Constant temperature gradient fluid mass flow transducer

A constant temperature gradient fluid mass flow transducer is described. The upstream and downstream ends of a measuring section of a capillary tube of the transducer are held at respective constant temperatures by separate temperature regulated heat sinks, the downstream end being hotter. A heat conducting outer tube surrounds the measuring section and joins the heat sinks to cause the measuring section temperature to assume a substantially linear profile at a constant gradient. An electrical heater supplies heat uniformly to the measuring section to replace that transferred to the flowing fluid within the capillary tube and thereby keep the temperature and gradient constant. The voltage across the heater, proportional to the square root of mass flow rate, is taken as the output signal.

FIELD OF THE INVENTION 
This invention relates to the field of fluid flow measurement and control. 
More particularly, it relates to thermal mass flow transducers, which 
produce an electrical signal indicative of the mass flow rate of a fluid 
through a measuring channel. 
BACKGROUND OF THE INVENTION 
The ability to measure and control the flow of fluids, both liquid and gas, 
is vital not only to research and development, but also to small and large 
scale production processes. Fortunately, the way in which a fluid stream 
divides between a large delivery channel and a small bypass channel can be 
well defined. A small, accurate flow rate transducer, applied to measure 
the flow in a small loop tapped off a large pipeline can be calibrated to 
reflect the flow rate in the pipeline; its electrical output signal can be 
used to control the fluid flow in the pipeline. Accurate transducers, 
therefore, that respond quickly to changing flow rates, provide stable, 
repeatable output signals and are of small size, are in demand for small 
and large applications alike. 
One type flow rate transducer that can be made in a small package is the 
thermal mass flow transducer. It has long been known that the rate of heat 
transfer to a fluid in a laminar flow channel from the walls of the 
channel is a rather simple function of the temperature difference between 
the fluid and the channel, the specific heat of the fluid and the mass 
flow rate of the fluid within the channel. See, for example, P.B.S. 
Blackett, et al.; "A Flow Method for Comparing the Specific Heats of 
Gases"; Proc. R. Soc. London; A 126; pp. 319-354 (1930) (wherein the 
authors observed that where a laminar flow tube is provided with a 
constant gradient at zero flow, the nonlinear changes in the temperature 
profile of a tube to changes in the rate of gas flow through the tube is 
directly proportional to the product of the rate of flow and the specific 
heat of the gas flowing through the tube, p. 322) The thermal mass flow 
transducer is based on this relationship. Since the specific heat of a gas 
does not vary significantly with pressure or temperature, a thermal mass 
flow transducer calibrated for a particular gas can give true mass flow 
readings over a wide range of operating conditions. 
Thermal mass flow transducers therefore include one or more heating 
elements for transferring heat energy to a fluid stream flowing in a small 
laminar flow tube, sometimes known as a capillary tube. The heating 
elements are usually made of an alloy having a high temperature 
coefficient of resistance. The tube is usually thin, and the elements are 
usually wound tightly around the outside of the tube to provide effective 
heat transfer to the fluid without disturbing the fluid flow within the 
tube. The high temperature coefficient makes these heating elements also 
very good devices for sensing the temperature of the tube, and they are 
often employed in that double capacity. For clarity, such double duty 
heating/sensing elements will be referred to herein as thermal elements. 
Thermal fluid flow transducers have tended to develop into two basic 
varieties, which may be designated the differential sensing variety and 
the constant temperature variety. In the differential sensing variety of 
flow rate transducer, as disclosed by U.S. Pat. Nos. 3,851,526 and 
4,548,075, for example, two identical thermal elements may surround a 
laminar flow tube in a symmetrical tandem arrangement, one element being 
upstream of the other. A constant current electrical source feeds both 
elements in a series circuit arrangement. The temperature differential 
between the elements is used as the measure of mass flow. The response of 
this transducer to a change in flow rate is relatively slow because of the 
need to reestablish equilibrium in the channel temperature profile for 
each reading. 
In the constant temperature variety of flow rate transducer, as disclosed 
for example in U.S. Pat. No. 4,464,932, the laminar flow channel may be 
heated to a controlled temperature that is above the ambient. The power 
required to maintain the temperature of a single thermal element located 
within the temperature controlled area is used as the measure of fluid 
mass flow. Since the average temperature of the flow channel is held 
constant, this type transducer reacts much more quickly to flow rate 
changes than does the differential sensing variety, and it has met with 
considerable commercial success. In the known constant temperature flow 
transducers, however, the temperature profile of the flow channel does not 
in fact remain constant. As the flow rate increases, portions become 
cooler while other portions become hotter. Reestablishing thermal 
equilibrium involves the thermal inertia of the channel, and does take 
some time. Another disadvantage is that the output is not zero when there 
is no flow. It must be balanced by an offset voltage, introducing the 
problem of stability of readings. 
