CN113495001B - Device and method for measuring entrainment flow ratio of disk cavity of gas compressor - Google Patents
Device and method for measuring entrainment flow ratio of disk cavity of gas compressor Download PDFInfo
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Abstract
The invention aims to provide a device for measuring the entrainment flow ratio of a disc cavity of an air compressor, which is used for measuring the entrainment flow ratio of the disc cavity of the air compressor under the real engine test working condition. The invention also aims to provide a method for measuring the entrainment flow ratio of the disc cavity of the compressor, which adopts the test device to measure the entrainment flow ratio of the disc cavity. The method for measuring the entrainment flow ratio of the disk cavity of the compressor to achieve the aim comprises the following steps: setting a compressor disk cavity between any two adjacent stages of compressor disks in the multi-stage compressor disks as a measurement object disk cavity, wherein the measurement object disk cavity is provided with a disk cavity inlet which is open towards a compressor disk mandrel; setting a plurality of temperature measuring points; and acquiring a plurality of temperature data of the temperature measuring points, and calculating the entrainment flow ratio of the disc cavity to be measured according to the plurality of temperature data.
Description
Technical Field
The invention relates to a device and a method for measuring the entrainment flow ratio of a disk cavity of an air compressor.
Background
Aircraft engines typically require a portion of the compressed air to be bled from the compressor and then flow axially rearwardly through the compressor disk core for cooling the compressor disk and providing a portion of the cooling air for cooling the turbine disk, which is also commonly referred to as the axial through-flow of the compressor disk core.
As shown in fig. 1, when the compressor disk center axial through flow 9 passes through the multistage compressor disk cavity 8, a part of the air flow 9a is sucked into the disk cavity 80 due to the centrifugal action of the disk rotation and participates in the heat exchange of the disk cavity, and due to the mass conservation, the part of the air flow flows radially inwards again through the middle lower part of the disk cavity, joins the disk center main flow 9b, and is mixed with the main flow 9.
The entrainment flow of the disk cavity is input for calculating the heat exchange boundary condition of the compressor disk, and can influence the prediction precision of the temperature of the compressor disk and the prediction precision of the temperature rise of the airflow along the axial through flow, and even influence the reliability of the whole engine design scheme. According to the content, the flow condition at the opening of the disc cavity of the air compressor is very complex, and the traditional flow meter measuring method has the problems of inconvenience in installation and difficulty in capturing the specific entrainment position. For example, in the prior art, a PIV technology is adopted to monitor the entrainment flow of the disc cavity, however, although the PIV technology can display a flow field, the entrainment flow ratio of the disc cavity of the compressor is further counted, and a light transmission window must be opened on the compressor disc when the PIV is used for speed measurement, so that the safety risk is high for the conditions of high rotating speed, high temperature and high pressure during real engine test.
Therefore, a new testing device for the entrainment flow ratio of the disc cavity of the air compressor is needed to be provided, so that the entrainment flow ratio of the disc cavity of the air compressor is measured under the real engine test working condition.
Disclosure of Invention
The invention aims to provide a device for measuring the entrainment flow ratio of a disc cavity of an air compressor, which is used for measuring the entrainment flow ratio of the disc cavity of the air compressor under the real engine test working condition.
The invention also aims to provide a method for measuring the entrainment flow ratio of the disk cavity of the compressor, which adopts the testing device to measure the entrainment flow ratio of the disk cavity.
The method for measuring the entrainment flow ratio of the disk cavity of the compressor to achieve the aim comprises the following steps:
setting a compressor disk cavity between any two adjacent stages of compressor disks in a multi-stage compressor disk as a measurement object disk cavity, wherein the measurement object disk cavity is provided with a disk cavity inlet which is open towards a compressor disk mandrel;
setting a plurality of temperature measuring points, wherein the temperature measuring points comprise:
a plurality of first temperature measurement points set between the compressor disk and the compressor disk mandrel upstream of the disk cavity inlet;
a plurality of second temperature measurement points set between the compressor disk and the compressor disk mandrel on a downstream side of the disk cavity inlet; and
a plurality of third temperature measurement points set on an inner wall surface of the measurement target disk chamber on a downstream side of the disk chamber inlet;
acquiring a plurality of temperature data of the temperature measuring points, wherein the temperature data comprises:
average temperature data T of the plurality of first temperature measurement points1；
Average temperature data T of the plurality of second temperature measurement points2(ii) a And
average temperature data T of the plurality of third temperature measurement pointsout；
Calculating the entrainment flow ratio of the disc cavity of the measurement object by the formula (1)
Wherein, Cp,1Is the specific heat capacity of the air flow at the first temperature measuring point, Cp,2Is the specific heat capacity of the air flow at the second temperature measuring point Cp,outAnd the specific heat capacity of the air flow at the third temperature measuring point.
