A Three-Dimensional Euler Solver for Turbomachinery Blade Rows

1985 ◽  
Vol 107 (2) ◽  
pp. 258-264 ◽  
Author(s):  
D. G. Holmes ◽  
S. S. Tong
Keyword(s):  
Boundary Condition ◽  
Coordinate System ◽  
Centrifugal Compressor ◽  
Spatial Interpolation ◽  
Three Dimensional ◽  
Interpolation Scheme ◽  
Wall Boundary Condition ◽  
Absolute Flow ◽  
Euler Solver ◽  
Volume Method

This paper describes a three-dimensional Euler solver for turbomachinery blade rows. The algorithm used is based on the explicit, four-step, finite volume method advocated by Jameson. Some of the issues addressed include the spatial interpolation scheme compatible with the wall boundary condition; the appropriate interpolation scheme for correctly interpolating a uniform absolute flow in a rotating coordinate system; smoothing techniques that assure global conservation; and code vectorization. The Euler solver has been tested on turbine nozzles, turbine rotors, centrifugal compressor rotors, transonic fans, and propellers, in all cases without any modification to the code or any parameter adjustment.

scholarly journals Prediction of Heat and Mass Transfer in a Rotating Ribbed Coolant Passage With a 180 Degree Turn

1998 ◽  
Author(s):  
David L. Rigby
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Turbulence Model ◽  
Heat Mass Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wall Boundary Condition ◽  
Wall Boundary

Numerical results are presented for flow in a rotating internal passage with a 180 degree turn and ribbed walls. Reynolds numbers ranging from 5200 to 7900, and Rotation numbers of 0.0 and 0.24 were considered. The straight sections of the channel have a square cross section, with square ribs spaced one hydraulic diameter (D) apart on two opposite sides. The ribs have a height of 0.1D and are not staggered from one side to the other. The full three dimensional Reynolds Averaged Navier-Stokes equations are solved combined with the Wilcox k-ω turbulence model. By solving an additional equation for mass transfer, it is possible to isolate the effect of buoyancy in the presence of rotation. That is, heat transfer induced buoyancy effects can be eliminated as in naphthalene sublimation experiments. Heat transfer, mass transfer and flow field results are presented with favorable agreement with available experimental data. It is shown that numerically predicting the reattachment between ribs is essential to achieving an accurate prediction of heat/mass transfer. For the low Reynolds numbers considered, the standard turbulence model did not produce reattachment between ribs. By modifying the wall boundary condition on ω, the turbulent specific dissipation rate, much better agreement with the flow structure and heat/mass transfer was achieved. It is beyond the scope of the present work to make a general recommendation on the ω wall boundary condition. However, the present results suggest that the ω boundary condition should take into account the proximity to abrupt changes in geometry.

scholarly journals Three-Dimensional Flowfield Calculation of High-Loaded Centrifugal Compressor Diffusers

1986 ◽  
Author(s):  
Ingolf Teipel ◽  
Alexander Wiedermann
Keyword(s):  
Coordinate System ◽  
Centrifugal Compressor ◽  
Classical Theory ◽  
Three Dimensional ◽  
Curvilinear Coordinate System ◽  
Centrifugal Compressors ◽  
Curvilinear Coordinate ◽  
Side Walls ◽  
Twisted Shape

In this paper a method for calculating inviscid three-dimensional flowfields in vaned diffusers of high-loaded centrifugal compressors will be considered. Following the classical theory of Wu different kinds of stream surfaces have been introduced. The complete three-dimensional result is approximated by a combination of blade to blade stream surfaces (S1-surface) and S2-surfaces between the side walls of the diffuser. The geometry of the stream sheets depends on each other. A special curvilinear coordinate system has been introduced to take into account the twisted shape of the surfaces.

SIMULATION OF FLOW PAST A CIRCULAR CYLINDER USING ENTROPIC LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 25 (01) ◽  
pp. 1340024 ◽  
Author(s):  
CHUAN GU ◽  
SHYAM S. CHIKATAMARLA ◽  
ILIYA V. KARLIN
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Wall Boundary Condition ◽  
Flow Past ◽  
Wall Boundary ◽  
Stability And Accuracy ◽  
Boltzmann Method

The entropic lattice Boltzmann method (ELBM) has been demonstrated to bring unconditional stability and accuracy to sub-gird flow simulations. However, the application of ELBM to engineering flows were restricted so far due to the lack of a matching wall boundary condition that retains the accuracy of the method for both resolved and under-resolved simulations. To this end, we show that the recently proposed wall boundary condition for ELBM is reliable and accurate for both these regimes. Three-dimensional (3D) flow past a circular cylinder is taken as a benchmark to show that ELBM is both stable and accurate for range of Reynolds numbers and grid sizes. Several key parameter of this flow are studied in detail.

Numerical Analysis of the Three-Dimensional Swirling Flow in Centrifugal Compressor Volutes

1994 ◽  
Vol 116 (3) ◽  
pp. 462-468 ◽  
Author(s):  
E. Ayder ◽  
R. Van den Braembussche
Keyword(s):  
Centrifugal Compressor ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Elliptical Cross ◽  
Hexahedral Elements ◽  
Flow Mechanisms ◽  
Radial Forces ◽  
Finite Volume Approach ◽  
Euler Solver

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge–Kutta time-stepping scheme. The artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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