Abstract
This study investigates a number of u-P, primitive variables, finite element algorithms based on 3D Lagrangian brick elements for simulation of steady incompressible confined fluid flow. These were applied to flow through a tight 90° bend of circular cross section, and compared to available experimental measurements on this geometry for laminar flows at Re=500 and Re=1093, and for turbulent flow at Re=43000. Three distinct pressure approximations were investigated: (1) discontinuous linear, (2) discontinuous tri-linear, and (3) continuous tri-linear, all of these combined with a 27 noded tri-quadratic approximation for velocity. Also studied were the penalty method, Galerkin weighting, and an inconsistent version of the SUPG method. Turbulence was simulated with a k — e model. Computations were carried out on a Cray XMP supercomputer with an SSD for efficient I/O. Discontinuous pressure elements were more stable in the presence of convection than continuous pressure elements for both laminar Reynolds numbers studied. The discontinuous approximation is less restrictive than the continuous approximation for the modelling of strong pressure gradients present inside the 90° bend — a fact which may account for such an observation. Flow simulations at Re=1093 gave an estimate of the distortion of the test space required for good non-linear convergence and accuracy, when implementing the inconsistent SUPG method. The turbulence simulations revealed the importance of a near wall model able to capture strong secondary flows near pipe walls.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.Boussinesq.Essai surla theorie des eaux courantes. Mem. pres. Acad. Sci. XXIII, vol. 4, no. 1, pg. 1–680, Paris 1877
C.A. Brebbia. The unification of finite elements and boundary elements in Unification of finite element methods. Ed. H. Kardestuncer. North-Holland Mathematics Studies 94, Elsevier Science Publishers B.V., 1984.
A.N. Brooks and T. J. R. Hughes. SUPG formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp. Meth. Appl. Mech. Engng., vol. 32, pg. 199–259, 1982.
W.R. Dean. The streamline motion of a fluid in a curved pipe. Phil. Mag., vol 7, no. 4, pg 208, and no. 5, pg. 673, 1928.
M.M. Enayet, M.M. Gibson, A.M.K.P. Taylor and M. Yianneskis. Laser doppler measurements of laminar and turbulent flow in a pipe bend. NASA contract report 3551. Contract NASW-3258, May 1982.
P. Hood. Frontal solution program for unsymmetric matrices. Int. J. Num. Meth. Engng., vol. 10, pg. 379–399.
D. Howard. Numerical Techniques for the Simulation of Three Dimensional Swirling Flow . Ph.D. thesis, University College of Swansea, 1988.
D. Howard, W.M. Connolley and J.S. Rollett. Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation . Int. J. Num. Meth. in Fluids, vol. 10, pg. 925–45, 1990.
T.J.R. Hughes. The finite element method: linear static and dynamic finite element analysis. Prentice-Hall International Inc., 1987.
H. Iacovides. Momentum and heat transfer in flow through 180° bends of circular cross section. PhD thesis. UMIST 1986.
B.E. Launder and D.B. Spalding. The numerical computation of turbulent flows . Comp. Meth. Appl. Mech. Engng., vol. 3, pg. 269–289, 1974.
D.S. Malkus and T.J.R. Hughes. Mixed FEM - Reduced and selective integration techniques: A unification of concepts. Comp. Meth. Appl. Mech. Engng., vol. 15, pg. 63–81, 1978.
G.L. Mellor and H.J. Herring. A survey of the mean turbulent field closure models . AIAA Journal, vol. 11, no. 5, pg. 590–599, May 1973.
S. Nakazawa. Finite element analysis applied to polymer processing. PhD thesis, Chemical Engineering, University College of Swansea, 1982.
C. Taylor, J. Rance and J.O. Medwell. A note on the imposition of t ra ction bondary conditions when using the FEM for solving incompressible flow problems. Proc. Int. Conf. Num. Meth. Lam. and Turb. Flow, pg. 345–352, 1985.
C. Taylor, C.E. Thomas, and K. Morgan. Analysis of turbulent flow with separation using the FEM. in chap. 10 of Computational techniques in transient and turbulent flow. Ed: C. Taylor and K. Morgan, Pineridge Press, Swansea 1981.
C.E. Thomas. Analysis of confined turbulent flows. PhD thesis, Civil Engineering, University College of Swansea, 1982.
C.-C.Yu and J.C.HeinrichPetrov—Galerkin method for multidimensionaltime—dependent convective—diffusion equationsInt. J. Numer. Meth. Engng.vol. 24, 2201–2215, 1987.
O.C. Zienkiewicz, J. P. Villotte and S. Toyoshima. Iterative method for constrained and mixed approximation. An inexpensive improvement of FEM performance. Internal report C/R/489/84, Inst. for Num. Meth. in Engng., Univ. College of Swansea, 1984.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Computational Mechanics Publications
About this chapter
Cite this chapter
Howard, D. (1991). Study of Incompressible Flow with 3D Finite Elements. In: Brebbia, C.A., Peters, A., Howard, D. (eds) Applications of Supercomputers in Engineering II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3660-0_20
Download citation
DOI: https://doi.org/10.1007/978-94-011-3660-0_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-695-9
Online ISBN: 978-94-011-3660-0
eBook Packages: Springer Book Archive