sensors Article Coaxial Thermocouples for Heat Transfer Measurements in Long-Duration High Enthalpy Flows Shizhong Zhang 1, Qiu Wang 1, Jinping Li 1,

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1 sensors Article Coaxial rmocouples for Heat Transfer Measurements Long-Duration High Enthalpy Flows Shizhong Zhang 1, Qiu Wang 1, Jpg Li 1, *, Xiaoyuan Zhang 1 Hong Chen 1,2 1 State Key Laboratory High Temperature Gas Dynamics, Institute Mechanics, Chese Academy Sciences, Beijg 119, Cha; zhangshizhong@imech.ac.cn (S.Z.); wangqiu@imech.ac.cn (Q.W.); zhangxiaoyuan@imech.ac.cn (X.Z.); hongchen@imech.ac.cn (H.C.) 2 School Engeerg Science, University Chese Academy Sciences, Beijg 149, Cha * Correspondence: lijpg@imech.ac.cn Received: 12 August 22; Accepted: 11 September 22; Publhed: 14 September 22 Abstract: Coaxial rmocouples have advantages fast response good durability. y widely for transfer measurements transient facilities, researchers have also considered ir use for long-duration transfer measurements. However, model thickness, transverse transfer, changes physical parameters materials with creasg fluence accuracy transfer measurements. A numerical analys rmocouples conducted to determe above fluences on measurement deviation. mimum deviation obtaed if rmal effusivity chromel that changes with to derive from. deviation less than 5.5% when Fourier number smaller than.255 1% when Fourier number smaller than.52. results provide guidance for design test models rmocouples long-duration transfer measurements. numerical calculation results verified by a laser radiation g experiment, transfer measurements usg rmocouples an arc tunnel with a test time several seconds performed. Keywords: transfer measurement; rmocouple; long-duration; semi-fite; high enthalpy 1. Introduction accurate prediction aerodynamic g important design development hypersonic flight vehicles. peak g rate combustion chamber a scramjet enge also a significant parameter rmal, structural design enge [1]. However, aerodynamic g prediction remas a difficult problem modern computational fluid dynamics. Due to high cost flight tests, most aerodynamic g experiments conducted ground facilities. Generally, data obtaed usg sensors that flush-mounted wall test model. time-resolved data n processed to calculate usg a physical conduction model with few simplified assumptions. Different ground test facilities have different measurement environments different test periods; thus, requirements for sensor variable [2,3]. Transient transfer measurements with a test time milleconds (i.e., a pulse shock tunnel environment) require a fast response sensor. Commonly transient sensors clude th-film restance rmometers fast-response rmocouples [4]. However, long-duration transfer measurements (i.e., contuous tunnel environment) have relatively low requirements sensor response, commonly long-duration sensors clude Gardon meters [5] Schmidt Boelter meters [6]. refore, it crucial to select a sensor that suitable for test environment. Sensors 22, 2, 5254; doi:1.339/s

2 Sensors 22, 2, In supersonic combustion experiments a direct-connected facility, enge generally runs a few seconds. flow field calibration an arc tunnel also performed with a few seconds [7]. When transfer measurements conducted th long-duration environment, model will crease significantly. Thus, sensor needs to be cooled most cases generally has a large size with a diameter more than 2 mm. However, ternal space enge direct-connected facilities limits application long-duration sensors. coolg system sensor also complicates system design. Flow field calibrations arc tunnels also require miaturized sensors to obta sufficient spatial resolution. Coaxial rmocouples based on one-dimensional (1D) semi-fite conduction ory has advantages fast response, strong antierosion capacity, low production cost; diameter se sensors generally 1 2 mm. Thus, se sensors easy to stall due to ir small size convenient for transfer measurements under se conditions. Coaxial rmocouples widely for transient transfer measurements, test time order milleconds meets assumption 1D semi-fite conduction. Researchers performed numerous vestigations to improve measurg accuracy rmocouples. Serson [8] Mareau [9] conducted studies on structural design manufacturg method rmocouples found that sensor response time was related to structure junction. Li [1] performed a numerical analys transfer, cludg junction rmocouple, observed a two-dimensional transfer effect near junction due to fluence sulatg layer. Li also vestigated fluencg mechanm junction size, thickness sulatg layer, effect rmal conductivity on transfer measurements. Mareau [9], Buttsworth [11], Mohammed [12], Chen [13] conducted calibration experiments on effective rmal effusivity ρck rmocouples; large differences were observed rmal effusivity for different junction grdg processes. Wang [14] researched impact different materials on transient transfer measurements obtaed from rmocouples; measurement errors up to 2% were obtaed 1 ms measurement periods. Sce many factors fluence accuracy measurements, such as gauge stallation, gauge calibration sensitivity tests, data reduction procedures, uncertaties, accuracy transfer measurements obtaed from rmocouples a transient environment ±1% for some simple model shape [15], which might be larger for more complex model shape [16]. In view advantages rmocouples ir creased use research on transient transfer measurements, rmocouples have also been for transfer measurement long-duration facilities (on order seconds). Coblh [17] conducted transfer measurements on a 25/55 double-cone model usg rmocouples No. 9 hypersonic tunnel (HVWT9) at Arnold Engeerg Development Center (AEDC); effective test time was 15 s. Kirk [18] rmocouples for aerodynamic g measurements on Orion Crew Module model HVWT9 tunnel, effective test time was 1 s. Both experiments provided meangful results, but complex flow structure or nonuniformity resulted challenges analys use rmocouples long-duration experiments. Additionally, few error analyses were conducted to date long-duration transfer measurements based on 1D conduction ory. Furr vestigations also required on changes effective rmal effusivity ρck resultg dcrepancies at a rmocouple several hundred degrees. In th study, we vestigate use mature fast-response rmocouples developed laboratory for long-duration measurements order several seconds to extend application sensors. First, fluencg factors on long-duration transfer measurements obtaed from rmocouple analyzed, cludg model thickness, transverse transfer, changes physical parameters materials with creasg. Second, accuracy numerical results verified usg a laser radiation g experiment, measurements order several seconds obtaed an arc tunnel. Th study

