TEC EXPERT DX8020 USER GUIDE Moscow 2010 Version 1.20 RMT Ltd. DX8020 User Guide CONTENTS 1. FOREWORD ................................................................................................................ 4 2. DX8020 DESCRIPTION ............................................................................................... 5 2.1. Objectives and Technical Data................................................................................... 5 2.1.1. Objectives .................................................................................................................. 5 2.1.2. Technical Data ........................................................................................................... 6 2.2. Standard Kit ............................................................................................................... 7 2.3. DX8020 Arrangement................................................................................................. 8 2.3.1. Connection of Cables ............................................................................................... 11 2.3.2. How to Install TE Module to Be Tested..................................................................... 11 2.3.3. Vacuum Pumping System Operation........................................................................ 15 2.4. 3. 3.1. Maintenance............................................................................................................. 16 DX8020 OPERATION PROGRAM ............................................................................. 17 Program Preparation ................................................................................................ 17 3.1.1. System Requirements .............................................................................................. 17 3.1.2. Program Installation ................................................................................................. 17 3.2. Connection............................................................................................................... 18 3.3. Disconnection........................................................................................................... 18 3.4. Main Window "DX8020 Operation Program" ............................................................ 19 3.5. TE Module Selection from the Database .................................................................. 21 4. 4.1. MEASURING METHODS ........................................................................................... 23 Standard Mode......................................................................................................... 24 4.1.1. Measurement of ∆T(I), U(I) at Q=0 ........................................................................... 25 4.1.2. Measurement of Q(∆T) ............................................................................................. 30 4.2. Expert Mode............................................................................................................. 36 4.3. Z-R-τ-Metering ......................................................................................................... 39 4.3.1. TE Module Free in the Ambient ................................................................................ 39 4.3.2. TE Module with the Hot Side Temperature Stabilized............................................... 43 4.4. TE Properties Testing............................................................................................... 45 5. Mathematical Annex I. Estimation of Convectional Heat Exchange Coefficient........... 48 6. Mathematical Annex II. Estimation of Radiation Heat Exchange Coefficient ............... 50 7. Mathematical Annex III. Additional Thermal Conductance between Pellets ................ 51 8. Mathematical Annex IV. Passive Heat Flux along the Leading Wires ......................... 52 9. Mathematical Annex V. n-Power Polynomial Interpolation .......................................... 55 10. Mathematical Annex VI. Measurement of Imax, ∆Tmax.............................................. 57 11. Mathematical Annex VII. Qmax Measurement and ∆Tmax Correction............................. 58 12. Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit ....................... 60 Version 1.20 2 RMT Ltd. DX8020 User Guide REFERENCE 1. Materials Useful Properties........................................................................ 62 REFERENCE 2. Terms and Definitions................................................................................ 63 Version 1.20 3 RMT Ltd. 1. DX8020 User Guide FOREWORD The given User’s Guide is to provide thorough information for studying and handling the TEC Expert model DX8020 (for brevity further can be referred to as the DX8020). It is only the personnel acquainted with all the sections of this guide who can operate the facilities. The DX8020 combines direct measurement and Z-R-τ Meter capabilities and are meant for measuring parameters of thermoelectric (TE) single-stage modules (direct measurements and Z-R-τ Meter) and multistage TE modules (direct measurements). The equipment DX8020 enables the measurement of the following parameters – see Table 1.1. Table 1.1 Measured Parameter Designation TE module temperature difference versus electric current at zero heat load ΔТ=f(I) TE module maximum temperature difference at zero heat load ΔТmax Electric current at which ΔTmax is achieved Imax TE module electric voltage versus electric current at zero heat load U=f(I) Electric voltage at which ΔTmax is achieved Umax TE module temperature difference versus heat load available at electric current fixed Q=f(ΔТ) Maximum heat load capacity at Imax (ΔT=0) Qmax TE module Figure-of-Merit Z TE module electric resistance R TE module time constant at 0.01Imax τ Average Seebeck coefficient of TE material α Average electric conductivity of TE material σ Notes Direct measurements Z-metering The DX8020 provides automatic capability to measure full specifications of a TE module at one measuring cycle in given ambient conditions. The equipment DX80200 is intended for acceptance, qualification and research testing of TE modules. Version 1.20 4 RMT Ltd. DX8020 User Guide 2. DX8020 DESCRIPTION 2.1. Objectives and Technical Data 2.1.1. Objectives The ranges of the parameters of single- and multistage TE modules measured by DX8020 are given in Table 2.1. Table 2.1 Measured parameter Designation Units Range Accuracy Measured temperature Т ºC -120…85 ±0.3 ºС Maximum temperature difference ΔТmax ºC 0…140 ±0.3 ºC TE module electric current I A 0…7 ±3 mA TE module electric voltage U V 0…16 ±3 mV Maximum heat load Qmax W 20 Maximum electric power Pmax W 30 0.6 %, but AC electric resistance АС R Ohm 0…100 TE module Figure-of-Merit Z *1000 1/K 0…4 Time constant τ s 0…10 Average Seebeck coefficient of TE material in the TE module α µV/K 100…300 Average electric conductivity of TE material in the TE module σ 1/Ohmּcm 400…2500 Version 1.20 not better than 0.01 Ohm 5 RMT Ltd. DX8020 User Guide 2.1.2. Technical Data 2.1.2.1 Technical data of the facilities DX8020 are given in Table 2.2. Table 2.2 Parameter Designation Units Range Accuracy Tested TE module substrate max dimensions CxD mm² 30х30 Tested TE module max height Н mm 30 Tested TE module electric current Q A 0…6 0.005 Tested TE module heat load Qadd W 0…0.5 0.005 Additional heat load on a stage of a multistage TE module Тhot W -10…85 0.2 Thermostabilizing surface temperature Qhot ºC 0…40 Maximum heat rejection ∆I W 0.001 Minimum electric current modification step ∆Тhot A 1 Minimum thermostabilizing temperature modification step Stabilization time From 10 s to 30 min Time of temperature stabilizing Trace gases pressure Not exceeding 1х10-2 mm Hg 0.2 2.1.2.2 Electric power consumption: • • AC voltage: - 220 +10/-15 V; Electric power consumption: not exceeding 500 W. 2.1.2.3 The equipment DX8020 is meant for laboratory measurements at the ambient temperature 25±3ºC and relative humidity up to 80%.. Version 1.20 6 RMT Ltd. DX8020 User Guide 2.2. Standard Kit The equipment comprises the following: • • • • • • vacuum table; sample holder; control block; pumping system Mini-TASK; software; interface cables set. Version 1.20 7 RMT Ltd. 2.3. DX8020 User Guide DX8020 Arrangement 1) The testing part of the device is a vacuum table (see Figure 2.3-1) with the base thermally stabilized. There is a sample holder on it. A TE module to be tested is mounted on the sample holder. 