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Flow Measurement and Instrumentation 15 (2004) 167–177

www.elsevier.com/locate/ﬂowmeasinst

Eﬀects of upstream installations on the reading

of an ultrasonic ﬂowmeter

C. Ruppel, F. Peters

Str¨ mungslehre, Universit¨ t Essen, D-45127 Essen, Germany

Abstract

The downstream ﬂow of two typical installations in piping systems, the 90 v bend and the double bend, is experimentally ident-

iﬁed by ﬂow angle measurements at the pipe wall. The identiﬁed downstream ﬂow patterns are stable when the installation inﬂow

is stabilized. An ultrasonic ﬂowmeter is exposed to the downstream ﬂow at various positions and circumferential angles. At each

position the error shift of the ﬂowmeter is recorded. A unique assignment between ﬂow pattern and error shift is found paving

the way for an intelligent correction of ﬂowmeters.

1. Introduction

that the error is not the smallest possible one. Holden

and Peters [1] show how these limits are found for an

ultrasonic ﬂowmeter in high pressure gases.

Any look up-table procedure gives up on the chance

to see a direct relationship between the ﬂow structure

upstream of the meter and the behavior of the meter as

a reaction to it. Whenever this relationship can be

established it can be used to predict the meter reaction

on basis of the ﬂow situation. This second approach is

called the intelligent meter correction [2,3] .

It is important to emphasize what the conditions and

limitations of the intelligent meter are. The ﬂow

upstream of the meter, which is downstream of the

installation, must not be chaotic. It must have a detect-

able and reproducible structure. Fortunately, this is the

case for typical installations. They mainly generate

superpositions of elementary disturbances as described

by Gersten and Klika [4] . Yet, for good results the

resulting ﬂow has to be stationary which means a ﬁxed

ﬂow pattern at a ﬁxed position. Otherwise, the assign-

ment between ﬂow pattern and error shift would be

time dependent and not feasible or at least not very

fruitful. Generally, the intelligent correction depends

mainly on the uniqueness of the upstream ﬂow.

On the instrumentation side it must be possible to

identify the ﬂow downstream of the installation by a

simple measurement. Simple because a complex instru-

mentation cannot be implemented into a real piping

system where the intelligent corrections are needed. We

A ﬂowmeter designed to accurately measure the ﬂow

rate in a pipe has to take into account the upstream

ﬂow situation which is normally governed by a typical

installation. A bend, for example, is typical and a

meter is likely to be placed downstream of it. Other

typical installations are combinations of bends, T-

joints, obstructions and alike. The need to consider the

upstream situation has long been recognized by

researchers in ﬂuid mechanics and signal processing as

well as by manufacturers of ﬂowmeters. This paper

deals with the ﬂows generated by bend and double

bend and the corresponding reactions of an ultrasonic

meter from the ﬂuid mechanics point of view.

Obviously, various approaches are conceivable on

the way to the ‘‘perfect’’ meter of which two general

ones may be distinguished. One is to subject a meter to

as many installation situations as possible and create a

kind of look-up table telling the user what error shift is

to be expected in what situation. This is a laborious

approach which can never be completed. As a manu-

facturer can hardly spend the time and expense for

such a table he will rather specify the possible error

within deﬁned limits of application taking into account

Corresponding author. Tel.: +49-201-183-2061; fax: +49-201-183-

3945.

E-mail address: franz.peters@uni-essen.de (F. Peters).

doi:10.1016/j.ﬂowmeasinst.2003.12.004

168

C.Ruppel, F.Peters / Flow Measurement and Instrumentation 15 (2004) 167–177

have developed an appropriate pressure probe for that

purpose [5] which detects the swirl angle close to the

wall on the circumference of the pipe. It will be shown

that the swirl angle is capable of identifying the ﬂow

pattern. It provides only a limited information which

narrows the spectrum of ﬂows to the typical instal-

lation ﬂows. Yet, this compromise can be acceptable

when a substantial correction for a real (typical) ﬂow

situation can be achieved.