3 Sensors 22, 2, x FOR PEER REVIEW 3 18 creasg Sensors 22, 2, Second, accuracy numerical results verified usg a laser 3 18 radiation g experiment, measurements order several seconds obtaed an arc tunnel. Th study provides oretical guidance for design provides oretical guidance for design rmocouples analys long-duration rmocouples analys long-duration measurements. measurements. 2. Influencg Factors on Accuracy Long-Duration Heat Transfer Measurements Usg a 2. Influencg Factors on Accuracy Long-Duration Heat Transfer Measurements Usg Coaxial Coaxialrmocouple 2.1. Configuration Prciple Coaxial rmocouple structure rmocouple shown Figure A constantan wire 1. 1.mm diameter serted ly to a mached chromel cylder 2. mm diameter. two rmocouple elements lectrically sulated from fromeach each or or radial radial direction, direction, except except at at front front.. thickness thickness sulation sulation approximate approximate 1 μm. 1 µm. junction junction sensor sensor sed sed to ensure to ensure a smooth a smooth for for test testmodel. junction n obtaed based on Seebeck effect. Th type-e rmocouple has has been been widely widely transient transient measurement measurement because because rmal rmal properties properties chromel chromel constantan constantan similar, similar, reby reby reducg reducg detrimental detrimental lateral lateral conduction conduction between between two materials. two materials. rmocouple rmocouple has advantages has advantages fast response fast good response durability. good durability. Chromel Connectg leads Front sensor Electrical sulation layer Constantan Figure 1. Schematic diagram rmocouple. Figure 1. Schematic diagram rmocouple. measured by rmocouple, thus, a mamatical relation measured by rmocouple, thus, a mamatical required to derive from. Commonly, it assumed that relation required to derive from. Commonly, it assumed that conduction side a rmocouple 1D conduction side a homogeneous semi-fite conduction side a rmocouple 1D conduction side a homogeneous solid; thus, two straightforward solutions obtaed [19]: semi-fite solid; thus, two straightforward solutions obtaed [19]: 1 t t T(t) π ρck q q (τ) (τ) T(t) = dτ dτ π ρck t t τ τ (1) (1) q (t) ρck t π dt 1. ρck t dt 1 q(t) = dτ π dτ t dτ τ dτ t τ (2) (2) where where q q. ; ; ρ, ρ, c, c, k k density, density, specific specific,, rmal rmal conductivity conductivity material, material, respectively; respectively; T T measured measured ; ; t t time, time, τ τ tegral tegral variable. variable. model thickness sensor size need to be considered if semi-fite assumption required model thickness transfer measurement. sensor size need Sce to be considered test time if transient semi-fite assumption measurements required only on order transfer milleconds, measurement. it easier Sce to meet test time semi-fite transient assumption. measurements However, if a only on rmocouple order milleconds, Equation it (2) easier to for meet long-duration semi-fite measurements, assumption. However, assumption if a 1D semi-fite rmocouple conduction Equation will (2) be more challengg. for long-duration measurements, assumption 1D semi-fite conduction will be more challengg Effects Limited Thickness For an fite flat plate with limited thickness l, can be modeled as 1D unsteady-state transfer. flat plate can be determed accurately usg 1D unsteady-state differential equation [18]:.

4 Sensors 22, 2, Effects Limited Thickness For an fite flat plate with limited thickness l, can be modeled as 1D unsteady-state transfer. flat plate can be determed accurately usg 1D unsteady-state differential equation [18]: T(x, t) = T + q l k αt l x2 2l 2 x l 2 π 2 n=1 ( ) 1 nπx n 2 cos l e α( nπ l ) 2 t where T(x, t) ; x depth plate, x = defed as ; T itial ; q applied uniform constant at plate; l thickness plate; α rmal diffusivity material defed as: (3) α = k ρc (4) penetration time t p provided by Hightower [2] : t p = l2 ln(2) (5) απ2 rmal penetration time t p can be calculated from thickness plate l rmal diffusivity α. Once penetration time t p exceeds a specific value, semi-fite assumption not applicable anymore. Equation (5) can be to obta mimum model thickness required under assumption semi-fite conduction for a given test time t: l > π αt ln (2) = 3.77 αt 4 αt (6) expression l = 4 αt describes charactertic length under semi-fite conditions. However, charactertic lengths vary for different materials due to differences rmal diffusivity. In transient transfer measurements, material test models commonly staless steel, which has an effective rmal effusivity ρck close to that sensor material. Th material mimizes fluence transverse transfer between sensor model. rmophysical parameters constantan, chromel, staless steel at 3 K lted Table 1. Table 1. rmophysical parameters materials at 3 K [21]. Materials Constantan Chromel Staless Steel ρ, kg/m c, J/(kg K) k, W/(m K) α, m 2 /s (ρck).5, W s.5 /(m 2 K) nondimensional Fourier number F to obta universal results for different materials th study: F = αt/l 2 (7) F < 1/16 obtaed by combg Equations (6) (7), i.e., 1D semi-fite conduction satfied if Fourier number less than 1/16 for different plate materials thicknesses.

5 Thickness (mm) Sensors 22, 2, plate with thickness l obtaed by settg x = Equation (3): T(t) = T + q l k αt l π 2 n=1 e α( nπ l ) 2 t Sensors where 22, T(t) 2, x FOR PEER REVIEW plate. can be derived from th 5 18 usg 1D semi-fite calculation method. Equation (2) can be expressed dcretely as follows [17]: ρck n T(t i ) T(t i 1 ) q q = 2 2 ρck n π π T(t i) T(t i 1 ) tn t i + (9) (9) t n t i + t n t n t i 1 t i 1 i=1 i=1 results versus Fourier number for various materials shown Figure calculated dplayed usg nondimensional form form q/qq/q,, where where q q represents loadg loadg at at model model.. Values Values q/qq/q closer closer to to one one dicate a a smaller fluence on on measurement results results vice vice versa. versa. 1D 1D semi-fite conduction satfied when when Fourier number smaller than 1/16, calculated equals loaded value. As As Fourier number creases, deviation between calculated loaded loaded value value gradually gradually creases. creases. deviations deviations 1% 1% 1% when 1% when Fourier Fourier numbers numbers , respectively..52, respectively. refore, refore, long-duration for long-duration measurements, measurements, thickness thickness plate can be creased plate can to be obta creased a lower to obta Fourier a lower number Fourier smaller number measurement smaller deviation. measurement deviation. (8) % 2% F =.948 q/q 1.1 1% F = % F = 1/16 F =.255 F = semi-fite F = t/l 2 Figure2. 2. Calculated versus Fourier number for for 1D 1D conduction. A Atest test duration 1 1s s considered here, thicknesses plate plateneed needto tomeet meet requirements two two different Fourier numbers shown Figure3. 3. At At1 1s, s, charactertic lengths under semi-fite conditions (F (F = 1/16) constantan, chromel, staless steel 31, 31, 28, 28, mm, mm, respectively. However, actual actual experiments, model model thickness thickness usually usually limited limited due due to to requirements model model weight weight strength strength support support system. system. thickness thickness above above three three materials materials can becan reduced be reduced to 15.4, to 14, 15.4, 14, 13 mm, 13 respectively, mm, respectively, when when Fourier Fourier number number equals.255, equals.255, measurement measurement deviation deviation only 1%. only 1% Constantan Chromel Staless steel F = 1/16 l = 4( t) 1/ F =.255 l = 2( t) 1/