2) The sample holder temperature is stabilized by the TE module ТМ-127-1.4-6.0, its consumption controlled. 3) The heat from the hot side of the thermostablizing TE module is rejected by the electric fan CNPS7000А-Cu. 4) The leading wires of thermal resistors and the wires of the heaters are soldered to the mounting pads of the printed circuit board of the sample holder according to the diagram given in Figure 2.3-2. Figure 2.3-1 Version 1.20 8 RMT Ltd. DX8020 User Guide Figure 2.3-2 5) The leading wires of the testing circuits and the circuits of power supply of the thermostabillizing TE module as well as those of the tested TE module and of the heaters are soldered to the vacuum-tight connectors "Lemo". 6) The vacuum chamber is closed by the cover which is held down to the ring gasket. 7) The pumping is accomplished through the nipple by the pumping system Mini-TASK (see Figure 2.3-3). Version 1.20 9 RMT Ltd. DX8020 User Guide Figure 2.3-3 8) Residual gases level is controlled by the vacuum pressure gauge (EYESYS ConvecTorr). 9) The DX8020 control and signals processing is fulfilled by the control unit with the help of PC and the software "DX8020 Operation Program". The measuring methods and necessary mathematics are given hereinafter. 10) The temperature of the base and that of the tested TE module cold side is measured by platinum thermal resistors (Pt resistors, also temperature sensors or thermistors) of the nominal resistance 100 Ohm, type HEL-700-T-1-A. The measuring accuracy is ±0.3 ºC. Version 1.20 10 RMT Ltd. 2.3.1. DX8020 User Guide Connection of Cables All the connectors of the cables included in the kit are different, and allow an unambiguous connection. 2.3.2. How to Install TE Module to Be Tested 1) Prepare a TE module to be tested for measurement: identify the TE modules in the database or input the module data into the database if it is newly developed (see Section 3.5); 2) Mount the TE module to the substrate: apply either the solder 52%In-48%Sn (melting temperature 117ºC), or Rose's alloy (melting temperature 94ºC), or a thermal grease; use the solder Sn-63%, Pb-37% (melting temperature 183ºC) to connect the TE module wires outlets with the print circuit (observe the TE module polarity – see Figure 2.3-2. IMPORTANT: It should be kept in mind that mounting by soldering provides more accurate test results. However we do not recommend soldering mounting for large TE modules (the linear dimensions exceeding 20 mm) to prevent effect of materials tempera- Version 1.20 11 RMT Ltd. DX8020 User Guide ture expanding coefficients mismatch. Furthermore, it should be kept in mind that soldering is only possible for TE modules with outer surfaces metalized. 3) Use either the solder 52%In-48%Sn (melting temperature 117ºC), or Rose's alloy (melting temperature 94ºC), or a thermal grease to mount a ceramic or a copper substrate onto the TE module cold side, with a microheater and the temperature sensor (the platinum thermal resistor of the nominal resistance 100 Ohm, type HEL-700-T-1-A). 4) Solder the outlets of the temperature sensors (Pt resistors) and the wires of the heater on the print circuit of the sample holder according to the diagram given in Figure 2.3-2. It should be borne in mind that thermistor 1 (see Figure 2.3-2) is used to measure the temperature of the base (the "hot" side of the module), and thermistor 2 (see Figure 2.3-2) - to measure the temperature of the "cold" side of the module. Circuitry of the facilities is such that the thermistors work in pairs: One pair thermistors 1 and 2, and another one - thermistors 3 and 4. When using only one additional thermistor 3 or 4, the contacts of another should be connected together (shorted). 5) Insert the sample holder with the TE module mounted into the fastening guides of the vacuum table (Figure 2.3-1), pre-lubricating the mating surfaces with silicone oil. Version 1.20 12 RMT Ltd. DX8020 User Guide 6) Connect the connectors of the sample holder to the vacuum-tight connectors of the vacuum table. 7) Close the table by the cover and press it to the gasket by the hold-down. 8) Turn on the vacuum-pump and pump out to residual pressure less than 1·10-2 mm Hg (see Section 2.3.3). 9) Turn on the control unit and perform the tests according to the methods and software - see Chapters 3, 4. Version 1.20 13 RMT Ltd. DX8020 User Guide 10) Having finished the tests, turn off the equipment, vacuum pump and let the air into the vacuum chamber (see Section 2.3.3). Version 1.20 14 RMT Ltd. 2.3.3. DX8020 User Guide Vacuum Pumping System Operation The vacuum pumping system should be assembled according to the scheme given in Figure 2.3-3. How to switch the vacuum pumping system ON: 1) Connect by the cable the control block of the pumping system to the vacuum pumping system Mini-Task Mini-Task (Figure 2.3-1). 2) Connect by the cable the electromagnetic valve to the control block of the pumping system (Figure 2.3-1). 3) Plug the power supply cable into the control block of the pumping system. 4) Switch on the vacuum pumping system Mini-Task. 5) By the switch, switch on the control unit of the pumping system (the green light "In operation" is blinking). 6) Press the button "Start" on the control block of the pumping system (the green lamp "In operation" is on; the vacuum pumping system starts pumping the air out of the closed chamber). 7) If after 3.5 min the red lamp "Leakiness" is on, a leakiness is detected in the vacuum system. In this case the control block turns off the vacuum pumping system Mini-Task. It is possible to switch on the system again in 8 min. The leak should be stopped. 8) On the chamber pressure reaching 1х10-2 mm Hg the green lamp "System ready" is on and the equipment is ready for measurement (the pressure is indicated by the vacuum pressure gauge "Eyesys ConvecTorr"). How to switch the vacuum pumping system OFF: 1) After the measurements, press the "Stop" button and hold it down for a few seconds. The isolation valve closes on the system Mini-Task (Figure 2.3-3, valve #1) and the air admittance valve opens (Figure 2.3-3, valve #2). 2) The yellow lamp "Standstill" turns on. It is possible to switch on the system again by the button "Start" in 8 min after the lamp "Standstill" goes out. Version 1.20 15 RMT Ltd. DX8020 User Guide 2.4. Maintenance 1) Perform the following monthly maintenance: • • wipe the vacuum table with ethyl alcohol; clear the fan ribs of dust by a vacuum cleaner. 2) Once in a month control the data of the Pt resistors (temperature sensors) comparing them with the data of the standard thermometer. The admissible accuracy is ±0.3ºC. 3) Once in a month control the data of Z-meter by the standard resistors.the Pt resistors. 4) When in operation do not bar the vent-holes of the equipment DX8020 control unit. Version 1.20 16 RMT Ltd. 3. DX8020 User Guide DX8020 OPERATION PROGRAM 3.1. Program Preparation 3.1.1. System Requirements The DX8020 software allows all the necessary interaction with the device DX8020. To work with the program one must be of minimal knowledge of working with MS Windows operating system. To work with the program you need: • mended); • • • IBM PC compatible computer with WINDOWS 98/2000/XP (2000/XP recomfree serial port; 10 MB free disk space; 256 MB RAM. The recommended screen resolution is 1024х768. 3.1.2. Program Installation The program distributive is supplied on the CD delivered with the facilities. Insert your CD into the appropriate drive and start the Setup program – Figure 3.1-1 Figure 3.1-1 Follow all the installation steps. When the installation is over, the program icon will appear on the desktop and in the "Start" menu. Version 1.20 17 RMT Ltd. DX8020 User Guide 3.2. Connection To connect with the device it is necessary: • connect the device DX8020 and computer by the interface wire; • select the menu item "Main Menu"-"File"-"Connect"-"Settings". In the resulting window, select the port you are connecting to, and set baud rate 115200. _ • select the menu item "Main Menu"-"File"-"Connect"-"Connect". If the connection is successful, the status says "DX8020 ver. 100 found at COM1(2)"– Figure 3.2-1. Figure 3.2-1 If the connection fails, the message of an unsuccessful attempt to connect to the device appears – Figure 3.2-2. Figure 3.2-2 To solve this problem, follow these steps. • • • • • Check the connection of the device with your computer; Check the power supply unit; Turn off and on the device; Restart the software; If nothing helps, contact the program author. 