A "hybrid" arrangement is described in pending U.S. Application No. 581,285 
filed Sep. 12, 1990 in the name of Charles F. Mariano and assigned to the 
present assignee. This hybrid arrangement includes the principal 
advantages of both the differential sensing variety and the constant 
temperature variety of flow rate transducer without the disadvantages. 
An object of the present invention is a flow rate transducer that responds 
quickly to flow rate changes. 
Another object of the present invention is a constant temperature type flow 
rate transducer that is very stable. 
SUMMARY OF THE INVENTION 
A mass flow transducer embodied according to the invention comprises a 
laminar flow channel, means for establishing a substantially constant 
temperature gradient along a defined portion of the flow channel, 
temperature regulating means including heating means for maintaining the 
temperature profile, and hence the gradient in the presence of an 
undetermined flow rate within the channel, and output means responsive to 
the energy consumed by the heating means for indicating the mass flow rate 
within the channel. 
With the temperature profile of the flow channel held substantially 
constant, only the flowing fluid being measured undergoes a temperature 
change. The invention therefore provides a substantially faster response 
to changes in flow rate than a conventional constant temperature type flow 
transducer. In addition, since the heating means need supply no heat in 
the absence of flow, a stable zero reading may be obtained. 
Other objects of the invention will in part be obvious and will in part 
appear hereinafter. The invention accordingly comprises the apparatus 
possessing the construction, combination of elements and arrangement of 
parts exemplified in the following detailed disclosure, and the scope of 
the application of which will be indicated in the claims.

DETAILED DESCRIPTION 
The physical structure of an exemplary mass flow transducer that embodies 
the invention is shown in the cross sectional drawing of FIG. 1. In this 
embodiment, a capillary flow tube 11, which may advantageously be of 
stainless steel, runs through the center of the transducer. A thermal 
clamp 13 which may be of copper or brass, for example, surrounds and is 
tightly coupled thermally to the entrance, or upstream end of tube 11. 
Another thermal clamp 15 is similarly coupled to the downstream end of 
tube 11. Thermal elements 17 and 19, which can sense temperature as well 
as supply heat, are wound around thermal clamps 13 and 15, respectively, 
in a close heat-exchanging relationship. These elements are used to hold 
the respective temperatures of the thermal clamps constant. A third 
thermal element 21 may be wound around the section of tube 11 between 
thermal clamps 13 and 15. This section of the capillary tube, designated 
section 24, is the measuring section. A heat-conducting tube 23 surrounds 
section 24 and element 21 and is thermally connected to both thermal 
clamps 13 and 15. Finally, insulating material 25 may surround tube 23 and 
thermal clamp 15 to reduce heat losses and make the system less suseptable 
to ambient fluctuation effects. 
The embodiment of FIG. 1 operates to provide improved transducer 
performance in the following manner: With zero flow through tube 23 
thermal elements 17 and 19, thermal clamps 13 and 15 and heat-conducting 
tube 23 establish a thermal profile in flow tube 11 as described by 
elementary heat analysis and such as that illustrated by solid line 27 in 
the graph of FIG. 2. In this Figure, the ordinate is the temperature of 
the capillary measuring tube, and the abscissa is the distance along the 
tube from the upstream side of thermal clamp 13. Thermal clamp 13, 
therefore is heated by element 17 to a first temperature T.sub.1, that may 
be only slightly above the ambient temperature, and thermal clamp 15 is 
heated by element 19 to a higher temperature T.sub.2. Electrical circuits 
to be described later hold these thermal clamps at the respective 
temperatures. Outer tube 23 conducts enough heat between the thermal 
clamps to establish a constant temperature gradient (i.e., a linear 
temperature profile), as illustrated by the sloping part of curve 27. As 
will become evident, maintaining the linearity of the temperature profile 
for all mass flow rates is important. Heat loss from tube 23, whether by 
convection, radiation or conduction, introduces nonlinearities into the 
temperature profile. Insulation 25, therefore, minimizes the convective 
heat loss outside the transducer and helps toward establishing linearity 
of the temperature profile. External heat loss from the thermal clamps, on 
the other hand, does not affect the linearity of the temperature profile, 
but does increase the power required to maintain the respective constant 
temperatures. Since temperature T.sub.1 is not much above the ambient, 
thermal clamp 13 may electively be uninsulated and even thermally 
connected to a large and stable thermal heat sink. In the absence of fluid 
flow within it, therefore, the temperature of capillary flow tube 11 
assumes a profile similar to curve 27. That is, the input section of the 
tube within thermal clamp 13 is at temperature T.sub.1, the output section 
within thermal clamp 15 is at temperature T.sub.2, and the temperature of 
measuring section 24 rises linearly from input to output. In this zero 
flow condition, no heat energy need be supplied by thermal element 21 to 
maintain this profile. 