6 Thickness (mm) requirements two different Fourier numbers shown Figure 3. At 1 s, charactertic lengths under semi-fite conditions (F = 1/16) constantan, chromel, staless steel 31, 28, 26 mm, respectively. However, actual experiments, model thickness usually limited due to requirements model weight strength support system. thickness Sensors 22, above 2, three 5254 materials can be reduced to 15.4, 14, 13 mm, respectively, when Fourier 6 18 number equals.255, measurement deviation only 1% Constantan Chromel Staless steel F = 1/16 l = 4( t) 1/ F =.255 l = 2( t) 1/ Figure 3. Thickness plate versus time for different Fourier numbers. Figure 3. Thickness plate versus time for different Fourier numbers Effects Transverse Heat Transfer above calculation based on 1D conduction without considerg effects transverse transfer between different materials. Although rmal effusivity constantan, chromel, staless steel similar, effects transverse transfer still ext. Numerical simulations were conducted to underst fluence transverse transfer on accuracy transfer measurements long-duration experiments. governg equation axymmetric unsteady conduction equation: T (r, z, t) t = k ( i 2 T ρ i c i r ) T r r + 2 T z 2 (i = 1, 2, 3) (1) where r z radial axial coordates physical space; or quantities same as those Equations (1) (2); subscripts 1, 2, 3 denote constantan, chromel, staless steel, respectively. rmocouple simplified to chromel constantan, ignorg fluence sulatg layer, which reasonable because error ca by sulatg layer will decrease rapidly with a few milleconds. details were described our previous paper on rmocouples [11]. Inside sensor model materials, satfy contuity condition at terface between two different materials. With followg boundary condition on top ( ) T = q (i = 1, 2); t > (11) z z= k i adiabatic conditions on or s, Equation (1) solved usg fite difference method for spatial dcretization fourth-order Runge Kutta method for time tegration. A code developed C++ was th study; it was verified reference [1]. itial T = 3 K, a constant q = 1. MW/m 2 occurs on. physical materials parameters calculations lted Table 1. computational model considered here assumed to be axymmetric as shown Figure 4. diameter sensor d, with a d/2 diameter constantan center. junction located at half sensor radius. Because ma purpose th calculation to analyze fluence transverse transfer between different materials on measurement, contact rmal restance between different materials not considered.

7 computational model considered here assumed to be axymmetric as shown Figure 4. diameter sensor d, with a d/2 diameter constantan center. junction located at half sensor radius. Because ma purpose th calculation to analyze fluence transverse transfer between different materials on measurement, contact rmal restance between different materials not considered. Sensors 22, 2, d/2 d/4 q Junction l Ax symmetry Constantan (i (i = 1) 1) Chromel (i = 2) Adiabatic boundary Model:Staless steel (i = 3) Figure4. 4. Two-dimensional numerical calculation model (not to scale, units mm). Structured grids applied; zones near sensor/model terface corporated with clustered pots to provide good spatial resolution. A grid convergence study was conducted for three different grid resolutions, thicknessl l = 1 1 mm was as as an example. Sensors re 22, was 2, a negligible x FOR PEER difference REVIEW junction normalized by loadg 7 for all 18 grids, as shown Figure 5. Sce junction rmocouple located between chromel constantan, average value chromel constantan, i.e., effusivity calculation average value chromel constantan, ρck i.e., = 8644 ρck (W= s )/(m(w 2 K). s.5 )/(m Fally, 2 K). Fally, grid with grid 4 with 4 4 grid pots 4 grid was pots was present study. present study q/q Figure 5. Junction for three grid resolutions. First, model thicknesses l l = = 55mm mm 1 1 mm mm considered considered here, here, where where diameter diameter rmocouple rmocouple d = d 2 = mm 2 mm (regular (regular homemade homemade sensors). sensors). calculation calculation time time 1 s. 1 s. s s atsensor sensor junction junction derived derived from from se se s s usg usg 1D semi-fite 1D semi-fite calculation calculation method method (Equation (Equation (9)) (9)) shown shown Figure oretical obtaedfrom Equation (1) (1) plotted plottedas aswell, ρck ρck average values chromel constantan, i.e., 8644 (W s (W s.5.5 )/(m )/(m 2 K). 2 K). crease crease for for different model thicknesses constent with with that that oretical at at itial itialtime; time; subsequently, sensors deviates from oretical value, differences crease over time. error error between between calculated calculated loaded value creases over time. At t = 1 1s, s, calculated values q/q q/q for for two two model thicknesses 1.71, 1.11, respectively. correspondg Fourier number also shown Figure 6, where rmal diffusivity α average rmal diffusivity chromel constantan. If Fourier number F =.255 considered, as dcussed Section 2.2, calculated q/q for model thicknesses 5 1 mm, i.e., deviation 3% 4%, respectively, correspondg time 1.16 s 4.65 s. After considerg effects transverse transfer, deviation exceeds calculation result 1% Figure 2 under one-dimensional conduction.

8 Temperature (K) Temperatue (K) Temperature (K) Temperatue (K) Sensors 22, 2, Sensors 22, 2, x FOR PEER REVIEW 8 18 q/q F mperature (l = 5mm) mperature (l = 1 mm) oretical 1.15 oretical 9 Heat (l = 5 mm) Heat (l = 1 mm) 8 8 Sensors , 2, x FOR PEER REVIEW q/q F mperature (l = 5mm) oretical 4.8 Heat (l = 5 mm) (a) q/q F F mperature (l = 1 mm) oretical Heat (l = 1 mm) Figure : (a) (a) l l = 5 mm; (b) l l = 1 mm. Different correspondg model thicknesses Fourier number diameters 3also shown.9 considered Figure 6, to where obta universal rmal diffusivity results 3 α provide average guidance rmal for diffusivity model design chromel long-duration constantan. tests. If results Fourier number F = versus.255 considered, Fourier number as dcussed shown Section Figure 2.2, 7; y calculated cover a wide range q/q 1.3 l/d from 1.4 for to 1. model In (a) (b) thicknesses calculations, 5 sensor 1 mm, diameters i.e., deviation range from 3% 1 to 2 mm 4%, respectively, (typical sensor correspondg sizes), time model 1.16 sthickness 4.65Figure s. ranges After 6. considerg from 1 to 2 mm. effects Compd transverse : to (a) l sgle-material = 5 mm; transfer, (b) l = 1 mm. deviation conduction exceeds with limited calculation thickness, result transverse 1% Figure 2 under transfer one-dimensional between sensor conduction. model material has an fluence Different on model value thicknesses q/q. diameters diameters considered considered to obta to obta universal universal results results provide provide guidance guidance for model for design model design long-duration long-duration tests. tests. results results versus versus Fourier Fourier number number shown shown Figure 1.4 7; Figure y cover 7; y a wide cover range a wide l/drange from 1.l/d to 1. from In 1. to calculations, 1. In calculations, sensor diameters sensor range diameters from 1 range to 2 mm l/d from = (typical 1.1 to 2 mm (typical sensor sizes), sensor model sizes), thickness model l/d = 2.5 rangesthickness from 1 toranges 2 mm. from Compd 1 to to mm. Compd l/d = sgle-material to 5. sgle-material conduction with limited conduction thickness, with limited transverse thickness, transfer transverse between transfer sensor l/d = 1between model sensor material has anmodel fluence material on has value an fluence q/q. on value q/q. q/q q/q l/d = 1 Sgle material % % l/d = 1. l/d = l/d = F =.52 l/d = 1 l/d = F1 =.255 F =1/16 Sgle material % 1.1 F = t/l 2 5.5% Figure 7. Effects transverse transfer F on calculated. = F =.255 When l/d = 1., q/q very F =1/16 close to 1. at itial moment F <.255. However, when l/d.9 = 2, thickness model. far exceeds.2.4 diameter.6.8 sensor, 1. q/q close to 1.5, even at itial moment F < 1/16. reason for th F = t/l result 2 that when thickness far exceeds diameter, even a smaller Fourier number means a long physical test time, Figure sensor Effects approaches transverse transfer on staless calculated steel. However,. effusivity calculation average value chromel constantan, i.e., 8644 (W s.5 )/(m 2 K), which When 5% l/d l/d higher = = 1., 1., q/q q/q than very very effusivity close close to staless 1. toat 1. at steel itial itial 821 moment moment (W s.5 F )/ (m 2 < K) F < Under However,.255. However, or calculation when l/d = when conditions, 2, l/d = thickness 2, i.e., when thickness l/d model between far model exceeds far 1. exceeds 1, diameter curves diameter sensor, q/q sensor, q/q gray close q/q shaded to 1.5, close part even to at 1.5, Figure even itial at 7. moment itial moment F value < 1/16. q/q creases F reason < 1/16. with for an th reason crease result for th l/d that result for when same that thickness when Fourier far thickness number. exceeds As far diameter, exceeds Fourier number even diameter, a creases, smaller even a Fourier smaller value number Fourier number q/q gradually means means a creases, long a long physical physical test test trend time, time, similar to result sgle material. sensor approaches staless staless steel. steel. However, However, effusivity effusivity calculation effects calculation average transverse average value transfer value chromel have chromel constantan, to be considered constantan, i.e., 8644 (W s long-duration i.e., )/(m 2 K), (W swhich aerodynamic.5 )/(m 2 K), 5% which g 5% measurements higher than if high-accuracy effusivity staless measurement steel 821 results (W s.5 )/ desired. (m 2 K). However, Under or calculation maximum conditions, deviation i.e., less when than l/d 5.5% between when 1. F <.255 1, 1.8% curves when q/q F <.52. refore, gray shaded an acceptable part Figure 7. value q/q creases with an crease l/d for same Fourier number. As Fourier number creases, value q/q gradually creases, trend similar to result sgle material. q/q (b) 6 5 4

