Abstract

This study experimentally and computationally investigates the heat transfer capability of supercritical carbon dioxide (sCO2) single jet impingement. The evaluated jet Reynolds number range is between 80,000 and 600,000, with a nondimensional jet-to-target surface spacing of 2.8. CO2-impinging jet stagnation conditions were maintained at approximately 200 bar and a temperature of ∼400 °C for most experiments. The goal is to understand how changes in the aforementioned parameters influence heat transfer between the working fluid and the heated surface. Additionally, due to the elevated Reynolds numbers and difference in thermodynamic properties between air and CO2, air-derived impingement correlations may not be appropriate for CO2 impingement; these correlations will be evaluated against experimental sCO2 impingement data. At the time of this study, no sCO2 impingement data was available relevant to sCO2 power cycles. The target surface is a 1.5-in. diameter copper block centered on the 3 mm jet orifice. A mica heating element bolted to the bottom of the copper block provides a uniform heat flux. Thermocouples embedded in the copper block are used to determine the surface temperature. Nusselt numbers obtained from experimental sCO2 test data are compared to area-averaged Nusselt numbers from air-derived correlations. The comparisons showed that air correlations drastically underpredict the heat transfer when sCO2 is used as the working fluid. A modified sCO2 correlation using experimental data at discussed conditions is derived based on an existing air correlation. A CFD study is also performed to further investigate sCO2 heat transfer characteristics, and assess the numerical model applicability to this problem type.

Introduction

Power cycles can be said to be the heartbeat of modern civilizations. Engines provide power to vehicles for transportation, and turbines for generating electricity. The working fluid, whether air, steam, or some other substance, moves through the various components in a careful design system to achieve effective and efficient power output. In a power plant, the working fluid in the cycle propels the turbine's blades into angular motion. This motion, paired with an electrical generator, provides most of society's energy needs. Due to the ever-increasing energy demand associated with the progress of society, the need to increase the thermal efficiency of these cycles is of the utmost importance [1]. Considering the Carnot cycle as the ideal cycle to which the Brayton cycle can be compared, the goal is to approach this standard by increasing cycle efficiency. The three main avenues for increasing the efficiency of a cycle are: increasing the turbine inlet temperature, improving the design of turbomachinery components, and augmenting the cycle, e.g., intercooling, regeneration, or reheating. Increasing the inlet temperature in the turbine is the predominant approach to improving efficiency. Several methods are used to improve cooling internally and externally for the blade and increase the turbine inlet temperature. The internal methods are impingement, rib turbulators, and pin fins [2]. Impingement cooling is primarily used along the leading edge, which is subjected to the highest temperatures; and also along the midchord of the blade or vane. From there, the cooling flow moves through rib turbulators providing some heat transfer between the cooling fluid and the turbine walls via turbulence. At the trailing edge, pin-fin cooling provides heat transfer from the channel end walls to the pins and the cooling fluid. The external method is film cooling; after impingement, the fluid is bled through the film-cooling holes or showerheads, creating a protective coolant layer on the blade.

Impingement cooling is used along nearly all paths in contact with the hot inlet gas, providing the most significant cooling capability compared to other single-phase heat transfer methods [3]. Therefore, increasing the cooling capacity for jet impingement is of great concern, since increasing the inlet temperature in the turbine will provide greater thermal efficiency.

sCO2 Turbines.

In addition to increasing thermal efficiency, lowering cost and pollution outputs are essential. Supplying higher efficiency, sCO2 power cycles are capable replacements for steam Rankine cycles, as shown by Subbaraman et al. [4]. Additionally, the higher density of the working fluid results in a lower plant footprint. The working fluid, CO2, at a supercritical state—meaning above its critical pressure and temperature—allows it to expand to fill a volume like a gas and have a density similar to a liquid. This occurs for CO2 above a pressure of 73.8 bar and temperature of 31.1 °C.

Small changes in pressure and temperature can significantly impact the density of sCO2. For example, sCO2 at a higher density, results in less compression work, and higher cycle efficiency. This can be exploited to reduce the size of cycle components, thus reducing plant costs while increasing efficiency by approximately 5% [4].

Literature Review

Fluid Mechanics.

An impinging jet is a high-velocity mass ejected from an orifice or slot that impacts a heat transfer surface. Gauntner reviewed the structure of single jet impingement and defined the flow field into three main regions—shown in Fig. 1 [6].