In one or more embodiments, the plurality of first temperature measurement points includes: a plurality of groups of first temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of first temperature measuring points comprises a plurality of first temperature measuring points;
the plurality of second temperature measurement points include: and the plurality of groups of second temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of second temperature measuring points comprises a plurality of second temperature measuring points.
In one or more embodiments, the plurality of first temperature measurement points includes: 3 or 4 groups of first temperature measuring points distributed in the circumferential direction of the compressor disk.
In one or more embodiments, each set of first temperature measurement points includes 3 to 5 first temperature measurement points distributed along a radial direction of the compressor disk.
In one or more embodiments, the plurality of second temperature measurement points includes: 3 or 4 groups of second temperature measuring points distributed in the circumferential direction of the compressor disk.
In one or more embodiments, each set of second temperature measurement points includes 3 to 5 second temperature measurement points distributed along a radial direction of the compressor disk.
In one or more embodiments, the plurality of third temperature measurement points includes: and the plurality of groups of third temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of third temperature measuring points comprises a plurality of third temperature measuring points.
In one or more embodiments, the plurality of third temperature measurement points includes: 3 or 4 groups of third temperature measuring points distributed in the circumferential direction of the compressor disk.
In one or more embodiments, each set of third temperature measurement points includes 3 to 5 third temperature measurement points distributed along a radial direction of the compressor disk.
In one or more embodiments, the method further comprises providing an armored thermocouple at each of the first, second, and third temperature measurement points.
In order to achieve the above another object, a device for measuring a ratio of a suction flow rate of a disk cavity of a compressor is used for measuring a ratio of a suction flow rate of a disk cavity to be measured, where the disk cavity to be measured is a compressor disk cavity between any two adjacent stages of the compressor disks in a multi-stage compressor disk, and the device includes:
a plurality of first temperature measuring devices disposed between the compressor disk and the compressor disk mandrel on an upstream side of the disk cavity inlet;
a plurality of second temperature measuring devices disposed between the compressor disk and the compressor disk mandrel on a downstream side of the disk cavity inlet;
a plurality of third temperature measuring devices provided on an inner sidewall surface of the measurement target disk chamber on a downstream side of the disk chamber inlet; and
and the processing unit is used for receiving the temperature information sent by the first temperature measuring device, the second temperature measuring device and the third temperature measuring device and calculating the entrainment flow ratio of the disc cavity of the measuring object.
In one or more embodiments, the first temperature measurement devices, the second temperature measurement devices, and the third temperature measurement devices are each sheathed thermocouples.
The gain effect of the invention is that: the invention indirectly measures the entrainment flow ratio in the disc cavity by measuring the relative total temperature of the upstream side and the downstream side of the inlet of the disc cavity of a certain stage of the compressor and the disc cavity according to the principles of mass conservation and energy conservation. The method provides more reasonable and accurate boundary conditions for the heat transfer design of the compressor disk, improves the accuracy of the calculation results of the temperature field of the compressor disk and the temperature rise of the disk core airflow along the way, further improves the reliability of the air system and the heat transfer design scheme, and provides important support and guarantee for the reliability design of the whole aircraft engine.
Drawings
The above and other features, properties and advantages of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings and examples, in which:
FIG. 1 is a schematic view of the axial through-flow direction of the compressor disk center;
FIG. 2 is a schematic diagram schematically illustrating a compressor disk cavity in a cross-sectional view;
FIG. 3 is a schematic flow chart of a method for measuring a suction flow ratio of a disc cavity of a compressor;
fig. 4 is a schematic view of the disk center axis in the disk chamber to be measured in the direction of flow of the through flow.