In this paper, we apply the pressure probe for the

identiﬁcation of the ﬂow behind the installations 90 v

bend and double bend. In the same set-up we record

the error shift of an ultrasonic ﬂowmeter. The ultra-

sonic meter presently investigated is of the transit-time

type [6] . It makes use of the fact that sound is carried

by the ﬂuid at an eﬀective speed with respect to the

wall which is either the diﬀerence or the sum of its own

speed and the ﬂuid velocity. The sound is directed

across the streaming ﬂuid as a beam such that velocity

information is collected along a line (line sensor) in

terms of time shift or frequency without being able to

reconstruct the velocity proﬁle. Therefore, there is a

principle ambiguity in determining the mean transport

velocity when the proﬁle is not known. Various designs

try to circumvent this problem by multiple paths

arrangements which penetrate the stream in more than

one direction. Some designs claim [1,6] to attain mea-

suring uncertainties below 1%. These remarkable

achievements together with the crucial beneﬁts of an

unblocked cross section and applicability to both gases

and liquids have led to a great success with a variety of

models on the market.

In the present investigation, it is shown in a ﬁrst step

how to secure a stationary (stable) installation ﬂow and

that the pressure probe is suitable for the identiﬁcation

of the ﬂow structure. In a second step, the ultrasonic

ﬂowmeter is subjected to the stationary ﬂow down-

stream of the installation in two ways. Firstly, the reac-

tion of the meter is studied as it moves away from the

installation. As the meter remains a line sensor despite

multiple paths, it can be expected to be sensitive to the

angular position of mounting relative to the orientation

of the installation. Therefore, secondly, measurements

are carried out for angular positions. Beyond that the

inﬂuence of the Reynolds number is looked at. The

results are quantiﬁed in terms of error shift with

respect to developed pipe ﬂow entering the meter.

Both steps, the identiﬁcation of the ﬂow and the

measurement of the error shift are preliminary for an

intelligent correction of the meter which is to be dealt

with in a follow-up paper.

2. Experimental set-up

The experiments were carried out in our multi-

functional ﬂow rate test rig sketched in Fig. 1 . A speed

controlled blower circulates room air through the test

and reference sections made of precision piping of 150

and 100 mm inner diameter, respectively.

The test section is segmented and assembled by ﬂan-

ges to allow variable conﬁgurations of pipe lengths and

installations including the ultrasonic meter and the

pressure probes.

The reference section incorporates a venturi at 20 d

upstream of the blower and 36 d downstream of a con-

striction which reduces the wider pipe to the smaller

one. The venturi was calibrated against another refer-

ence based on developed pipe ﬂow which can be placed

Fig. 1. Experimental set-up (multifunctional ﬂow rate test rig).

C.Ruppel, F.Peters / Flow Measurement and Instrumentation 15 (2004) 167–177

169

optionally on the downstream side of the blower [2] .

By means of pressure and temperature measurements

in the venturi the venturi diﬀerential pressure reading is

converted into mass ﬂux. The mass ﬂux reproducibility

is better than 0.2% over all tested conﬁgurations in

the test section upstream of the constriction ( Fig. 1 ).

This is an important feature because we are looking for

error shifts. The absolute measuring uncertainty is less

important.

3. Installations and their downstream ﬂow

Fig. 3. Vortex ﬂow formation downstream of a 90 v bend (left) and

a double bend (right) in the case of undisturbed inlet conditions.

Two typical installations, the 90 v bend and the dou-

ble bend, are studied. Their radius to diameter ratio is

1.5 following DIN 2605. Fig. 1 shows how they are

mounted and Fig. 2 provides the angular orientation

necessary when discussing the ﬂow.

When axial pipe ﬂow (free of swirl) enters the 90 v

bend a counter rotating vortex pair appears at the exit

( Fig. 3 , left) that was already described by Dean [7] .It

was conﬁrmed by CFD calculations [8] and measure-

ments [9] . When the bend merges into a straight pipe

this vortex pair looses strength along the pipe, yet it

maintains its circumferential position, i.e., the pattern

in Fig. 3 (left) remains in the angular position shown.

