A thermal anemometer or mass flow meter having temperature and
flow velocity sensor elements is provided in which a thin film temperature
sensor is provided in the heated sensor of the fluid velocity sensor
element of the system. The thin-film sensor is captured at least
partially within a spacer or interface member, the spacer being
received within a housing. The thermal anemometer is constructed
to offer sufficient precision and accuracy in its design to be suitable
for sensitive scientific and industrial applications. This goal
is achieved while using cost effective parts--as in the thin film
temperature sensor(s)--in connection with a construction approach
minimizing or eliminating gaps or other system configuration variability.
That being said, I claim:
1. An apparatus for use in a mass flow meter for immersion in a
fluid, comprising: a velocity sensor element comprising an elongate
body for extending into the fluid, said elongate body comprising
a housing shell, a distal end of said housing shell receiving and
closely holding a spacer therein, said spacer comprising a solid
body of metal receiving and closely holding a thin-film Resistance
Temperature Detector (RTD) sensor therein, said sensor comprising
an active area and electrical leads to carry current to said active
area from a proximal end of said shell, said active area in substantially
gap-free contact with an internal abutting spacer area.
2. The apparatus of claim 1 further comprising a second temperature
3. The apparatus of claim 2 wherein said second temperature sensor
is a thin-film RTD sensor.
4. The apparatus of claim 1 wherein said spacer is in substantially
gap-free contact with said housing shell.
5. The apparatus of claim 1 further comprising a temperature sensor
element comprising a fluid temperature sensor.
6. The apparatus of claim 5 wherein said fluid temperature sensor
element comprises two temperature sensors within a housing.
7. The apparatus of claim 6 wherein said temperature sensors are
thin-film RTD temperature sensors.
8. The apparatus of claim 5 further comprising a computer processor.
9. The apparatus of claim 5 further comprising an open protective
housing adapted to axially receive said velocity and temperature
10. The apparatus of claim 9 wherein said open protective housing
includes at least one feature proximal to a distal end of either
sensor element at the exterior of the housing to redirect the axial
component of the velocity vector of the fluid flowing over the exterior
of the housing.
11. The apparatus of claim 9 wherein a distal end of said housing
12. The apparatus of claim 10 wherein said feature comprises a
13. The apparatus of claim 5 configured as an insertion flow meter.
14. The apparatus of claim 5 configured as an in-line flow meter.
15. The apparatus of claim 1 wherein said spacer comprises a powdered
metal fabricated piece.
16. The apparatus of claim 15 wherein said powdered metal comprises
17. The apparatus of claim 15 wherein said housing shell comprises
18. The apparatus of claim 1 wherein said housing shell exerts
radial force upon said spacer and said spacer exerts force holding
said temperature sensor in stable position.
FIELD OF THE INVENTION
 This invention relates to mass flow meters, particularly
regarding their manufacture at decreased cost, yet of such quality
for critical applications.
BACKGROUND OF THE INVENTION
 The mass flow rate of a fluid (defined by its average velocity
multiplied by its mass density multiplied by the cross-sectional
area of the channel through which the flow travels) is a measured
quantity of interest in the control or monitoring of most practical
and industrial applications, such as any chemical reaction, combustion,
heating, cooling, drying, mixing, fluid power, etc. Generally speaking,
a thermal anemometer is used to measure the mass velocity at a point
or small area in a flowing fluid--be it liquid or gas. The mass
velocity of a flowing fluid is its velocity referenced to standard
or normal temperature and pressure. The mass velocity averaged over
the flow channel's cross-sectional area multiplied by the cross-sectional
area is the standard or normal volumetric flow rate through the
channel and is a common way of expressing the total mass flow rate
through the channel.
 The thermal anemometer is sometimes referred to as an immersible
thermal mass flow meter because it is immersed in a flow stream
or channel in contrast to other thermal mass flow meter systems,
such as those which sense the total mass flow rate by means of a
heated capillary tube mounted externally to the flow channel. The
operational principles of thermal anemometers derives from the fact
that a heated sensor placed in a fluid stream transfers heat to
the fluid in proportion to the mass flow rate of the fluid. In a
thermal anemometer, one such heated sensor is provided together
with another sensor that detects fluid temperature. In the constant-temperature
mode of operation, the heated sensor is maintained at a constant
temperature above the fluid temperature. The temperature difference
between the flowing fluid and the heated sensor results in an electrical
power demand in maintaining this constant temperature difference
that increases proportional to the fluid mass flow rate and that
can be calculated. Alternately, some thermal anemometers operate
in a constant-current mode wherein a constant current or power is
applied to the heated sensor and the fluid mass flow rate is calculated
from the difference in the temperature of the heated sensor and
the fluid temperature sensor, which decreases as mass flow rate
increases. Thermal anemometers have greater application to gases,
rather than liquids, because their sensitivity in gases is higher
than in liquids.
