Sommario
La forza di accoppiamento fluido-solido in campi bidimensionali multiconnessi e periodici può essere determinata mediante lo studio del flusso locale in un microelemento di dimensioni pari alla lunghezza d'onda della soluzione. Le equazioni di Navier-Stokes, scritte su un microelemento, ammettono una sola soluzione periodica nella velocita e nel gradiente della pressione, ma non nella pressione stessa, che e data dalla somma di un termine incognito periodico e un termine lineare assegnato. La soluzione numerica locale delle equazioni del moto è ottenuta con tecnica alle differenze finite in coordinate curvilinee generalizzate, sostituendo le condizioni al contorno su parte della frontiera con condizioni di periodicità. Allo scopo di verificare l'accuratezza del modello proposto sono state eseguite, in galleria idrodinamica, misure della caduta di pressione e visualizzazioni del flusso trasversale attraverso un fascio di cilindri. I risultati numerici sono confrontati con i dati sperimentali e con altre soluzioni numeriche e misure sperimentali per numeri di Reynolds inferiori ad 800.
Summary
The fluid-solid interaction force in two-dimensional multi-connected periodic domains can be determined by a local flow solution in a periodic microelement. Integration of Navier-Stokes equations in the microelement yields a unique solution in velocity field and in pressure gradient, but not in pressure itself, which is given by the sum of an unknown periodic term and an assigned linear term. The numerical solution of the equations of motion in general curvilinear coordinates is obtained by a finite difference technique, assuming periodic boundary conditions. Pressure drop measurements and flow visualization through arrays of cylinders in different configurations have been conducted for the validation of the proposed method. Comparisons of present numerical results with experimental data and other numerical solutions, for Reynolds number up to 800 and different geometrical configurations of cylinders, are presented and discussed.
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Abbreviations
- d :
-
diameter of cylinders
- D d :
-
hydraulic diameter
- f, f c , v :
-
friction factors
- g ij :
-
metric tensor
- n :
-
number of cylinder rows
- N :
-
number of larger restrictions of flow
- p :
-
pressure
- P′ :
-
periodic pressure
- R d :
-
Reynolds number, d3 αρ/μ 2
- R * d :
-
Reynolds number based on averaged velocity in the minimum section and cylinder diameter
- Re :
-
Reynolds number based on averaged velocity in theME and cylinder diameter
- R v :
-
Reynolds number based on averaged velocity in the minimum section and hydraulic diameter
- S l :
-
longitudinal center-to-center distance from a tube in transverse row to nearest tube outside of that row
- S t :
-
center-to-center distance between tubes in a transverse row
- \(\bar v\) :
-
velocity
- υ * :
-
reference velocity
- υ :
-
mean velocity in the minimum section
- \(\bar v\) :
-
mean velocity in theME
- x k :
-
position vector
- α i :
-
mean pressure gradient
- ∂Ω:
-
solid boundary of theME
- Δ p :
-
total pressure drop
- μ :
-
viscosity
- ξ, η:
-
curvilinear coordinates
- p :
-
density
- Ω :
-
fluid region
- i :
-
contravariant components
- \i :
-
contravariant derivatives
- i :
-
covariant components
- \i :
-
covariant derivatives
References
Fujii M., Fujii T.,A Numerical Analysis of Laminar Flow and Heat Transfer of Air in a In-Line Tube Bank, Num. Heat Transfer,8, pp. 89–102, 1984.
Sha W.T.,An Overview of Rod-Bundle Thermal Hydraulic Analysis, NUREG/CR-1825 ANL-79-10, Argonne National Laboratory, 1980.
Sanchez-Palencia E.,Homogenization Method for the Study of Composite Media, Survey Paper in ≪Asymptotic Analysis II≫, ed. Verholst, Lect. Notes in Maths.,985, 1983.
Whitaker S.,The Equations of Motion in Porous Media, Chem. Eng. Sci.,21, pp. 291–300, 1966.
Slattery J.C., ≪Momentum Energy and Mass Transfer in Continua≫ McGraw-Hill, 1972.
Vafai K., Tien C.L.,Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media, Int. J. Heat Mass Transfer,24, pp. 195–203, 1981.
Beavers G.S., Sparrow E.M.,Non-Darcy flow through fibrous porous media, J. Appl. Mech.,36, pp. 711–714, 1969.
Guj G., De Matteis G.,Fluid-Particles Interaction in Particulate Fluidized Bed: numerical and experimental analysis, Phisico-Chemical Hydrodynamics,7, pp. 145–160, 1986.
Thom A., Apelt C.J., ≪Field Computations in Engineering and Physics≫, Van Nostrand, London, 1961.
Launder B.E., Massey T.H.,The Numerical Prediction of Viscous Flow and Heat Transfer in Tube Banks, J. Heat Transfer,100, pp. 565–571, 1978.
Patankar S.V., Lin C.H., Sparrow E.M.,Fully developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area, J. Heat Transfer,99, pp. 180–186, 1977.
Ene I., Sanchez-Palencia E.,Equations et Phenomenes de Surface pour le Ecoulement dans un Modele de Milieu Poreux, J. Mecanique,14, pp. 73–108, 1975.
Thompson J.F.,Thomas F.C.,Mastem C.N.,Boundary Fitted Curvilinear Coordinate Systems for Solution of Partial Differential Equations of Fields Containing Any Number of Arbitrary Two-Dimensional Bodies, NASA-CR-2729, 1977.
Flugge W., ≪Tensor Analysis and Continuum Mechanics≫, Springer-Verlag, 1972.
Di Carlo S., Piva R., Guj G.,A Study on Curvilinear Coordinates and Macro-Elements for Multiply Connected Flow Fields, Lecture Notes in Physics, Springer-Verlag,90, p. 161–168, 1979.
Bergelin O.P., Brown G.A., Hull H.L., Sullivan F.W.,Heat Transfer and Fluid Friction During Viscous Flow Across Banks of Tubes-III. A Study of Tube Spacing and Tube Size, Trans. ASME,72, pp. 881–888, 1950.
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Guj, G., de Matteis, G. Fully developed flow in periodic multi-connected domains: Numerical and experimental study. Meccanica 22, 185–192 (1987). https://doi.org/10.1007/BF01573811
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DOI: https://doi.org/10.1007/BF01573811