9 Sensors 22, 2, higher than effusivity staless steel 821 (W s.5 )/ (m 2 K). Under or calculation conditions, i.e., when l/d between 1. 1, curves q/q gray shaded part Figure 7. value q/q creases with an crease l/d for same Fourier number. As Fourier number creases, value q/q gradually creases, trend similar to result sgle material. Sensors 22, 2, x FOR PEER REVIEW 9 18 effects transverse transfer have to be considered long-duration aerodynamic g measurements if high-accuracy measurement results desired. However, maximum deviation measurement deviation can be obtaed with proper consideration l/d Fourier number, less than 5.5% when F < % when F <.52. refore, an acceptable measurement even if transverse transfer exts. deviation can be obtaed with proper consideration l/d Fourier number, even if transverse 2.4. Effects transfer exts. Sensor Length 2.4. Effects length Sensor Length sensor above calculation same as thickness model. Actually, length sensor generally longer than model thickness for convenient length sensor above calculation same as thickness model. Actually, stallation. effects sensor length on measurement a long-duration test length sensor generally longer than model thickness for convenient stallation. determed. calculation model similar to that Figure 4, except that length sensor effects sensor length on measurement a long-duration test determed. considered. length 2 mm. Similarly, we use model thickness l = 5 mm 1 mm as calculation model similar to that Figure 4, except that length sensor considered. an example; calculated q/q for a constant sensor length 2 mm shown Figure 8. length 2 mm. Similarly, we use model thickness l = 5 mm 1 mm as an example; For comparon, results for same length sensor thicknesses model also calculated q/q for a constant sensor length 2 mm shown Figure 8. For comparon, shown Figure 8. results for same length sensor thicknesses model also shown Figure l = 5 mm, sensor length 5 mm l = 5 mm, sensor length 2 mm l = 1 mm, sensor length 1 mm l = 1 mm, sensor length 2 mm 1.4 q/q Figure 8. Effects sensor length on. Figure 8. Effects sensor length on. When model thickness l = 5 mm, q/q decreases from 1.71 to 1.68 as length sensor When model thickness l = 5 mm, q/q creases from 5 to 2 mm at t = 1 s; th represents a decreases reduction from only %. to However, 1.68 as when length model sensor thickness creases l = 1 mm, from re 5 to 2 no mm reduction at t = 1 s; th represents value q/q a reduction only 3%. However, when as sensor length creases. refore, model thickness l = 1 mm, re no reduction value q/q an crease sensor length has little fluence on calculated as sensor q/q length creases.. refore, an crease sensor length has little fluence on calculated q/q Effects Physical Parameters 2.5. Effects Physical Parameters In numerical calculations, fluence crease on rmophysical parameters In numerical material calculations, has not beenfluence considered. In transient crease measurements, on rmophysical effect parameters material creasehas on not effective been considered. rmal effusivity In transient generally not measurements, considered. However, effect long-duration crease transfer on measurements, effective rmal effusivity generally sensor not considered. model However, can reach long-duration a few hundred degrees transfer ifmeasurements, high. In th case, it necessary sensor to evaluate model effect can reach a few hundred crease degrees on if rmophysical high. parameters In th case, it measurement necessary to evaluate accuracy. effect fluencecrease on rmophysical creaseparameters on rmophysical measurement parameters accuracy. type-e rmocouples fluence has been extensively vestigated crease on by several rmophysical researchers [12,22,23]. parameters We type-e rmocouples equation developed has been by Mohammed extensively [12] vestigated to determe by several specific researchers [12,22,23]. rmal conductivity We equation chromel developed constantan by Mohammed with creasg [12], to determe as well specific as rmophysical rmal parameter conductivity fittg chromel equation for staless constantan steel with creasg by Mills [24]., changes as well as effective rmophysical rmal effusivity parameter versus fittg equation for staless steel by Mills [24]. changes effective rmal effusivity versus chromel, constantan, staless steel shown Figure 9. results normalized by effective rmal effusivity at 3 K, as shown Table 1. rmal effusivity three materials creases with. changes rmal effusivity staless steel chromel with creasg relatively small;