 Because the parts of the heated sensor of known thermal
anemometers are not sufficiently reproducible dimensionally or electrically,
known thermal anemometers require multi-point flow calibration of
electrical output versus mass flow rate, usually in the actual fluid
and with the actual ranges of fluid temperature and pressure of
the application. For industrial applications, the heated sensor
and fluid temperature sensor of known thermal anemometers typically
have their respective sensors encased in a protective housing (e.g.,
thermowell or metallic tube sealed at its end, etc.). Usually, the
encased heated sensor is inserted into the tip of the housing and
is surrounded by a potting compound, such as epoxy, ceramic cement,
thermal grease, or alumina powder.
 In such a system, "skin resistance" and stem conduction
are two major contributors to non-ideal behavior and measurement
errors in thermal anemometers constructed in this manner. Skin resistance
is the thermal resistance between the encased heated sensor and
the external surface of the housing exposed to the fluid flow. The
well-known hot-wire thermal anemometers have zero skin resistance,
but thermal anemometers with a housing do have skin resistance.
The use of a potting compound substantially increases the skin resistance
because such potting compounds have a relatively low thermal conductivity.
 Skin resistance results in a temperature drop between the
encased heated sensor and the external surface of the housing which
increases as the electrical power supplied to the heated sensor
increases. Skin resistance creates a "droop" and decreased
sensitivity in the power versus fluid mass flow rate calibration
curve which is difficult to quantify and usually varies from meter
to meter because of variations both in the parts of construction
and in installation. The ultimate result of these skin-resistance
problems is reduced accuracy. Furthermore, the use of a surrounding
potting compound can create long-term measurement errors caused
by aging and by cracking due to differential thermal expansion between
the parts of the heated sensor.
 Stem conduction causes a fraction of the electrical power
supplied to the encased heated sensor to be passed through the stem
of the heated sensor, down the housing, lead wires, and other internal
parts of the heated sensor, and ultimately to the exterior of the
fluid flow channel. Stem conduction couples the electrical power
supplied to the encased heated sensor to the ambient temperature
outside the channel. If the ambient temperature changes, stem conduction
changes, and measurement errors occur. Similarly, stem conduction
is responsible for errors in the encased fluid temperature sensor's
measurement because it too is coupled to the ambient temperature.
 Further discussion of the operational principles of known
immersible thermal mass flow meters, their several configurations,
particular advantages, uses, skin resistance, and stem conduction
are presented in section 29.2 entitled "Thermal Anemometry"
by the inventor hereof as presented in The Measurement Instrumentation
and Sensors Handbook, as well as U.S. Pat. Nos. 5880365; 5879082;
and 5780736 all assigned to Sierra Instruments, Inc., and each
incorporated by reference herein in its entirety.
 As noted in the referenced material, resistance temperature
detectors (RTDs) may be employed in the heated sensor and the fluid
temperature sensor, when one is provided. Alternative sensors for
either the heated sensor or the fluid temperature sensor include
thermocouples, thermopiles, thermistors, and semiconductor junction
thermometers. RTD sensors are generally recognized as being more
accurate and stable than any of these alternatives.
 RTD sensors operate on the principle of electrical resistance
increasing in accordance with increasing temperature. In known thermal
anemometers, the RTDs are provided most commonly in the form of
wire-wound sensors, but also as thin-film sensors (such as provided
on an alumina chip) and least commonly as micro-machined sensors
(such as provided in a silicon wafer). The most common wire-wound
RTD sensors are usually manufactured via hand winding and hand resistance
trimming, as well as other manual operations. This makes them vulnerable
to human error in production and subject to irreproducibilities.
The labor content, as well as the high cost of platinum wire, make
them quite costly. Variations in the dimensions of the circular
mandrel (e.g., alumina) over which the wire is typically wound and
the insulating coating (e.g., glass) over the wound wires cause
further dimensional and electrical-resistance irreproducibilities
in wire-wound RTD sensors. Micro-machined RTD sensors have even
worse dimensional and electrical resistance tolerances. As such,
neither type of sensor is ideal for use in thermal anemometers.