Fig. 1
Impinging flow field [5]
Fig. 1
Impinging flow field [5]
Close modal

The three main regions are the free jet, stagnation, and wall jet regions. The review compared theoretical and experimental works detailing the velocity distribution in the flow regions. In addition, techniques for determining how the jet velocity and pressure profiles develop are provided for impingement cooling designs. The first phase for an impinging flow field is the development of the free jet region. The free jet region occupies the space just before hitting the plate. Axial velocity is highest at the center of a single free jet and decreases radially outward. The decrease is due to shearing and entrainment with the environment, which generates turbulence in the shear layer surrounding the potential core [7]. The potential core, where the nozzle exit velocity is maintained, is an approximate laminar region between the shear layers with a sharp v-like profile. The potential core length is approximately four to eight nozzle widths downstream from the nozzle exit. Viskanta defined the developing, and fully developed regions as the final parts of a free jet [8]. The developing region encompasses the decaying jet, and the fully developed region occurs once the decaying jet profile becomes Gaussian. Bradbury covers general velocity distribution and jet axial velocity decay, providing vital information on single-free jet fluid mechanics [9]. Figure 1 shows after hitting the surface, the structure of the stagnation region forms, and the outward spent jet create the wall jet regions that further turbulate the fluid in the environment. Flow is highly turbulent at, and near the impingement region; the stagnation region typically begins 1.2 diameter lengths above the surface for a round jet [10]. The stagnation region marks the beginning of a nonuniform flow turning accompanied by large normal, and shear stresses that heavily influence the local transport properties: viscosity, thermal conductivity, and diffusivity. In addition, vortex stretching occurs due to the nonuniform flow path within the region, increasing turbulence. Maurel and Solliec's experimental work outlines the influences and development of the Reynolds stresses within the stagnation region [11]. After impingement, a thin boundary layer is formed within the stagnation and wall jet region. The boundary layer thickness is inversely proportional to the square root of the Reynolds number (Re). Reynolds number is a ratio of inertial to viscous forces, and the Prandtl number (Pr) is a ratio of momentum diffusivity to thermal diffusivity. In practical applications, Reynolds numbers can be of the order of magnitude of 104 or more; the boundary layer thickness can be as low as one-hundredth of the nozzle diameter. The outward flow from the stagnation region eventually develops the wall jet region. The thickness of the region can be determined by measuring the height where the flow speed is 5% of the max speed in the wall jet parallel to the surface. The boundary layer in the stagnation region increases to a maximum of 1% of the jet diameter within the wall jet region [10].

Heat Transfer.

The effects turbulence has on heat transfer in the stagnation region for round jets were studied by Kataoka [12]. The work shows heat transfer enhancement by large-scale eddies by renewing turbulence on the surface. Hrycak's literature review discussed the results of Huang, Gardon, and Waltz's [13]. The review focused on how the spacing from the nozzle to the impingement surface (z/D or H/D) influenced the heat transfer coefficient. Huang observed that an adjustment within 1 < z/D < 10 showed minimal impact on the heat transfer coefficient, with a general agreement for Daane and Han's work [14]. Conversely, Gardon showed peak heat transfer rate increasing as z/D decreased with Waltz's work supporting. Gardon stated later that the heat flow gage could have had a calibration error of 40% [13]. Hrycak's literature review also discussed the results of Brdlik and Savin, which showed that for z/D < 6.2, there was little to no impact on the heat transfer coefficient when the standoff distance was adjusted within the stated range for laminar flow [15]. Additionally, Kataoka showed that a z/D between 5 and 8 will produce a maximum stagnation point Nusselt number, and a maximum turbulent intensity occurs at a z/D of 7. Viskanta reviewed the effect of Reynolds number and z/D [8]. For circular jets, various Reynolds numbers and z/D less than one can produce dominating secondary peak in the heat transfer distribution. This is because the acceleration of the fluid from the impingement surface creates a thinning boundary layer at r/D = 0.5. The secondary peaks can be attributed to this acceleration, but it may not be the only reason. Additionally, increasing the Reynolds numbers increases the amplitude of the secondary peaks [16].

sCO2.

