Note: Descriptions are shown in the official language in which they were submitted.
~1~7S74
- A method and a meter for measuring quantities of heat. -
~ack~round of the Invention
Field of the Invention
The invention relates to a method and a meter for mea~uring the
quantity of heat abstracted from a circulating flow of liquid by
a consumption unit based upon the indirect measurement of the
volume flow rate of the liquid, while maintaining a sub heat flow
from or to the main heat flow transported by the flow of liquid
and measuring the temperature at some points by means of tempera-
ture sensors. Such a heat may for instance be provided in city
wide heating networks for consumption on small æcale by the con-
sumers.
Description of Prior Art
.
In the future, city heating networks will be used in a progres-
sively increasing number of towns and districts in which each house
will obtain a connection to a public heating network instead of
its own boiler for central heating. From this conneotion the con-
sumer will obtain the hot water for his home heating system andtap water supply either directly or indirectly by means of a heat
exchange.
It has become evident that consumption by individual consumers
(and thus total consumption) in such city heating system decreases
when the amount of heat consumed by the individual ccnsumer is
measured. From the heat quantity meter the consumer will then have
an idea of the cost of his heating. For this reason the installa-
tion of heat quantity meters for consumption on small scale is
considered to be useful.
Existing meters such as, for instance evaporation meters, often
have the drawback that they are not accurate enough. With respect
to others, such as meters including turbine parts, the initial cost
and/or maintenance cost are too high.
Summar~ of the Invention
~0 The object of the invention is to provide a method and a heat
quantity meter not exhibiting the above mentioned drawbacks among
other things by the complete absence of moving parts or measuring
.
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flanges in the flowing liquid so that there are no obstructions in
the supply and return conduits. This will lead to a considerable
decrease in maintainance of the meter.
In accordance with the invention this object is attained in that
the volume flow rate of the liquid is determined on the basis of
the flow rate dependent heat transfer in the boundary layer of the
flow of liquid at the location where the sub heat flow leaves or
enters. The temperature differential across the boundary layer and
the sub heat flow passing through said boundary layer i8 determined,
while measuring at least one absolute temperature of the flow of
liquid for correcting the temperature dependency of the material
constants of the liquid involved in the determination of the volume
flow rate.
~rie~ Description of the Drawin~s
The present invention will now be elucidated further with refe-
rence to the annexed drawings in which like numerala denote like
element :
Fig. 1a shows a basic sketch of the conduit sections including
a thermal shunt connection of the heat quantity meter;
Fig. 1b shows a side elevation of a part of a conduit section
having a bar shaped shunt connection according to fig. 1a fastened
thereto by means of an angular junction;
Fig. 1c discloses a diagrammatioal view of the heat quantity me-
ter including its temperature measuring points and the imaginary
heat resistances R1 to R4, inclusive;
Fig. 1d discloses the relation between the measured volume flow
rate and the measured temperatures;
Fig. 2 shows a side elevation of a production embodiment of the
heat quantity meter;
Fig. 3a, b, c, and d shows a side elevation of four variants of
the junction of the shunt connection to a conduit section; and
Fig. 4 shows a side elevation of a variant of the location of
a temperature sensor.
Description of a Preferred Exem~lar~ Embodiment
The operation of the heat quantity meter in accordance with the
present invention is based solely on the measurement of a number
il~757~
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of temperatures. Use is made of the fact that the heat transfer
between the heat carrier or flowing liquid and a body, in which
or along which this liquid i8 transported, is dependent among
other things on the flow rate of the liquid at the relevant loca-
tion. The more this flow rate increases the better the heat trans-
fer will become. It is now aimed at measuring this coefficient of
heat transfer.
When employing this method easily measurable temperature diffe-
rentials occur without being accompanied by large (and consequent-
ly unacceptable) heat losses in the main flow as in a thermal flow-
meter. In a known flowmeter as i9 for instanoe known from the
French Patent Specification 2,353,045 one tries to minimize the in-
fluence of the laminar sub or boundary layer among others by a
special shape of the wall surrounding the flow of liquid. In the
present method and meter a measurement is made of the coefficient
of heat transfer of the laminar sub layer of the flow of liquid
considered to be turbulent.
Where this measurement can not be performed directly a sub or
leakage heat flow is allowed to form which is dependent on the
coefficient of heat transfer. For this purpose there is provided
an energy connection or, in particular, a thermal connection be-
tween the supply and drain or return conduit.