 On the other hand, thin-film RTD sensors are mass produced
using automated production operations, employing technologies such
as photolithography and lasers. This results in the comparatively
high reproducibility, accuracy, stability, and cost-effectiveness
of thin-film RTD sensors. Yet, prior to the teaching offered by
the present invention, some thermal anemonmeters have used thin-film
RTD's that were not entirely encased in a protective housing and
which had their surfaces directly exposed to the fluid. Due to the
fragility, poorer dimensional tolerances, and the oscillating and
turbulent flow around the thin-film RTD body, etc., such devices--standing
alone--have only proven suitable for light duty, low-end, low-accuracy/precision
 Prior to the solution offered by the present invention,
the best accuracy typically achievable in current thermal anemometers
for industrial applications was approximately 2% to 3% of reading
error in accuracy over a mass flow rate range of 10% to 100% of
full scale and over a relatively smaller temperature and pressure
range. The construction of the heated sensor selected is what limits
the accuracy. Most commonly, a wire-wound RTD sensor and, less commonly,
a thin-film RTD sensor is encased in the tip of a metallic tube
(e.g., 316 stainless steel) sealed at its end and surrounded by
a potting compound (e.g., epoxy, ceramic cement, thermal grease,
or alumina powder).
 Sensor fabrication with such potting compounds is inherently
irreproducible due to variations in their composition, amount used,
insufficient wetting of surfaces, and/or air bubbles. In the case
of wire-wound sensors, this irreproducibility is added to previously
mentioned irreproducibilities associated with wire-wound RTD sensors
themselves. These irreproducibilities, combined with the previously
mentioned high skin resistance and potential for long-term instability
associated with the use of potting compounds, limits the overall
accuracy of known thermal anemometers constructed in this manner.
 The thermal anemometer described in U.S. Pat. No. 5880365
avoids the accuracy degrading use of potting compounds by forming
the encasing housing over the wire-wound RTD sensor by means of
forces external to the housing. This construction has high stability
and improved accuracy but is relatively expensive and may have irreproducibilities
associated both with wire-wound RTD sensors and with variations
from meter to meter in the gap between the wire-wound RTD and the
internal surface of the housing.
 However, the present invention employs a thin-film RTD not
prone to such problems. It does so in a manner not heretofore contemplated,
thereby offering the advantage of the sensor type's relative benefits,
but in a highly accurate meter. As such, the present invention offers
a significant advance in the art.
SUMMARY OF THE INVENTION
 Where a thermal anemometer is desired for use in a given
application, the quality of the device may be quite significant.
The present invention offers a mode of device construction or packaging
in connection with thin-film RTD sensors (TFRTD) that is able to
leverage the cost advantage offered by such products, but still
attains and improves the measurement quality required of scientific
and industrial applications. Namely, systems according to the present
invention offer performance with as low as 1% to 1.5% or 2% of reading
error in accuracy over a mass flow rate range of 10% to 100% of
full scale (or larger) and over a relatively larger fluid temperature
and pressure range.
 When coupled with computations based on heat-transfer correlations
and other corrective algorithms, reducing the dimensional and electrical
(e.g., resistance) tolerances of the parts of the heated sensor
as is possible with the present invention yields important cost-reducing
and accuracy-enhancing benefits. These potential benefits include:
fewer flow calibration points required; calibration with a low-cost
surrogate flow calibration fluid (e.g., air for other gases); and
better accuracy over wider ranges for mass flow rate, fluid temperature,
and fluid pressure. In the ultimate case of negligible tolerances
(i.e., perfect reproducibility), no flow calibration whatsoever
 To achieve one or more of these benefits, the present invention
provides an approach for using a TFRTD temperature sensor(s) in
an immersible thermal mass flow meter. The meter may be configured
in connection with relevant hardware for use as an insertion or
as an in-line type device. The meters include temperature and velocity
sensor elements. The velocity sensor element has a heated TFRTD
sensor and may also include a secondary temperature sensor to enable
compensation for stem conduction. The temperature sensor element
may also include a second temperature sensor for stem-conduction
compensation as described in U.S. Pat. No. 5879082. The meter's
sensor elements are typically used in connection with a programmed
general-purpose computer or dedicated electronic control hardware--either
example of such hardware including a data processor.
 In each variation of the invention, the heated sensor in
the velocity sensor element is a TFRTD sensor. Although the preferred
embodiment of the present invention uses TFRTDs for the remaining
temperature sensors in both the velocity sensor element and the
temperature sensor element, alternative types of temperature sensors
can be used in these locations.
 Means of producing the heated TFRTD of the velocity sensor
element include printed circuit technology, photolithography, laser
milling, and MEMs approaches, etc., whereby a temperature sensing
element is provided on a silicon wafer, by thin-film platinum, nickel,
or other metal on an alumina or other electrically insulating chip,
or otherwise. By virtue of the manner in which the heated TFRTD
is held or captured within the velocity sensor element, spacing
or gaps between it and adjacent thermally conductive material are
minimized or effectively eliminated.