3.3. Disconnection To disconnect, select the menu item "Main Menu"-"File"-"Connect"-"Disconnect". Version 1.20 18 RMT Ltd. DX8020 User Guide 3.4. Main Window "DX8020 Operation Program" After starting the program, the software main window depicted in the figure appears. Figure 3.4-1 The main window can be divided into three fields. • • • Main menu; Temperature sensors panel; Status panel. Main Menu The main menu structure is shown below. Figure 3.4-2 In the Z-Meter mode there is an additional menu item "Z-Meter History". Figure 3.4-3 Version 1.20 19 RMT Ltd. DX8020 User Guide Temperature sensors panel is located in the right-hand part of the main window (see Figure 3.4-4). Figure 3.4-4 The telemetry data from the sensors "T1" (Hot side temperature) and "T2" (Cold side temperature), as well as the difference between the two values is displayed continuously except the periods of measurement. To set the hot side temperature is only available at a testing mode selected. Status Panel This panel is intended for the output of: • • • • • device identification; device mode; temperature stabilization status; vacuum status; corrections status. Figure 3.4-5 Version 1.20 20 RMT Ltd. 3.5. DX8020 User Guide TE Module Selection from the Database To select a TE module from the database choose from the Main Menu the item "Main Menu"-"Tests"-"TE Cooler selection". The following window will be displayed: Figure 3.5-1 By default a list of RMT TE modules is displayed. For a TE module selected, in the right-hand window part one can see its specification involved. For adding a TE module not included it is necessary to choose "USERBASE" from combo box – see Figure 3.5-2. Figure 3.5-2 Then press the button "New" - Figure 3.5-3. Figure 3.5-3 You are supposed to input the values of parameters required and save the new TE module specification pressing the button "Add" - Figure 3.5-4. Version 1.20 21 RMT Ltd. DX8020 User Guide Figure 3.5-4 It is possible to proceed with measurements without identifying the TE module to be tested (except the mode "TE Materials Properties Testing"). In this case no corrections will be calculated. Version 1.20 22 RMT Ltd. 4. DX8020 User Guide MEASURING METHODS The equipment DX8020 provide the following testing modes: 1. STANDARD: testing TE module standard performance plots in vacuum 1.1 At the zero heat load within electric current range: ∆T(I), U(I); 1.2 At varied heat load at a certain electric current: Q(∆T) 2. EXPERT: testing of a TE module parameters in the given operational point (given operating current, heat load and stabilizing temperature). 3. Z-R-τ Metering 3.1 TE module is free in the ambient: 3.1.1 The ambient is air; 3.1.2 The ambient is vacuum 3.2 TE module hot side temperature is stabilized (vacuum) 4. Testing of TE Materials PROPERTIES in a TE module (vacuum) Before the measurements, select the type of the module tested. Version 1.20 23 RMT Ltd. DX8020 User Guide 4.1. Standard Mode The major task of the standard measurements is to measure Standard Performance Plots and to confirm the tested TE module standard specifications, i.e. the following parameters: ∆Tmax, Qmax, Imax, Umax in vacuum. The tested TE module hot side temperature Thot can be fixed within the range available (Table 2.2). The characteristics measured in this mode are: • ∆T(I) – temperature difference dependent on electric current at the cooling capacity Q=0. The plot is used to obtain Imax and ∆Tmax of a TE module. • U(I) – volt-ampere characteristics at the cooling capacity Q=0. The plot is used to obtain Umax. • Q(∆T) – Temperature difference versus cooling capacity ∆T(Q, I) and voltage versus temperature difference U(∆T, I) at a certain current up to Imax. The results are Qmax and ∆Tmax at the current chosen. The testing conditions are as follows. 1) A base with a heater and a thermal resistance is mounted onto the TE module cold side (see Section 2.3.2, 3). 2) The TE module hot side is mounted onto the sample holder mounting surface (see Section 2.3.2, 2). 3) The TE module leading wires are soldered to the connecting plates according to the TE module polarity. 4) The thermostabilizing module is switched on. The temperature Thot of the thermostabilizing surface is fixed within the range available (see Table 2.2). 5) The cover is closed; 6) The vacuum chamber is pumped out to pressure of residual gases not exceeding 1·10-2 mm Hg. Version 1.20 24 RMT Ltd. DX8020 User Guide Measurement of ∆T(I), U(I) at Q=0 4.1.1. This mode is to enable building the dependences of the TE module temperature difference ∆T and the voltage U on electric current I, as well as obtaining the values ∆Tmax(Imax), Umax, Imax – see Section Mathematical Annex VI. Measurement of Imax, ∆Tmax. The additional requirement: the heater is off. The testing procedure in the automatic mode is as follows: 1) Set the required temperature of the thermostabilized surface Thot. 2) Choose the TE module stabilization time tstab and wait until the base temperature is steady. 3) Set the limiting testing electric current values (see Mathematical Annex VI. Measurement of Imax, ∆Tmax); 4) Set the electric current step. 5) Start measuring. Consistently the TE module is fed by a constant electric current, beginning from ∆I, TE module is maintained at a given current during tstab to achieve steady-state. 6) For each electric current value I the TE module temperature difference ∆T(I) and voltage U(I) are captured: in a steady state the following parameters are registered: TE module electric current, voltage drop, the base temperature; temperature difference between the base and TE module cold surface; 7) 8) The data ∆T(I) are processed; the values Imax, Umax, ∆Tmax are calculated with no corrections applied (see Mathematical Annex VI. Measurement of Imax, ∆Tmax). To enter this mode of measurement, you must select "Main Menu"-"Tests""Standard tests"-"dT(I), U(I)". The window of measurements looks as shown (Figure 4.1-1). It should be noted that after starting measurements the thermal stabilization of the base is done in accordance with set. The temperature of the set point can be changed "Set hot side temperature". Version 1.20 25 RMT Ltd. DX8020 User Guide Figure 4.1-1 The window is divided into several fields. • • • • Field of plots dT(I) and U(I); Field of current values dT, I, U; Table of measured points; Control Panel. Field of plots dT(I) and U(I) Field of plots dT(I) and U(I) is shown in Figure 4.1-2. Version 1.20 26 RMT Ltd. DX8020 User Guide Figure 4.1-2 The graphs depict the points measured. If indicating by the mouse to a point on the plot, the values and parameters of this point are highlighted by the red colour in the summary table, see – Figure 4.1-3. Figure 4.1-3 Mistaken and unnecessary points can be deleted. To do it just approach the point you want to delete by the mouse cursor until it is enclosed in the red circle. Press the right button of the mouse to obtain the context menu – Figure 4.1-4. Figure 4.1-4 Choose "Delete point". Field of current values dT, I, U This field displays current values dT, I, U of the tested TE module. In the manual mode with the help of these values it is possible to estimated if the module is stabilized or not. Figure 4.1-5 Version 1.20 27 RMT Ltd. DX8020 User Guide Table of Measured Points This table contains the measured values as well as the value of the electric current. The bottom line summarizes the measured values dTmax, Imax, Umax and the values dTmax, Imax, Umax calculated by a polynomial. Figure 4.1-6 The red-coloured line corresponds to the point indicated by the mouse. Control Panel This field allows control of the testing procedure. Figure 4.1-7 Before starting the test it is necessary to set the temperature of the