10 Surface Surface (K) (K) Changes Changes rmal rmal effusivity effusivity Sensors 22, 2, chromel, constantan, staless steel shown Figure 9. results normalized by effective rmal effusivity at 3 K, as shown Table 1. rmal effusivity three materials creases with. changes rmal effusivity Sensors staless 22, steel 2, x FOR chromel PEER REVIEW with creasg relatively small; however, effusivity 1 18 constantan Sensors 22, 2, changes x FOR PEER significantly REVIEW with. At a material 6 K, effective 1 18 steel rmal effusivity 19%, 5%, values 23% chromel, higher than constantan, that at 3 K. staless Th result steel shows 19%, 5%, effect 23% higher than crease that steel at 3 on 19%, K. Th 5%, effective result 23% shows rmal higher effusivity effect than that at 3 materials. K. Th crease result shows on effective effect rmal effusivity crease materials. on effective rmal effusivity materials Staless steel Constantan Chromel Staless steel Constantan Chromel Temperature 6 7 (K) Temperature (K) Figure 9. Changes rmal effusivity versus. Figure 9. Changes rmal effusivity versus. Figure 9. Changes rmal effusivity versus. Numerical simulations change rmal effusivity also conducted to vestigate Numerical simulations change rmal effusivity also conducted to vestigate its its fluence Numerical on simulations. numerical change model rmal effusivity same as that also described conducted Section to vestigate 2.3, fluence on. numerical model same as that described Section 2.3, its fluence model thickness on remas. constant numerical at 1 mm. model same as that described crease Section junction 2.3, model thickness remas constant at 1 mm. crease junction different model from thickness results remas constant Section at (Figure mm. 7) when changes crease rmophysical junction different from results Section 2.3 (Figure 7) when changes rmophysical parameters parameters different from considered, results as shown Section Figure 2.3 (Figure 1. After 7) when changes loaded for 1 rmophysical s, considered, as shown Figure 1. After loaded for 1 s, parameters crease considered, 686 as K when shown Figure physical 1. parameters After chromel, loaded constantan, for 1 s, staless crease 686 K when physical parameters chromel, constantan, staless steel change steel change with crease 686 K when 741 physical K when parameters physical chromel, parameters constantan, three materials staless with 741 K when physical parameters three materials rema constant rema steel change constant with at 3 K. 741 K when physical parameters three materials at 3 K. rema constant at 3 K Constant rmophysical parameters three materials at 3 K Changed rmophysical parameters three materials with Constant rmophysical parameters three materials at 3 K Changed rmophysical parameters three materials with 4 l = 1 mm, q = 1. MW/m 2 4 l = 1 mm, q = 1. MW/m K Figure Effect Effect changes rmophysical parameters on on junction Figure 1. (q (q Effect = 1. 1.MW/m changes 2 2 ). ). rmophysical parameters on junction (q = 1. MW/m 2 ). effective rmal effusivity sensor required to derive from effective rmal effusivity sensor required to derive from crease sensor. Durg unsteady conduction, effective rmal effusivity ρck effective crease rmal sensor effusivity. Durg sensor unsteady required to conduction, derive effective from rmal model changes over time as creases. It unreasonable to use a effusivity ρck crease model sensor. changes Durg over unsteady time as conduction, effective creases. rmal It constant rmal effusivity to calculate from. However, unreasonable effusivity ρck to use a constant model rmal effusivity changes to over calculate time as from creases.. It sensor was measured by rmocouple can be to calculate However, unreasonable to use a constant rmal sensor effusivity was to measured calculate by rmocouple from. can be However, to calculate accurate rmophysical sensor was measured parameters by at different rmocouple pots. can refore, be to Equation calculate (9) can be accurate rewritten rmophysical as follows: parameters at different pots. refore, Equation (9) can be rewritten as follows: q = 2 1 n n π1 (ρck) T(t i ) T(t i 1 ) T(t i ) (12) T(t ) T(t ) 741 K 686 K

11 Sensors 22, 2, accurate rmophysical parameters at different pots. refore, Equation (9) can be rewritten as follows: 1 n T(t i ) T(t i 1 ) q = 2 (ρck) π T(ti ) tn t i + (12) Sensors 22, 2, x FOR PEER REVIEW t n t i 1 i=1 where ti t i time, T(ti) i ) measured at atti, t i, (ρck) (ρck) T(ti ) T(ti ) rmal effusivity at att(ti). i ). primary primarydifference differencebetween betweenequations (12) (12) (9) (9) that that fluence fluence re reon on physical physicalparameters parameterswas wasconsidered. constant constantrmal rmaleffusivity effusivity calculation calculation Section Section average average effusivity effusivity chromel chromel constantan constantan at at 3 3 K because K because ir ir values values similar similar at th at. th. However, However, rmal rmal effusivity effusivity different materials different varies materials significantly varies significantly with. with. Thus, it critical Thus, toit choose critical to appropriate choose rmal appropriate effusivity rmal to calculate effusivity to calculate.. Six Six different different calculation calculation methods methods were were to derive to derive from from crease: crease: effusivity effusivity sgle materials sgle materials chromel, constantan, chromel, constantan, staless steel; staless steel; average effusivity average effusivity value chromel value chromel constantan; constantan; average effusivity average value effusivity value three materials; three materials; constant effusivity constant value effusivity value results shown results Figure shown 11. Figure Sgle staless steel Sgle chromel Sgle constantan Average chromel constantan Average three materials Constant value 8644 q/q l = 1 mm, q = 1. MW/m 2 Figure 11. Effect usg different values rmal effusivity materials on calculated Figure 11. (q Effect usg different values rmal effusivity materials on calculated = 1. MW/m 2 ). (q = 1. MW/m 2 ). calculated has a large deviation from loaded value when rmal effusivity constantan calculated changed with has a large deviation because from loaded change value rmal when effusivity rmal effusivity constantan varies constantan greatly changed with with. As a result, regardless because change wher rmal average effusivity value chromel constantan constantan varies or greatly average with value. three As materials a result, regardless, calculated wher average values value chromel significantly different. constantan When or average constant value value 8644 three materials, calculated, calculated decreases over values time. Th significantly method different. not suitable When for constant present analys, value where 8644, rmal calculated physical parameters decreases changg over with time. Th. method not Insuitable contrast, for if -dependent present analys, where rmal rmal effusivity physical chromel parameters or staless steel changg, with value q/q. changes from In 1. contrast, to 1.9 or if from -dependent rmal effusivity chromel or staless steel, value q/q.95 to 1.5 with 1 s, which means errors with 1%. When parameters staless changes steel from, 1. to calculated 1.9 or from.95 value to 1.5 with about 5% 1 lower s, which than means when errors parameters with chromel 1%. When because parameters rmal staless effusivity steel, staless calculated steel about 5% lower value than about that 5% lower chromel. than when Although parameters model chromel sensor because fields have rmal some spatial effusivity nonuniformity staless steel durg about unsteady 5% lower conduction, than that chromel. calculatedalthough value model q/q sensor fields have some spatial has mimum deviation when rmal nonuniformity durg unsteady conduction, calculated value q/q effusivity chromel after considerg effects physical parameter changes has with mimum. deviation when rmal effusivity chromel after considerg effects physical parameter re changes model with. sensor under different loadg conditions different, changes re rmal effusivity model related sensor to under. different loadg To verify conditions se results, different, changes rmal effusivity related to. To verify se results, three or loadg values selected, i.e., 2.,.5,.1 MW/m 2. calculated values for different loadg conditions shown Figure 12.

