impossible situation. A moving boundary technique is applied to improve the numerical solution and bring it into agreement with physical reality. Since a convergence proof for a numerical algorithm for nonlinear partial differential equations with a moving boundary is not available, a grid study has been performed to demonstrate convergence. The agreement between the solutions of different grid sizes and the experimental data is taken to show that the numerical algorithm was convergent. This three dimensional spring simulation model can be used in the simulation of high-speed mechanical machinery utilizing helical springs, and in particular, for design optimization of automotive valve springs.

The Aerodynamic Significance of Fillet Geometry in Turbocompressor Blade Rows

1980 ◽  
Vol 102 (4) ◽  
pp. 984-993 ◽  
Author(s):  
L. L. Debruge
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Polyhedral Approximation ◽  
Corner Flow ◽  
Fillet Radius ◽  
Dimensional Boundary ◽  
Modified Power Law

This paper describes a theoretical investigation of the influence of fillet radius on the aerodynamic behavior of turbocompressors. The fillet is that found at the intersection of an airfoil and a hub or shroud where no relative motion or gap is present. A modified power law velocity is used in conjunction with experimental estimates of the three-dimensional corner boundary layer extent to obtain values of the interference displacement and friction coefficient for the 90 deg corner flow which are in fair agreement with Gersten’s experimental results. Likewise, interference displacement and friction coefficient are obtained in the case of a corner flow in a dihedral > 150 deg for which experimental data is unavailable but where the low curvature of the stream surfaces allows the three-dimensional boundary layer extent to be calculated from Bertotti’s integral momentum equation. The boundary layer characteristics thus obtained are then applied, by means of a polyhedral approximation, in the evaluation of the influence of 90 deg corner fillet on corner flow separation. Some guidelines are provided relating the fillet radius to physical dimensions of the blading.

Three-Dimensional Effects in Supersonic and Transonic Compressor Rotors: An Experimental and Computational Study

1982 ◽  
Author(s):  
K. D. Broichhausen ◽  
H. E. Gallus
Keyword(s):  
Experimental Data ◽  
Computational Study ◽  
Three Dimensional ◽  
Experimental Results ◽  
Computation Method ◽  
Rotational Flow ◽  
Transonic Compressor ◽  
Dimensional Effects ◽  
Flow Through ◽  
Data Result

A computation method for the three-dimensional rotational flow through transonic and supersonic rotors is described and discussed by means of a comparison with experimental results. The computation treats subsonic and supersonic flows with different algorithms. The compression shocks are calculated as real three-dimensional discontinuities on the basis of the Rankine-Hugoniot-equations. The experimental data result from measurements in transonic and supersonic compressor rotors. A comparison of the data shows to what extent these three-dimensional effects are covered by the described theory.

Sign in / Sign up

Export Citation Format

Share Document