stabilizing basement and wait some time to achieve the stabilization. Figure 4.1-8 The test can be done either manually or automatically. Testing Manually Set the electric current value and click "apply", see Figure 4.1-9. Figure 4.1-9 Version 1.20 28 RMT Ltd. DX8020 User Guide After achieving a steady-state temperature of the module cold side press the button "Get point" – see Figure 4.1-10. Figure 4.1-10 Testing Automatically It is necessary to set the starting and finishing values of the electric current the TE module is to be tested at, the electric current step and the hot side stabilization time – Figure 4.1-11. Figure 4.1-11 To start the measuring cycle press the button "Start". The data will be taken automatically within the settings given. After the test is over, a square-law polynomial is built by all the measured points. The measured values dTmax, Umax, Imax and the values dTmax, Umax, Imax extracted from the polynomial are displayed. If needed, it is possible to set limiting current values for the polynomial. To do it you are to choose a point, click the right button on the mouse; select "First Point of polynomial" or "Last Point of polynomial" from the context menu. By narrowing the interval of polynomial the values dTmax, Umax, Imax can be obtained more exactly. Version 1.20 29 RMT Ltd. DX8020 User Guide 4.1.2. Measurement of Q(∆T) This mode is intended for obtaining the dependence of the TE module heat load Q on the module temperature difference dT at the given electric current I, as well as for calculating the maximum heat to be pumped Qmax and extracting the corrected value dTmax at the given current. See Mathematical Annex VII. Qmax Measurement and ∆Τµαξ Correction. The additional requirement in this option: the heater is off. The testing procedure is as follows. 1) Set the required temperature of the thermostabilized surface Thot. 2) Choose the TE module stabilization time tstab and wait until the base temperature is steady. 3) Set the current I through the TE module. To measure the specification value Qmax, the condition is I = Imax, where Imax is obtained either during the measurements (see Measurement of ∆Τ(Ι), U(I) at Q=0), either by calculation. 4) For the automatic testing define the upper limit of the heat to be loaded Qlim at the electric current selected. We recommend: Q lim = 1 Q max , 2 (4.1.1) where Qmax is the TE module maximum cooling capacity estimated by calculations at the chosen current. 5) At the given current the TE module temperature difference ∆T is measured for 5 values of the heater power: Q=(0, 0.25, 0.5, 0.75, 1)Qlim. For each measurement the TE module stabilization time is tstab. 6) Build the curve Q(∆T) by the measured points using linear interpolation (See Mathematical Annex VII. Qmax Measurement and ∆Τµαξ Correction). 7) For each measured ∆T at the given current I the correction for the passive heat load from the wires is calculated: Qpas ( ∆T ) = Q wire ( ∆T ) (4.1.2) (see Mathematical Annex IV. Passive Heat Flux along the Leading Wires). 8) The new curve is built Q′( ∆T ) = Q( ∆T ) + Qpas ( ∆T ) 9) Find Qmax, ∆Tmax at a given current (see Mathematical Annex VII. Qmax Measurement and ∆Tmax Correction) 10) Find Q’max, ∆T’max at a given current (see Mathematical Annex VII. Qmax Measurement and ∆Tmax Correction). IMPORTANT: If you need to consider amendments to the passive heat flows through the wires before you go into this mode of measurement, specify the necessary characteristics of the wires in the box "Main Menu" - "Tests" - "Qpas Parameters", Bocused bookmark "Standard test : Q(dT)" see Figure 4.1-12. Version 1.20 30 RMT Ltd. DX8020 User Guide Figure 4.1-12 The wires are divided into two types: • • Type 1 - Wire Pt resistor; Type 2 - wire heater. To enter the measurements of Q (dT), must choose the "Main Menu" - "Tests" "Standard tests" - "Q (dT)". Window measurements looks as shown in Figure (Figure 4.1-13). Version 1.20 31 RMT Ltd. DX8020 User Guide Figure 4.1-13 The window contains several fields: • Fields of the plots Q(dT) and Q`(dT) • Field of current values dT, I, Q • Table of the measured points; • Control panel. Field of the Plots Q(dT) and Q`(dT) The left plot offers the results with no corrections applied; the right plot does those corrected taking into account passive heat flows through the wires (see Figure 4.1-14). Figure 4.1-14 Version 1.20 32 RMT Ltd. DX8020 User Guide If indicating a point on the plot by the mouse, the values of this point as well as the corresponding parameters are highlighted by the red colour in the table – see Figure 4.1-15. Figure 4.1-15 Mistaken and unnecessary points can be deleted. To do it just approach the point you want to delete by the mouse cursor until it is enclosed in the red circle. Press the right button of the mouse to obtain the context menu as shown – Figure 4.1-16. Figure 4.1-16 To delete a point choose "Delete point". Field of current values dT, I, Q This field displays current values dT, I, Q of the tested TE module. Figure 4.1-17 In the manual mode with the help of these values it is possible to estimate if the module is stabilized or not. Table of the Measured Points This table contains the measured values as well as the value of the electric current. The bottom line summarizes the calculated values Qmax, dTmax with no corrections applied and Qmax’, dTmax’ corrected by the passive heat load – Figure 4.1-18. Figure 4.1-18 The red-coloured line corresponds to the point indicated by the mouse cursor. Version 1.20 33 RMT Ltd. DX8020 User Guide Control Panel This field allows control of the testing procedure – see Figure 4.1-19. Figure 4.1-19 Before starting the test it is necessary to set the temperature of the stabilizing base and wait during the time tstab to achieve the stabilization (Figure 4.1-20). Figure 4.1-20 The test can be done either manually or automatically. Testing Manually Set the electric current and heat load values and click "apply" – Figure 4.1-21. Figure 4.1-21 After achieving a steady-state temperature by the module cold side press the button "Get point". Testing Automatically Set the electric current value and click “apply" – Figure 4.1-22. Figure 4.1-22 Set the hot side stabilization time and 5 values of the heat to be pumped – see Figure 4.1-23. Version 1.20 34 RMT Ltd. DX8020 User Guide Figure 4.1-23 To start the measuring cycle press the button "Start". The data will be taken automatically within the settings given. After the test is over a linear polynomial is built by all the measured points. The values the calculated values Qmax, dTmax with no corrections applied and Qmax’, dTmax’ corrected by the passive heat load are displayed. Version 1.20 35 RMT Ltd. DX8020 User Guide 4.2. Expert Mode The Expert Mode objective is to measure the widened range of TE module parameters at a specified electric current with no corrections. It is possible to apply an additional measuring temperature channel and an additional heater. In the Expert mode all the measuring telemetry can be obtained for the conditions assigned as fully as possible. The telemetry comprises the following parameters to test and control: • Four-sensor temperature data (T1, T2, T3, T4); • Double-channel heat loads (Q1, Q2); • Tested TE module electric current; • Tested TE module voltage; • Thermostabilizing TE module voltage; • The electrical resistance of thermistor (if there is one on the tested TE module) The testing conditions are as follows: 1) A base with a heater and a thermal resistor is mounted onto the TE module cold side (see Section 2.3.2); ; the heater power equals the necessary value; 2) The TE module hot side is mounted onto the sample holder mounting surface (see Section 2.3.2); 3) The TE module leading wires are soldered to the connecting plates according to the TE module polarity; 4) The thermostabilizing module is switched on. The temperature Thot of the thermostabilizing surface is fixed within the range available (see Table 2.1); 5) 6) mm Hg. The facilities cover is closed; The vacuum chamber is pumped out to residual pressure not exceeding 1·10-2 The testing procedure is as follows. 