Temperature Sensitive Paint Heat Flux Measurements in Hypersonic Tunnels

Transcription

1 Temerature Senitive Paint Heat Flux Meaurement in Hyeronic Tunnel Tianhu Liu, Z. Cai, B. Wang Wetern Michigan Univerity, Kalamazoo, MI J. Rubal, J. P. Sullivan, S. Schneider Purdue Univerity, Wet Lafayette, IN 47907

2 Objective To develo data-reduction method and algorithm for the determination of heat flux field from tranient temerature enitive aint (TSP) meaurement in hyeronic tunnel articularly in the Purdue Mach-6 Quiet Ludwieg Tube

3 Outline Overview 1D Analytical Invere Method 1D Numerical Invere Method Correction for Lateral Heat Conduction Effect Hitorical Effect of Warming-U Proce of Model Determination of Coating Thickne Concluion & Further Invetigation

4 Overview Aroximate Fourier Law q(t ) ki [T1(t ) T ] / L Aumtion: T i aroximately the initial temerature for a high-conductive bae (e.g. Al) in a hort run time. Liu et al. (1994, 1995), Matumura et al. (003, 005) Hubner et al. (00)

5 Overview Cook-Felderman Method The olution on a emi-infinite bae for TSP in hyeronic tunnel q ( t ) k c n T( ti ) T( ti1 ) t i 1 n ti tn ti1 Cook & Felderman for thin-film enor (1966) Merki et al. for thermograhic hohor (1998, 1999) Main Problem TSP layer affect the time hitory of urface temerature, and direct alication of the C-F method lead to a ytematic error in TSP heat flux meaurement (Nagai et al. 007)

6 1D Analytical Invere Method Invere Solution of 1D Heat Conduction Equation The heat flux at the olymer urface in the Lalace tranform lane: Q ( ) ( k / a ) ( )K( ) where ) (,L ) i the tranformed urface temerature ( K( ) 1 1 ex 1 ex L L / / a a The relevant arameter: ( 1 ) /( 1 ) k c / k b c b b

7 Evaluation of the integral: Invere Lalace Tranform Contour k( t ) 1 i i i ex( t )K( )d 1D Invere Solution: q (t ) k (1 a ) t 0 W ( t, ) t d ( ) d d The effect of the olymer layer i given by W (t, ) ex( ) d 0 1 co( L / a t )

8 The Dicrete Form of the Analytical Invere Solution for a thin olymer layer on a bae of any material n k (1 ) (ti ) ( ti1 ) q( tn ) W ( tn ti ) W ( tn ti1 a t t t t i1 n i n i1 ) where W (t, ) ex( ) d 0 1 co( L / a t ) For a emi-infinite bae 0 W (t,0 ) 1 The Cook-Felderman Method

9 TSP Surface Temerature & TSP-Meaured Temerature TSP-Meaured Temerature T TSP ( t ) L 1 0 L T( t, y ) dy TSP Surface Temerature T (t ) T TSP (t ) 0.5q (t )L / k Iteration i required for temerature correction for high heat flux

10 Simulation: Validation of Analytical Invere Method 0.01 mm Thick PVC Layer on Al Bae Ste Change followed by a Sinuoidal Change in Heat Flux Simulated heat flux in a hyeronic tunnel Temerature obtained by numerically olving the unteady 1D heat conduction equation

11 Recovered Heat Flux uing the Analytical Method for 0.01 mm Thick PVC Layer on Al Bae

12 Simulation: Validation of Analytical Method 0.01 mm Thick PVC Layer on Nylon Bae Ste Change Followed by a Sinuoidal Change in Heat Flux Temerature Recovered heat flux larger time contant

13 Senitivity Analyi for the Analytical Invere Method Total Uncertainty in Heat Flux: Elemental Error: thickne L / L k thermal conductivity q / k / q ratio between thermal roertie / a / a thermal diffuivity thickne Al thermal conductivity Al Nylon Nylon

