Venturi Tube Design

Abstract

This chapter describes the main design specifications for classical Venturi tubes : it points the reader to important parts of ISO 5167 and gives reasons for the requirements in the standard. It covers the different types: their shape and their discharge coefficient. It includes the tappings, the dimensional measurements, the effect of roughness and the pressure loss. Gas flow at high Reynolds number and the effect of upstream fittings are not covered here: they are in Chaps. 7 and 8 respectively. The basic instruction remains to follow ISO 5167-4, probably with only one tapping, instead of four tappings, in each plane.

Appendix 3.A: Effect of Roughness: Computational Fluid Dynamics

3.1.1 3.A.1 General

In the work at NEL described in this appendix the effect of the roughness of Venturi tubes and upstream pipes was computed (Reader-Harris et al. 2000). The results are summarized here. The tappings were not included in the computation. In this appendix roughness is described using the arithmetical mean deviation of the roughness profile, R _a , (the average of the absolute values of the deviation from the mean).

3.1.2 3.A.2 Venturi Tube Roughness

3.1.2.1 3.A.2.1 Effect of Venturi Tube Roughness Height

Except for two points for R _a /d equal to 10⁻² increasing the roughness of Venturi tubes of diameter ratio 0.4 and 0.75 caused a decrease in the discharge coefficient, as shown in Tables 3.A.1 and 3.A.2 (because the friction loss increases). The pressure spike at the corner between the convergent section and the throat is smaller for rough Venturi tubes, and there is a significant pressure loss in the throat itself. These factors reduce the pressure at the throat tapping, increasing the measured pressure difference across the Venturi tube, thus reducing C. Very rough walls cause difficulty in CFD calculations.

Table 3.A.1 Predicted discharge coefficient for a range of Reynolds numbers and Venturi tube roughness heights: β = 0.4, inlet pipe R _a /D = 10⁻⁵

Table 3.A.2 Predicted discharge coefficient for a range of Reynolds numbers and Venturi tube roughness heights: β = 0.75, inlet pipe R _a /D = 10⁻⁵

3.1.2.2 3.A.2.2 Effect of Reynolds Number

For smooth Venturi tubes, increasing Reynolds number causes an increase in C (because the friction loss as a fraction of the differential pressure reduces): this can be seen in Table 3.A.1 for β = 0.4. For β = 0.75 C increases from 0.988 when Re _D  = 10⁶ to 0.992 when Re _D  = 2 × 10⁷ provided that both the Venturi tube and the upstream pipe are smooth (i.e. for the Venturi tube R _a /d = 0 and for the upstream pipe R _a /D = 0). However, the discharge coefficient of rough Venturi tubes appears to be independent of Reynolds number over the range tested. The decrease in C shown by one very rough Venturi tube is likely to be due to numerical errors in the CFD.

3.1.2.3 3.A.2.3 Effect of Venturi Tube Roughness Type

In the Fluent 5 CFD code roughness is specified in terms of an actual roughness height and a shape factor C _Ks . The C _Ks value is varied to account for the shape and distribution of the roughness. For example, a riveted surface which has rivets of height 2 mm could be represented by setting the actual roughness height to 2 mm and C _Ks to an appropriate value. A ribbed surface which has 2 mm high ribs would also be represented by setting the actual roughness height to 2 mm, but a different value of C _Ks would be used. Setting C _Ks to 0.5 reproduces sand roughness. Unfortunately, very little information is available which links values of C _Ks to particular roughness patterns. Figure 3.A.1 shows that varying C _Ks significantly affects the extent to which discharge coefficient varies with roughness height, particularly for very rough Venturi tubes. This implies that the shift in discharge coefficient caused by, say, 100 μm grooves eroded to run parallel to the flow could differ significantly from the shift caused by 100 μm grooves running across the flow.

Fig. 3.A.1

Variation of discharge coefficient with roughness shape factor, C _Ks : β = 0.75, Re _D  = 10⁶

3.1.3 3.A.3 Pipe Roughness

Tables 3.A.3 and 3.A.4 show that increasing the roughness of the pipe upstream of a Venturi tube causes an increase in C (a peakier velocity profile results in a smaller differential pressure); this effect is small in magnitude compared with the effect of roughening the Venturi tube itself to an equivalent degree. The effect of pipe roughness increases with β as would be expected.

Table 3.A.3 Predicted discharge coefficient for a range of Reynolds numbers and pipe roughness heights: β = 0.4, Venturi tube R _a /d = 10⁻⁵

Table 3.A.4 Predicted discharge coefficient for a range of Reynolds numbers and pipe roughness heights: β = 0.75, Venturi tube R _a /d = 10⁻⁵

3.1.4 3.A.4 Effect of Rounding the Corner Between the Convergent Section and the Throat

Figure 3.A.2 shows how rounding the corner between the convergent section and the throat reduces the magnitude of the pressure spike upstream of the throat. The figure shows the pressure profile for a β = 0.4 Venturi tube with a sharp and with a 4.839 d radius corner. In addition to reducing the magnitude of the pressure spike, the rounded corner reduces the straight length of throat upstream of the throat tapping. This causes the spike to recover later in the throat, reducing the pressure at the throat tapping and thus increasing the measured pressure drop and decreasing the discharge coefficient.

Fig. 3.A.2

The pressure profile through a Venturi tube: β = 0.4

Figure 3.A.3 shows that rounding the corner of a smooth Venturi tube has a more significant effect on small β Venturi tubes. ISO 5167-4:2003 defines an “as cast” Venturi tube as having a radius of 3.625 d at the join of the convergent and the throat. The greatest difference seen between the discharge coefficient of a Venturi tube with a sharp corner and that of a rounded Venturi tube of this radius was −0.3 % (for the β = 0.4 Venturi tube). This difference in discharge coefficient is only slightly affected by Reynolds number.

Fig. 3.A.3

The effect of rounding the corner between the convergent section and the throat: r _c is the radius of that corner. The Venturi tube and upstream pipe were both smooth

• NOTE Data collected in 1400 mm Venturi tubes are presented by Han et al. (1998): the 13 Venturi tubes had discharge coefficients in water of 0.985 ± 1 %. There was very little difference in discharge coefficient between rough-welded and machined convergent Venturi tubes.