By H. Versteeg, W. Malalasekra

ISBN-10: 0582218845

ISBN-13: 9780582218840

This article goals to supply info for amateur CFD clients who, when constructing CFD talents by utilizing software program, want a reader that covers the basics of the fluid dynamics at the back of advanced engineering flows and of the numerical resolution algorithms on which CFD codes are established.

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**Additional info for An Introduction to Computational Fluid Dynamics: The Finite Volume Method Approach**

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In order to avoid errors, caused by the variation of the velocity proﬁle in the intake region, the pressure must be measured further downstream. 139) and comparing it with the distance between the position of the boreholes for the pressure measurements and the entrance of the pipe. 7 Turbulent Pipe Flows The Hagen-Poiseuille law looses its validity when the Reynols number exceeds a certain value. Experiments show, that irregular velocity ﬂuctuations set in, which cause an intensive intermixing of the various layers in the ﬂow.

If the exponents are set αi = 1, then the products can be formulated as K1 K2 K3 K4 = = = = γ1 ∆p ρβ1 um D δ1 , β2 γ 2 µ ρ u m D δ2 , γ3 l ρβ3 um D δ3 , β4 γ 4 k ρ u m D δ4 . 56) The similarity parameters K1 to K4 are obtained as follows K1 = ∆p µ l k , K2 = , K3 = , K4 = ρ u2m ρ um D D D . 57) 40 2. 58) . 59) or ∆p = f2 Re, ρ u2m k D l , D The form of the function cannot be determined with the method of dimensional analysis. However, the number of inﬂuence quantities has been reduced from six to three.

The change of mass per unit time in the volume element is equal to the diﬀerence between in- and out-ﬂowing mass. 9) Again there is obtained ∂ρ + ∇ · (ρ v) = 0 . 10) The change of mass per unit time in the control volume is expressed by the partial derivative ∂ρ , the mass ﬂow through its surface is given by the expression ∇ · (ρ v). 2 The Navier-Stokes Equations The equilibrium of forces acting on a volume element of ﬂuid can be described with the momentum theorem. The time rate of change of the momentum of a closed volume is equal to the sum of the external forces acting on the volume.

### An Introduction to Computational Fluid Dynamics: The Finite Volume Method Approach by H. Versteeg, W. Malalasekra

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