A new flowmeter for the dynamic flow rate measurement

RESEARCHANDTECHNICALNOTES

A new flowmeter for the dynamic flow rate measurement W. Reichel

Nomenclature

possible. An alternating current bridge circuit is the only electronics unit required. Commercial carrier-frequency measuring amplifiers can be directly connected with the flowmeter for information processing.

A

diaphragm surface

a, b

geometrical quantities of inductance

C

resistance coefficient

Theoretical fundamentals

F

force acting on the diaphragm surface

When a body is approached by a fluid, a force F acts on it:

L

inductance

R

electrical resistance

Re

Reynolds-number

s

gap width

U

voltage

V-'

flow rate

v

deflection of diaphragm

l+'

fluid velocity

x

galvanometer deflection

/J

permeability

p

fluid density

(1)

F = C A p W2/2

and the body will be deformed, if the design is suitable. In our case, a thin-walled invar diaphragm is used (Fig. 1). The diaphragm with a hole is deformed proportionally to the action of force, v ~

F

(2)

and the gap between the diaphragm and the induction coils is thus varied ~ effecting a variation of inductance. 2

aI.II,

= -

as/((a

(3)

+ b)/u + S)

If the opposite coils one and two are connected within a bridge circuit, the bridge voltage of the deflection can be measured.

In general, turbine or oscillator flowmeters are used for the flow rate measurement in cryogenics. Such flowmeters have a relatively high time constant and are subject to wear. The electronic equipment for analysis of the measuring signal is quite complex. The new flowmeter is simply designed and does not have any moving components in bearings. It consists of a variable diaphragm the deflection of which, in the direction of flow, is a measure of the flow rate. The deflection is found by a non-contact measurement with the induction coils arranged axially around the diaphragm (Fig. 1). The new flowmeter has a very low time constant and can measure pulsating flows below 100 Hz. The measuring device operates independently of the direction of flow. Thus, flow rate measurements on the back-flowing fluid have become The author is at Technische Universitat Dresden, 8027 Dresden, Mommsenstra#e 13, Sekt. Energieumwandlung, GDR. Received 19 June 1978

CRYOGENICS . JANUARY 1979

Induction coil 2 " ~ ~

~

lnduction coil I

Fig. 1 Diagramshowing the design of the flowmeter

55

U ~- v

(4)

x

~

cw

2 ~

cr n

(s)

(6)

C = f(Re)

The circuit is represented in Fig. 2 where the bridge is supplied with alternating current. In the case of pulsating flow rates, the loop oscillograph can be advantageously used for the voltage measurement. The galvanometer deflection x is proportional to the square of the fluid velocity and resistance coefficient

Fig. 3 shows a flowmeter. The two halves of the casing were made of stainless-steel and contain the induction coils. The diaphragm is held by the two halves of the casing. In its range of measurement, the flowmeter can be varied within wide limits by means of the diaphra~n thickness and the diameter of the diaphragm hole. Fig. 4 shows a characteristic calibration curve, recorded at p = 0.2 MPa LN2 with a loop oscillograph and a 150 Hz mirror galvanometer.

~2

With the measurement technique used, at pulsating flow rates below 100 Hz a measuring error of 1.0% is achieved. -

Li

L2

IOO

/P3

~4

80

U~

Fig. 2 The circuit diagram showing the alternating current bridge

60 E E

40

20

0

2'0

4'0

6'0

80

I00

I)j cm 3 5-I Fig. 4 The characteristic calibration curve of the f l o w m e t e r recorded at 0.2 MPa LN 2

References Fig. 3

Photograph of the flowmeter

Woschni, E.G. Mel3gr6t3enverarbeitung S. Hirzel Verlag Leipzig 1969 GDR Patent WP GO 1 F/199 789

Precision table for surface scattering in foils V. Groger The surface scattering of conduction electrons has been described by several physical models Fuchs, 1 Br~ndli and Cotti, 2 Parrott, 3 and Soffer.4 In practice the Fuchs I model is usually favoured for the interpretation of experimental results because in most cases there is no appreciable difference in its results from the more sophisticated models. The Fuchs 1 boundary conditions assume the electron to be scattered at the surface either specularly (with a probability, p) or diffusely. The surface parameter p describes the surface conditions and was often supposed to be zero. Since unfortunately complicated numerical calculations are involved, a short table for generalized variables should be very useful if the accuracy could be high enough. The author is at the Tieftemperaturphysik, Universit~t Wien. Received 2 October 1978.

56

Dworschak et al s give a table with 341 data points describing foils with parameter values p = 0, 0.2, 0.4, 0.6. The maximum error seems to be 8 x 10 -a. Later critical investigations on rolled high purity copper foils (Schwartz and Stangler, 6 Gr6ger and Stangler 7) have shown, that p values of 0.7 or 0.8 can also be realistic. Chopra et al s' 9 have found p = 0.8 for evaporated Ag and Au films. Therefore a tabulation should include the whole physical range of p values. An improvement in accuracy would also be desirable in a table which is as short as possible. The table which we have established is given below and it satisfies these conditions. The expression for the electrical resistivities of foils given by Dworschak et al s (equation 1) was generalized further in this paper for thermal resistivities (equation 2) using the

CRYOGENICS. JANUARY 1979