Measurement of radiation heat transfer in supercritical carbon dioxide medium

Accepted Manuscript Measurement of radiation heat transfer in supercritical carbon dioxide medium Sagar Khivsara, Matta Uma Maheswara Reddy, K.P.J. Reddy, Pradip Dutta PII: DOI: Reference:

S0263-2241(19)30221-0 https://doi.org/10.1016/j.measurement.2019.03.012 MEASUR 6447

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

24 September 2018 3 March 2019 5 March 2019

Please cite this article as: S. Khivsara, M.U.M. Reddy, K.P.J. Reddy, P. Dutta, Measurement of radiation heat transfer in supercritical carbon dioxide medium, Measurement (2019), doi: https://doi.org/10.1016/j.measurement. 2019.03.012

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MEASUREMENT OF RADIATION HEAT TRANSFER IN SUPERCRITICAL CARBON DIOXIDE MEDIUM Sagar Khivsara1, Matta Uma Maheswara Reddy1, K. P. J. Reddy2, Pradip Dutta1* 1Department 2Department

of Mechanical Engineering, Indian Institute of Science, Bangalore, India of Aerospace Engineering, Indian Institute of Science, Bangalore, India * Corresponding author: Email: [email protected] Tel.: +91-80-22933521

Abstract In this work, a novel experimental method for measurement of radiation emitted by supercritical carbon dioxide (s-CO2) at high pressure and high temperature is presented. Due to high pressure conditions, use of conventional spectroscopic methods to measure radiative properties of s-CO2 is challenging. In the present method, supercritical conditions are created in a shock tube by using carbon dioxide (CO2) as the driven gas. The radiative emission by sCO2 is measured using a platinum based thin film sensor. The total emissivity for s-CO2 is estimated and the value compares favourably with that predicted theoretically using a standard method available in literature. It is estimated that the total emissivity value of supercritical conditions is nearly 0.2 for the conditions studied, implying that s-CO2 acts as a participating medium for radiation heat transfer. The outcome of this study will have significant impact on the design of heat transfer equipment such as solar thermal receivers and heat exchangers typically used in s-CO2 based closed Brayton cycle, for which participating medium radiation heat transfer has been neglected traditionally. Keywords: Radiation, emissivity, supercritical, carbon dioxide, shock tube

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1. Introduction Over the past decade, research on power generation using supercritical carbon dioxide (sCO2) as the working fluid in closed-loop Brayton cycle has gained popularity. This cycle, which has the potential for improved efficiency, is being actively considered for nuclear [1] as well as concentrating solar power (CSP) applications [2]. Compared to the air Brayton cycle which typically requires high temperature operation, the s-CO2 cycle has the potential to realise high efficiencies even at moderate conditions. This is because of the superior thermophysical properties of s-CO2 [3, 4]. An in-depth knowledge of the thermal behaviour of s-CO2 is necessary for optimally designing the system and its components. Niu et al. [5] and Kim et al. [6] undertook experimental studies to evaluate the thermal characteristics for flow of s-CO2 through tubes. In addition to experiments, computational modelling tools have also been used for development of s-CO2 based equipment [7-9]. In none of the above studies, the participating nature of supercritical carbon dioxide has been considered in radiation modelling. While it is well established that CO2 is nearly transparent to the spectrum of direct solar radiation, infrared radiation absorption by CO2 at ambient conditions is well recognized [10]. Radiation heat transfer in such conditions is prevalent in several applications of high temperature heat exchange with s-CO2 flowing in tubes and micro-channels. In the supercritical regime, it is expected that the absorption-emission spectrum is likely to be different. It is essential to quantify the emissive characteristics of the fluid in supercritical conditions, and assess its role in the overall heat transfer. In a previous study, Khivsara et al. [11] attempted to use radiative property data from HITRAN and performed a parametric numerical study to estimate the magnitude of the radiation component for flow through a circular tube. It was found that radiation absorption is significant for moderate Reynolds number applications. In case of highly turbulent flow, however, it is expected that forced convection heat transfer coefficient will be significant, and hence radiation component can be negligible, as reported in Caliot and Flamant [12]. To the best of the authors’ knowledge, measurement of radiation heat transfer by s-CO2 and experimentally determined s-CO2 emissivity has not been reported in the literature. Hence, the present study focuses on experimental determination of radiation heat flux emitted by s-CO2, and the estimation of its magnitude in the context of overall heat transfer. Due to very high pressure, use of conventional spectroscopic methods to measure the radiative properties of s-CO2 is challenging. The present experimental technique involves heat transfer 2