In the connection thus provided there will occur a heat flow de-
pendent on the difference in temperature between the hot water in
the supply conduit and the cooled water in the return conduit as
well as on the total heat resistance. This total heat resistance
consists of a fixed component determined by the thermal connec-
tion possibly in combination with the walls of the conduits, and
of a variable component mainly determined by the flow of the
liquid in the thermal boundary layers. ~he magnitude of this
branched heat flow may be measured by means of a temperature diffe-
rential measurement. ~he magnitude of the temperature differential
across one or both of the boundary layers together with the ma~-
nitude of the heat flow through the connection determine the coef-
ficient of heat transfer in situ.
In the general case of an energy connection, apart from the heatflow by conduction, radiation or convection, a heat transport due
to thermo-electric effects may also occur if the connection is
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electrically conductive. The electric current generated
in this case (possibly by the Seebeck effect) will then be
a measure for this form of energy or heat transport.
The absolute temperatures of the flows of liquid at
the location of the boundary layers are also of importance,
because the relevant material constants, like the coefficient
of heat conduction ~ , the specific heat c (weakly), and
the viscosity ~ (strongly), are dependent on temperature.
The coefficient of heat transfer together with the
several material constants fixedly determine the velocity
gradient in the boundary layer. If the velocity profile
in the conduit is also governed and reproduceable, then
there will be an unambiguous relation between several tem-
peratures and the volume flow rate of the liquid, and conse-
quently between these temperatures and the net heat flowrate.
The signals supplied by the temperature sensors are
processed in accordance with an empirically determined
relation by an electronic unit into a quantity of heat per
each unit Gf time or a time pulse per quantity o heat. By
employing an integrating, summing or pulse counter circuit
in the electronic unit, a total supplied quantity of heat
per each chosen period of time can be accumulated,
By having the meter constructed symmetrically both
the volume flow rate in the hot supply conduit and in the
colder drain conduit may be determined and compared with
each other.
With reference now to Fig. la there is shown a basic
sketch of a meter in accordance with the present invention,
in which the reference numeral 1 indicates the supply
conduit, the reference numeral 2 indicates the drain or
return conduit and the reference numeral 3 indicates the
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- 4a -
bar shaped thermal shunt connection. The temperatures
Ti, Tb, To, T or temperature differentials may be measured
by means of sensors 4, such as thermo~couples, to which
a sensitive amplifier is connected. The thermo-couples
mav be soldered onto or into the material.
With reference to Fig. lb there is shown a side
elevation of a cross section of the angular junction of
the thermal shunt connection 3 to one of the conduits
1 or 2. Likewise the laminar boundary layer 7 of the
liquid at the tube wall of the conduits has
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1~47S7
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been indicated. ~he reference numeral 4 denotes the junction
contact of the temperature differential sensor. This temperature
differential sensor may be also consist of two separate absolute
temperature sensors.
~or this type of heat transfer problems concerning the boundary
layer one may apply a theory known in the theory of flows as the
so called "film theory". In turbulent flowæ of liquid (as will
occur in the supply and the drain conduits) one may consider
the larger part of the velocity gradient and the entire tempe-
rature gradient to be in the laminar sub layer at the wall. Ingeneral one may start from the empirical relation:
~'
,
,
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Nu = 0~024 (1 + L) 0~66 ReO'8 PrO'33 (~vl ) '14 (1)
in which:
Nu is the Nusselt number which is a measure for the coef-
ficient of heat transfer of the boundary layer.
(1 + L) is a correction factor accounting for the inlet or
starting area of the thermal boundary layer and in-
cluding therein the ratio of the conduit or pipe di~-
meter D and the distance L over which the heat trans-
fer occurs.
10 Re is the Reynolds number relating the specific mass p ,
the rate of flow v and the conduit diameter D with the
viscosity ~ of the liquid.
Pr is the Prandtl number indicating the ratio between
impulse transport (friction) and heat transport. This
is an zssembly of material constants, such as the spe-
cific heat c, the viscosity ~ and the specific conduc-
tivity A of the liquid. This therefore is a (tempera-
ture dependent) material constant per se.
(~wl) is a correction term for the fact that the viscosity
of the liquid in the turbulent center portion differs
from that directly at the wall where a different tem-
perature will prevail.