14 Senitivity Analyi for the Analytical Invere Method Total Uncertainty in Heat Flux: q / q Ratio between the thermal roertie Thermal diffuivity Nylon Al Al Nylon

15 0 (y,t) θ y a t 1D Numerical Invere Heat Tranfer Method Iterative Solution through Otimization Method for Variable Thermal Proertie of Polymer and Bae Polymer temerature: Bae temerature: in T T (y,t) θ 0 (y,t) θ y a t b b Boundary condition at : 0 y / θ k q y L Boundary condition at infinity: in b b T T (y,t) θ 0 t), ( θ b Matching condition at : y / θ k y / θ k b b 0 y b θ θ

16 1D Numerical Invere Heat Tranfer Method Numerical Scheme Algorithm 1. Iterative Algorithm Inut: meaured urface temerature θ (TSP data) Initialization: initialize error tolerance ε and contruct matrix Φ comute coare determination of heat flux q uing 1 k=1 While T err ε, reeat from the direct heat conduction equation, comute calculate the temerature error Ste 1. from the matrix form Ste. q K 1 q K q err err Ste 3. comute urface temerature Ste 4. udate T Ste 5. K K 1 End Outut: heat flux etimate ' err θ θ K 1 K 1 T ' err θ θ 1 Φq T, comute q err θ err ' K 1 θ Φq ' θ 1 uing the direct heat conduction equation Minimize the urface temerature q error to find heat flux

17 Simulation: Validation of Numerical Invere Method 0.01 mm Thick PVC Layer on Al Bae Ste Change Followed by a Sinuoidal Change in Heat Flux Convergence Comarion with the analytical invere method

18 5 o /45 o Indented Cone at Mach 11 in 48-inch Shock Tunnel at Calan-Univerity of Buffalo Reearch Center Hubner, J. P., Carroll, B. F., and Schanze, K. S., Heat-Tranfer Meaurement in Hyeronic Flow Uing Luminecent Coating Technique, Journal of Thermohyic and Heat Tranfer, Vol. 16, No. 4, 00,

19 5 o /45 o Indented Cone at Mach 11 in 48-inch Shock Tunnel at Calan-Univerity of Buffalo Reearch Center t = m t = 6 m

20 5 o /45 o Indented Cone at Mach 11 Iteration for Surface Temerature Correction Surface Heat Flux Ditribution along a Ray at the max heating oint Gauge Data (Hubner et al. 00)

21 5 o /45 o Indented Cone at Mach 11 Time-Averaged Surface Heat Flux Ditribution Cut lot

22 Correction for Lateral Heat Conduction Effect Equivalent to Image Deconvolution Problem Baed on an analogy between 3D and 1D olution, 1D heat flux olution i interreted a a Gauian average of the correonding 3D olution. Convolution-Tye Integral Equation q ( 1D ) (t,x,z ) g ( t ),x x',z z' q t,x',z' r dx' dz' where the Gauian filter i g 1 t,x,z ex r ( t ) r ( t ) x z Unknown to be determined

23 Two-Ste Method Combination of the 1D method and image deconvolution method

24 Simulation: Ste Heating on Square Region Surface Temerature Evolution Surface Heat Flux Calculated by the 1D Invere Method

25 Simulation: Ste Heating on Square Region Surface Heat Flux Calculated by the 1D Invere Method Surface Heat Flux Corrected by the Image Deconvolution Method

26 Simulation: Ste Heating on Square Region

27 The Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue Univerity

28 Exerimental Condition Table 3. Tet Condition for the Aluminum Cone (10/1/009) Run 1 Run Run 3 Run 4 0 (initial) 65 kpa 896 kpa 51 kpa 896 kpa T 0 (initial) 43 K 43 K 435 K 430 K T w (re-run) 98 K 301 K 305 K 307 K Re D Time 1:59 m 1:48 m :30 m 3:10 m