measurement in a shock tube, for estimation of the total emissivity of s-CO2. Numerical simulation using ANSYS Fluent is also performed to evaluate the magnitude of convective heat transfer, which is then compared with the experimentally determined radiation component. 2. Experiment Details a. Shock tube description A typical shock tube consists of a driver section containing gas at a high pressure, a driven section containing gas at a lower pressure, along with a diaphragm separating the two sections. A normal shock wave can be generated when the diaphragm bursts. In the present experiments, CO2 is kept in the driven section, with the objective of suddenly increasing its pressure and temperature as the primary shock traverses this section. After the primary shock reaches the other end of the driven section, it reflects back and results in further elevation of pressure and temperature to reach supercritical conditions. This characteristic behaviour of a shock tube is utilized to obtain stagnant s-CO2 for a short time (~ millisecond). For this short time scale, any measured heat flux can be attributed to the radiation mode only. In the present experiments, a platinum based thin film sensor is used to measure the rise in temperature, and the data is subsequently used to estimate the radiation flux by an algorithm presented in Cook and Felderman [13]. The driver and driven sections of the present shock tube are 2 m and 5.12 m long, respectively, and have 12.5 mm thick walls made of stainless steel SS304. The tube, which is qualified for gas pressures up to 275 bar, has 50 mm inner diameter and 75 mm outer diameter. The driver side is filled with gas from high pressure cylinders through a port after pressure regulation. The driven section is filled with the test gas (CO2 in this case) to a desired pressure through ports, after evacuation using a vacuum pump. The speed of the primary shock wave is estimated by pressure readings from two fast response piezoelectric pressure transducers (PCB Piezotronics Ltd., USA), one mounted near the end wall of the driven section while the other one 0.38 m away from it. The former sensor is mounted very close to the tube end such that it records the stagnation pressure labelled as P5 (pressure at state 5, as per standard shock tube nomenclature). By observing the time difference between the triggering of the two pressure sensors placed at known locations, the primary shock Mach number is calculated. Using the primary shock Mach number and the value of P5, the temperature of the shocked gas (T5) can be calculated from standard shock tube relations, which can be obtained in literature (e.g. Anderson [14], Kumar et. al. [15]). Figure 1 shows 3

the HST-2 shock tube schematic and the location of the pressure and thin film platinum sensor used in the present experiment.

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Fig. 1: Schematic of HST-2 shock tube The driver and the driven chambers.are separated by an aluminium diaphragm having a diameter of 113 mm and thickness ranging from 1 to 3 mm. Two perpendicular V-grooves made on the driver side of the diaphragm ensure proper rupture, clean petal formation, consistency and good control of the rupture pressure. The diaphragm used in this experiment is 2 mm thick and grooved to 1/3rd of its thickness. Figure 2 shows the ruptured diaphragm after the experiment. The petals open uniformly and remain attached to the body of the diaphragm.

Fig. 2: Burst diaphragm after the test b. Experimental conditions It is important to create a strong primary shock in the driven section such that the reflected shock produces supercritical pressure and temperature condition of CO2. For this to occur, the driver gas section is filled with a low molecular weight gas. Due to the hazards associated with hydrogen, helium is chosen as it has low molecular weight, is inert as well as cheap. The driven gas in this case is CO2. Once the driver and driven gases are known, the required 4

Mach number for producing primary shock in the driven section can be calculated by knowing the initial pressure and final desired conditions for the shocked gas (i.e. P5 and T5). Equations to determine the same are straightforward and available in literature as well as in various existing online resources such as Wisconsin Shock Tube Laboratory Gas dynamics calculator [16]. For the required approximate conditions of pressure (P5 = 90 bar) and temperature (T5 = 1000 K), the following theoretical estimates (Table 1) are obtained and the same conditions are executed in the shock tube HST-2. Table 1: Shock tube conditions Driver Gas