1) Set the required temperature of the thermostabilizing surface Thot; 2) Set the required heat load Q0 (the heater power); 3) Set the required electric current I0; 4) Wait until the thermostabilizing is steady, observing the stabilizing temperature data; 5) Measure the temperature difference ∆T of the TE module at the given values Q0 and I0; IMPORTANT. In order to calculate corrections to ∆T in the expert mode it is necessary to measure Q(∆T) in the vicinity of the operating point (that is, to measure Q(∆T) at a given current I in the standard mode). For the expert testing of a TE module it is necessary to choose "Main Menu""Tests"- Expert Mode". The window can be viewed in Figure 4.2-1. Version 1.20 36 RMT Ltd. DX8020 User Guide Figure 4.2-2 The window contains two functional fields: • • table of measured points; control panel. Table of Measured Points The table contains current values of parameters of a tested TE module (grey line) and those taken for the test results (white lines) – see Figure 4.2-3. Рисунок 4.2-4 Control Panel In this field you may change the device mode and set the parameters at which the TE module is to be tested – Figure 4.2-5. Version 1.20 37 RMT Ltd. DX8020 User Guide Figure 4.2-6 For example, in the figure given (Figure 4.2-6), the mode is the following: the device mode is thermal stabilization of the hot side (the base), heater 1 is on; the measurement parameters: the base temperature is 30 ºC, TE module electric current is 100 mA, the heater is 200 mW. To take the measured result, press the button "Get point". Version 1.20 38 RMT Ltd. DX8020 User Guide 4.3. Z-R-τ-Metering In these testing modes the following TE module parameters are measured: electrical resistance AC R; Figure-of-Merit Z; time constant τ. See Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit. Similar to the series of Z-R-τ meters developed by RMT for complex express testing the facilities DX8020 enable testing the following parameters of TE modules: • • • AC resistance (AC R); Figure-of-Merit (Z); Time constant (τ) The TE module Figure-of-merit Z is measured by the Harman method. Here all the limitations common for the Z-R-τ meters are to be followed (see Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit). The methods of the DX8020-100 are meant for measuring Z of single-stage TE modules. IMPORTANT: The testing of the value Z for two-stage TE modules are rather estimative. For multistage TE modules the Harman method is not applicable. The quality of TE modules with more stages can be estimated by measuring the module electric resistance AC R and the time constant τ For brevity we call Z-R-τ-Meter as Z-Meter. 4.3.1. TE Module Free in the Ambient In this testing mode the TE module to be tested is in free heat exchange with the air/vacuum environment. The aim of this option is: • to offer express assessments of TE module quality and necessity of its direct measurements by testing the values Z, R, τ of a TE module at room temperature ~ 300 K; • ensure a correlation between measurements of Z, R, τ in vacuum and air, and evaluate the accuracy of mathematical estimation of air impact on the results of measurements. The testing conditions are as follows. 1) Both the TE module sides are free. 2) The TE module leading wires are soldered onto the connecting plates. 3) The thermostabilizing TE module is off. 4) The DX8020-100 cover is closed. 5) For testing in vacuum the chamber is pumped out to residual pressure not exceeding 1·10-2 mm Hg. The testing procedure is as follows. 1) Measure the ambient temperature Та. 2) Measure the TE module AC R (hereinafter this value comprises both the TE module and its wires electric resistance AC R: R=RTEC+Rwires). 3) Set the overall measuring time МТ. 4) Set the TE module electric current Itest=0.01Imax (see the TE module Standard Specifications); press the button “measure". The automatic testing procedure is started. 5) The automatic testing procedure is as follows: Version 1.20 39 RMT Ltd. DX8020 User Guide 5.1) The temporal dependences of the TE module total voltage U(t)± and the Seebeck voltage Uα(t)± are measured within the time range [0.. MT] sequentially at the current ±Itest; the telemetry Uα(t)± is displayed; 5.2) The curves Uα(t)± are interpolated by the exponents: U α ( t ) ± = Ust α ± (1 − e − t / τ ± ) ; (4.3.1.1) As a result of this interpolation the corresponding time constants τ± and the steadystate voltage values Uαst(t)± are obtained for both polarities. IMPORTANT: To proceed with the Z-R-τ-meter measurements be sure that the period ttest is enough for the module to achieve the steady state, which can be controlled by the visual telemetry. 5.3) The TE module time constant is found as the average: τ av = 0.5(τ + + τ − ) 5.4) For each polarity the ohmic voltage is found via averaging over the last 10 measured points: UR ± = 1 ∑ (U(t i ) ± − Uα ( t i ) ± ) ; 10 i≥( N−10 ) (4.3.1.2) 5.5) With no account of the corrections the values Z± are calculated as: Z± = 1 Ust α ± ; Ta UR (4.3.1.3) ± Then the average Z is calculated as: 1 Zav = (Z + + Z − ) ; 2 (4.3.1.4) 5.6) With the help of calculated corrections it is possible to allow for the inequality between the ambient temperature and the average temperature of the module (bT), heat flow between the pellets (bth) and thermal losses on the wires (br). IMPORTANT: The corrections are only applied to the value Zav: ( ) Z av Z′ = 1 + b th (1 + b r ) av (1 + b ) T (4.3.1.5) Therefore the whole correction can be written as: corr = (1 + bth) (1 + br ) , 1 + bT (4.3.1.6) All the expressions for the corrections are given in Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit. It is only the corrections values that the choice of the environment (air/vacuum) tells upon. To select this testing mode choose from the Main Menu bar the command "Main Menu"-"Tests"-"Z-meter"- "TE Module Free in the air" or "TE Module Free in vacuum". The measurement window is illustrated in Figure 4.3-1. Version 1.20 40 RMT Ltd. DX8020 User Guide Figure 4.3-2 The window consists of three fields: • • • results field; temporal behaviour of the Seebeck voltage; control panel. Results Field This field is shown in Figure 4.3-3. Figure 4.3-3 The following results are displayed: Version 1.20 41 RMT Ltd. • • • • • • • DX8020 User Guide Tamb – ambient temperature; ACR – TE module electrical resistance (alternating current); ACR` – ACR referred to Tref; Z – TE module Figure-of-Merit; Z` – TE module Figure-of-Merit with corrections applied; Corrections – correction coefficient to Z; Time Const – TE module time constant. Temporal behaviour of the Seebeck voltage This curve (see Figure 4.3-4) displays the dynamics of the Seebeck voltage at the test current of two polarities. Each experimental curve is accompanied by the interpolation one. Figure 4.3-4 Control Panel The control panel allows setting the measurement parameters – see (Figure 4.3-5). Figure 4.3-5 The following parameters are to be set: • • Reference temperature (Tref) – temperature ACR is referred to; Current – TE module electric current (0.01Imax is recommended); Version 1.20 42 RMT Ltd. • • DX8020 User Guide Measuring Time; Time Step (recommended to increase for longer testing). 4.3.2. TE Module with the Hot Side Temperature Stabilized The mode is intended for Z-R-τ- testing of a TE module at the given temperature. See Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit. In this mode one side of a TE module is stabilized at a temperature Thot. The measurements are performed in vacuum. The aim of this option is to measure the parameters Z, R, τ at a given temperature, which may differ from the room temperature. The testing conditions are as follows. 1) One side of the TE module is free, the other is mounted onto the thermostabilized surface (see How to Install TE Module to Be Tested Section 2.3.2). 2) The TE module leading wires are soldered onto the connecting plates. 3) The thermostabilizing TE module is on. The thermostabizing surface temperature Thot is fixed within the range available (see Table 2.2); 4) The DX8020-100 chamber cover is closed; 5) The chamber is pumped out to residual pressure not exceeding 1·10-2 mm Hg. The testing procedure is as follows: 1) Set the temperature of the thermostabilizing surface Thot; wait until the thermostabilizing is steady. 