Detailed Description
The following discloses a variety of different implementation or examples implementing the subject technology. Specific examples of components and arrangements are described below to simplify the disclosure, but are by way of example only and are not intended to limit the scope of the present application. For example, if a first feature is formed over or on a second feature described later in the specification, this may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features are formed between the first and second features, such that the first and second features may not be in direct contact. Additionally, reference numerals and/or letters may be repeated among the various examples throughout this disclosure. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. Further, when a first element is described as being coupled or joined to a second element, the description includes embodiments in which the first and second elements are directly coupled or joined to each other and also includes embodiments in which the first and second elements are indirectly coupled or joined to each other with the addition of one or more other intervening elements.
It should be noted that, where used, the terms upper, lower, left, right, front, back, top, bottom, positive, negative, clockwise, and counterclockwise in the following description are used for convenience only and do not imply any particular fixed orientation. In fact, they are used to reflect the relative position and/or orientation between the various parts of the object.
It is noted that these and other figures which follow are merely exemplary and not drawn to scale and should not be considered as limiting the scope of the invention as it is actually claimed. Further, the conversion methods in the different embodiments may be appropriately combined.
It should be noted that the reference numeral system described hereinafter is independent of the reference numeral system of the background art.
For further understanding, the terms herein are to be interpreted as follows: disk cavity entrainment flow ratio (the intake flow ratio of disk cavity): the ratio of the entrainment flow of the disc cavity to the total flow of the main flow of the disc core. Axial through-flow (the axial through flow in compressor) of the compressor core: the air compressor guides air and then passes through the disk centers of all stages and flows backwards along the axial direction, and the air flow is mainly used for turbine cooling and bearing sealing and heat insulation. Temperature rise along the path (temperature rise along the flow path): the secondary flow of the engine and the wall surface of the disc cavity can exchange energy by acting or heat transfer in the flowing process of the secondary flow in the disc cavity, so that the temperature of the air flow along the path is changed.
Referring to fig. 2, fig. 2 schematically shows a schematic view of a compressor disk cavity in a cross-sectional state, where the compressor disk cavity includes a multi-stage compressor disk 1 and a compressor disk spindle 2, it can be understood that the compressor disk spindle 2 is in a revolving structure, and the multi-stage compressor disk 1 is disposed around the compressor disk spindle 2, where a compressor disk cavity 10 exists between any two adjacent stages of compressor disks 1.
Fig. 3 shows a procedure for measuring the entrainment flow ratio of the compressor disk cavity shown in fig. 2, please refer to fig. 2 and fig. 3 in combination.
First, execution S1: a measurement target is specified, specifically, a compressor disk cavity between any two adjacent stages of the compressor disks in the multi-stage compressor disk is set as a measurement target disk cavity, and as a measurement target disk cavity 100 is schematically selected in fig. 2, the measurement target disk cavity 100 has a disk cavity inlet 100a opening toward the compressor disk spindle 2.
Subsequently, S2 is executed to determine a test position, specifically, set a plurality of temperature measuring points, where the temperature measuring points include: a plurality of first temperature measurement points 31 set between the compressor disk 1 and the compressor disk spindle 2 on the upstream side of the disk chamber inlet 100a, a plurality of second temperature measurement points 32 set between the compressor disk 1 and the compressor disk spindle 2 on the downstream side of the disk chamber inlet 100a, and a plurality of third temperature measurement points 33 set on the inner side wall surface of the measurement target disk chamber 100 on the downstream side of the disk chamber inlet 100 a.
To further clarify the location of the temperature measurement point, referring to fig. 4, the disk chamber 100 to be measured is selected in fig. 4 and the flow direction of the through flow 4 in the axial direction of the disk center is schematically drawn out, it being understood that the upstream side and the downstream side of the disk chamber inlet 100a are referred to the flow direction of the through flow 4 in the axial direction of the disk center.
Subsequently, in the engine test run state, step S4 is executed to acquire temperature data, specifically, a plurality of temperature data of the temperature measurement points, which includes the average temperature data T of the first temperature measurement points 311Average temperature data T of a plurality of second temperature measurement points 322And average temperature data T of a plurality of third temperature measurement points 33out. The average temperature data may be an arithmetic average or a weighted average of the plurality of first temperature measurement points 31, the plurality of second temperature measurement points 32, and the plurality of third temperature measurement points 33.