Helium

Driven Gas

Carbon Dioxide

Initial Temperature

Ambient (300 K)

Initial Pressure (CO2)

2 bar

Mach Number

2.75

Pressure (P5)

90 bar

Temperature (T5)

1018 K

Rupture Pressure

36 bar

c. Platinum thin film sensor preparation and calibration Fast response platinum thin film gauges which exhibit typical response time ~5 microseconds are widely used in heat transfer measurements in shock tubes. For the present study, these gauges are prepared by depositing a thin platinum film on a ceramic backing material such as MACOR. The gauge is supplied with a constant current, and when its temperature rises due to heat transfer from s-CO2, the resistance of the gauge increases. The instrumentation is designed to keep the current constant at the initial supply value despite the rise in resistance. Therefore, the rise in voltage across the gauge recorded by the data acquisition system corresponds to the temperature recorded by the sensor. Preparation of the gauge: The base material for the thin film gauge is MACOR, which has good thermal insulation and machinability. MACOR also has a high melting point and maintains the integrity of its properties at elevated temperatures. For MACOR, with a thermal diffusivity of 7.94×10−7 m2/s, the thickness of the sensor should be greater than 5 mm [17]. Once the MACOR is shaped according to the mounting arrangement on the end flange cavity, the location of platinum deposition is finalized. Holes of 0.9 mm diameter are drilled at appropriate locations 5

on the substrate for drawing electrical leads. On the top surface, the drilled holes are given a countersink of 1.5 mm diameter to facilitate electrical connection. Presence of dust particles and other impurities on the MACOR surface affects the adhesiveness of platinum. Before the platinum layer is applied, the MACOR is cleaned thoroughly using an acetone bath inside an ultrasonic vibrator. After cleaning, platinum is deposited on the MACOR by hand painting. Thin strips of metallo-organic platinum ink (N.E. Chemcat Corporation, Japan), comprising of platinum in liquid form along with a chemical binding agent, are applied on the MACOR. Once painted, the MACOR pieces are transferred to an oven in which it is initially dried at a temperature of 125°C, at which point the chemical binding agents evaporate. After about 10 minutes, the temperature is raised to 620°C for curing. At this higher temperature, the surface of the MACOR softens and the platinum gets embedded into the molecular structure of the backing material. The sensor is then left to cool down to room temperature naturally, leaving a thin layer of platinum and resulting in a gauge of initial resistance of around 30 – 50 Ω. After platinum is deposited on MACOR, a thin layer of conducting silver paste procured from Hanovia Gold (USA) is coated within the countersink of each drilled hole, so that it makes good contact with the cured platinum. The sensor is again heated to 450°C and allowed to cool down naturally. Electrical leads are then soldered to the silver coating and the wires are drawn from the back face of the sensor, passing through the drilled holes. Care is taken to ensure that the solder filled the countersunk holes on the MACOR surface and does not protrude out. Figure 3 below shows a typical gauge consisting of three identical handdrawn sensors.

Fig. 3: Typical gauge with three sensing elements

Calibration of the gauge: The change in resistance per unit change in temperature (defined as the coefficient α) is an important parameter in deducing the temperature data from platinum thin film sensors. The 6

coefficient α is measured in an oil-filled chamber, in which the gauge and an attached thermometer are suspended into an empty beaker and the sensor is heated by convection using hot air. This arrangement is used to attain a gradual change in temperature of the gauge. For a constant current through the gauge, the change in voltage with temperature is measured by connecting a voltmeter connected across the gauge. The temperature of the gauge is increased from room temperature to 100 °C, and the corresponding voltage is noted after every 5 °C rise in temperature. The alpha calibration curve and the final value is discussed in section 4. Another important parameter required for post-processing the measured signal (voltage) from a thin film gauge is β, which is defined as