A small number of experimental studies pertaining to sCO2 jet impingement around the pseudo-critical point have been conducted. Chen et al. demonstrated that the local heat transfer coefficient increases near the stagnation point when the inlet temperature is lower than the pseudo-critical temperature, and the impinging surface temperature is slightly higher than it [17]. Chen also performed a numerical study validated by the above-mentioned experimental results [18]. Kim numerically studied sCO2 jet impingement in oxy-fuel sCO2 turbines, focusing on changes in the heat transfer coefficient when heat flux varies [19]. They found secondary peaks appear at a radial location further down than air, and the sCO2 inlet values should be determined with respect to the heat flux range of the impinging surface. Potential experimental studies may consider examining extreme cases, such as ultrahigh Reynolds numbers. Cormier showed that a RANS model simulation with a v2f turbulence model handled ultrahigh Reynolds numbers and temperatures the best [20]. Though a number of experimental studies using sCO2 for microcooling applications have been conducted [17,21], there is a lack of practical studies for cooling applications for gas turbines. This lack of studies could be attributed to difficulties in maintaining, troubleshooting, and operating experiments under such challenging conditions (high-temperature/pressure). The work presented here aims to provide experimental heat transfer data for gas turbine applications. The primary conditions of this study are 200 bar with a jet temperature of 400 °C. Data at these conditions will be valuable to the heat transfer community for jet impingement studies at relevant sCO2 turbine conditions.

Overview.

This section provides an overview of the content of this work. The “Methodology” describes components, test setup and procedures, data reduction, and uncertainty analysis. The “Results and Discussion” examines air and sCO2 data. The “Conclusion” summarizes the essential takeaways from this investigation. Critical terms for understanding this work are bolded and italicized when accompanied by their definition.

Methodology

This section begins with the specifics of the benchtop test and the heat transfer setup, followed by the experimental setup and procedures for the air validation and sCO2 tests. Finally, critical empirical analyses are provided; the sections included are “Surface Temperature Calculation,” “Heat Loss,” and “Data Reduction.”

The benchtop tests are jet impingement experiments open to ambient conditions, shown in Fig. 2. Benchtop tests are done to validate experimental procedures and data reduction. The “rig,” refers to the assembled top and bottom flange assemblies instrumented on the pressure vessel. The details of the rig are discussed in later sections. The rig air tests also validate experimental procedures and data reduction, providing confidence in the experimental setup and its ability to obtain accurate data for the sCO2 test.

Fig. 2
Benchtop experimental schematic
Fig. 2
Benchtop experimental schematic
Close modal

Benchtop Test.

The schematic for the benchtop test is shown in Fig. 2. The copper block is instrumented with three thermocouples. The mica heater is held in place by threading at the bottom of the copper block. The copper block and all attached components are referred to as the heat transfer setup. The impinging flow travels along the z-axis shown in Fig. 2. The distance between the jet nozzle and surface is shown as H. The convective heat is represented by Qconv and heat loss from the copper block is depicted as Qloss. The heat flux from the mica heater is represented as qflux.

To begin the experiment, the compressor is turned on, and the flowrate is adjusted using a needle valve and measured using the mass flowmeter. The flow then exits the nozzle, travels along the z-axis shown in Fig. 2, and impinges on the copper block. The copper block is a cylinder with a radius of 0.75 in. and a height of 1 in. Copper was selected due to its high thermal conductivity allowing for near-isothermal conditions.

At the time of this study, other sCO2 experiments were performed at pressure and temperature conditions substantially lower than turbine cooling conditions necessary for a direct-fired sCO2 cycle; thus, power and temperature measurements could be provided from a micro-electro-mechanical system (MEMS) chip [17]. But at the pressure, temperatures, and other conditions of this study – 200 bar and 400 °C—such an approach would not be feasible. The mica heater was selected due to its survivability at the primary conditions of the sCO2 tests. The mica heater is electrically powered by a variable AC voltage regulator or (variac). A standard wall outlet powers the variac. The variac allows for the voltage across the heater to be controlled. The mica heater is held in place by the backing plate screwed into the copper block. The mica heater supplies the heat flux (qflux) to the block. The block is heated, so a temperature difference (dT) occurs between the impinging fluid and the block. dT refers to the temperature difference between the surface and the jet. The block's temperature is measured via three embedded J-type thermocouples. Minco, the manufacturer, provides documentation that is used to determine the maximum allowable voltage at a specified temperature. The resistance of the mica heater is measured using a ohmmeter.

The alumina silicate holder, shown in Fig. 2 is used to hold the rest of the assembly and mitigate heat loss from the copper block since the material's thermal conductivity is sufficiently low (< 2 W/mK). Radial heat loss is further reduced by wrapping the assembly in an insulating ceramic sheet. This allows most of the heat to be transferred upward from the top surface with the impinging fluid. Subsequent sections discuss how the surface temperature and heat loss are determined.

Rig Components

Bottom Flange Assembly.