The entire ﬂow disturbance induced by the bend van-

ishes after roughly 50 D and developed pipe ﬂow pre-

vails. This was shown experimentally by Schl¨ter and

Merzkirch [10] .

When axial pipe ﬂow (free of swirl) enters the double

bend CFD calculations [8] and measurements [9] show

an excentric main vortex with an embedded smaller

one ( Fig. 3 , right). The smaller one disappears rapidly

along the pipe while the excentric pattern of the bigger

one rotates about the pipe axis with the ﬂow. At a

ﬁxed axial position in the pipe the pattern stays put.

Decay of the main vortex is rather slow with developed

pipe ﬂow restored only after 100 D [9,10] .

In a real piping system, the bend will be fed from an

upstream pipe or just another bend or installation of

some sort which means that the inlet conditions to the

bend creating the vortex ﬂow is a disturbed ﬂow itself.

Any numerical calculation on the bend ﬂow or any

experiment has, in principle, to take into account the

individual inlet conditions which they normally do not.

Fiedler [11] makes an illuminating contribution in this

context. Because of lacking lab space we cannot extend

the inlet pipe to a length that provides developed ﬂow.

In order to secure at least stable axial inlet conditions,

irrespective of the radial proﬁle, we found the Akashi

ﬂow straightener [12] to work well in contrast to an

inlet nozzle which suggests smooth ﬂow but enhances

swirl and instabilities. (It is a widespread misconcep-

tion that the bend ﬂow itself is instable.)

In order to analyze and characterize the ﬂow down-

stream of the installations one can, in principle, apply

powerful techniques as LDA, PIV or hot wire. We

wanted a simple method that can be ﬂange mounted

not requiring any support except the pipe itself. Such a

measuring ﬂange can be placed in any position includ-

ing envisaged future applications outside the lab.

For this purpose, we developed a special pressure

probe the design and calibration of which is being pub-

lished elsewhere [5] . It detects the swirl angle close to

the wall which is in pipe direction for undisturbed ﬂow

and diﬀerent from it when vortices are present.

The probe protrudes from the wall into the ﬂow for

a few millimeters. It is wedge-shaped with the edge

pointing straight upstream. A pressure diﬀerence is

recorded between two taps symmetrically located on

the two sides. This pressure reads zero when the ﬂow

close to the wall is in pipe direction and it rises pro-

portional to the ﬂow direction in the range up to 20 v .

By this probe the circumference of the pipe can either

be sampled and the ﬂow direction can be plotted vs cir-

cumferential angle H ( Fig. 5 ) providing a clear picture

of the vortex ﬂow formation. Either a single or an

array of probes can be used. The single probe has to be

moved stepwise through 360 v while the array needs less

an angle. In this work a ﬂange with eight equally

spaced probes was preferably used each ﬁtted with two

diﬀerential pressure transducers ( Fig. 4 ). When the

ﬂange is turned stepwise by 5 v it collects 80 data points

at 72 stations.

The pressure signals were digitized by the A/D

board DAQ Pad 6020Eof National Instruments at a

sampling frequency of 1000 Hz averaging over 60 s.

Fig. 2. Bend arrangements with circumferential angle H.

170

C.Ruppel, F.Peters / Flow Measurement and Instrumentation 15 (2004) 167–177

straightener is required for stable, reproducible con-

ditions.

These results for both installations were consistently

found in the investigated Reynolds numbers range

from 150,000 to 300,000.

4. Ultrasonic meter

Fig. 4. Flange with eight pressure probes.

After we have seen that the downstream ﬂow of a

typical installation can be identiﬁed especially when

measures are taken to stabilize the inlet conditions we

can now proceed to study the reaction of an ultrasonic

meter to these ﬂow cases.