Ck s . β is a combination of properties related to

the backing material (MACOR). The value of β for MACOR used in the present experiment is taken from Srinivasa [18], in which stagnation point heat flux was estimated using a similar platinum based sensor on a cylinder placed in a shock tunnel. The calculation of stagnation point heat flux was based on the expression given in Fay and Riddell [9]. Using this value of convection heat flux in Eqn. (1) below, along with a known value of α, the numerical value of

Ck s was calculated to be 1700 W/m2Ks1/2 [18]. As the MACOR used in the present experiment is same as that used in [18], the same value of β is used here. Knowing α for the thin film gauge and β for the MACOR, the voltage signal measured from the sensor can directly be used to estimate the heat flux with the help of the Cook and Felderman algorithm [13]. The algorithm is applied to the heat transfer equation obtained from 1-dimensional semi-infinite heat conduction analysis of the gauge, as detailed by Kumar [20]. The final form of the transient heat conduction equation, obtained from Kumar [20], is shown in equation 1 below:

q (t ) 

  E f

 E ( t n ) n 1  tn   i 1 



E ( t n )  E ( ti ) t n  ti



E ( t n )  E ( t i 1 ) t n  t i 1

2

E ( t i )  E ( t i 1 ) t n  t i  t n  t i 1



E ( t n )  E ( t n 1 ) t

  

(1)

The procedure for iteratively solving equation 1 is programmed in MATLAB to calculate the heat flux in the time interval (0, t) at n discrete points. E f is the initial voltage for the platinum sensor which is recorded before the diaphragm ruptures, while α and β and are determined using the methods described above. d. Sensor mounting

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Due to mechanical failure of the thin film sensor, three geometric configurations of sensor mounting are attempted to obtain the radiation heat flux. The three configurations are discussed briefly below: Configuration 1: The platinum sensor is mounted at the centre of the end flange of the shock tube by milling a 7 mm deep slot, and a thin quartz glass piece is used to separate the sensor from CO2. An adhesive is used to fill the gap between the walls of the sensor and the cavity to ensure proper sealing. After mounting the quartz glass, the system is covered with Kapton tape and the experiment is conducted. Due to the large exposed area and the impact of shock, the quartz glass shattered and the sensor cracked as seen in figures 4a and 4b. Configuration 2: After mechanical failure of the first sensor, the next design incorporated a smaller area of quartz along with a metal adapter and rubber padding to absorb the impact of the shock. The adapter design model in CATIA and the one manufactured are shown in figure 4c. Figure 5 shows the end flange system and the assembled system.

(a)

(b)

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(c) Fig. 4: a) Shattered quartz glass b) Cracked sensor after removal of tape and quartz c) Adapter for configuration 2 Configuration 2 was tested and the quartz glass shattered due to the metal adapter and glass contact, but the sensor was intact. Configuration 3: In this attempt, a new flange with a mounting port and a bolt-adapter (figure 6) is designed such that a protective O-ring could be placed between the sensor and the metallic part of the adapter. Also, the exposed area of quartz and sensor assembly was reduced.

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Fig. 5: Configuration 2 concept and assembled flange

Fig. 6: Flange centre port and bolt-adapter for sensor mounting This aluminium flange has an outer diameter of 240 mm and thickness of 34 mm. The dimensions of the quartz glass is 7mm diameter and 2 mm thickness. The circular exposed area has a diameter of 5.5 mm. The MACOR piece is circular with 5 mm radius and 13 mm cylindrical height. Figure 7 shows the platinum thin film sensor and the sensor-flange unit. Configuration 3 is used to perform the experiment to obtain radiation heat flux data.