12 Temperature (K) Sensors 22, 2, Sensors three22, or 2, x FOR PEER loadg REVIEW values selected, i.e., 2.,.5,.1 MW/m 2. calculated12 18 values for different loadg conditions shown Figure 12. F q =.1 MW/m 2 11K q =.5 MW/m 2 9 q = 1. MW/m 2 q = 2. MW/m 2 8 F Constant rmophysical parameters three materials at 3 K Changed rmophysical parameters three materials, q =.1 MW/m % Changed rmophysical parameters three materials, q =.5 MW/m 2 Changed rmophysical parameters three materials, q = 1. MW/m 2 Changed rmophysical parameters three materials, q = 2. MW/m K q/q 1.5 4% 5 54K 4 343K (a) F =.52 F = (b) Figure 12. calculated results for for different different loaded loaded values: values: (a) Temperature; (a) Temperature; (b) Calculated (b) Calculated usg rmal usg effusivity rmal chromel effusivity that changes chromel with that changes. with. When load.1 MW/m 2, maximum junction 343 K, representg When anload crease only.1 43 MW/m K. Due 2, to maximum small crease, junction rmophysical 343 K, representg parameters an crease material change only 43 only K. Due slightly; to hence, small calculated crease, curve rmophysical similar to that parameters when physical material parameters change only calculation slightly; hence, do not depend calculated on curve ( Section similar 2.3). to that When when loaded physical parameters 2. MW/m calculation 2, maximum do not depend on 11 K, ( Section rmal 2.3). effusivity When chromel loaded 42.6% higher 2. MW/m than 2, parameter maximum at 3 K, as shown 11 K, Figure 9. However, rmal effusivity calculated chromel 42.6% q/q similar higher to than or parameter calculation at results 3 K, under as shown different Figure loadg 9. However, conditions when calculated rmal effusivity q/q chromel similar that to changes or with calculation results under different to derive loadg conditions (Equation when (12)). rmal effusivity chromel that changes with to derive refore, after considerg (Equation (12)). changes rmophysical parameters with, if refore, -dependent after considerg rmal effusivity changes chromel rmophysical, maximum parameters deviation with less, than 4% when if F < -dependent.255 1% when F < rmal.52 (Figure effusivity 12). se chromel results, constent maximum with those deviation Section 2.3. less than measurement 4% when F deviation <.255 can be 1% mimized when F if < l/d.52 reduced. (Figure 12). se results constent with those Section 2.3. measurement deviation can be mimized if l/d reduced. 3. Long-Duration Heat Transfer Measurement Experiments 3. Long-Duration Heat Transfer Measurement Experiments 3.1. Laser Radiation Heatg Experiment 3.1. Laser We use Radiation a laserheatg radiation Experiment g method to validate numerical calculation results conduct long-duration transfer measurements usg rmocouples. composition laser We use a laser radiation g method to validate numerical calculation results g system shown Figure 13. A high-power laser as energy source. After conduct long-duration transfer measurements usg rmocouples. composition laser spot foc on tegrator through multiple reflections homogenization, a uniform laser g system shown Figure 13. A high-power laser as energy source. spot formed at exit tegrator as loaded. A trigger to control After laser spot foc on tegrator through multiple reflections homogenization, a laser output time. A power meter to determe output power laser. quality uniform spot formed at exit tegrator as loaded. A trigger to laser beam analyzed with a laser beam measurg strument to ensure uniformity control laser output time. A power meter to determe output power laser. loadg. An electronic shutter stalled between test model tegrator outlet. quality laser beam analyzed with a laser beam measurg strument to ensure shutter opened after a stable laser output obtaed, stard applied to uniformity loadg. An electronic shutter stalled between test model model. tegrator outlet. shutter opened after a stable laser output obtaed, stard applied to model.

13 Sensors 22, 2, x FOR PEER REVIEW Sensors 22, 2, 5254 Sensors 22, 2, x FOR PEER REVIEW Trigger: DG535 Trigger: DG535 QBH Laser:IPG QBH Laser:IPG Beam Sampler Beam Sampler Beam Integration Beam Integration Laser head Laser head rmocouples rmocouples Staless steel plate Staless steel plate Energy Digital detector oscilloscope Energy Digital detector oscilloscope Figure 13. Laser radiation g system. Figure Laser Laserradiation radiationg gsystem. system. Figure test model a 5 5 mm staless steel flat plate. thickness 1 mm. Three test test model model aa 5 5at tervals 5 mm mm staless staless steel flat plate. thickness 1 1 mm. mm. Three Three rmocouples stalled 5 mm.steel flat diameter rmocouple 2 mm, 5 plate. thickness rmocouples stalled at tervals 5 mm. diameter rmocouple mm, length 2 mm, which commonly dimensions laboratory products. sensors rmocouples stalled at tervals 5 mm. diameter rmocouple 22mm, length 2 mm, which commonly dimensions laboratory products. sensors labeled as No. 1 to 3. After sensor, model was pated black a length 2 mm, whichstallg commonly dimensions laboratory products. usg sensors labeled labeled as as No. No. tobody 3. After After stallg sensor, sensor, model model was pated pated black usg aa high- black coatg (Pyromark 25, Tempil Co., New York, NY, USA) to reduce 11 to 3. stallg was black usg high- black body (Pyromark Tempil Co., York, NY, USA) reduce reflectivity black coatg model material.25, Thus, model regarded astormally high- body coatg (Pyromark 25, Tempil Co.,New New York, NY, USA) to reduce reflectivity model material. Thus, model regarded as rmally black, black, absorption coefficient.95.material. AlthoughThus,thickness pat affects reflectivity model model regarded asresponse rmally absorption coefficient.95. thickness enough pat response time time rmocouples, test time ouralthough experiments long to ignore th fluence. black, absorption coefficient Although.95. thickness affects pat affects response rmocouples, test time our experiments long enough to ignore th fluence. conduction pat was not considered th study. time rmocouples, test time our experiments long enough to ignore th fluence. conduction pat was not considered th study. was sensor 32 time for loadg 6 s. itial conduction pat not considered K, th study. itial itial three sensor sensor 32K, K, shown time time for loadg s rmocouples for Figure 14a. curves 32 loadg 66s.s. s three rmocouples shown Figure 14a. curves three sensors very similar, maximum about 47 K after 6 s s three rmocouples shown Figure 14a. curves three three sensors very very similar, maximum about about 47 K K after after loadg. calculated curves maximum presented Figure 14b. rmal effusivity sensors similar, ss loadg. calculated curves presented Figure 14b. rmal effusivity chromel that changes with to derive from loadg. calculated curves presented Figure 14b. rmal effusivity 2 chromel that changes with to derive from,, with loaded by laser.55 MW/m In derive first 3 s, error chromel that changes.to between from 2. In first 3 2s, error between loaded loaded by laser by.55 MW/m loaded measured values with MW/m gradually over time., loaded laser3%..55. In first 3decreases s, error between measured values with 3%. gradually decreases over time. reason that reason that emsivity black body coatg material creases with. loaded measured values with 3%. gradually decreases over time. emsivity black body coatg material creases with. laser radiation radiation g experiments show thatcoatg calculation usg physical laser reason that emsivity black body material creases with. g show that calculation physical parameters chromel parameters chromelg accurate reliable. laserexperiments radiation experiments show that usg calculation usg physical accurate reliable. parameters chromel accurate reliable. 5 NO.1 NO.2 NO.1 NO.3 NO.2 NO Heat (MW/m2) Heat (MW/m2) 45 Temperature (K) Temperature (K).8 NO.1 NO.2 NO.1 NO.3 NO.2 NO Time (s) (b) (a) (b) (a) Figure 14. Results rmocouple laser radiation g experiment. (a) Surface Figure 14. Results rmocouple laser radiation g experiment. (a) Surface ; (b)(b) Heat Figure 14. Results. rmocouple laser radiation g experiment. (a) Surface ; Heat. ; (b) Heat Heat Transfer Measurement ArcTunnel Tunnel 3.2. Heat Transfer Measurement anan Arc 3.2.As Heat Transfer Measurement an Arc Tunnel Asdcussed dcussedabove, above, rmocouples rmocouplescan canbebe long-duration long-duration transfer transfer measurements appropriate Fourier number. small size rmocouples measurements if if anan appropriate Fourier number. size rmocouples As dcussed above, rmocouples can besmall long-duration transfer facilitates stallation. Hence, sensor can be flexibly various transfer measurement measurements if an appropriate Fourier number. small size rmocouples facilitates stallation. Hence, sensor can be flexibly various transfer measurement