When the temperatures of thermal clamps 13 and 15 are set and maintained 
respectively at T.sub.1 and T.sub.2, the temperature profile of the tube 
becomes substantially that represented by the solid line 27 of FIG. 2 (a 
constant temperature gradient), and will remain as such regardless of the 
flow rate through the tube. The temperature profile of fluid flowing 
through the tube at a given flow rate is shown by the dotted line 29. The 
dashed line 31 represents the fluid temperature profile when flowing at a 
relatively higher rate than that depicted by line 29. Thus, the 
temperature of the fluid flowing through the tube between the thermal 
clamps assumes a linear profile at a temperture differential .DELTA.T 
below that of the tube. Different flow rates will establish different 
.DELTA.T's as shown in FIG. 2 by .DELTA.T.sub.29 and .DELTA.T.sub.31. 
However, for a given flow the heat flux transferred from the tube to the 
gas is uniform along the tube since heat flux depends directly on 
.DELTA.T. Thus, a resistive heating element 21 may supply a uniform heat 
flux to maintain the tube's temperature profile as depicted by the solid 
line 27. If heat is added uniformly along this section, therefore, the 
gradient still remains the same. Thermal element 21 is designed to do just 
that. Thus, when the average temperature of the measuring section 24 is 
kept constant according to the invention, the entire temperature profile 
of the section remains constant. Since the energy supplied to thermal 
element 21 goes almost entirely to replace that lost to the fluid by 
measuring section 24, the rate at which it is supplied, i.e., the power 
dissipated by the element, is a linear measure of the mass flow in the 
tube. 
The mass flow transducer just described provides several significant 
advantages over current popular types. First of all, it has a 
substantially quicker response to changes in fluid flow rate. The response 
time of thermal mass flow transducers in general depends upon the amount 
of thermal mass that must change temperature and the magnitude of the 
temperature change. Since, according to this invention, the measuring 
section of the capillary tube undergoes no significant temperature change, 
but only the fluid being measured, the mass involved in a flow rate change 
is only that of the fluid, and the response of the transducer is extremely 
fast. A computer simulation of the embodiment of FIG. 1, using a stainless 
steel capillary tube of 0.026 inches I.D. and 0.042 inches O.D., yielded 
response times in the order of ten milliseconds. 
A second advantage is that at zero fluid flow, there is little or no output 
signal. With prior constant temperature devices, it takes considerable 
heat, supplied by the device sensor to maintain the temperature of the 
sensor above the ambient. The voltage across the sensor, therefore, is 
high at no flow, being as high as three quarters the full range. This 
leaves much less voltage for the measurement, providing a lower 
signal-to-noise ratio, and introduces instability if the zero flow voltage 
is balanced out to give a zero no flow reading. With the transducer of the 
invention, the only power supplied to the sensor at zero flow is that 
needed to measure temperature. This uses up typically in the order of 
one-quarter the full range value, the rest being available for flow 
sensing. 
A third significant advantage to this invention arises from the fact that 
the flow rate is proportional to the power used to keep the measuring 
section profile constant, while the actual output signal is conveniently 
the voltage across the sensor, thermal element 21 in FIG. 1. Since the 
thermal profile of element 21 remains constant, its total resistance 
remains constant, and the power it dissipates is proportional to the 
square of the voltage drop across it. The measured flow rate is thus 
proportional to the square of the output signal. This means that the 
sensitivity increases as the signal gets smaller. The result is more 
precision with less noise and drift at low values and an increased range. 
A fourth advantage is a simple design. With only one heater on the 
measuring tube, connections are easy to make and several options exist. 
In the design of a specific embodiment, the dimensions and material of 
outer tube 23 can be chosen to keep total losses within power limitations. 
One design uses a stainless steel outer tube of 0.180 inches I.D. and 
0.250 inches O.D.; it takes about one watt to keep T.sub.1 at 40.degree. 
C. and T.sub.2 at 60.degree. C. 
Other arrangements for the space between element 21 and outer tube 23 are 
also possible. For example, the space could be filled with insulation, or 
additional conducting or nonconducting tubes could be mounted 
concentrically therein. It will also be recognized that thermal clamps 13 
and 15 need not be made only out of copper or brass. Other materials 
having high thermal conductivity, such as, for example aluminum or silver 
could be used successfully. 
For best results, the temperature gradient of the measuring section 24 
should be as constant as it is practical to attain for all flow rates. 