2) The measurements 2) – 5) of Section 4.3.1. Eq. (4.3.1.3) is modified as: Z± = 1 Ust α ± ; Thot UR (4.3.2.1) ± The value Z is measured and corrected (see Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit) for a TE module with Thot=const. The corrections only include the leading wires correction (see Mathematical Annex IV. Passive Heat Flux along the Leading Wires) and radiation (see Mathematical Annex II. Estimation of Radiation Heat Exchange Coefficient, Mathematical Annex III. Additional Thermal Conductance between Pellets). Choose the command "Main Menu"-"Tests"-"Z-meter"-"TE module with the Hot Side Temperature Stabilized". The measurement window is shown in Figure 4.3-6. Version 1.20 43 RMT Ltd. DX8020 User Guide Figure 4.3-6 Before testing it is necessary to set the TE module base temperature and wait until the base is stabilized (the red indicator at the bottom turns to green). The testing procedure, parameters, functional fields and results form are the same as in the modes "Z-R-τ-Meter for TE Module Free (air/vacuum)". Version 1.20 44 RMT Ltd. DX8020 User Guide 4.4. TE Properties Testing This testing mode enables experimental estimate of TE matrials properties of the tested TE module: the Seebeck coefficient α and electrical conductivity σ at temperature available. The objective of the given option is to estimate the properties of TE materials of the TE module pellets at the given temperature Thot or in a temperature range available using the measurements of the parameters Z and R, as well as the stationary Seebeck voltage value Uα and the corresponding value of the temperature difference ∆T. The TE properties to be obtained are: • Electrical conductivity; • Seebeck coefficient The estimates obtained are the average values for the n- and p- type materials. IMPORTANT: It is only one-stage TE modules with known geometrical parameters that can be tested in this option. The testing conditions are as follows. 1) One side of the TE module is stabilized at the temperature Thot. 2) The TE module leading wires are soldered onto the connecting plates. 3) The thermostabilizing TE module is on. The thermostabizing surface temperature Thot is fixed within the range available (see Table 2.2); 4) The chamber cover is closed; 5) The chamber is pumped out to residual pressure not exceeding 1·10-2 mm Hg. The testing procedure is as follows. 1) Set the temperature of the thermostabilizing surface Thot; wait until the thermostabilizing is steady. 2) Repeat the Z-R-τ-metering of the TE module with the hot side temperature Тhot stabilized; the values of AC R and Z of the TE module are found (with / with no corrections applied. 3) By the measured AC R at the given temperature Thot the electrical conductivity σ [1/Ohm·m] of the TE material is estimated as: a. R pellet = (R − 2r − NR me ) , N b. ρ = R pellet c. σ = (4.4.1) s , l 1 , ρ Here N is the TE module pellets number. The electrical resistance R me is calculated as: R me = ρ Cu d + 2 / 3w , wl me (4.4.2) where d is the distance between pellets of the TE module, w is their width, lme is the metal junctions thickness. Version 1.20 45 RMT Ltd. DX8020 User Guide 4) By the known polynomial temperature dependence κ=1/2(κn+κp) the Seebeck coefficient is calculated by: α= Zκ σ ; (4.4.3) The corrected parameter α corresponds to the corrected Figure-of-Merit Z. Among the three parameters α, σ, κ the parameter κ is the least sensitive to charge carriers properties, that is why a standard κ(T) can serve for estimating the coefficient α. In Figure 4.4-1 the dependence κ(T) averaged for n- and p-type room temperature optimized TE materials is given. This curve is a default function the DX8020-100 software offers. Figure 4.4-1 IMPORTANT: The function κ(Т) can be changed by introducing new factors of the polynomial (see the file DX8020/Parameters.ini). If necessary, items 1-7 are performed for a new Thot Version 1.20 46 RMT Ltd. DX8020 User Guide Choose the command "Main Menu"-"Tests"-"TE Materials Properties Testing". The measurement window is shown in (Figure 4.4-2). Figure 4.4-2 The testing procedure, parameters, functional fields are similar to the mode "TE Module with the Hot Side Temperature Stabilized". Version 1.20 47 RMT Ltd. 5. DX8020 User Guide Mathematical Annex I. Estimation of Convectional Heat Exchange Coeffi- cient Coefficient of Convection heat exchange per surface unit α conv [W/(m2·K)] is written as α conv = κ Nu , Nu = C(Gr Pr)n x (5.1) where Nu is the Nusselt number; Gr, Pr are the Grashof and Prandtl numbers, respectively. The Grashof number is described as: Gr = gβ∆Tx 3 , ν2 (5.2) where g=9.8 m/c2, β=1/T [1/K] is linear expansion coefficient for the ambient gas at given conditions (usually at normal ones), T [K] is the gas absolute temperature; ∆T is temperature difference considered, x [m] is characteristic linear size of the object (we recommend it to be the bigger side of the surface involved in the heat exchange), ν [m2/s] is kinematic viscosity. The Prandtl number and gas thermal diffusivity a can be calculated as: ν , a (5.3) κ , c pρ (5.4) Pr = a= where ρ [kg/m3] is gas density, c p [J/(kg·K)] is gas heat capacity at constant pressure. If 1< Pr <1000 and 103< Gr ⋅ Pr <109, we deal with a laminar flow and then the coefficients in Eq. (1) are the following C=0.75, n=0.25, i.e.: α conv = κ 0.75(Gr Pr)0.25 x (5.5) Table 5.1 offers dry air parameters at normal pressure and temperature 20 ºC and 30 ºC. Table 5.1 Т, ºС ρ, kg/m 3 ср, J /( kg • K) κ, W/(m • K) ν·10 , m /s 6 20 1.205 1000 0.0260 15.06 30 1.165 1000 0.0268 16.00 2 Consider an example of calculations. For ∆T=3K (approximately true in Z-metering). In Table 5.2 the estimates for α conv are given for some TE modules in the air at 20 ºC. Table 5.2 Version 1.20 3 TE module type х·10 , m αconv, W/m K (20ºС) 1МС04-004-хх 3.2 10.87 1МС06-018-хх 6.0 9.29 1МС04-070-хх 9.6 8.26 1МС06-105-хх 15.0 7.38 2 48 RMT Ltd. DX8020 User Guide The full passive convectional flow onto the surface F1 (the TE module substrate, including lateral sides) is: Qpas conv = α conv F1∆T Version 1.20 (5.6) 49 RMT Ltd. 6. DX8020 User Guide Mathematical Annex II. Estimation of Radiation Heat Exchange Coeffi- cient We designate: "1" - object (TE module): Surface – F1, m2 (TE module surface); A1 – emissivity; T1 – temperature. "2" - hemisphere cover: Surface – F2, m2; A2 – emissivity; T2 – temperature. General data: The hemisphere cover surface, m2: F2=2πRcover2=0.062 m2 (Rcover=10 cm) Emissivities: A1=0.8 (common for ceramics) A2=0.45 (common for stainless steel). The method of estimating effective emissivity between bodies 1 and 2 can be obtained as: A 12 = 1 F 1 1 + 1 − 1 A 1 F2 А 2 (6.1) For micro modules F2<<F1 and effective emissivity nearly coincides with the value A1. Further we consider this case. In the Standard option the radiation heat exchange coefficient αrad [W/m2K] can be estimated as: 2 2 αrad = σ SB A1( Thot + Tcold )(Thot + Tcold ) , (6.2) where σSB is the Stefan-Boltzmann constant. For testing a TE module in the Z-R-τ-metering option, free heat exchange mode the value αrad equals the following: α rad = 4σ SB A 1Ta3 , (6.3) For testing a TE module in the Z-R-τ-metering option and the base side temperature stabilized at Thot, the value αrad is defined via Thot: 3 α rad = 4σ SB A 1Thot . (6.4) Then the full passive radiation flow onto the surface F1 (the TE module substrate, including lateral sides) is: Qpas conv = αradF1∆T Version 1.20 (6.5) 50 RMT Ltd. 7. DX8020 User Guide Mathematical Annex III. Additional Thermal Conductance between Pellets Consider one stage of a TE module. The correction bth characterizes additional thermal conductivity between the pellets: κ′ = κ(1+ b th ) , (7.1) where κ is p-n type average thermal conductivity of TE material. The value bth is estimated as the sum of corrections for thermal conductivity in the air and radiation: b th = Bair + Brad , (7.2) where B air is the correction for thermal conductivity in the air; Brad is that for radiation. Introduce β as the pellets filling coefficient: β= ns , S (7.3) where n is the pellets number, s is a pellet cross-section, S is the cold substrate surface. The value B air is calculated as: B air = κ air κ 1 − 1 , β (7.4) The correction for radiation can be written as: B rad = l γσSB 1 − 1(Thot β κ + Tcold )( T 