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Fig. 7: Platinum thin film sensor and sensor-flange unit 3. Numerical Modeling For estimating the contribution of radiative heat flux component as a percentage of the total heat transfer rate (radiation + convection), the measured radiation emission by s-CO2 in the present experiment is compared with the typical convective heat flux value for a low Reynolds number turbulent flow obtained using a computational fluid dynamics (CFD) model. A circular geometry of the tube is chosen as it is a common configuration element used by researchers to design high pressure receivers and heat exchangers for use in the sCO2 Brayton cycle [7, 8]. Low Reynolds number turbulent flow with Re = 6000 is chosen for the comparison as previous studies have revealed that radiation heat transfer may be comparable to convection for low-speed flows, while it has a negligible impact for highly turbulent flows [11, 12]. Figure 8 shows a 2D axisymmetric computational domain and boundary conditions for flow of s-CO2 through a circular tube. The length and diameter of the tube are fixed at 600 mm and 12 mm, respectively. It is specified that s-CO2 enters the tube at 100 bar and 990 K. An irregular structured quadrilateral grid is obtained using ANSYS ICEM CFD. Mesh sensitivity analysis is carried out by progressively refining the grid system until it is observed that further refinement yields negligible difference in the solution of parameters of interest. While the number of control volumes in the grid was varied from around 7500 to 30000, it was found that a grid system containing around 15000 cells was adequate. The grid spacing was non-uniform with more number of control volumes near the wall compared to the tube core.

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Fig. 8: Computational domain of a two-dimensional axisymmetric model A pressure based finite-volume solver ANSYS Fluent employing the SIMPLE algorithm is used to numerically solve the transport equations [21]. The standard k-ε model with enhanced wall functions is implemented to model the turbulent flow. For ensuring convergence, fluxes of mass and energy are monitored after every iteration, and convergence is declared once the residuals monotonically drop below 10-3. The thermo-physical property values for s-CO2 are obtained by linking ANSYS with REFPROP, which is a thermodynamic database maintained by NIST [22]. The s-CO2 properties for this database are calculated using an equation of state given in Span and Wagner [23]. The radiative transport equation is not solved in the numerical model and participation of s-CO2 is hence, neglected. The hot high-pressure s-CO2 loses heat to the colder tube wall by convection and diffusion only. 4. Results and Discussion a. Thermal coefficient of resistance (α) calibration The α-calibration for the sensor used in configuration 3 is performed by the method discussed in section 2. Figure 9 shows the alpha calibration data. The change in voltage as a response to change in temperature is recorded and the thermal coefficient of resistance is calculated using equation 2:



1 V IR T

(2)

where I and R are the constant current supplied to the gauge and the initial resistance, respectively. The value of V / T is the slope of the graph in figure 10. The value of thermal coefficient of resistance calculated from equation 2 is 0.00085 K-1.

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Fig. 9: Thermal coefficient of resistance calibration b. Variation of pressure in driven section The measured pressure variation in the driven section is shown in figure 10. The first sensor (Pressure Sensor 1) is triggered when the primary shock wave passes it, raising the pressure and temperature of the gas. As the shock wave moves forward, the second sensor (Pressure Sensor 2) is triggered.

Fig. 10: Pressure variation for s-CO2 in the driven section

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The second jump in Pressure Sensor 2 happens when the reflected shock traverses it, raising the pressure (P5) to 85 bar. The Mach number is 2.75 and the temperature of the shocked gas is calculated from equation 3, as obtained from Kumar et. al. [15]. T5 Tinitial



2

1





 1M 12  3   1  3 1  1M 12  2 1  1  2  12 M 12

(3)

where, Tinitial is the initial temperature of CO2, viz. 300 K,  1 is the ratio of specific heats of CO2 at initial pressure (2 bar) and temperature (300 K), viz. 1.297 and M1 is the primary shock Mach number (2.75). The temperature (T5) of the shocked gas calculated from equation 3 is 990 K. At the critical point, the pressure and temperature of CO2 are 73.9 bar and 304.1 K, respectively. Hence, the measured condition is in the supercritical regime. Further, for the Mach number measured in the shock tube during this experiment, shock tube relations also predict that CO2 would attain a pressure of 90 bar, as outlined in Table 1. Such pressures and temperatures are routinely observed in shock tubes. Within a few milliseconds of peaking, the pressure and temperature of CO2 drop due to diffusion of helium and CO2, giving an effective test time of about 600 microseconds for measuring the radiation heat flux. The heat flux is measured after the CO2 reaches supercritical conditions (85 bar and 990 K) and before the onset of diffusion, as reported below. c. Radiation heat flux measured by the platinum thin film sensor The heat flux variation with time measured by the platinum sensor is shown in figure 12.