Heat losses from outer tube 23, therefore should be kept to a minimum. 
An electrical arrangement that cooperates with the physical arrangement of 
FIG. 1 to form the exemplary embodiment of the invention is shown in the 
schematic diagram of FIG. 3. In this embodiment, thermal elements 17, 19 
and 21 are each a part of a respective Wheatstone bridge circuit that 
regulates its temperature. In a first regulating circuit the bridge input 
nodes are labelled 40 and 41, and the output nodes are labelled 43 and 44. 
Thermal element 17 forms the bridge arm between nodes 44 and 41, and a 
resistor 45 with a low temperature coefficient forms the arm between nodes 
43 and 41. The other two arms are formed by low temperature coefficient 
resistors 46 and 47, respectively. DC power is supplied to bridge input 
node 40 from positive supply terminal B.sup.+ via the parallel combination 
of a resistor 49 and a transistor 51. The other input node, 41, is 
connected to ground. The inverting input of a differential amplifier 53 is 
connected to output node 44; the non-inverting input of amplifier 53 is 
connected to the other output node 43. The output of amplifier 53 is 
connected via a resistor 55 to the base of transistor 51. 
The bridge operates to hold the temperature of the thermal element constant 
as follows: As previously mentioned, thermal elements such as elements 17, 
19 and 21 have high temperature coefficients of resistance. The resistance 
of thermal element 17, therefore, is very much a function of its 
temperature, which is closely tied to that of thermal clamp 13. When that 
temperature starts to drop, because of an increase in fluid flow or 
otherwise, the element resistance decreases. Since the other three arms of 
the bridge are low temperature coefficient resistors (and are not 
connected to the sensor), however, their respective resistances remain 
substantially constant. The resulting lower voltage at bridge node 44, 
compared to the relatively constant voltage at node 43, causes amplifier 
53 to increase the base current of transistor 51, hence increasing the 
current to the bridge. The current increase flows through the both sides 
of the bridge and thus creates more heat by the element 17. The heating 
effect of the increased current flow through the element raises its 
temperature to restore equilibrium. The temperature of thermal element 17, 
and because of close thermal coupling , that of thermal clamp 13 and the 
input end of the measuring section of capillary tube 11 are therefore held 
substantially constant in accordance with the invention. The regulating 
circuit for element 19 is substantially identical and operates to hold the 
temperature of thermal clamp 15 and the output end of the measuring 
section of tube 11 substantially constant, albeit at a higher temperature. 
Although slightly different, the regulating circuit for element 21 operates 
in substantially the same manner. The difference in this illustrated 
embodiment is that, because element 21 supplies only the heat lost to the 
fluid by the measuring center section of the capillary tube, there is no 
need for the extra current amplification of a transistor such as 
transistor 51. Differential amplifier 61 provides sufficient output to 
supply element 21 and keep the bridge in balance. The DC supply to 
amplifier 61 is, of course, implicit. Diode 63 avoids improper bias on the 
amplifier. Finally, an output terminal V.sub.out, connected to the high 
side of thermal element 21, provides a transducer output signal that is in 
fact the voltage across element 21, the voltage being proportional to the 
square root of the mass flow rate through the channel 11. It should be 
appreciated that the output signal can be provided from other points on 
the bridge circuit. 
It should be mentioned that while very convenient, it is not necessary to 
the operation of the invention that thermal elements 17, 19 and 21 be dual 
duty thermal elements. An alternative arrangement that uses separate 
heating and heat sensing elements and can be substituted for each of the 
series connected sensing bridge regulating circuits of FIG. 3 is shown in 
FIG. 4. In this arrangement, a temperature sensing element 65 takes the 
place of the thermal element in the sensing bridge. A separate heater 67 
is controlled by the transistor 70 that is in turn driven by the 
differential amplifier 71 in response to the bridge output voltage. Sensor 
65 may, in the case of a heat sink regulator, for example, be a thermistor 
embedded within the thermal clamp. In the case of the measuring section 
regulator, it could be a thermocouple sensing one point on the measuring 
tube, or even a uniform film covering the whole measuring section. Heater 
67 may in each case be a heating wire wound as shown for the thermal 
elements in FIG. 1. In the measuring section, a uniform semiconductive 
film for heater 67 might be particularly useful, in order to supply the 
heat to the section more uniformly and keep the gradient even more nearly 
constant. 
I have thus described a new and improved mass flow rate transducer that has 
a fast response to flow rate changes, high stability and sensitivity with 
a wide range, and is simple to make. Other arrangements will occur to 
those skilled in the art which do not depart from the spirit and scope of 
my invention, as defined by the appended claims.