The relation (1) indicates that the coefficient of heat
transfer a is about proportional to the output or volume flow
rate to the power 0.8.
~ second relation, i.e. the generally known relation also
applies to the meter of ~ig. 1a, b:
Qm = ¦ ~ c 0 ~ Ti Udt (2)
in which
30 Q is the quantity of heat that the meter will have to
indicate
y is the specific mass of the liquid
c is the specific heat capacity
.~ .
75~7
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0 is the output or the volume flow rate
i,u the difference in temperature between supplied and
discharged flow
dt is the factor time to which the integration is per-
formed.
When one takes the derivative ofrelation(2)(because thisprovides
for a simple electronic analog), and combines both the rela-
tions (1) and (2) the result will be
Qm = f( A, ~ ~ ~W~ c, D, ~ '2.56 Ti u (3)
in which
Q is the first derivative of the quantity of heat, i.e.
the heat flow per each unit of time
f(/~ ,c,D,~) is a function of the aforesaia meterial con-
stants and of the dimensions of the meter. When used
in practice f will be mainly a function of Ti and to
a lesser degree of ~ ~i u
i8 the expected actual coefficient of heat
transfer.
~ i,u is the difference in temperature between the supplied
and discharged flow.-
Consequently relation (3) may also be written as follows
' 1,25
Qm f(~ i,u)~ i,u (4)
~ his makes it clear that for determining Qm it suffices to de-
termine ~ and a Ti U- ~his may be performed by measuring four
temperatures in the meter box.
~ ig. 1c diagrammatically shows the æupply and the return con-
duit including the thermal shunt connection. In th~se parts there
have been drawn the imaginary heat resistances R1 to R4 inclu-
sive while it has been indicated diagrammatically at which points
the four temperatures Ti, Tu~ Tb, ~O are mea9ured-
~herein:
~1 is the heat resistance of the boundary layer at the
hot side,
R2 is the heat resistance of the tube raw material and
~1~7574
the composite body,
R3 is the heat resistance of the thermal shunt connection,
and
R4 is the heat resistance of the boundary layer and the
material resistance at the colder side.
~he first resistance R1, the boundary layer resistance, is
formed by the coefficient of heat transfer a(which haa to be de-
termined)and the surface area F across which the thermal shunt
connection abstracts heat from the flow in the conduit. ~his
surface area is substantially fixed by the dimensioning of the
meter. ~he edges are subject to some di~placement beyond the
original area, and the heat transfer by the pipe w~lls outside
the composite body also will play a role upon decreasing flow of
liquid. ~his increase of surface area will be indicated below as
the border (line) effect.
The second indicated resistance R2 i9 formed by the intermedia-
te material because a direct measurement of the wall temperature
is difficult. The third resistance R3 i9 that of the shuntconnection
between ~b and ~0, which resistance determines the heat trans-
port by the first two resistances.
~he coefficient of heat transfer may be determined by measu-
ring ~ ~i b and the heat transport in accordance with
R1 (5)
and
R1 + R2 R~ (6)
a ~i b ~ b,o
which may be combined as follows
3 ~ = ( FR3 x ~ 2 ) (7)
b,o
~y combining the relation (7) with the relation (4) the follo-
wing i9 obtained
~, J~
1~47574
g
~ Ti b
Qm = f1 (Ti- a Ti,u) f2 (~ Tb ) ~ Ti,U (8)
~ ased on this theory it appears to be possible indeed to deter-
mine the heat consumption by measuring four temperatures.
~rom these temperatures the differential values a Ti U~ ~Ti b
and ~ Tb O as well as the quotient of the latter two may be cal-
culated. Subsequently these arguments are translated with the aid
oi` tables and the two above mentioned function values, whereupon
two multiplication operations provide the instantaneous
heat consumption Qm.
The above notedfunction curves(f1, ~)have beendetermined empiri-
cally.In orderto explain thismeasurement,relation (2) should~ be
compared with relation (8). It then appears that it will be ne-
cessary to investigate the relation between on the one hand ~ c0
and on the other hand
~ ~i b
~ Tb ' Ti and ~ Ti u .