14 Sensors 22, 2, Sensors 22, 2, x FOR PEER REVIEW facilitates conditions. stallation. In th study, Hence, transfer sensor measurements can be flexibly conducted variousdurg transfer calibration measurement conditions. parameters In th an arc study, tunnel flow transfer field. measurements conducted durg calibration parameters Currently, an arc tunnel most common flow field. device for cold wall transfer measurements arc tunnels Currently, copper calorimeter. most common An air device gap or for sulatg cold wall material transfer generally measurements added between arc tunnels copper copper block calorimeter. model An air for gap sulation. or sulatg However, material local generally ablation added between sensor copper occurs block experiments, modelreby for sulation. affectg However, life local ablation sensor. refore, sensor rmocouples occurs experiments, to reby obta affectg wall transfer life measurement sensor. refore, arc tunnel, rmocouples results to obta compd wall with transfer calorimeter measurement measurements. arc tunnel, results compd with calorimeter measurements. test test conducted usg usg arc arc tunnel tunnel equipment equipment with with a tubular a tubular arc er, arc er, as shown as shown Figure Figure 15a. 15a. equipment equipment consts consts an arc er, an arc aer, high-speed a high-speed nozzle, anozzle, test section, a test section, a vacuum a system. vacuum Asystem. two-dimensional A two-dimensional rectangular rectangular nozzle (12 nozzle 6 mm) (12 6 selected mm) toselected generate to high-speed generate high-speed flow (around flow 2 (around m/s). 2 m/s). model stalled model close stalled to close nozzle to exit. nozzle Cleanexit. Clean dry high-pressure dry high-pressure air jected air to jected arc to er arc forer g. for After g. After acceleration acceleration expansion expansion nozzle, nozzle, test flow test fieldflow formed field at formed outlet. at outlet. model model at a negative a angle negative attack angle with attack nozzle with outlet nozzle when outlet flow when field flow establhed field establhed so that so model that model does not does crease. not crease. When When flow fieldflow stable, field stable, model model quickly adjusted quickly adjusted to an angle to an angle attack attack 6, aerodynamic 6, aerodynamic g g applied applied to to model. model. A stable A flow stable field flow field loaded loaded on on model model for about for about 5 s, 5 s, model model adjusted adjusted to a to negative a negative angle angle attack attack aga aga to fh to fh calibration test. test. test test model aa squ staless steel steel plate with with aa size size mm, aa thickness 1 1 mm, 99 sensors. Sensors copper calorimeters, sulation material between copper block staless steel steel glass-fiber-reforced plastic plastic (FRP). (FRP). C1 C3 C1 C3 rmocouples. rmocouples. location location measurement measurement pots presented pots presented Figure 15b, where Figure 15b, airflow where from airflow right trom left. right signals to left. from signals sensors from were acquired sensors were by a signal acquired conditioner by a signal conditioner were processed were on a PC-based processed data on a acquition PC-based data system acquition at a samplg system rate at a samplg 1 Hz. rate 1 Hz. High-pressure coolg water Test cab Arc chamber Nozzle Model Vacuum Argon & Air Cathode Air jection Argon & Air Anode (a) 4 5 C1 1 6 C2 1 C3 2 3 (b) 1 Figure Schematic arc tunnel arc tunnel test model test with model stalled with sensors. stalled (a) sensors. Arc tunnel (a) equipment Arc tunnel diagram; equipment (b) diagram; Mounted(b) position Mounted position sensors on sensors plate model. on plate model. re re values values obtaed from from rmocouples shown shown Figure Figure values were values calculated were calculated from from by usg by rmal usg effusivity rmal effusivity chromel. It observed that decreases from C1 to C3, sce y arranged from front to back sequence on plate. curves relatively stable.

15 Heat Heat (MW/m 2 ) 2 ) Heat Heat (MW/m 2 ) 2 ) Sensors 22, 2, chromel. It observed that decreases from C1 to C3, sce y arranged from Sensors front to 22, back 2, x FOR sequence PEER REVIEW Sensors 22, 2, FOR PEER REVIEW on plate. curves relatively stable Temperature (K) (K) 6 6 rmocouple C1 rmocouple C1 55 rmocouple C2 55 rmocouple rmocouple C2 C3 rmocouple C (a) (a) 1.4 rmocouple C1 1.4 rmocouple rmocouple C1 C2 rmocouple rmocouple C2 C3 rmocouple C Figure 16. Results arc tunnel flow field calibration tests. (a) Temperatures Figure 16. Results arc tunnel flow field calibration tests. (a) Temperatures rmocouple; (b) Heat obtaed from rmocouples. rmocouple; (b) Heat obtaed from rmocouples. On model, rmocouple C2 copper calorimeter 3 same dtance from front edge edge plate. plate. Thus, a comparon measurements obtaed from se two sensors shown shown Figure Figure response response time time time rmocouple rmocouple much much much faster faster faster than than than that that that copper copper copper calorimeter; calorimeter; calorimeter; however, however, however, measured measured measured by by copper copper copper calorimeter calorimeter calorimeter slightly slightly slightly higher higher higher than that than than bythat by by rmocouple. rmocouple. rmocouple. (b) (b) rmocouple C2 rmocouple C2 Calorimeter 3 Calorimeter Figure 17. Heat obtaed from rmocouple (C2) copper calorimeter (3). Figure 17. Heat obtaed from rmocouple (C2) copper calorimeter (3). Figure 17. Heat obtaed from rmocouple (C2) copper calorimeter (3). average value values 2 5 s as measurements. measurement results average average lted value value Table 2. Sixteen-bit AD converters values values were s acquition as measurements. as measurements. board. overall measurement measurement error results results th lted lted measurement Table Table system 2. Sixteen-bit 2. Sixteen-bit was calibrated AD converters AD converters was were were found to be.15%. acquition acquition board. overall measurement error th measurement system was calibrated was found to board. overall measurement error th measurement system was calibrated was found to be.15%. be.15%. Table 2. Comparon obtaed from copper calorimeters rmocouples at same location arc tunnel. Table 2. Comparon obtaed from copper calorimeters Table 2. Comparon obtaed from copper calorimeters rmocouples Sensor at Type same location arc tunnel. Calorimeter rmocouple rmocouples at same location arc tunnel. Sensor No C1 C2 C3 Sensor Type Calorimeter rmocouple MeasuredSensor Type (MW/m 2 ) Calorimeter rmocouple Sensor No C1 C2 C3 Sensor No. C1 C2 C3 Measured (MW/m Measured (MW/m 2 2 ) Table 2 dicates that measured by copper calorimeter about 1% higher Table dicates that measured by copper calorimeter about 1% higher than that measured by rmocouple at same location. reason that FRP than that measured by rmocouple at same location. reason that FRP rmal sulation material between copper block model that has low rmal rmal sulation material between copper block model that has low rmal