 In the subject heated TFRTD of the velocity sensor element
of mass flow meters according to the present invention, an outer
layer is provided by a housing that captures a spacer or interface
member (gland), that--in turn--captures the TFRTD. During manufacture,
gaps between the TFRTD and the spacer adapted to receive the same
are minimized or eliminated using a method in which the ductile
metal forming the spacer is compressed around or about the TFRTD.
Such an approach may take place prior to insertion or encasement
of the spacer into an outer housing (e.g., thermowell or tube).
 Beyond selecting a ductile material for the spacer, certain
other material-choice considerations, in any combination, may be
considered pertinent. For one, the spacer material may have a high
thermal conductivity in order to minimize skin resistance and to
provide a more uniform axial temperature distribution along the
length of the spacer, thereby simplifying the use of heat-transfer
correlations and other corrective algorithms for the velocity sensor
element. For another, it may be desirable to produce the spacer
from powdered metal for the sake of economy in producing the desired
shape. Alternatively, the spacer material may be selected in coordination
with that of the housing and TRFTD in order to match or substantially
match thermal expansion properties.
 In any case, the approach to heated TFRTD capture within
the tightest tolerances using an interface member is a major reason
why the velocity sensor element--and thus--thermal anemometers according
to the invention offer the requisite accuracy and precision for
industrial and scientific applications. Yet, it is the inexpensive
nature, reproducible dimensions and electrical characteristics of
using a thin-film RTD temperature sensor (at least as the heated
sensor of the velocity sensor element) that make systems according
to the present invention economical.
 The tangible benefits to users of immersible thermal mass
flow meters according to the present invention may include reduced
cost, higher accuracy, and higher stability than know alternatives
The features of the invention yield these benefits by solving the
problems of known thermal anemometers described in the Background
section above as follows: the use of a TFRTD as the heater of the
velocity sensor element reduces cost and enhances reproducibility
issues; the high thermal conductivity interface member assembled
with minimal gaps reduces skin resistance and simplifies the use
of heat-transfer correlations and corrective algorithms; the "dry"
sub-assembly of the heated sensor of the velocity sensor element
fabricated without the use of potting compounds increases long-term
stability and reproducibility; an additional optional temperature
sensor in the velocity sensor element and/or temperature sensor
element compensates for stem conduction. In the above features improved
reproducibility yields the benefit of reduced costs; simplified
heat-transfer correlations and corrective algorithms yield the benefits
of better accuracy and reduced cost; and reduced skin resistance
and stem-conduction compensation both yield the benefit of better
 In sum, the present invention includes systems comprising
any of the features described herein. As for these features and
possible advantages enjoyed in connection therewith, only the use
of at least one TFRTD is required in the invention. All other advantageous
aspects are optional. Methodology, especially in connection with
manufacture, also forms part of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
 Each of the figures diagrammatically illustrates aspects
of the invention. Of these:
 FIGS. 1A and 1B show front and side views, respectively,
of a thin-film RTD (TFRTD) sensor element;
 FIGS. 2A and 2B show an end view and a side sectional view
taken along line A-A of a spacer interface member for the temperature
sensor shown in FIGS. 1A and 1B;
 FIG. 3 is a partial side-sectional view of a velocity sensor
element in accordance with the present invention incorporating the
hardware shown in FIGS. 1A-2B;
 FIGS. 4A and 4B show front and side views, respectively,
of another temperature sensor as may be used in the present invention;
 FIG. 5 shows a partial sectional view of the velocity sensor
element including the sensor in FIGS. 4A and 4B housed therein to
provide compensation for stem conduction;
 FIG. 6 shows a partial side-sectional view of a complete
thermal anemometer sensor assembly including velocity and temperature
sensor elements according to the present invention;
 FIG. 7 shows a partial sectional view of a preferred temperature
 FIG. 8 shows a partial side-sectional view of a sensor head
of a thermal anemometer with an insertion-type configuration according
to the present invention with the assembly of FIG. 6 set therein;
 FIGS. 9A and 9B show a partial side-sectional view and an
end view, respectively, of a thermal anemometer according to the
present invention of the insertion-type configuration having a tubular
 FIG. 10 shows a partial side-sectional view of an alternative
insertion-type meter configuration;
 FIGS. 11A and 11B show an end view and a side-sectional
view taken along line B-B, respectively, of a thermal mass flow
meter according to the present invention of the in-line-type configuration;
 FIGS. 12A and 12B show partial side-sectional views of two
alternative in-line-type configurations.