A commercially available ultrasonic ﬂowmeter for

gas measurements was used. It is built for the pipe

diameter of 150 mm with ﬂange attachments according

to DIN 2633. Its design is based on two V paths. The

beams are not directed radially and not even in a radial

plane. They penetrate a measuring volume in an opti-

mized fashion the background of which we do not know

and do not need to know for the time being. The meter

is sold for the volume ﬂow rate range 14–1600 m 3 /h

corresponding to the mass ﬂux range 5–533 g/s under

our test conditions.

The manufacturer recommends a distance of 3 D to

the next upstream installation to keep accuracy speciﬁ-

cations. There is no restriction as to the kind of instal-

lation and consequently there is no requirement for a

particular angular orientation of the meter.

As we do analyze particular installations (bend and

double bend) and their eﬀect on the meter reading we

include the relative angular position as a parameter. To

do so the zero reference line is chosen in the middle

between the two V paths. The zero position for the

second parameter, the downstream distance, lies in the

center between the two ﬂanges which is also the center

of the housing. Measured from this point the pipe

begins at 0.75 D.

The reading of the meter is in m 3 /s. As for the venturi

we convert to mass ﬂux by measuring pressure and tem-

perature continuously 1 D downstream of the meter.

The output signal of the meter is a current between

4 and 20 mA proportional to the ﬂow rate which is

processed by a PCI 6024 by National Instruments.

Integration time is 90 s at a sampling frequency of

1000 Hz. The instrument was calibrated against the

venturi for developed pipe ﬂow to conﬁrm the pro-

portionality.

Data processing was carried out by LabView 6i of

National Instruments.

Results concerning the ﬂow structure downstream of

the two installations are plotted in Fig. 5 . Figs. 2 and 3

help with the orientation for H. The ﬂow angle h is

plotted vs H. It is zero when the ﬂow direction is axial

and would be 90 v for tangential ﬂow. Looking in

ﬂow direction h < 0 when the ﬂow turns clockwise. We

see that the range 20 v covers all data points. The fol-

lowing observations are worth mentioning.

In the 90 v bend case with ﬂow straightener the

h-curves are smooth with zero points at 90 v and 270 v

and maxima to both sides of the 270 v point. In com-

parison with Fig. 3 , the double vortex is clearly ident-

iﬁed. Moving downstream the zero points stay put

conﬁrming that the vortex pattern does not revolve.

The amplitude decays and dies out at 20 D. The inser-

ted CFD calculation was carried out by Ernst and

Schm¨cker [13] for the present bend geometry

assuming a square inlet proﬁle. It agrees remarkably

well with the measurements just that the damping of

the amplitude is a little too weak. The most important

ﬁnding is that the curve is not reproducible when the

ﬂow straightener is replaced by the inlet nozzle.

Clearly, under these circumstances any attempt of an

intelligent correction is less promising than in the

stable case with ﬂow straightener.

In the double bend case, the overall turn of the

vortex pattern along the pipe leads to generally nega-

tive angles h. Following the curves from top to bottom,

it is seen that the curve moves to the right reﬂecting the

revolution of the vortex pattern which is predicted by

the CFD calculations [13] . Just the predicted rotational

speed is a little low. The damping prediction turns out

better now possibly because it is weaker now as the

double bend vortex stays on to 100 D. Again the ﬂow

5. Results for the ultrasonic meter

The ultrasonic meter is now subjected to the ﬂows

downstream of the two typical installations considered

in this work. Circumferential angle H, Reynolds num-

ber and distance are varied. The error shift of the

C.Ruppel, F.Peters / Flow Measurement and Instrumentation 15 (2004) 167–177

171

Fig. 5. Flow angle h close to the wall vs circumferential angle H at various positions downstream of the 90 v bend (left) and the double bend

(right) Re 250 ; 000; measured data with Akashi ﬂow straightener; h measured date with inlet nozzle; u calculated data—CFD.

meter is measured in % according to

DF ½ % ¼ m ref m usm

m ref

ð 1 Þ

where m usm is the mass ﬂux measured by the ultrasonic

meter and m ref the reference one measured by the

venturi.

100

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