Fig. 11: Measured radiation heat flux

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This measured value of heat flux is derived from the numerical solution of equation 1, using the Cook and Felderman algorithm [13] as outlined in section 2(c). The absorptivity of the sensor is also taken into account. As seen in figure 11, a peak radiation heat flux value of about 0.95 W/cm2 is measured by the sensor. d. Estimation of emissivity of s-CO2 The emissivity of s-CO2 is estimated by comparing the radiation heat flux measured by the thin film platinum sensor with the blackbody emissive power corresponding to the temperature of s-CO2, i.e. 990 K. The total emissivity value is calculated as:

 s  CO

2 , total



Radiation Heat Flux of Gas Tb4

(4)

where σ is the Stefan Boltzmann constant and Tb is the blackbody temperature. Based on the above formulation, the emissivity of supercritical carbon dioxide at 85 bar and 990 K is calculated to be 0.17. The radiation heat flux variation shown in fig. 12 is measured over a very short time period of about 0.4 milliseconds. The estimated reflected shock speed for the current shock tube conditions is about 250 m/s, the shocked gas path length when the radiation heat flux is measured is 4 cm. The emissivity value for a gas is typically specified along with the pressure (bar), temperature (K) and the product of pressure, p, and path length, L [i.e. product pL (bar-cm)] for which the measurement/calculation of emissivity is performed. For the current measurement, the pressure is 85 bar and the path length is about 4 cm when the radiation heat flux peak value is measured. The pL product is obtained as: pL  85(bar ) * 4( cm )  340 bar  cm

(5)

For a pressure of 1 bar, temperature of 1000 K and a pL product equal to 340, the value of total emissivity for CO2 is predicted using an analytical method by Farag and Allam [24]. The data from this reference is reproduced in figure 12. For 1 bar, 1000 K and 340 barcm, the value of emissivity is estimated to be about 0.2. For an elevated pressure of 85 bar at the same temperature (1000 K) and pL (340 bar-cm), the prediction of total emissivity can be obtained from the following equation suggested by Modest [25]:

  ( a  1)(1  pE ) ( pL) m  1 exp  c log10   s( pL,1 bar, Tg ) a  b  1  pE pL   s( pL, p, Tg )

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2

   

(6)

where p E (effective pressure), a, b, c and (pL)m are correlation parameters which are described in Modest [25]. Using the values of pressure, temperature and the pL product for the present case, equation 6 predicts that the emissivity at the present elevated pressure is found to be almost same as that at 1 bar. Thus, the measured value of emissivity (0.17) in the present work is in close agreement to the theoretically predicted value.

Figure 12: Emissivity of CO2 for 1 bar at varying temperature and pL [24]

e. Measurement Uncertainties For the current measurements, uncertainties can occur with respect to various measured parameters such as shock speed, pressure, and the heat flux. The uncertainty estimate presented here is based on the analysis reported in Singh [26], in which the same equipment and devices were used as in the present case. These uncertainties are based on the root mean square of the uncertainties of various factors affecting each instrument. The uncertainties estimated are ±2.65 % in the shock speed measurement, ±3.15 % in the pressure measurement and ±5.65 % in the heat transfer measurement. The uncertainty in the estimated stagnation temperature of the shocked gas is ±4.72 %. 16

f. Comparison with convection heat flux As the hot s-CO2 at 990 K enters the circular tube and loses its energy to the constant temperature wall at 300 K, its temperature drops gradually along the length. The transfer of heat from s-CO2 to the wall is purely by convection-diffusion in the simulated case. The purpose of this simple numerical experiment is to provide a reference convection heat flux with which the radiation heat flux measured experimentally can be compared. The centre line temperature variation of s-CO2 is plotted along with the wall temperature, which is constant at 300 K (figure 13). As seen in figure 13, the fluid cools and decelerates as it travels along the tube. Postprocessing in ANSYS Fluent reports that the convection heat flux is about 55 kW/m2., averaged over the tube length. The relative percentage of the measured radiation heat flux with respect to the simulated convective heat flux is 17.4 %.