 Variation of the invention from that shown in the figures
is contemplated. Fluid flow direction is indicated in many of the
figures by arrows.
 Before the present invention is described in detail, it
is to be understood that this invention is not limited to particular
variations set forth and may, of course, vary. Various changes may
be made to the invention described and equivalents may be substituted
without departing from the true spirit and scope of the invention.
In addition, many modifications may be made to adapt a particular
situation, material, composition of matter, process, process act(s)
or step(s), to the objective(s), spirit or scope of the present
invention. All such modifications are intended to be within the
scope of the claims made herein.
 Methods recited herein may be carried out in any order of
the recited events which is logically possible, as well as the recited
order of events. Furthermore, where a range of values is provided,
it is understood that every intervening value, between the upper
and lower limit of that range and any other stated or intervening
value in the stated range is encompassed within the invention. Also,
it is contemplated that any optional feature of the inventive variations
described may be set forth and claimed independently, or in combination
with any one or more of the features described herein.
 All existing subject matter mentioned herein (e.g., publications,
patents, patent applications and hardware) is incorporated by reference
herein in its entirety except insofar as the subject matter may
conflict with that of the present invention (in which case what
is present herein shall prevail). The referenced items are provided
solely for their disclosure prior to the filing date of the present
application. Nothing herein is to be construed as an admission that
the present invention is not entitled to antedate such material
by virtue of prior invention.
 Reference to a singular item, includes the possibility that
there are plural of the same items present. More specifically, as
used herein and in the appended claims, the singular forms "a,"
"and," "said," and "the" include plural
referents unless the context clearly dictates otherwise. It is further
noted that the claims may be drafted to exclude any optional element.
As such, this statement is intended to serve as antecedent basis
for use of such exclusive terminology as "solely," "only"
and the like in connection with the recitation of claim elements,
or use of a "negative" limitation. Unless defined otherwise
herein, all technical and scientific terms used herein have the
same meaning as commonly understood by one of ordinary skill in
the art to which this invention belongs.
 Turning now to FIGS. 1A and 1B, these show a view of the
type of temperature sensor 2 employed in the present invention.
The sensor shown is a "thin film" type sensor as described
above. The particular sensor shown is a thin-film Platinum Resistance
Temperature Detector (PRTD) as commonly available. An active region
12 of the device is provided, over which area the PRTD is self-heated
by current during use. Sensor 2 includes lead wires 4 connected
to weld pads leading to active region 12 and covered by a glass
strain relief 10. The body 8 of the sensor is made of high-purity
alumina, preferably held to a thickness tolerance within about .+-.0.002
to 0.001 inches as commonly available. A thin layer of glass electrical
insulation is provided over the PRTD active area. Of course, the
PRTD is only exemplary as other such TFRTDs may be employed in the
 FIGS. 2A and 2B, show a member for receiving the RTD therein.
The interface member or spacer 20 comprises a metal such as copper.
The material should be highly thermally conductive. For example,
other metals and alloys (such as bronze) including aluminum, aluminum
alloy, silver, gold, alloys thereof, etc. could be employed.
 Space 20 is advantageously constructed of molded powdered
metal. In that manner it is cost-effectively constructed to define
a hole or bore 22 suited to closely fit temperature sensor 2. Other
techniques, such as broaching and electric discharge machining,
may be employed in producing the part. However, as a molded powdered
metal piece, the item is inexpensive to produce.
 Still further, as a powdered metal piece, the inventor hereof
observed an unexpected result. Namely, when the sensor was inserted
into the hole, any gap between the sensor and the bore is permanently
collapsed by squeezing the exterior of the spacer in a simple chuck.
Such ease of plastic deformation of the piece is believed (at least
in part) to result from the nature of the powdered metal matrix.
 Yet, whether the spacer is a powdered metal piece or otherwise
formed, more aggressive forming techniques can be applied to reduce
any gaps between the sensor and facing material. Particularly, a
hydroforming procedure such as described in the '365 patent referenced
above may be employed. It should be noted that such forming techniques
should not apply forces on sensor 2 sufficient to generate electrical
resistance changes caused by strains in sensor number 2. Our tests
have shown that with simple mechanical compression of a powdered
metal copper spacer and release from the compression, sensor 2 is
not easily pressed from hole 20 (when opened at a distal end 24
to allow such action).
