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  • Thermocouple TransientResponse Characteristics

    Thermal Systems Laboratory

    ME 4351 - 141

    Instructor: Dr. Jerry R. Dunn

    Lab Group

    John Burroughs, Group LeaderKim ShinnJay Spikes

    Barry Webster

    Date dueSept. 30, 1997

  • i

    Executive Summary

    The objective of this laboratory was to experimentally determine the effects of flow

    conditions and bead diameter on thermocouple transient response characteristics and to

    compare the measured response characteristics with predictions from theory. The transient

    temperature response was measured experimentally for two type T, exposed junction,

    sheathed thermocouple assemblies. The two assemblies had a bead diameter of 1/8 in. and

    1/16 in. respectively. The response of each assembly was measured at free stream flow

    velocities of 20 ft/s and 40 ft/s and a free stream temperature of 180 F. The initial

    temperature was kept at 80F for each test. Each thermocouple assembly was suddenly

    exposed to a step change in free stream temperature and the response of the sensor

    measured at 1 sec. intervals for each set of test conditions. Results were plotted and

    compared with theory from convection and transient conduction heat transfer.

    Measured time constants ranged from 2.5 to 9.8 sec. These were slightly faster than values

    predicted from theory which ranged from 2.7 to 10.7 sec. for the conditions of this test.

    The time constant decreased as bead diameter decreased and as free stream velocity

    increased. A factor of two decrease in bead diameter had a significantly greater effect on

    time constant, a change of 10.7 to 3.7 sec, than a factor of two increase in velocity, a

    change of 10.7 to 7.6 sec. This was because of a decrease in bead diameter resulted in an

    increase in heat transfer coefficient and a decrease in the mass, thermal capacitance, of the

    thermocouple. Flow stream turbulence and the uncertainty associated with the correlation

    for heat transfer coefficient were possible causes for the difference between theoretical and

    measured values of time constant.

  • ii

    Table of Contents

    Page

    Executive Summary i

    List of Tables iii

    List of Figures iv

    I. Introduction 1

    II. Theory 2

    III. Test Setup 6

    IV. Test Procedure 8

    V. Results and Discussion 9

    VI. Conclusions 12

    VII. References 12

    Appendices 13

    Data Sheets and Predicted Theoretical Response

    Sample Calculations

    Handout

  • iii

    List of Figures

    Figure No. Page

    2.1 Representation of a bead thermocouple 2

    2.2 Theoretical TC Transient response 5

    3.1 Schematic of Test Section 6

    4.1 Transient Temperature vs Time, D = 1/8 in. 11

  • iv

    List of Tables

    Table No. Page

    1. Equipment List 7

    2. Transient Temperature Response Test Matrix 8

    3. Heat Transfer Coefficient Calculation 9

    4. Predicted Thermocouple Time Constant 10

    5. Thermocouple Response Data, D = 1/8 in. 14

    6. Predicted Thermocouple Response, D = 1/8 in. 15

  • 1

    I. Introduction

    Reliable and accurate temperature measurement is an important and necessary element

    in many of todays engineering problems and designs. Accurate temperature measurements

    are typically important to the control, performance, and normal operation of many

    engineering processes and operating equipment. Typical examples range from cooking,

    heating and cooling, temperature measurement and control in processes such as

    combustion, steam generation, and chemical production, and maintaining acceptable

    operating conditions for temperature sensitive equipment such as electronics and energy

    conversion systems.

    Devices used to measure temperature include the basic thermometer, thermocouples,

    thermisters, resistance temperature detectors (RTDs), and optical pyrometers. These

    devices have a wide range of temperature measurement capability, accuracy, and

    characteristics. The measurement characteristics of each must be understood in order to

    select the correct sensor for a given measurement application. This is particularly true

    when dynamic response characteristics are important to the given measurement application.

    Not only is there a wide difference in response characteristics between devices such as a

    thermocouple and a thermometer, but also the transient response of a given device such as a

    thermocouple can vary significantly depending on the design and operating conditions of

    the sensor.

    Therefore, it is the objective of this experiment to determine the transient response

    characteristics of a bead thermocouple for various values of thermocouple bead diameter

    and flow conditions.