Finally, when the temperature data is collectedAfter that, step S5 is executed to calculate the entrainment flow ratio of the disk cavity to be measured
The specific calculation formula (1) is as follows:
wherein, Cp,1Is the specific heat capacity of the air flow at the first temperature measuring point 31, Cp,2Is the specific heat capacity of the air flow at the second temperature measuring point 32, Cp,outIs the specific heat capacity of the air flow at the third temperature measuring point 33.
To further illustrate the principle of the measurement method, the deduction process of the aforementioned calculation formula is as follows.
First, according to the energy conservation of the disk center flow path, the change of the relative total enthalpy on the upstream side and the downstream side of the disk chamber inlet 100a should be equal to the energy transferred to the gas flow by the disk chamber wall surface (assuming that the energy is Q), that is, the following formula (2):
Cp,2GT2-Cp,1GT1＝Q (2)
wherein G represents the core airflow mass flow rate, respectively.
And according to the conservation of energy in the disc cavity, the relative total enthalpy entering the disc cavity and the energy Q transferred to the airflow by the wall surface of the disc cavity are equal to the relative total enthalpy leaving the disc cavity. The following formula (3) is obtained
Cp,1GinT1+Q＝Cp,outGoutTout (3)
Wherein G isin、GoutRepresenting the mass flow of air entrainment into the disc chamber (i.e., upstream of the disc chamber inlet) and out of the disc chamber (i.e., downstream of the disc chamber inlet), respectively.
Due to mass conservation, the mass flow into the disc chamber should be equal to the mass flow out of the disc chamber, and therefore there is equation (4):
Gin＝Gout (4)
the above formulae (2) to (4) can be combined to obtain the above formula (1):
wherein, Cp,1Is, Cp,2、Cp,outThe calculation can be directly obtained by the gas flow temperature, specifically, the calculation can be performed by the following formula (5):
Cp,i＝0.9956+0.000093(Ti-273.15) (5)
where i is 1, 2 or out, represents a parameter at a different location, i.e. Cp,1＝0.9956+0.000093(T1-273.15)；Cp,2＝0.9956+0.000093(T2-273.15)；Cp,out＝0.9956+0.000093(Tout-273.15)。
As can be seen from the above, the average temperature data T of the plurality of first temperature measurement points 31 is measured1Average temperature data T of a plurality of second temperature measurement points 322And average temperature data T of a plurality of third temperature measurement points 33outNamely, the entrainment flow ratio of the disc cavity of the measured object can be calculated
The invention measures the relative total temperature of the upstream side and the downstream side of the inlet 100a of the disc cavity of a certain stage of compressor and the disc cavity, and indirectly measures the entrainment flow ratio in the disc cavity according to the principles of mass conservation and energy conservation. The method provides more reasonable and accurate boundary conditions for the heat transfer design of the compressor disk, improves the accuracy of the calculation results of the temperature field of the compressor disk and the temperature rise of the disk core airflow along the way, further improves the reliability of the air system and the heat transfer design scheme, and provides important support and guarantee for the reliability design of the whole aircraft engine.
Another aspect of the present invention is to provide a device for measuring a suction flow ratio of a compressor disk cavity, which is used for measuring the suction flow ratio of the disk cavity of a disk cavity to be measured as described above. The temperature measurement device comprises a plurality of first temperature measurement devices, a plurality of second temperature measurement devices, a plurality of third temperature measurement devices and a processing unit. The plurality of first temperature measuring devices are arranged corresponding to the plurality of first temperature measuring points 31, the plurality of second temperature measuring devices are arranged corresponding to the plurality of second temperature measuring points 32, and the plurality of third temperature measuring devices are arranged corresponding to the plurality of third temperature measuring points 33.
The processing unit is used for receiving the temperature information sent by the first temperature measuring device, the second temperature measuring device and the third temperature measuring device and calculating the entrainment flow ratio of the disc cavity of the measuring object. The processing unit may be a computer that calculates the entrainment flow rate ratio of the measurement target disk chamber by the foregoing formula (1).