16 Surface (K) Sensors 22, 2, Table 2 dicates that measured by copper calorimeter about 1% higher Sensors than that 22, measured 2, x FOR PEER by REVIEW rmocouple at same location. reason that 16 FRP 18 rmal sulation material between copper block model that has low rmal conductivity. conductivity. crease FRP much higher than that sensor crease FRP much higher than that sensor. refore,. refore, transverse transfer occurs on model. energy transferred transverse transfer occurs on model. energy transferred from FRP to from FRP to copper block. Figure 18 shows s copper copper block. Figure 18 shows s copper calorimeter. calorimeter. highest at FRP position. energy transferred from highest at FRP position. energy transferred from model to copper model to copper block, resultg high copper calorimeter. Ablation block, resultg high copper calorimeter. Ablation commonly occurs due to high commonly occurs due to high FRP, small particles accumulate FRP, small particles accumulate appear flow, which results appear flow, which results measurement errors over time. rmocouple measurement errors over time. rmocouple rmally matched with staless rmally matched with staless steel material, re no significant crease steel material, re no significant crease on ; thus, re no rk on ; thus, re no rk local ablation. results dicate that local ablation. results dicate that rmocouple provides more accurate reliable rmocouple provides more accurate reliable results than copper calorimeters for results than copper calorimeters for transfer measurements order several seconds transfer measurements order several seconds an arc tunnel. an arc tunnel t =.1 s t = 1. s t = 2. s t = 3. s Insulation sleeve Test model Oxygen free copper rmocouple x (mm) Figure 18. Surface dtributions copper calorimeter at different test times. Figure 18. Surface dtributions copper calorimeter at different test times. 4. Conclusions 4. Conclusions A rmocouple measures based on crease under assumption A 1D rmocouple semi-fitemeasures conduction. For long-duration based transfer measurements, crease under it assumption necessary to consider 1D semi-fite several fluencg conduction. factors. For Inlong-duration th study, effects transfer measurements, fite thickness, it necessary transverse to consider transfer, several fluencg physical factors. parameters In th study, on effects transfer fite measurements thickness, transverse analyzed usg atransfer, two-dimensional numerical physical simulation parameters on unsteady transfer conduction. measurements analyzed calculation usg a two-dimensional results dicate numerical that simulation effects unsteady changes conduction. transverse transfer physical calculation parameters results dicate due to creasg that effects s changes have to be considered transverse long-duration transfer aerodynamic physical parameters g measurements. due to creasg deviation s calculated have to be considered q/q long-duration cannot be reduced aerodynamic g measurements. deviation calculated q/q only by creasg length sensor. mimum deviation obtaed if rmal cannot effusivity be reduced chromel only by creasg to derive length fromsensor. mimum. deviation deviation obtaed if rmal less effusivity than 5.5% when chromel F to derive from. <.255 1% when F <.52. Th formation can be for deviation less than 5.5% when F <.255 1% when F design test models rmocouples long-duration transfer measurement. <.52. Th formation measurement can be error for design three sensors test models laser radiation rmocouples g test long-duration less than 3% 3 s, transfer which measurement. verifies numerical calculation results demonstrates accuracy rmocouples measurement long-duration error three transfer sensors measurements. laser radiation For g calibration test less than 3% field 3 parameters s, which verifies arc numerical tunnel, calculation obtaed results fromdemonstrates rmocouples accuracy more stable rmocouples than that obtaed long-duration from copper calorimeters. transfer measurements. In addition, For response calibration time field parameters rmocouples also arc tunnel, faster than that obtaed copperfrom calorimeter rmocouples better describes more physical stable process than that aerodynamic obtaed from g. copper calorimeters. In addition, response time rmocouples also faster than that copper calorimeter better describes physical process aerodynamic g. present study provides oretical guidance for design analys long-duration measurements usg rmocouples.

17 Sensors 22, 2, present study provides oretical guidance for design analys long-duration measurements usg rmocouples. Author Contributions: Conceptualization, S.Z.; formal analys, X.Z.; vestigation, S.Z.; methodology, J.L.; supervion, H.C.; writg origal draft preparation, S.Z.; writg review editg, Q.W. All authors have read agreed to publhed version manuscript. Fundg: Th research was funded by Cha Scholarship Council National Natural Science Foundation Cha (Grant Nos ). Conflicts Interest: authors decl no conflicts terest. References 1. Song, K.D.; Choi, S.H.; Scotti, S.J. Transpiration coolg experiment for scramjet enge combustion chamber by high es. J. Propul. Power 26, 22, [CrossRef] 2. Loehle, S.; Nawaz, A.; Herdrich, G.; Fasoulas, S.; Martez, E.; Raiche, G. Comparon Heat Flux Gages for High Enthalpy Flows NASA Ames IRS. In Proceedgs 46th AIAA rmophysics Conference, Washgton, DC, USA, June Childs, P.R.N.; Greenwood, J.R.; Long, C.A. Heat measurement techniques. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 1999, 213, [CrossRef] 4. Flaherty, W.; Aust, J. Comparative transfer measurements hypervelocity flow. J. rmophs. Heat Transfer 211, 25, [CrossRef] 5. Gardon, R. An strument for direct measurement tense rmal radiation. Rev. Sci. Instrum. 1953, 24, 366. [CrossRef] 6. Kidd, C.T.; Adams, J.C. Fast-response - sensor for measurement commonality hypersonic wd tunnels. J. Spacecr. Rockets 215, 38, Terrazas-Salas, I.; Carballo, J.E.; Driver, D.; Balboni, J. Comparon Heat Transfer Measurement Devices Arc Jet Flows with Shear. In Proceedgs AIAA/ASME Jot rmophysics Heat Transfer Conference, Chicago, IL, USA, 28 June 1 July Serson, S.R.; Sturtevant, B. Transient measurement usg a junction rmocouple. Rev. Sci. Instrum. 22, 73, [CrossRef] 9. Mareau, E.; Hornung, H. Modelg Calibration Fast-Response Coaxial Heat Flux Gages. In Proceedgs 47th AIAA Aerospace Sciences Meetg cludg New Horizons Forum Aerospace Exposition, Orlo, FL, USA, 5 8 January 29; p Li, J.; Chen, H.; Zhang, S.; Zhang, X.; Yu, H. On response rmocouples for transient aerodynamic g measurements. Exp. rm. Fluid Sci. 217, 86, [CrossRef] 11. Buttsworth, D.R. Assessment effective rmal product junction rmocouples on millecond microsecond time scales. Exp. rm. Fluid Sci. 21, 25, [CrossRef] 12. Mohammed, H.A.; Salleh, H.; Yusf, M.Z.; Campo, A. rmal product type-e fast response sensors. J. rm. Sci. 21, 19, [CrossRef] 13. Chen, H.; Frankel, J.I. Calibration Co-Axial rmocouple Usg A Quantified High Heat Flux AlN Heater. In Proceedgs AIAA SciTech Forum, California, CA, USA, 7 11 January 219; p Wang, Q.; Olivier, H.; Ehf, J.; Li, J.; Zhao, W. Influence test model material on accuracy transient transfer measurements impulse facilities. Exp. rm. Fluid Sci. 219, 14, [CrossRef] 15. Wang, Q.; Li, J.; Zhao, W.; Jiang, Z. Comparative study on aerodynamic gunder perfect nonequilibrium hypersonic flows. Sci. Ch. Phys. Mech. Astron. 216, 59, [CrossRef] 16. Peng, Z.; Shi, Y.; Gong, H.; Li, Z.; Luo, Y. Hypersonic aerog predictiontechnique its trend development. Acta Aeron. Astronaut. S. 215, 36, Coblh, J.; Smith, M.; H, T.; Cler, G.; Nompel, I. Double-Cone Experiment Numerical Analys at Aedc Hypervelocity Wd Tunnel No. 9. In Proceedgs 43rd AIAA Aerospace Sciences Meetg Exhibit, Reno, NV, USA, 1 13 January 25; p Kirk, B.S. Multidimensional assessment modelg error typical high-speed wd-tunnel -transfer data-reduction schemes. J. rmophs. Heat Transf. 29, 23, [CrossRef]

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