Figure 3 shows the copper block's position inside the pressure vessel. Positioning the assembly inside the pressure vessel is a rather delicate procedure since the surface of the copper block must be maintained normal to the issuing flow. Tight machining tolerances require precise positioning, or experimenters risk damaging the heat transfer setup. Although such tolerances complicate the assembly, they allow for proper angularity of the jet-to-target surface. Once assembled within the rig, a visual inspection is performed through the 2 NPT sight openings. With machining and assembly tolerances, the jet axis to the impingement surface angle is perpendicular within 1 deg. After confirming no damage, the openings are closed by 2 in NPT plugs, which can also be used as sight windows if optical diagnostics are to be used. When the heat transfer setup is seated on the bottom flange, and connected to the gland fittings, the collective is referred to as the “Bottom Flange Assembly.”

Fig. 3
Interior view of the flow path in rig
Fig. 3
Interior view of the flow path in rig
Close modal

Top Flange Assembly.

The top flange assembly consists of the top flange, deflector chamber, plenum, jet plate, and associated features. For the rig tests, the fluid travels through a quad fitting, through the flange into the deflector chamber, where the fluid strikes the splash plate, diffuses through the deflector chamber openings into the plenum, and travels down to the jet plate. The purpose of the splash plate is to break up the inlet flow from the loop and to better ensure stagnant conditions for the flow through the 3 mm nozzle on the jet plate. The flow then impinges on the copper block and is driven up and out of the pressure vessel. A metal sheet is wrapped around the heat transfer setup to direct the flow upward and not into the sight window openings. The flow path and top flange assembly components are shown in Fig. 3.

The Rig.

Figure 4 shows the fully assembled experimental apparatus, which will be referred to as the ‘rig.’ The rig is composed of the top and bottom flange assemblies instrumented onto the pressure vessel. A hydraulic torque wrench tightens the 1 bolts that fix the flanges onto the pressure vessel. An R28 soft iron RTJ gasket is wedged between the flanges to create the seal.

Fig. 4
Thermocouple and air inlet positions
Fig. 4
Thermocouple and air inlet positions
Close modal

Rig Air Tests.

The benchtop and Rig air tests have essentially the same experimental setup. Air travels from the air compressor to the quad fitting, where pressure and temperature are measured, as shown in Fig. 4, and then impinges on the copper block surface. The needle valve regulates the mass flow measured using a mass flow sensor. The DAQ records the measured data. The preliminary air tests verify that the setup, data acquisition, and reduction procedures are correct by validating experimental Nusselt numbers to well-known correlation values from literature [2225]. This is a crucial first step, before transitioning to using sCO2 as a working fluid. The correlations are discussed in the “Air Validation” section.

Rig Loop Integration.

Figure 5 shows the rig integrated into the sCO2 experimental loop. The sCO2 experimental loop, or the loop, consists of the components that generate, regulate, and heat the flow. The flow enters the inlet pipe following the inlet lines into the quad fitting on top of the top flange. After impingement, the flow exits the rig from the outlet piping, following the outlet arrows back to the loop. The thermocouple in the normal position to the top flange measures the flow temperature into the plenum and is used to extrapolate the jet temperature. The rig is insulated later to minimize heat loss during the experiment with ceramic fiber insulation with a thermal conductivity of ∼0.029 W/(m K)

Fig. 5

sCO2 Experimental Loop.

Figure 6 details the sCO2 experimental loop. The black arrow lines outline the flow path. The location where heating is applied is referred to as preheaters, the booster pump is where CO2 is pumped into the system, and the jet impingement experiment is located after the busbar power supply section, where additional heat is added to the flow. The test facility where the system is located is equipped with a ventilation system that quickly removes any leaked CO2 outside the room. CO2 concentration sensors are also located throughout the room and notify personnel if the concentration exceeds 1000 ppm (parts per million).

Fig. 6
sCO2 experimental loop
Fig. 6
sCO2 experimental loop
Close modal

Before the test begins, the loop is vacuumed, removing any air or nitrogen in the loop. While running these experiments, only CO2 should be in the lines, and the purity of the CO2 in the cylinders is 99.9%. To begin, the exhaust valve is open, and the loop depressurizes to atmospheric conditions. Then the vacuum pump is connected to the loop, turned on, and the loop begins to approach vacuum conditions. Once a sufficient vacuum has been established—approximately the lowest achievable vacuum by pump (–18 psi to -26 psi)—a shut-off valve is closed, and the vacuum pump is turned off. The next step is pressurizing the loop by opening the valves around the buffer tank and the recirculating pump. This will increase the pressure in the loop to around 40–55 bar. The goal is to get the pressure to 200 bar. Next, the recirculating pump is turned on at the operating panel to get the flow going in the loop. This flow will be tuned to the desired flowrate as the value will change throughout the experiment due to changing conditions like temperature and pressure. The components for cooling the loop are also turned on; these components are for keeping the temperature of the CO2 in the recirculation pump within its operating range. For adding more CO2 into the loop, two booster pumps in series, pump CO2 from the cylinders to the loop. The loop is pressurized between 130 and 150 bar before a shut-off valve is closed to turn the booster pumps off and then to seal the cylinders. The loop is also isolated from the booster pumps via an on-off valve that is closed to allow the booster pump lines to be vented and detached from the loop and the cylinders. These pumps are then moved and attached to the recuperator and nitrogen cylinders to fill the recuperator shell.