Fig. 13: Variation of centreline fluid temperature and wall temperature 5. Conclusions A novel experimental technique for investigating the radiative properties of s-CO2 as a participating medium is presented in this work. It is found that s-CO2 acts as a participating medium, and the percentage contribution of radiation towards the total heat exchange in a typical heat transfer equipment can be significant. Traditionally, such effects were not considered in the design of heat exchangers used in s-CO2 based power cycles involving high

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temperatures. Hence, the results of the present work will have tremendous implication in such designs. However, it is important to note that any estimation of total emissivity value of s-CO2 under such extreme conditions will have a good deal of uncertainty [25]. Hence, the value estimated using the present method should be considered only as an approximate one, and it opens up a wide scope for making more accurate and detailed measurements of spectral radiative properties of s-CO2 for different path lengths. Nevertheless, the present study serves the important objective of making researchers consider s-CO2 as a participating medium in radiation heat transfer calculations. Acknowledgment The authors would like to acknowledge the financial support of Ministry of New and Renewable Energy (MNRE) under Grant No. No.15/11/2015-16/ST. Also acknowledged are the numerous inputs from members of LHSR, with a special mention of Mr. Jeevan and Mr. Srinath. The authors would also like to acknowledge the contribution of Prof. Jeffrey M. Gordon, Ben-Gurion University of the Negev, Israel for his valuable comments and inputs. 6. References 1. V.Dostal, A supercritical carbon dioxide cycle for next generation nuclear reactors, PhD thesis, MIT-ANP-TR-100, 2004. 2. C. S. Turchi, Z. Ma, T.W. Neises, M.J. Wagner, 2013. Thermodynamic Study of Advanced Supercritical Carbon Dioxide Power Cycles for Concentrating Solar Power Systems. Journal of Solar Energy Engineering, 135 (2013) 041007-1 3. P. Garg, P. Kumar, K. Srinivasan. Supercritical carbon dioxide Brayton cycle for concentrated solar power, The Journal of Supercritical Fluids, 76 (2013) 54– 60. 4. B. D. Iverson, T. M. Conboy, J. J. Pasch, A. M. Kruizenga, Supercritical CO2 Brayton cycles for solar-thermal energy, Applied Energy, 111 (2013) 957–970. 5. Niu, X. D., Yamaguchi, H., Zhang, X. R., Iwamoto, Y., & Hashitani, N. (2011). Experimental study of heat transfer characteristics of supercritical CO 2 fluid in collectors of solar Rankine cycle system. Applied Thermal Engineering, 31(6), 1279-1285. 6. Kim, H. Y., Kim, H., Song, J. H., Cho, B. H., & Bae, Y. Y. (2007). Heat transfer test in a vertical tube using CO2 at supercritical pressures. Journal of nuclear science and technology, 44(3), 285-293. 18