In one or more embodiments, the plurality of first temperature measurement points 31 includes a plurality of sets of first temperature measurement points distributed in the circumferential direction of the compressor disk 1, each set including a plurality of first temperature measurement points. It will be appreciated that, as the compressor disk 1 is arranged around the compressor disk spindle 2, there are a plurality of positions between the compressor disk 1 and the compressor disk spindle 2 in the circumferential direction of the compressor disk 1, and the plurality of first temperature measurement points 31 are sets arranged in the circumferential direction a of the compressor disk 1, each set of first temperature measurement points 31 comprising a plurality of first temperature measurement points.
Specifically, in one embodiment, while the plurality of first temperature measurement points 31 are arranged in 3 or 4 groups in the circumferential direction a of the compressor disk 1, each group of first temperature measurement points 31 includes 3 to 5 first temperature measurement points in the radial direction b of the compressor disk 1. With the arrangement, a plurality of points in the circumferential direction a of the compressor disk 1 can be measured respectively during measurement, and a plurality of points in the radial direction of the compressor disk 1 can be measured at the same circumferential position, so that the measurement error can be reduced.
In one or more embodiments, the plurality of second temperature measurement points 32 includes a plurality of groups of second temperature measurement points distributed in the circumferential direction of the compressor disk 1, each group of second temperature measurement points including a plurality of second temperature measurement points. Specifically, in one embodiment, while the plurality of second temperature measurement points 32 are arranged in 3 or 4 groups in the circumferential direction a of the compressor disk 1, each group of second temperature measurement points 32 includes 3 to 5 second temperature measurement points in the radial direction b of the compressor disk 1.
In one or more embodiments, the plurality of second temperature measurement points 32 includes a plurality of groups of second temperature measurement points distributed in the circumferential direction a of the compressor disk 1, each group of second temperature measurement points including a plurality of second temperature measurement points. Specifically, in one embodiment, while the plurality of second temperature measurement points 32 are arranged in 3 or 4 groups in the circumferential direction a of the compressor disk 1, each group of second temperature measurement points 32 includes 3 to 5 second temperature measurement points in the radial direction b of the compressor disk 1.
In one or more embodiments, the plurality of third temperature measurement points 33 includes a plurality of sets of third temperature measurement points distributed in the circumferential direction of the compressor disk 1, each set of third temperature measurement points including a plurality of third temperature measurement points. Specifically, in one embodiment, the plurality of third temperature measurement points 33 are arranged in 3 or 4 groups in the circumferential direction of the compressor disk 1, and each group of third temperature measurement points 33 includes 3 to 5 third temperature measurement points in the radial direction b of the compressor disk 1.
In one or more embodiments, the plurality of first temperature measuring devices, the plurality of second temperature measuring devices, and the plurality of third temperature measuring devices are respectively armored thermocouples, and the measuring method further includes: s3: armored thermocouples are provided, in particular at the first 31, second 32 and third 33 temperature measurement points, respectively, which may be connected, for example by welding. The armored thermocouple can resist high temperature and high pressure, and the maturity is higher, so that the measurement requirement of the entrainment flow ratio of the disc cavity of the air compressor under the real trial run environment of the engine can be met.
Although the present invention has been disclosed in terms of the preferred embodiment, it is not intended to limit the invention, and variations and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention. Therefore, any modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope defined by the claims of the present invention, unless the technical essence of the present invention departs from the content of the present invention.
Claims (12)
1. A method for measuring the entrainment flow ratio of a disc cavity of a compressor is characterized by comprising the following steps:
setting a compressor disk cavity between any two adjacent stages of compressor disks in a multi-stage compressor disk as a measurement object disk cavity, wherein the measurement object disk cavity is provided with a disk cavity inlet which is open towards a compressor disk mandrel;
setting a plurality of temperature measuring points, wherein the temperature measuring points comprise:
a plurality of first temperature measurement points set between the compressor disk and the compressor disk mandrel upstream of the disk cavity inlet;
a plurality of second temperature measurement points set between the compressor disk and the compressor disk mandrel downstream of the disk cavity inlet; and
a plurality of third temperature measurement points set on an inner wall surface of the measurement target disk chamber on a downstream side of the disk chamber inlet;
acquiring a plurality of temperature data of the temperature measuring points, wherein the temperature data comprises:
average temperature data T of the plurality of first temperature measurement points1；
Average temperature data T of the plurality of second temperature measurement points2(ii) a And
average temperature data T of the plurality of third temperature measurement pointsout；
Calculating the entrainment flow ratio of the disc cavity of the measurement object by the formula (1)
Wherein, Cp,1Is the specific heat capacity of the air flow at the first temperature measuring point, Cp,2Is the specific heat capacity of the air flow at the second temperature measuring point Cp,outAnd the specific heat capacity of the air flow at the third temperature measuring point.