Heat is added to the flow using fifteen rope heaters along the yellow and red lines. Eight variacs regulate the power distributed to the rope heaters. The busbar section is composed of a DC power supply with two positive and negative terminals. A pair of copper wires connects to the terminals of a DC power supply, which also connect to the loop via nickel busbars uniformly covering about a half-inch cross section on the stainless-steel pipe. The busbars allow for joule heating to occur through the pipe which in turn heats the flow. As the flow is heated, the recuperator shell is filled with nitrogen. The shell is pressurized between 90 and 120 bar. Once the recuperator shell is pressurized to about 120 bar, the shell is isolated from the nitrogen cylinders. As the current recuperator casing is only rated for ∼120 bar, it is enclosed in a pressurized shell, which then splits that pressure difference so the recuperator only experiences pressures in its safety range. The mass flowrate required to meet the Reynolds number for each test is calculated using the primary conditions. The flowrate is monitored and adjusted using the loop's recirculating pump and the two valves surrounding it.

Surface Temperature Calculation.

This section will discuss how the surface temperature of the copper block is determined. The z-position refers to the coordinate normal to the copper blocks top surface but beginning at the bottom of the block. For example, z-positions of 0 and 1 in would be the block's bottom and top surfaces. The R-position refers to the radial position along the surface. The R-positions 0 and 0.75 in. are the center and radius of the copper block. The copper block has a 1 in. height or z-position of 1 in., and thermocouples 1 and 2 are at a z-position of 0.87 in. Thermocouple 1 is positioned directly under the stagnation point or R-position 0. Thermocouple 2 is at an R-position 0.375 in., which is between the center and radius of the block. The third thermocouple is at the same R-position as the first, but at a z-position of 0.51 in., this position is halfway up the block. The fourth position is not used.

For data analysis, temperature and mass flow are at steady conditions, constant heat flux is applied, and no heat is generated from within the copper block. A linearly extrapolated surface temperature is obtained from the three thermocouples discussed. The coefficients in the linear equation will depend on the temperatures at the thermocouple positions and are calculated for each test.

Heat Loss.

The heat loss test aims to quantify how much heat will be lost to the area surrounding the copper block during the tests with flow. The heat loss relationship is known a priori to be purely linear, four points are used herein. The heat loss experiment's setup and methodology are the same for the benchtop and rig tests.

As shown in Eq. (2), all the heat supplied is equal to the Qloss, or Ql, whereas, during the test shown in Fig. 2 and Eq. (1), the heat will also be transferred with the fluid as well
(1)
(2)

The mica heater is supplied with a voltage to obtain a specific block temperature. Then room temperature is subtracted from the measured blocked temperature to determine the temperature difference.

Data Reduction.

The area of the cross section for the jet nozzle is calculated using Eq. (3)
(3)
Similarly, the surface area of the impinging surface is determined by the following:
(4)
Supply power for heating the copper block is calculated using the voltage from the mica heater and the resistance across it
(5)
As discussed in “Heat Loss,” the heat loss is defined using the following equation:
(6)
Using supply power, heat loss, area of the impinging surface, and temperature difference between the jet and the impinging surface, the heat transfer coefficient can be determined
(7)
The nondimensional heat transfer coefficient, Nusselt number, is calculated using the heat transfer coefficient, jet diameter, and fluid property thermal conductivity, k. The thermal conductivity is determined by coolprop using temperature and pressure values from the experiment
(8)

Uncertainty Analysis.