 Accordingly, it has been surmised that one or more points
or sub-areas of the two larger-area surfaces 28 of the hole 22 in
spacer 20 are touching mating points or sub-areas of the two larger-area
surfaces 14 of temperature sensor 2 thereby clamping temperature
sensor 2 with forces substantially normal to the sensor, in an
immovable position relative to the spacer 20 and insuring long-term
stability of the subassembly. The gaps between the two smaller-area
surfaces of the hole 22 and the two smaller-area surfaces of the
temperature sensor 2 may be designed to be relatively larger and
thereby have little effect in the compression process.
 It is further surmised, based on material variations and
testing, that the total gap--the sum of the gap between one surface
28 of the hole 22 and its mating surface 14 of the temperature sensor
2 and the gap between the second pair of such surfaces--ranges from
about 0.003 inches to 0.0005 inches (and where mating surfaces touch
even smaller) and likely averages about 0.001 inches. That is to
say, the sensor thickness "ST" and gap width "GW"
as shown in FIGS. 1B and 2B respectively differ by between about
0.0005 and 0.003 inches, or on average about 0.001 to about 0.002
inches. Yet another way to view the interaction is in terms of a
resulting close fit or light press fit tolerances as commonly understood
by those with skill in the art.
 In the present invention, spacer 20 provides an intermediate
member between sensor 2 and the shell housing 32 of the velocity
sensor element 30. In the '365 patent, it is the housing that is
externally pressure formed. In the present invention, no such activity
occurs in connection with the housing. Instead, spacer 20 (together
with sensor 2) is press-fit into the housing. The rounded distal
end 24 of spacer 20 is pressed into a complimentary distal section
34 of housing 32. In this manner, gaps along the outer surface of
the bullet-shaped spacer subassembly are substantially eliminated.
 The fit between the spacer and its housing may be designed
as a close fit, a light press fit or even a heavy press fit. In
the latter cases, the housing exerts a radial force on the spacer
subassembly. This force may supplement any previously-applied compression
to the spacer 20 onto temperature sensor 2 or it may instead offer
the only compression onto temperature sensor 2 applied in some cases.
 Seeing as a goal of the spacer is to eliminate gaps (which
are more than an order of magnitude less thermally conductive than
the desired metal material) that increase skin resistance and thereby
decrease system accuracy and introduce variability interfering with
modeling of the system, the shape of bore 22 will depend on the
shape of the sensor. Regardless of the sensor shape, it is preferred
that at least the portion 26 of the spacer facing the active surface
12 of the RTD be shaped to facilitate direct and at least substantially
complete abutment of the surfaces.
 Still further, it is to be appreciated that the inventive
system is one in which no significant amount of fillers or potting
material such as epoxy, ceramic cement, thermal grease, alumina
powder, or another agent or compound is provided between sensor
2 spacer 20 and housing 32 of velocity sensor element 30. This
factor is important since introduction of such material introduces
in quantity (or at all) may introduce irreproducibilities in the
velocity sensor element. It may further introduce instability, for
example, by virtue of differential expansion during temperature
cycling. Still, one might add a very thin layer of thermally conductive
material, otherwise used as "potting compound" to all
gaps in effort to reduce skin resistance between elements. However,
such a film, veneer or wetting of components (likely performed prior
to their assembly) is different, in kind, to immersing or traditionally
"potting" an item in such material.
 On another front, due to thermal cycling it is also desirable
that at least spacer 20 and housing 32 have substantially or approximately
matched coefficients of thermal expansion. Such a result is possible
in the case of a pairing of copper and stainless steel for the spacer
and housing, respectively. Of course, other materials may be selected.
Yet, the copper/stainless combination has proven highly advantageous
by virtue of the ductility of the copper in the forming procedure
of the spacer against sensor 2 and further with respect to the good
material thermal expansion rate match the selection provides.
 As for further optional features of the invention, reference
is made to FIGS. 4A and 4B. Here, a second RTD 40 is shown. Like
that shown in FIGS. 1A and 1B, it includes leads 42 a substrate
44 strain relief 46 and active area 48. Yet, this sensor is not
self-heated. It is intended merely to measure temperature. When
optionally used in the velocity sensor element 30 its purpose is
to offer compensation for stem conduction as is known possible in
the art as possible in theory. However, the hardware implementation
offering potential for such calculations is unique to the present
 In addition to such other facets as one with skill in the
art will appreciate upon review of the present disclosure, FIG.