2hot + T 2cold ) (7.5) where σSB is the Stefan-Boltzmann constant, γ is emissivity of the inner side of the TE module substrate; Thot is the hot side temperature, Tcold is the cold side temperature. For small electric currents (for example while measuring Z) Thot ≈ Tcold ≈ Ta, and formula (III.5) can be rewritten as: B rad = 4l γσ SB 1 − 1Ta3 β κ (7.6) In Table 7.1 we give the calculated results for B air and Brad for typical TE modules at Ta=293 К for typical temperature of Z,R,τ-metering: Thot =293 К, Tcold =290 К (∆T=3 K). Table 7.1 Version 1.20 TE module type β Bair Brad 1МС04-004-05 0.25 0.055 0.005 1МС04-004-15 0.25 0.055 0.014 1МС06-018-05 0.36 0.032 0.003 1МС06-018-15 0.36 0.032 0.009 51 RMT Ltd. 8. DX8020 User Guide Mathematical Annex IV. Passive Heat Flux along the Leading Wires Consider a wire with no insulation, the crosssection is S, the length is L, the cross-section perimeter is U. Let α stand for the heat exchange coefficient per the wire surface unit. T hot=Ta If x=0 marks the hot end of the wire, the cold end has the coordinate x=L. The heat conduction equation for such a pellet exposed to the electric current of the density j has the following form in one-dimensional equation: 0 κ d2 T (x ) dx 2 Tcold х L Figure 8-1 + j 2 ρ + A(Ta − T( x )) = 0 , (8.1) where κ is the wire material thermal conductivity, ρ is its electrical resistivity, T(x) is temperature in the coordinate x. The value A is defined as: A=α U S (8.2) We take the following boundary conditions: the cold end temperature is Tcold, the hot end temperature is Thot: T(x ) x =0 = Thot , T(x ) x =L = Tcold (8.3) The heat flux arriving at the cold end equals Q = − κS dT dx (8.4) x =L Solving Eq. (8.1) we find the temperature distribution along the wire: T( x ) = Ta − where p = ( ) ( ) j 2 ρ px sh(px ) j 2 ρ px , e −1 + e − 1 − ∆T A A sh(pL ) (8.5) A , ∆T = Thot − Tcold . κ The passive heat flow onto the cold end is yielded (8.4) and (8.5): j 2 ρ pL j 2 ρ ch(pL ) Q pas = S Aκ e + 1 − e pL + ∆T , sh(pL ) A A ( ) (8.6) In vacuum the radiation heat exchange coefficient [W/(m2·K)] can be estimated as: α rad = γσ (Tav + Ta )(T 2av + T 2a) , SB (8.7) where Tav=1/2(Thot+Tcold), σSB is the Stefan-Boltzmann constant, γ is the emissivity of the wire surface. Ta is the ambient temperature, or the temperature of the cover, it is taken 20ºC=293 K by default. In the DX8020-100 methods the corrections on the passive heat flow along the wires are taken into account for the TE module cold side only (no corrections for intermediate substrates). There may be two different types of these wires: 1) Resistor wires (Pt); Version 1.20 52 RMT Ltd. DX8020 User Guide 2) Heater wires. Consider exemplary calculations for both the types. 1) The common parameters of thermoresistor wires: the material is copper, κ=400 W/mK, ρ=1.667·10-8 Ohm·m. The wire diameter is 0.07 mm, the length is L=40 mm. The electric current is 1 mA (approximately for the 100 Ohm thermoresistor). The ambient temperature TA=20ºC. The hot end temperature Thot=Ta. The cold end temperature Tcold is -50 °C (approximate minimal temperature of a single-stage TE module cold substrate at Imax and Ta=20ºC). The heat exchange for the wire surface is that of radiation. For copper we take the value of emissivity γ=0.02 (polished copper). Then the heat exchange coefficient α equals α = 0.095 W/(m2·K). At the small current (here j2ρ j2ρ <<∆T, ~0.173) and if the wire thermal conductance A A is high enough while the radiation heat exchange from the surface is low: pL<<1 (here the value pL is equal to 0.16), the temperature distribution along the wire is nearly linear – in Figure 8-2 you are given the results of the exact calculation: Figure 8-2 I.e. Eq. (8.5) can be rewritten as: T( x ) = Ta − ∆T sh(px) . sh(pL) (8.8) and the expression for the heat flow at the cold end of the wire: Qpas = κ S ∆T , L (8.9) The exact calculation resulted from Eqs. (8.5), (8.6): Q=7.189 mW. The result of the approximate calculation yields: Q=7.180 mW. We see the results are very close. In the software DX8020-100 Eq. (8.9). is applied for thermoresistors. For N wires Eq. (8.9). is written as: Q pas = Nκ S ∆T , L (8.10) For N=2 the thermoresistor wires with the parameters and at the conditions given provide the summed passive heat load onto the cold substrate 5.39 mW. 2) Consider the following parameters of the heater wires: the material is copper, κ=400 W/mK, ρ=1.667·10-8 Ohm·m. The wire diameter is 0.15 mm, the length is L=40 mm. The electric current is 1 A (approximately for the heater of the nominal 6.8 Ohm at the Version 1.20 53 RMT Ltd. DX8020 User Guide load 6.8 W). The ambient temperature TA=20ºC. For an estimation of the passive heat load in the standard Q(∆T) measuring option we take Tcold=-20 ºC. The heat exchange for the wire surface is that of radiation. For copper we take the value of emissivity γ=0.02 (polished copper). Then the heat exchange coefficient equals α=0.095 W/(m2·K). For this instance the temperature distribution along the wire is non-linear - Figure 8-3. Figure 8-3 In the calculations the exact formulae (8.5-8.6) are necessary. As a result we have Qpas=31 mW. The approximate Eq. (8.9), taking into account thermal conductance only would have been: Qpas=12 mW, which is too rough an underestimation. In the software DX8020-100 for the heater correction Eq. (8.6) is applied. For N wires Eq. (8.6) is written as follows: j2ρ pL j2ρ ch(pL ) Qpas = NS Aκ e + 1 − epL + ∆T sh(pL ) A A ( ) (8.11) For N=2 the heater wires with the parameters and at the conditions given provide the summed passive heat load onto the cold substrate 62 mW. Version 1.20 54 RMT Ltd. DX8020 User Guide 9. Mathematical Annex V. n-Power Polynomial Interpolation The polynomial Interpolation approach suggested is based on the least squares method. Let us take a two-dimensional set of N points y i ( xi ) . Consider an n-power polynomial: n y( x ) = A 0 + A1x + A 2 x 2 + ... + A n −1x n −1 + A n x n = ∑ A j x j j=0 (9.1) Introducing the following coefficients: bn = N N N N i =1 i =1 i =1 i =1 2n 2n −1 , …, a2 = ∑ x i 2 , a1 = ∑ x i , a 0 = N ; ∑ x i , a 2n −1 = ∑ x i a 2n = N N N N i =1 i=1 i =1 i =1 n n −1 ∑ y i x i , bn −1 = ∑ y i x i , …, b1 = ∑ x i y i b0 = ∑ yi (9.2) We solve the system of (n+1) equations and find the coefficient Aj: A n ⋅ a 2n + A n −1 ⋅ a 2n −1 + ... + A1 ⋅ a 2n − n + A 0 ⋅ an −1 − bn = 0 A n ⋅ a 2n −1 + A n −1 ⋅ a 2n − 2 + ... + A1 ⋅ a 2n −1 + A 0 ⋅ an − 2 − bn −1 = 0 ... A n ⋅ an +1 + A n −1 ⋅ an + ... + A1 ⋅ a 2 + A 0 ⋅ a1 − b1 = 0 (9.3) A n ⋅ an + A n −1 ⋅ an −1 + ... + A1 ⋅ a1 + A 0 ⋅ a0 − b 0 = 0 The mean square deviation is given by: N ∑ (P( xi ) − yi ) 2 (9.4) i =1 σ= N Let us consider an example of 2-power polynomial: y( x ) = Ax 2 + Bx + C , (9.5) If the following designations are true: a= N N N N i =1 i =1 i =1 i =1 4 3 2 ∑ x i , b = ∑ xi , c = ∑ xi d = ∑ xi , f = N , aa = N N N i =1 i =1 (9.6) ∑ y i x i , ab = ∑ y i x i , ac = ∑ y i 2 i =1 We solve the following set of equations and find A, B, C: A ⋅ a + B ⋅ b + C ⋅ c − aa = 0 A ⋅ b + B ⋅ c + C ⋅ d − ab = 0 (9.7) A ⋅ c + B ⋅ d + C ⋅ N − ac = 0 For the linear interpolation: y( x) = Ax + B (9.8) If we designate: Version 1.20 55 RMT Ltd. a= DX8020 User Guide N N i =1 i =1 2 ∑ xi , b = ∑ xi aa = N N i =1 i=1 (9.9) ∑ y i x i , ab = ∑ y i We solve the following set of equations and find the coefficients A, B: A ⋅ a + B ⋅ b − aa = 0 A ⋅ b + B ⋅ c − ab = 0 Version 1.20 (9.10) 56 RMT Ltd. 10. DX8020 User Guide Mathematical Annex VI. Measurement of Imax, ∆Tmax To obtain the values Imax, ∆Tmax we interpolate the part of the dependence I(∆T) in the vicinity of its maximum by a square-law polynomial (see Mathematical Annex V. nPower Polynomial Interpolation): ∆T(I) = AI2 + BI + C (10.1) The interpolation is taken at the electric current segment [I0, Ilim]. By default I0=0.5·Imax is the starting measured point, Ilim=1.2·Imax is that finishing (Imax is the value taken from specifications or estimations). Once the interpolation is over, the maximal Imax, ∆Tmax are obtained as: Imax = − B , ∆Tmax = ∆T(Imax ) 2A (10.2) Let us take an example. Suppose the following data are measured (see Figure 10.1). The interpolating limits are taken as Ilim=4.5 A, I0=1.5 A. The interpolation