The method used to determine the propagation of uncertainty in the analysis is described in the Test Uncertainty Standard PTC 19.1-2005 by the American Society of Mechanical Engineers (ASME) [26]. The relative expanded uncertainties in measured parameters for air and CO2 are shown in Tables 1 and 2. As the National Institute of Standards and Technology (NIST) suggested, the uncertainty in thermophysical properties from coolprop is neglected [27]. Nusselt number uncertainties for the sCO2 tests are shown in Figs. 12 and 15 in ‘sCO2 Results.’ Eq. (9) is the general equation for determining uncertainty. The absolute expanded uncertainty is uα; alpha is the independent variable. The sensitivity coefficient is theta; i is each dependent variable, and n is the last dependent variable. The absolute combined standard uncertainty for the i dependent variable is ui. Table 3 shows the independent variables and dependent variables. The propagation of uncertainty in the heat transfer coefficient is determined by inputting Qs, Ql, Dsurf, and dT into Eq. (9) as the independent variables
(9)
Table 1

Air test uncertainties

Parameter uncertainties at each Reynolds number for air
Re·(103)1006025
Nusselt number4%5%5%
Jet pressure0.5%0.8%1.36%
Temperature1.2 °C1.2 °C1.2 °C
Mass flow rate0.5%1%3%
Resistance2%2%2%
Voltage0.4%0.4%0.4%
Parameter uncertainties at each Reynolds number for air
Re·(103)1006025
Nusselt number4%5%5%
Jet pressure0.5%0.8%1.36%
Temperature1.2 °C1.2 °C1.2 °C
Mass flow rate0.5%1%3%
Resistance2%2%2%
Voltage0.4%0.4%0.4%
Table 2

CO2 test measured parameters uncertainty

Parameter uncertainties for the range of Reynolds number tested for CO2
MaximumMinimumAverage
Jet pressure2.0%0.5%1.00%
Temperatures1.2 °C1.2 °C1.2 °C
Mass flow rates0.4%0.1%0.2%
Resistance2%2%2%
Voltage0.4%0.4%0.4%
Parameter uncertainties for the range of Reynolds number tested for CO2
MaximumMinimumAverage
Jet pressure2.0%0.5%1.00%
Temperatures1.2 °C1.2 °C1.2 °C
Mass flow rates0.4%0.1%0.2%
Resistance2%2%2%
Voltage0.4%0.4%0.4%
Table 3

Independent variables and dependent variables

αi
Nuh, Dj
hQl, Qs, Dsurf, dT
QldT
QsV, R
αi
Nuh, Dj
hQl, Qs, Dsurf, dT
QldT
QsV, R

Results and Discussion

In order to determine if the results obtained in the rig are acceptable, the experimental setup is first validated with air cases. The correlations used are shown in Table 4, with the coefficients for the required correlations below in Table 5. The experimental Nusselt number is determined from Eq. (8) in the ‘Data Reduction’ section.

Table 4

Air correlations

AuthorReynolds numberH/DR/DNu correlation
Martin [22]2000–400,0002–122.5–7.5Pr0.42Dr11.1D/r1+0.1(HD6)D/rARen
Huang [23]6000–124,0001–100–10Pr0.42Re0.76[a+bH+cH2]
Sagot [24]10,000–30,0002–63–100.0623Re0.8[10.168(RD)+0.008(RD)2](HD)0.037
Goldstein [25]61,000–124,0006–1224|HD7.75|533+44(RD)1.394Re0.76
AuthorReynolds numberH/DR/DNu correlation
Martin [22]2000–400,0002–122.5–7.5Pr0.42Dr11.1D/r1+0.1(HD6)D/rARen
Huang [23]6000–124,0001–100–10Pr0.42Re0.76[a+bH+cH2]
Sagot [24]10,000–30,0002–63–100.0623Re0.8[10.168(RD)+0.008(RD)2](HD)0.037
Goldstein [25]61,000–124,0006–1224|HD7.75|533+44(RD)1.394Re0.76
Table 5

Air correlation coefficients

AuthorCoefficients
Martinfor 2,000 < Re < 30,000, A = 1.36, n = 0.574
for 30,000 < Re < 120,000, A = 0.54, n = 0.667
for 120,000 < Re < 400,000, A = 0.151, n = 0.775
Huanga=104[506+13.3R19.6R2+2.41R39.04×102R4]
b=104[3224.3R+6.53R20.694R3+2.57×102R4]
c=3.85×104[1.147+R]0.0904
AuthorCoefficients
Martinfor 2,000 < Re < 30,000, A = 1.36, n = 0.574
for 30,000 < Re < 120,000, A = 0.54, n = 0.667
for 120,000 < Re < 400,000, A = 0.151, n = 0.775
Huanga=104[506+13.3R19.6R2+2.41R39.04×102R4]
b=104[3224.3R+6.53R20.694R3+2.57×102R4]
c=3.85×104[1.147+R]0.0904

Air Validation.