  • 2

    II. Theory

    The development of the governing equations for the transient response characteristics

    of a temperature measurement device begins with the use of the First Law of

    Thermodynamics to perform an energy balance on the temperature sensing element. The

    development shown below follows the analysis presented by Incropera and DeWitt [1].

    Consider a mass, m, shown below in Fig. 2.1, which is at an initial temperature, Ti, and

    exchanges heat with the surroundings at a temperature, T, by convection. We will assume

    that the geometry of the mass is sufficiently small that internal temperature gradients can be

    neglected. Therefore, as energy is transferred to or from the mass, we will assume that the

    temperature of the mass (our temperature sensing device) changes uniformly throughout the

    volume and at any time, , has a single value at all points in the mass.

    U

    D

    T

    Fig. 2.1 Representation of a bead thermocouple

    Equating the energy transfer by convection to the rate of energy change of the control

    volume (the mass m), we obtain Eqn. 1.

    =( )h A T T CV dTdc c (1)

  • 3

    Defining a new variable, , as = T - T and separating variables, we obtain the

    following:

    V Ch Ac c

    d di

    = 0 (2)

    Integrating from time, , equal to zero, the equation becomes:

    V C

    h An

    c c il =

    (3)

    Taking the inverse of the natural log, we obtain:

    ih A

    V Cc c=

    exp(4)

    Defining the time constant, c , as

    c VCh Ac c=

    (5)

    we finally obtain the equation for the transient response in the form:

    i

    T TT Ti c

    = =

    exp(6)

  • 4

    We observe that Eqn. 6 has the following characteristics:

    * At = 0, / i = 1* At = , / i = 0* At = c, / i = 1 /e = 0.3678

    We therefore see that the time constant physically represents the time necessary for the

    temperature sensor to reach 63.22 % (1 - 1/e) of the maximum possible temperature

    change. Graphically, this response should appear as a decaying exponential and will

    approach the final, steady-state value asymptotically as shown in Fig. 2.2.

    0

    0.25

    0.5

    0.75

    1

    1.25

    /cFig. 2.2 Theoretical TC Transient Response

    /i

    We can see that after a time equal to three time constants, the sensor still has not reached the

    final steady-state value and that the longer the time constant, the longer the time required to

    reach steady-state. It is thus desirable to have a small time constant if rapid sensor

    response is important in a given engineering process. From Eqn. 5, it is seen that the time

    constant decreases as heat transfer coefficient and surface area increases and as mass and

  • 5

    specific heat decreases. This information is helpful to the engineer in selecting and

    designing temperature sensing devices.

  • 6

    III. Test Setup

    The apparatus used in this experiment was designed to have the capability to suddenly

    expose the bead of an exposed junction, sheathed thermocouple to a simulated step change

    in free stream temperature. The response of the thermocouple is then measured as a

    function of time to determine the transient response of the specific sensor being tested. The

    configuration of the apparatus test section designed to conduct this test is shown in Fig.

    3.1. The main air duct provides a conduit for the free stream air flow to which the

    thermocouple is to be exposed.

    U U

    Thermocouple

    Protection tube

    Flow tube

    T

    Ti air flow

    Fig. 3.1 Test Section Schematic

    The flow rate can be controlled by varying the opening of an air damper to the fan to

    provide a range of free stream velocities for the step temperature change. This results in the

  • 7

    ability to change the heat transfer coefficient for the conditions of the test. Air flow in the

    duct is heated to the free stream test temperature by an electric resistance duct heater located

    upstream of the test section. A spring loaded protection tube is inserted into the flow duct

    to initially shield the sheathed thermocouple from the free stream flow. An unheated stream

    of air is delivered to the protection tube to maintain the thermocouple at the initial

    temperature, Ti. The protection tube is then suddenly withdrawn exposing the

    thermocouple a step change in temperature and flow conditions. The output of the

    thermocouple is monitored as a function of time to provide a record of the transient

    response for the conditions of the test. A digital temperature indicator provides a visual

    display of the changing temperature during the test period. A seco

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