Fig. 1d shows the relation between the measured volume flow
rate and the measured temperatures when performing this type of
test . Along the ordinate the normalized value of thte product
~ c 0 has been plotted and along theabscissa the ~ quotient of the
measured temperature differentialsh Ti b and ~Tb O~ while the
temperature Ti occurs as parameter. These measurements have been
performed at a fixed value of ~ Ti u ~ased on a number of tests
(in which first of all special attention was paid to the repro-
ducability)it was concluded that it is possible to record
the course of the function of ~ c 0 andd ~i.b in one table
b,o
and that simple corrections of arithmetic nature could be intro-
duced in the table values to compensate for the influences of
. and ~ T
l , U
~y correctly shaping the shunt connection as regards length
3 and cross section inconjunction with the choice of mate-
rials for the connection and the tube,together with the asso-
ciated coefficients of heat conductivity,itTappears to be pos-
sible to keep the course of the quotient ~ , as the functionb,o
;' ~ .
.
,
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-1 O-
of the volume flow rate(over a C 0 measuring range of 1 to 40),
between the limits of 1/8 to 8. ~his provides acceptable mea-
surable temperature differentials ~ Ti b or a Tb at a given
minimum temperature differential between supplied and drained
flow (~ ~i u)f 10C.
~ he calculation of the differences, quotients, products and
the handling of the table including the introduction of arith-
metical corrections of the results is performed in this instance
by a micro computer in IC-format.
With reference to Fig. 2 there has been shown a possible embo-
diment of the heat quantity meter ac¢ording to the invenion. In
this figure the reference numerals 1 and 2 indicate the supply
and drain conduits, respectively, the reference numeral 10 the
housing of the meter, the reference numeral 8 the electronic
processing unit, the reference numeral 9 the electric power unit
and the reference numeral 11 the reading panel (display).
An electronic signal processing unit capable of computing the
total heat flow from four absolute temperatures on the basis of
relation (8) has been realized by means of micro elect~nics as
already used in pocket computers. In view of the micro electro-
nics already present this meter will possess additional posssi-
bilities such as telemetric reading, control of system functio-
ning, day/night/season tariff, etc.
Also within the scope of the invention the meter may be applied
solely for the determination of volume flow rates of liquids.
Some important aspects with regard to the measurement princi-
ple of the present heat quantity meter are among others:
a. The dimensions of tne heat transferring surface area within
the conduits and the dimensions or nature of the thermal
shu~t conneftion.
a sence o a
b. ~e~requirement of a shunt connection for creating a partial
or sub heat flow. Even a (measurable) heat exchangeAfrom the
surroundings offers the possibility to determine the proper-
ties of the boundary layer and consequently the volume flow
rate via temperatures.
c. The influence of foreign components in the water circulation
that might deposit on the wall and might consequently influ-
.. ~ ,
.: .
11~7574
ence the heat resistance of the boundary layer.
d. ~he flow profile of the flows of liquid and the contacting of
the heat transferring surfaces;
e. The choice of the temperature measurement points in or on the
thermal shunt'connection and the choice of the shape by means
of which the shunt connection is coupled to one or both of
the conduits.
With respect to item a above,
the surface in which the thermal connection i9 joined to the
conduit, is limited. The heat transport by this connection is
continued not only at the location of this junction but also in
the surrounding conduit walls. The influence of this border ef-
fect is dependent on the'wall thickness of the conduit, the co-
efficient of heat conductivity of the materials used and the co-
efficient of heat transfer of the flowing liquid to the'conduit
wall and consequently on the volume flow rate.
The border line effect tends to cause a deterioration of the
non-linear relation between the temperatures to be measured and
the heat flux to be determined. The influence of this border ef-
fect may be restricted by thinning the conduit wall at the lo-
cation of the edges with the thermal connection or by providinga piece of insulating material ~5 in Fig. 4).
With reference to Figs. 3a and b there are shown two
examplas of a conduit section including a shunt connection fas-
tened thereto by means of a point junction~gand3a)conduit section
including a s~uFnt co3n~ection 3 fastened thereto by means of an
annular junctlon~ In both the embodiments the border effects
will act differently. The ratio of edge length
to transfer area is larger for the point junction than for the
annular junction. Moreover,the point junction possesses edges in
the longitudinal direction of the flow whereas the annular junc-
tion possesses only edges in the transverse direction.
With reference to Fig. 3c there is shown a further vari-
ant of the annular juncticn in which the block shaped shunt con-
nection is brought in contact with the flows over a greater
length than width. The participation of the edges is thereby re-
r~ ;` latively small. ~ile junction pieces 14 consist of a good
757~
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heat conductive material, such as coppper, whereas the fixed re-
sistance part 3 between the junction pieces 14 is made however
of aless heat conductive material, such as stainless steel, so
that within a small volume efficient heat resistance is provided.