5 illustrates the desired placement of sensor 40 within the body
of velocity sensor element 30 in which the adjacent housing 32
of velocity sensor element 30 is in the full fluid flow stream substantially
identical to that of heated sensor 2. The use of sensor 40 to compensate
for stem conduction is greatly simplified if the distal length of
the velocity sensor element 30 from its far distal tip to the active
area of sensor 40 called the "active length," is in the
full fluid flow with a velocity profile over said active length
that is substantially uniform. These same considerations also are
applicable to the location of the second temperature sensor 70 in
FIG. 7 for stem conduction compensation in the temperature sensor
element 56. Nevertheless, the present invention encompasses, but
with reduced accuracy for stem conduction compensation, the placement
of sensor 40 at any location within the velocity sensor element,
including more proximal locations, including within the cavity noted
by location 81 in FIG. 8 or even at the base of the velocity sensor
element within sensor head 80 as noted by location 83 in FIG. 8.
Yet, in a preferred variation of the invention, the housing 32 of
velocity sensor element 30 that is adjacent to sensor 40 is in the
full flow stream because then the computations associated with determining
mass flow are comparably simple or elegant.
 FIG. 5 offers a cross-sectional view of the highlighted
section of the velocity sensor element in FIG. 6. In this sectional
view, the cavity in ferrule piece 50 into which sensor 40 is fit
is shown filled with the sensor. For the sole purpose of improving
the thermal contact between sensor 40 ferrule 50 and housing 32
a potting compound such as thermally conductive epoxy or ceramic
cement may surround sensor 40 in the cavity of ferrule 50. It should
be observed that said potting compound is outside of the velocity
sensing length of the velocity sensor element, and therefore any
of its previously described negative features do not affect accuracy
or long-term stability. In FIG. 3 no such sensor is provided, illustrating
the optional nature of the sensor.
 While including the sensor 40 offers certain advantages
in the ability to broadly provide compensation for stem conduction,
it still may be desired to provide a longitudinal spacer collar
54 to carefully define the distance between ferrule 50 (for when
it might carry a sensor 40) and spacer 20 which carries sensor 2.
 As for the more global construction of a thermal mass flow
meter according to the present invention, FIG. 6 illustrates the
velocity sensor element/assembly 30 and temperature sensor element/assembly
56 provided in a greater sensor housing assembly 60. The sensor
element assemblies are set within sensor head 62 with their respective
leads optionally potted in epoxy, cement (or the like) with insulated
wires 64 arranged for connection to a processor 66.
 While such constructional details are within the level of
those with skill in the art to handle without undue experimentation,
FIG. 7 illustrates a particular temperature sensor element 56 as
advantageously employed in the present invention. As illustrated,
the assembly preferably includes two TFRTDs as shown in FIGS. 4A
and 4B. The distal sensor 72 is the primary sensor for measuring
the temperature of the flowing fluid. The proximal sensor 70 compensates
for stem conduction as described in U.S. Pat. No. 5879082. In
some applications, such as those involving certain liquids and certain
gases at high velocity, stem-conduction errors are relatively small
and in those applications proximal temperature sensor 70 is not
needed. It is understood that proximal temperature sensor 70 is
optional to, and is not required by, the present invention. It is
further understood that, although TFRTDs are the preferred type
of temperature sensor for use as sensors 70 and 72 the present
invention encompasses the use, in any combination, of other types
of temperature sensors such as wire-wound RTDs, thermocouples, and
 Yet another advantageous innovation that may be desired
for use in connection with the present invention for thermal anemometers
of the insertion configuration is shown in FIG. 8. Here an open-ended
protective sensor head 80 is shown in partial cross section. The
sectional view reveals the placement of the velocity and temperature
sensor elements in the sensor head. On either side of the sensor
elements/assemblies, legs 82 defining an open channel and extending
beyond the sensor elements are provided. The legs are of particular
use when a technician is installing a completed meter into a pipe
section or other location. The legs prevent inadvertent damage of
the sensor elements during the installation procedure as well as
offering protection from mishandling in the meantime. Use of a protective
shield for the sensor elements of insertion thermal anemometers
has precedence, but such shields normally are closed at their distal
end. The shielding of sensor head 80 of the present invention is
open at its end and thereby eliminates the flow disturbance created
at the distal end of closed ended shields and consummates ultimately
in better accuracy.
 FIGS. 9A and 9B show a complete probe assembly of an insertion
meter of the present invention constructed with tubular stem 88
and the sensor head 80 of FIG. 8. This meter is sealed and connected
to the flow channel or stream by means of a compressing fitting,
flange or other like means. The constituent elements of the system
are as described and designated by numerals above. To facilitate
proper installation orientation by an end-user a pointer indicating
flow direction may be incorporated in the housing.
 FIG. 10 shows another insertion thermal anemometer configuration
of the present invention intended for applications not requiring
the highest accuracy. In contrast to the insertion meter of FIGS.