29 Tyical Hitorie of Surface Temerature and Heat Flux Surface Temerature Surface Heat Flux

30 7 o Half-Angle Nylon Circular Cone at Mach 6 in the Mach-6 Quiet Ludwieg Tube at Purdue Heat flux image given by the 1D invere method Heat flux image corrected by the deconvolution method t = 1.5

31 7 o Half-Angle Nylon Circular Cone at Mach 6 in the Mach-6 Quiet Ludwieg Tube at Purdue x = 0.18 m x = 0.6 m t = 3 t = 3

32 Hitorical Effect of Warming-U Proce of Model Problem in the Purdue Mach-6 Quiet Ludwieg Tube Time hitory of urface temerature meaured by a thermocoule in four equential run Tunnel Total Preure 1034 kpa Total Temerature 433 K Re/ft mall 6 Run Time 5 On a 7-deg Shar Cone T on Nylon Cone ~ 10 K T on Aluminum Cone ~ K Heat Flux in Laminar BL ~ 1000 W/m

33 Hitorical Effect of Warming-U Proce of Model Warming-u k q ( t ) (1 a ) trun t W ( t, ) d,run ( ) d t d trun 0 W ( t, ) d t Hitorical effect of warming-u roce Due to the warming-u, a model i not in thermal equilibrium with ambient environment jut before a ecific run a aumed in the olution. Thu, the hitorical effect may be ignificant, and it hould be corrected in TSP meaurement. Integral for a ecific run,rerun d ( ) d

34 Hitorical Effect of Warming-U Proce 7deg-Half-Angle Al Circular Cone at Mach 6 Run 1 where the Al model i in thermal equilibrium with ambient environment before the run Run 4 where the model wa heated u 9 deg above the initial ambient temerature Laminar BL olution Corrected heat flux Shift becaue the hitorical effect i not taken into account

35 Correction for Hitorical Effect of Warming-U Proce 7deg-Half-Angle Al Circular Cone at Mach 6 1D Analytical Method: k q (t ) (1 a ) t trun Heat flux enor & thermocoule on a cone W (t, ) t d,run ( ) d B d 0 ( L / Correction term L )[T (t run ) T The coefficient Bo i determined in itu uing a data given by a heat flux enor, and the time hitory of urface temerature i meaured by a thermocoule. St u e e q ( h aw h w Corrected heat tranfer arameter ) in ]

36 Determination of Coating Thickne by Utilizing Initial Raid Heating in the Ludwieg Tube Heating a hot ga ae through (the eak heating flux at 10 kw/m^) Heat Flux Ditribution in Run 4 Time hitory of heat flux meaured by a heat flux enor Cooling due to ueronic flow exanion in the tart-u Satial variation caued by nonuniform coating thickne

37 Intercetion-baed method: ln[ Determination of Coating Thickne Baed on TSP Meaurement on an Al Cone 0.48 q ( t )] 1.3ln( t ) ln ( 4 a ) Sloe-baed method: L 1.3 k Coating thickne (L) ditribution ln[ ( t )] ( t / ) 11.7 q ln k 0 L where L / 4a Averaged L meaured by a gage: 50 micron

38 Heat Flux Ditribution with Correction of Non-Uniform Coating Thickne Run 3 Run 4

39 Jutification of Simle Dicrete Fourier Law Method Combined with In-Situ Calibration For a thin olymer layer on a highly conductive model: q (t ) k L (t ) Further aroximation: q (t ) ( k / L ) k c (t ) t 1 t 0 ( t ) ( t ) 3 / ( ) d T (t ) T (t ) B ( L / L ) T (t ) T. b run 0 run in

40 Concluion The 1D analytical and numerical method are develoed for determination of heat flux from TSP meaurement Deconvolution method i develoed for correction of lateral heat conduction effect Procedure are develoed for correction of the hitorical effect of warming-u roce in the Ludwieg tube A imle method i develoed to determine coating thickne by utilizing the raid heating in the tart-u of the Ludwieg tube Jutification of the ue of the dicrete Fourier law