7. Ortega, J., Khivsara, S., Christian, J., Ho, C., Yellowhair, J., & Dutta, P., Coupled modeling of a directly heated tubular solar receiver for supercritical carbon dioxide Brayton cycle: Optical and thermal-fluid evaluation. Applied Thermal Engineering, 109, 970-978, 2016 8. Ortega, J., Khivsara, S., Christian, J., Ho, C., & Dutta, P., Coupled modeling of a directly heated tubular solar receiver for supercritical carbon dioxide Brayton cycle: Structural and creep-fatigue evaluation. Applied Thermal Engineering, 109, 979-987, 2016 9. Ortega J.D., Khivsara S.D., Dutta P., Christian J.M., Ho C.K., 2018, On-Sun Testing of a High Temperature Bladed Solar Receiver and Transient Efficiency Evaluation Using Air, Proceedings of the ASME 2018 Power & Energy Conference & Exhibition, PowerEnergy2018, Lake Buena Vista, FL, June 24-28, 2018 10. Fourier, J. B. J. (1827). Les temperature du globe terrestre et des espaces planétaires. Mémoires de l’académie royale des sciences de l’institut de France, Tome VII. 11. Khivsara, S. D., Srinivasan, V., & Dutta, P., Radiative heating of supercritical carbon dioxide flowing through tubes. Applied Thermal Engineering, 109, 871-877, 2016 12. Caliot, C., & Flamant, G. (2014). Pressurized Carbon Dioxide as Heat Transfer Fluid: Influence of Radiation on Turbulent Flow Characteristics in Pipe. AIMS Energy, 3(2), 172-182. 13. Cook W. J. and Felderman E.J. “Reduction of data from thin film heat transfer gauges: a concise numerical technique”, AIAA J. Vol. 4. No 3, 1966, pp 561-562. 14. Anderson, J. D. (1990). Modern compressible flow: with historical perspective (Vol. 12). New York: McGraw-Hill. 15. Kumar, C. S., Takayama, K., & Reddy, K. P. J. (2014). Shock waves made simple. Wiley-Blackwell. 16. http://silver.neep.wisc.edu/~shock/tools/gdcalc.html 17. Jagadeesh G., Reddy N.M., Nagashetty K., Reddy K.P.J., “Fore-body Convective Hypersonic Heat Transfer Measurements Over Large Blunt Cones”, Journal of Spacecraft and Rockets, 37-1, pp 137-139, 2000. 18. Srinivasa P., “Experimental Investigations of Hypersonic Flow over a Bulbous Heat Shield at Mach number of 6”, PhD Dissertation, Indian Institute of Science, Bangalore, 1991. 19. Fay J.A., Riddell F.R., “Theory of Stagnation Point Heat Transfer in Dissociated Air”, Journal of the Aeronautical Sciences, Vol. 25, No. 2, pp 73-85, 1958.

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20. Kumar, C. S. (2017). Experimental Investigation of Aerodynamic Interference Heating Due to Protuberances on Flat Plates and Cones Facing Hypersonic Flows, PhD Dissertation, Indian Institute of Science, Bangalore, 2017. 21. ANSYS Academic Research, Release 13.0, Help System, Fluent Theory Guide, ANSYS, Inc, pp. 1-18, 41-174, 577-640. 22. Lemmon, E.W., Huber, M.L., McLinden, M.O., (2013), NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg 23. Span, R., & Wagner, W. (1996). A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPa. Journal of physical and chemical reference data, 25(6), 1509-1596 24. Farag, I. H., & Allam, T. A. (1982). Carbon dioxide standard emissivity by mixed graygases model. Chemical Engineering Communications, 14(3-6), 123-131. 25. Modest, M. F. (1993). Radiative Heat Transfer. McGraw Hill International Edition, pp. 366. 26. Singh, T. (2009). Experimental investigation of Hypersonic Boundary Layer modifications due to Heat Addition and Enthalpy Variation over a Cone Cylinder configuration, M. Sc. (Engg.) Thesis Dissertation, Indian Institute of Science, Bangalore, 2009.

Nomenclature: a

correlation parameter for eqn. 6

b

correlation parameter for eqn. 6

c

correlation parameter for eqn. 6

C

specific heat of MACOR (J/kg-K)

E

voltage (mV or V)

I

current (mA)

k

turbulent kinetic energy (J)

ks

thermal conductivity of MACOR (W/m-K)

M

Mach number

P5

pressure of shocked gas after reflected wave has passed (bar) 20

PE

effective pressure

q

heat flux (W/m2)

R

resistance (Ω)

Re

Reynolds number

t

time (s or ms)

T

temperature (K)

T5

temperature of shocked gas after reflected wave has passed (K)

V

voltage (V)

Greek alphabets: α

temperature coefficient of resistance (K-1)

β

MACOR (backing material) parameter defined by

γ

ratio of specific heats

ρ

density (kg/m3)

ε

dissipation rate (J/kg-s) in k-ε turbulence model, emissivity

σ

Stefan-Boltzmann constant (W/m2-K4)

Ck s (W/m2-K1-s1/2)

Subscripts: b

black body

f

initial voltage

i, n

time step

1

initial Mach number



A first-of-its-kind measurement of radiation flux & emissivity of s-CO2 is presented



s-CO2 acts as a participating medium: ignoring radiation may bring substantial errors



Radiative heat transfer component was found to be significant in comparison to convection



The current measurement confirms need for detailed spectroscopic studies for s-CO2

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