9A and 9B, this meter has threaded process connection 32 and, for
purposes of strength, a closed-ended protective shield 80' around
the sensor elements.
 Whereas the largest portion of the flow of a fluid around
such known thermal anemometers of the insertion configuration flows
circumferentially and perpendicularly around the meter's perpendicularly-oriented
stem 88 and sensor head 80 of FIGS. 9A and 9B (head detailed in
FIG. 8), nevertheless a smaller fraction is inclined to flow axially
down the stem and sensor head, enter the volume between legs 82
and ultimately flow over the velocity sensor element 30. This effect
can cause the meter to erroneously measure a velocity higher than
the actual velocity. Since this axial flow varies with the depth
of insertion into the flow stream, its magnitude during flow calibration
may be different than that of the actual field application, thereby
impairing velocity measurement accuracy.
 Accordingly, insertion meter sensor head 80 of the present
invention is designed to reduce errors caused by such axial flows.
Shoulder 84 and inset 86 of sensor head 80 in FIG. 8 provide aerodynamic
features to redirect and divert said axial flow circumferentially
around the sensor head as indicated by the flow arrows, thereby
diminishing its magnitude passing over the velocity sensor element
30 and improving velocity measurement accuracy. Furthermore, one
with skill in the art of aerodynamics will recognize that one or
more shoulders 84 fins, or other alternate feature configurations
may be provided to redirect a portion of said axial flow circumferentially
and substantially perpendicularly around the insertion probe before
it passes over the velocity sensor element and causes errors. The
present invention encompasses the use of such elements intended
for the purpose stated and associated flow dynamic methodology.
 Turning to FIGS. 11A and 11B, these drawings illustrate
an immersible thermal mass flow meter of the in-line configuration
encompassed by the present invention. The mass flow meter assembly
90 is shown emplaced within an adapter 92 extending from pipe 94.
Because the velocity sensor element 30 and the temperature sensor
element 56 are intended to be enclosed within the pipe 94 as a delivered
unit for in-line placement within a system, the sensors require
no protective shield. In-line meter 90 is attached to the process
piping by means of flanges 98. Also pictured are two perforated
flow plates 96 in series and upstream of velocity sensor element
30 and temperature sensor element 56 in order that the flow reaching
the same may be substantially uniform and independent of upstream
 In most known insertion-type and in-line configuration immersible
thermal mass flow meters the velocity sensor and temperature sensor
elements are aligned substantially perpendicular to the main fluid
flow stream as shown in FIGS. 11A and 11B (and as indicated by the
double-line flow direction arrows in many of the preceding figures).
However, the in-line meters 100 and 110 in FIGS. 12A and 12B, respectively,
represent exceptions to this commonality and have their flow axial
to the sensor elements. These designs are designed primarily for
applications with low mass flow rates and therefore have relatively
small flow channels.
 Accordingly, meter 100 in FIG. 12A has flow channels machined
in flow body 102 which connect to manifold 106. Meter 110 in FIG.
12B has tubular flow channels 112 connected to manifold 104. Meter
100 has pipe-threaded process connections 104 and meter 110 has
tubular process connections 112. In both of these configurations,
the fluid flows axially over the sensor elements, as described in
U.S. Pat. No. 5780776 rather than perpendicular to the sensors
as in the meters previously described.
 The present invention is suited for use in connection with
various other flow meter configurations in addition to those shown
the various figures. As for other manners in which the present invention
may be implemented (i.e., housed or integrated in a flow system),
these are either known or readily appreciated by one with skill
in the art; further examples of which are sold by Sierra Instruments,
 The thermal anemometer of the invention retains advantageous
performance if operated with either digital or analog sensor-drive
electronics, or with a combination of both, in either the constant-temperature
or constant-current modes of operations, all as described in the
above mentioned book chapter authored by the inventor hereof. Digital
electronics may be preferred for reason of simplified computations
based on heat-transfer correlations and corrective algorithms, that
compensate for any changes (e.g., as referenced to flow calibration
conditions) in the fluid itself, fluid temperature, fluid pressure,
ambient temperature, and other variables and influence parameters,
thereby yielding higher system accuracy. Said heat-transfer correlations
and corrective algorithms are based on known empirical heat transfer
correlations, specific experimental data for the thermal anemometer
of the present invention, physics-based heat transfer theory, and
 Though the invention has been described in reference to
several examples, optionally incorporating various features, the
invention is not to be limited to that which is described or indicated
as contemplated with respect to each embodiment or variation of
the invention. The breadth of the present invention is to be limited
only by the literal or equitable scope of the following claims.