The validation tests are the benchtop and rig air tests. These tests confirm the heat transfer methodology, data reduction, and data acquisition systems are working properly. After performing the air test and obtaining results matching air correlations, the rig sCO2 test was performed. The experimental conditions for the benchtop, rig air, and sCO2 test are shown below:

Experimental Test Conditions

R/D = 6.35

Air

  • H/D = 2, 3, 6, 8 (Benchtop)

  • H/D = 3, 7.4 (Rig)

  • Reynolds Number = 25×103100×103

  • Target dT 50 °C

sCO2

  • H/D = 2.8

  • Reynolds Number = 82×1031000×103

Target dT = large as possible

Benchtop Test.

The benchtop test is the first validation test. The test is of a free, unconfined impinging jet; thus, confinement does not impact the experimental Nusselt number. The benchtop test consists of four different H/Ds: 2, 3, 6, 8. The Reynolds number range consisted of 25,000, 60,000, and 100,000. Figure 7 shows the Benchtop test for H/D = 2 with the experimental Nusselt number shown as diamonds and the correlations as different colored circles. This is consistent throughout all Nusselt number versus Reynolds numbers plots. The accuracy of the benchtop tests is maintained for H/Ds 3, 6, and 8. Note, Nusselt Number uncertainty (∼5%) is of the order of the marker size for the experimental results in Figs. 7, 8, and 10.

Fig. 7
Air benchtop test results in z/D = 2
Fig. 7
Air benchtop test results in z/D = 2
Close modal

The results demonstrate that the heat transfer methodology, data reduction, and data acquisition systems are appropriate. Though the conditions of these tests are turbulent, Fig. 8 shows that within the H/D range tested, the Nusselt number change remained relatively small, similar to the results shown by Brdlik and Savin, whose tests were conducted under laminar conditions [15].

Fig. 8
Air benchtop test Nu versus z/D, follows a similar trend shown by laminar cases
Fig. 8
Air benchtop test Nu versus z/D, follows a similar trend shown by laminar cases
Close modal

Rig Tests.

The second validation test is performed in the rig. Figure 10 shows the cluster of tests per Reynolds number. The Reynolds number range is the same as the Benchtop test. Seven tests were performed for the H/D = 3 case, and will be discussed in the subsequent section in relation to numerical validation.

RANS-based CFD models were used for all simulations. The SST (Menter) K-Omega model was selected for all cases. The gas was treated as ideal with the coupled flow and energy solvers used. The air validation simulations were run as steady-state, three-dimensional models with properties determined by star-ccm+ [28]. Dynamic viscosity and thermal conductivity are determined by Sutherland's law. Specific heat was calculated by a fourth-degree polynomial with a temperature interval range of 100–1000 K. The fluid domain used for all simulations is shown in Fig. 9. The fluid domain is three-dimensional, axis-symmetric, and is a 1/8th slice. Subsequent sCO2 simulations were performed with two commercial solvers, star-ccm+, and ansysfluent. Both solvers were explored to assess their applicability to the problem of interest, given the unique nature of the flow and thermophysical conditions. Both solvers utilized identical numerical grids, turbulence models, and boundary conditions. coolprop was used for the thermophysical property tables within star-ccm+, and the solver integrated nist tables were used in the ansysfluent simulations.

Fig. 9
Fluid domain used in all simulations
Fig. 9
Fluid domain used in all simulations
Close modal

Figure 10 shows the complete air dataset for z/D = 3, along with CFD cases for validation. The numerical model shows excellent performance in heat transfer prediction, and results fall within the measurement error of the experimental dataset.

Fig. 10
Experimental rig results w/air for z/D = 3 without correlations, max deviation of experimental data from average also shown
Fig. 10
Experimental rig results w/air for z/D = 3 without correlations, max deviation of experimental data from average also shown
Close modal

The mesh independence study is shown in Fig. 11. Here, mesh size is the total number of cells within the simulation, and is varied by changing the mesh base size. Mesh independence is explored for a wide range of numerical grids. For the current problem configuration, independence is reached between 2 and 4 × 106 cells. 6 × 106 cell grids were used for the sCO2 simulations.

Fig. 11
Mesh independence for air and CO2
Fig. 11
Mesh independence for air and CO2
Close modal

sCO2 Results.

In Table 6, starting from test 5, begins the tests that either meet or are close enough to be comparable to the primary conditions, i.e., jet temperature and pressure of 400 °C and 200 bar. The primary condition of a jet temperature of 400 °C is achieved for all the tests in Fig. 12. Only two tests, one at 95 bar and another at 179 bar are not at the intended pressure condition. Observing these two tests in Fig. 12, both test results have little deviation from the trend line. The test that was at 95 bar has a 6% deviation, and the 179 bar test had a 1% deviation.