The highly conductive junction pieces 14 lessen the critical
character of mounting the temperature sensors for measurement of
To and ~b.
With reference to Fig. 3d there has been shown a side eleva-
tion of a coupling body 6 arranged coaxially within a conduit
section 1, 2 at the end of the thermal connection 3. ~he coaxial
arrangement has the advantage that the flow rate in the center
of the conduit contributes most to the output. Moreover the flow
contacting form of the coupling body may be chosen in such a
manner that there will be a simple relation between the heat
transport through the conduit and the temperature differential
measured across the thermal connection. It has therein clearly
been indicated that a thermal insulationring 5 may be provided
between the thermal connection 3 and the wall of the conduit 1,
2 in order to suppress an optional heat transfer from or to the
wall of the conduit.
With respect to the foregoing item ~,
i~ those systems in which the supply and the drain are not near
enough to each other and the heat transport for the sub flow
by means of Peltier effects is impossible or i9 hampered by
practical considerations, it it possible to make the desired heat
transportoccur from thesu~ply conduit to the surroundingsor ~iceversa
or heatlng
by means of a cooling~body. In that case the drain conduit isno
longer necessary for determining the volume flow rate of
the liquid and/or the heat output. However, the sub heat flow
or from
to~the surroundings will have to be measured because this flow
keeps playing a roll in the electronic signal processin&.
~ he same may be performed with the drain conduit, however,
in that case the temperature differential with respect to the
surroundings will be much smaller and the direction Or the sub
heat flow will also run from the inside to the outside.
With respect to item c above, substances for preventing corrosion
are often added to the circulating water of the city heating net-
work. In the future, presum-
1147574
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~ly yet other substances may be added in order to operate at a
lower stowing force of the pumps (drag reduction). It may be
possible that some substances will influence the heat transfer
properties of the liquid boundery layer to the walls. No indi-
cations of this sort, however, have yet been found bytests including oxide particles, salt solutions and suspensions.
Accordingly the fear of such effects is greatly
lessened.
With respect to item d above,
the relation between the water output or volume flow rate of
the water and the variable heat resistance is determined by
physical effects in the boundery layer. In a turbulent flow of
liquid ~s is the case in the present heat mete~ one may presume
that substantially the main part of the flow rate gradient and
the entire temperature gradient is to be found in the laminar
boundary layer. This boundary layer has a thickness in ths mag-
nitude of some tenths of micrometers.
The profile of the flow determines the relation between the
output and the flow rate gradient at the location of the boun-
dary layer. The profile of the flow should therefore be control-
ledinorder to maintain the relation between temperatures and
heat flux.~ends, valves, couplings, etc have their own influence
on the profile of the flow, BO that the length of the conduit of
the heat meter is bound to a minimum, presently ten times its
own diameter. The interfering influences of the above mentioned
accessories may be suppressed by correctly shaping the inlet
opening so that a shorter length of the conduit of the heat me-
ter may suffice.
With respect to item e above,
in a connection constructed like represented in Fig. 4 the
field of isotherms,by means of which the heat flow via the
boundary layer manifests itself ln the materia~ of the conduit
wall and shunt connection,is notradially symmetric.~ symmetricalfield
is, of course,impossible because the heat ultimatelyhas to flow in
one direction, for instance towards the other conduit. The heat
flow occurring in the head side of the connection (at 4 in Fig.
4) will have to flow via the sides to the central middle por-
~1~L757~
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tion. Consequently an additional decrease in temperature will
occur in the sides. This additional decrease in temperature appears
to be dependent on the flow. ~his is because increa-
sing volume flow rate of the liquid~the boundary layer resis-
tanceto becomesmaller so that the material resistances will beco-
me of greater influence on the heat flow lines in the side~. As
a result thereof there will occur a different temperature dis-
tribution.
Empirically it has been found possible to give the junction
according to ~ig. 4 such dimensions that the change in the Ti b
signal, by measuring at the head side (point 4), causes such a
change in the quotient ~ ~i b/ ~b O that the relation between
this quotient and the volume flow rate or output of liquid may
be straigtrened within acceptable limits over the entire measu-
ring range from 1 to 40. ~he term "acceptable" should thereby beunderstood as 1% within the final answer.