polynomial is given in Eq. (10.3) and is illustrated in Figure 10.1. ∆T(I) = −3.913∆T 2 + 24.417∆T + 32.554 (10.3) The mean square deviation on the interval [1.5А, 4.5А]: σ=0.22 К. The values are Imax=3.12A, ∆Tmax=70.642K. Version 1.20 57 RMT Ltd. 11. DX8020 User Guide Mathematical Annex VII. Qmax Measurement and ∆Tmax Correction The measured points are linearly interpolated and the curve Q(∆T) is obtained (see Mathematical Annex V. n-Power Polynomial Interpolation): Q(∆T ) = A ⋅ ∆T + B (11.1) The value Qmax is defined as Q(0) = B : Q max = B (11.2) The value ∆Tmax for the current I is obtained from Eq. (11.1) при Q = 0 : ∆Tmax = − B A (11.3) Consider an example. Suppose the measured data are given in Figure 11.1. The calculated for the TEC Qmax=3.26 W, so we choose Qlim=1.6 W. The measured and interpolated results without corrections are given in Figure 11.1. Figure 11.1 The mean square deviation in the range [35.9K, 68.7K]: σ=0.025 W. Eq. (11.2) yields Qmax=2.929 W. With the help of Eq. (11.3) we obtain ∆Tmax=71.35K. If it is necessary to calculate corrections taking into account a passive heat flow Qpas through the wires, for each point ∆Ti the passive heat load is estimated (see Mathematical Annex IV. Passive Heat Flux along the Leading Wires). By the points obtained we get a new dependence Q’=Q+Qpas of ∆T. After interpolating the new dependence according to the above algorithm, we find the corrected values Q’max, ∆T’max (see the Standard Mode). An example of the corrected curves for the case illustrated by Figure 11.1 is given in Figure 11.2. Version 1.20 58 RMT Ltd. DX8020 User Guide Figure 11.2 The corrected value ∆T’max is 73.2 K. Version 1.20 59 RMT Ltd. 12. DX8020 User Guide Mathematical Annex VIII. Measurement of TE Module Figure-of-Merit The rate equations of the heat balance for a single-stage TE module can be written as: αITcold − αIThot a 12 I R − k ′(Thot − Tcold ) = cold (Ta − Tcold ) 2 N a 1 + I2R − k ′(Thot − Tcold ) = hot (Thot − Ta ) 2 N (12.1) L , where σ is the pelσs let material electrical conductivity, L is the pellet length, s is its cross-section), Tcold is the TE module cold side temperature, Thot is the TE module hot side temperature, Ta is the where I is the TE module current, R is the electrical resistance ( R = ambient temperature, N is the pellets number, a cold is the summed coefficient of the heat exchange of the cold side, a hot is the summed coefficient of the heat exchange of the hot side. The value k ′ is the TE module pellet effective thermal conductance taking into account heat flows between the pellets (see Mathematical Appendix III). Eqs. (12.1) are solved without allowing for TE properties temperature dependence, which can be accepted as the tested currents are very small (I~0.01Imax). We suppose that acold << k ′, N ahot k′ << k ′, I << . N α (12.2) Accurate within the first order of smallness of the values (12.2), we find the following expression Z=α2σ/κ: Z= 1 Uα (1 + b th )(1 + br ) . Ta UR av (1 + b T ) (12.3) U The ratio α in Eq. (12.3) must be averaged for two current directions to elimi UR av nate the terms depending on the current linearly and to extract the corrections bth, br, bT. The expressions for bth, br, bT are as follows: 1. bth is the correction for additional thermal transfer between the pellets: b th = Bcond + Brad , (12.4) where the values B cond and Brad are calculated as shown in Mathematical Appendix III. 2. br is the correction for electrical resistance of the leading wires: br = 2r R TEC (12.5) where r is the electrical resistance of one wire, RTEC is that of the TE module without the wires: RTEC = R - 2r. 3 bT is the correction allowing for non-equality of the average temperature Tav of the module and Ta: I2RN b T = b T0 + b T1(1 + b T0 ) + b T2 , b T0 = , (acold + a hot )Ta Version 1.20 (12.6) 60 RMT Ltd. b T1 = − DX8020 User Guide a a cold ahot − ahot (αI)2 N + , b T 2 = cold (a cold + ahot )kN (a cold + ahot )k a cold + ahot 2 I2R 2kTa The values a cold , a hot can be estimated considering natural convection in the air (if not in vacuum) and radiation: a cold / hot = (a conv + a rad )S cold / hot , where a conv and a rad are convection and radiation heat exchange coefficients, respectively (see Mathematical Appendices I, II). It is of vital concern that Eq. (12.3) remains true if the inequalities (12.2) are modified the following way: acold << k ′, N a cold << ahot , I << k′ α (12.7) It means that the method allows testing Z of a TE module if its hot side I in a rather intensive heat exchange. That is why the Z-R-τ-metering option can be used for testing a 1 =Rt is the header thermal resistance. аhot TE module mounted on some header. Then In the extreme case Ahot=∞ we come to the expression for Z of a TE module, its hot side stabilized at the temperature Thot: Z= 1 Uα Thot UR av (1 + b th )(1 + br ) 1− a cold I2 R + kN 2kThot (12.8) The measured Z of a single-stage TE module allows estimating the module ∆Tmax at the given Ta (Thot): ∆Tmax (Ta(hot ) ) = Ta(hot ) − Version 1.20 1 + 2ZTa(hot ) − 1 (12.9) Z 61 RMT Ltd. DX8020 User Guide REFERENCE 1. Materials Useful Properties In Table R1 some metals properties that may be used for reference are given. Table R1 Material Density, Thermal conductivity, kg/m3 W/mK Specific heat, J/kgK Electrical resistivity, 10-8 mOhm Aluminum 2700 237 900 2.8 Copper 8960 400 385 1.7 Gold 19320 317 128 2.3 Iron 7210 83 460 8.71 Lead 11210 35 130 19.3 Molybdenum 10220 138 249 5.6 Nickel 8910 90 448 6.1 Platinum 21450 72 133 10.9 Silver 10500 429 235 1.7 Stainless steel 8010 14.5 460 8.4 Tin 7310 64 226 10.1 Wolfram 19350 174 132 5.6 Zinc 7150 112 381 5.5 Version 1.20 62 RMT Ltd. DX8020 User Guide REFERENCE 2. Terms and Definitions In Table R2 useful terms and definitions are given. Term Ambient temperature Cold side temperature Hot side temperature Temperature difference Cooling capacity Heat load Active heat load Passive heat load TE module electric current TE module electric voltage TE module electric power Heat to be rejected Definition if necessary Temperature of a TE module external cold substrate surface Temperature of a TE module (TE module system) hot (heat rejecting) surface The difference of the values Thot and Tcold for a TE module (TE module system) A heat amount possible to be pumped from a TE module cold side per a time unit. A heat amount supposed to be pumped by a TE module per a time unit. It should equal the value Q. A heat load to be pumped directly from the object to be cooled A heat load that arises from the heat interchange with the ambient, thermal radiation and conduction accompanying processes Table R2 Symbol Units Ta К Tcold K Thot K ∆T К Q W Q W Qa W Qpas W I A U V Electric power consumed by a TE module P W A heat amount to be transferred from the hot side of a TE module (TE module system) Qhot W TE module electric resistance AC resistance at a specified temperature Ta R Ohm Maximum temperature difference Maximal achievable TE module (TE module system) temperature difference at the zero TE module heat load Q=0. ∆Tmax K Maximum electric current Current at which ∆Tmax is achieved. Imax A Qmax W Umax V R Ohm Z 1/K Maximal possible TE module cooling capacMaximum cooling capac- ity at the zero TE module (TE module sysity tem) temperature difference ∆T=0 and I=Imax. Maximum voltage TE module voltage at ∆T=∆Tmax and I=Imax. TE module electric resisAC resistance of a TE module tance The combination of TE material parameters: the Seebeck coefficient α, electrical conducFigure-of-Merit tivity σ and thermal conductivity κ as Z=α2σ/κ. Characterizes the material efficiency at the temperature given. Version 1.20 63 RMT Ltd. DX8020 User Guide Term TE module time constant Definition if necessary The time necessary for the raise of the TE module temperature difference from 0 up to 0.63 of steady-state value at the given current switch on TE module height TE module cold surface TE module hot surface Header Header thermal resistance Version 1.20 A design interface between the TE module hot side and heat sink providing a housing for the module and pin-out. The value characterizing temperature gradient on a header and equals this gradient divided by Qhot. Symbol Units τ sec H AxB, Scold CxD, Shot mm mm2 mm2 Rt K/W 64