Notes on CFD: General Principles

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8.8 Venturi tube

A Venturi tube is a device used to measure the ﬂow rate of a ﬂuid in a pipe. The device exploits the Venturi eﬀect⁴, i.e. that pressure reduces when the ﬂuid ﬂows through a restriction.

The volumetric ﬂow rate $\text{[math]}$ is calculated according to

C q ---- Q = -p----------A 2 p; D=Dt 1 \relax \special {t4ht=

(8.2)

where: $\text{[math]}$ is the decrease in kinematic pressure $\text{[math]}$ between the Venturi inlet and throat; $\text{[math]}$ and $\text{[math]}$ are the inlet and throat diameter, respectively; the cross-sectional area is $\text{[math]}$ ; and, $\text{[math]}$ is a discharge coeﬃcient. A coeﬃcient of $\text{[math]}$ satisﬁes the Bernoulli equation, $\text{[math]}$ , between the inlet and throat, where $\text{[math]}$ is the ﬂuid speed.

For $\text{[math]}$ , $\text{[math]}$ is calculated accurately using $\text{[math]}$ values between 0.97 and 1,⁵ but, for $\text{[math]}$ , suitable values of $\text{[math]}$ decrease signiﬁcantly below 1 in order to account for pressure losses due to viscous forces.

$PICT\relax \special {t4ht=$

A simulation was performed to calculate $\text{[math]}$ for a Venturi tube, shown in the ﬁgure, with $\text{[math]}$ and an inlet $\text{[math]}$ . The inlet velocity was speciﬁed using the quadratic proﬁle in Sec. 8.7 with a mean cross-sectional speed $\text{[math]}$ , corresponding to a maximum speed $\text{[math]}$ .

$PICT\relax \special {t4ht=$

The simulation used the steady-state algorithm in Sec. 5.12, with an incompressible ﬂuid with uniform $\text{[math]}$ . The mesh contained 57,600 cells, with a near-wall cell height of 1.5mm, which resolved the velocity proﬁles as shown below. The ﬂow recirculates near the wall downstream of the Venturi throat, causing inﬂow at the outlet boundary. Consequently, the total pressure and inlet-outlet-velocity boundary conditions, described in Sec. 4.7 and Sec. 4.15 respectively, were applied at the outlet to maintain stability.

$PICT\relax \special {t4ht=$

The ﬂow was laminar so no turbulence modelling was required. The solution converged to within an absolute tolerance $\text{[math]}$ , see Sec. 5.4 , in 292 iterations.

The pressure drop was $\text{[math]}$ between the centres of the inlet and throat sections, with a corresponding $\text{[math]}$ .

⁴Giovanni Battista Venturi, Recherches expérimentales sur le principe de la communication latérale du mouvement dans les ﬂuides appliqué a l’explication de diﬀérens phénomènes hydrauliques, 1797.

⁵ISO 5167-4, Measurement of ﬂuid ﬂow by means of pressure diﬀerential devices inserted in circular cross-section conduits running full – part 4: venturi tubes, 2003.

Notes on CFD: General Principles - 8.8 Venturi tube

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Notes on Computational Fluid Dynamics: General Principles

8.8 Venturi tube