2. The method of measuring compressor disk cavity entrainment flow ratio of claim 1 wherein said plurality of first temperature measurement points comprises: a plurality of groups of first temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of first temperature measuring points comprises a plurality of first temperature measuring points;
the plurality of second temperature measurement points include: and the plurality of groups of second temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of second temperature measuring points comprises a plurality of second temperature measuring points.
3. The method of measuring compressor disk cavity entrainment flow ratio of claim 2 wherein said plurality of first temperature measurement points comprises: 3 or 4 groups of first temperature measuring points distributed in the circumferential direction of the compressor disk.
4. The method for measuring the entrainment flow ratio of the compressor disk cavity of claim 3, wherein each set of first temperature measurement points comprises 3 to 5 first temperature measurement points distributed along the radial direction of the compressor disk.
5. The method of measuring compressor disk cavity entrainment flow ratio of claim 2 wherein said plurality of second temperature measurement points comprise: 3 or 4 groups of second temperature measuring points distributed in the circumferential direction of the compressor disk.
6. The method for measuring the entrainment flow ratio of the compressor disk cavity according to claim 5, wherein each set of second temperature measurement points comprises 3 to 5 second temperature measurement points distributed along the radial direction of the compressor disk.
7. The method of measuring compressor disk cavity entrainment flow ratio of claim 1, wherein said plurality of third temperature measurement points comprise: and the plurality of groups of third temperature measuring points are distributed in the circumferential direction of the compressor disk, and each group of third temperature measuring points comprises a plurality of third temperature measuring points.
8. The method of measuring compressor disk cavity entrainment flow ratio of claim 7 wherein said third plurality of temperature measurement points comprises: 3 or 4 groups of third temperature measuring points distributed in the circumferential direction of the compressor disk.
9. The method for measuring the entrainment flow ratio of the compressor disk cavity of claim 8 wherein each set of third temperature measurement points comprises 3 to 5 third temperature measurement points distributed along the radial direction of the compressor disk.
10. The method for measuring the entrainment flow ratio of the compressor disk cavity according to claim 1, further comprising providing an armored thermocouple at each of the first temperature measurement point, the second temperature measurement point, and the third temperature measurement point.
11. A device for measuring a compressor disk cavity entrainment flow ratio, wherein the method for measuring a compressor disk cavity entrainment flow ratio according to any one of claims 1 to 10 is used for measuring a disk cavity entrainment flow ratio of a disk cavity to be measured, wherein the disk cavity to be measured is a compressor disk cavity between any two adjacent stages of the compressor disks in a multi-stage compressor disk, and the device comprises:
the first temperature measuring devices are arranged corresponding to the first temperature measuring points and are arranged between the compressor disk and the compressor disk mandrel on the upstream side of the disk cavity inlet;
the second temperature measuring devices are arranged corresponding to the second temperature measuring points and are arranged between the compressor disk and the compressor disk mandrel on the downstream side of the disk cavity inlet;
a plurality of third temperature measuring devices which are arranged corresponding to the plurality of third temperature measuring points and are arranged on the inner side wall surface of the measuring object disk cavity on the downstream side of the disk cavity inlet; and
and the processing unit is used for receiving the temperature information sent by the first temperature measuring device, the second temperature measuring device and the third temperature measuring device and calculating the entrainment flow ratio of the disc cavity of the measuring object.
12. The apparatus for measuring compressor disk cavity entrainment flow ratio of claim 11 wherein each of said first temperature measurement device, said second temperature measurement device, and said third temperature measurement device is a sheathed thermocouple.
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