Fig. 12
sCO2 rig test results z/D = 3 at primary conditions
Fig. 12
sCO2 rig test results z/D = 3 at primary conditions
Close modal
Table 6

sCO2 test conditions with dT

P (bar), T (°C)Reynolds numberdT
1) 117, 15482,93253.4
2) 203, 204256,14715.0
3) 197, 2251,157,3802.6
4) 203, 320638,9933.2
5) 194, 413105,0928.5
6) 95, 412197,39310.6
7) 209, 416249,9847.7
8) 197, 415401,1035.2
9) 179, 413470,1124.9
10) 191, 405583,4434.2
11) 202, 400601,5304.0
P (bar), T (°C)Reynolds numberdT
1) 117, 15482,93253.4
2) 203, 204256,14715.0
3) 197, 2251,157,3802.6
4) 203, 320638,9933.2
5) 194, 413105,0928.5
6) 95, 412197,39310.6
7) 209, 416249,9847.7
8) 197, 415401,1035.2
9) 179, 413470,1124.9
10) 191, 405583,4434.2
11) 202, 400601,5304.0

Additionally, a significant difference is shown between the air-derived correlations and the experimental sCO2 Nusselt numbers. Five numerical cases, shown in Fig. 12 for sCO2, were run using the previously mentioned methodology. Blue cases were performed in Star-CCM+, with green cases being performed in ansysfluent. The simulations' Reynolds numbers are 100,508, 194,768, 249,985, 470,112, and 601,616. Due to HPC access, the higher Reynolds number cases were run in fluent, however, several cases were run at matching Reynolds numbers, and both solvers showed nearly identical performance. As seen, both solvers show excellent agreement with experimental Nusselt numbers throughout the Reynolds number range of interest. The CFD results also corroborate the discrepancy between the experimental results and the air-derived correlations. This lack of agreement between the dataset, CFD, and the correlations shows that the air correlations cannot be used to determine the Nusselt number for sCO2 jet impingement. Additionally, given the differences in thermophysical properties between air and sCO2, experimenters, before experiments, hypothesized air correlations would not properly quantify sCO2 heat transfer. This experiment determined the extent of the difference in heat transfer between air and sCO2. The percent Nusselt number increase from air to CO2 between a Reynolds number 106–107 is shown in Table 7. Additionally, in all figures in the ‘sCO2 Results’ section, the air correlations are extrapolated outside of their working ranges. This is simply for reference of what the air performance could be with respect to sCO2.

Table 7

Increase in Nusselt number from air to CO2

NuCO2NuAirReynolds numberNu % increase
182150100,00022%
352230200,00053%
692390400,00078%
1032550600,00088%
1372710800,00093%
17128701,000,00097%
NuCO2NuAirReynolds numberNu % increase
182150100,00022%
352230200,00053%
692390400,00078%
1032550600,00088%
1372710800,00093%
17128701,000,00097%

An additional concern is whether or not CO2 will behave as a real gas at primary conditions. The compressibility factor or z-factor is 1.01 for CO2 at primary conditions and, thus, will behave similarly to an ideal gas. Contrast this to CO2 near the critical point, where pressure and temperature are 7.38 MPa, and 31.8 °C producing a z-factor of 0.4. For comparison, the z-factor for air at primary conditions is 1.09. Table 8 shows the property differences for air and CO2 at primary conditions at a Reynolds number of 249,984.

Table 8

Property difference in air and CO2 at primary conditions

CO2Air% difference
Density (kg/m3)1599763%
Thermal conductivity (W/(m K))5.47 × 10–25.48 × 10–2–0.24%
Kinematic viscosity (m2/s)2.12 × 10–73.64 × 10–7–42%
Dynamic viscosity (Pa·s)3.4 × 10–53.6 × 10–5–5%
Pr0.760.725%
Specific heat constant pressure (kJ/(kg K))1229111211%
CO2Air% difference
Density (kg/m3)1599763%
Thermal conductivity (W/(m K))5.47 × 10–25.48 × 10–2–0.24%
Kinematic viscosity (m2/s)2.12 × 10–73.64 × 10–7–42%
Dynamic viscosity (Pa·s)3.4 × 10–53.6 × 10–5–5%
Pr0.760.725%
Specific heat constant pressure (kJ/(kg K))1229111211%

Figure 13 shows the four other tests—the first four tests in Table 6—that were performed but did not meet the primary condition of a 400 °C jet temperature. The “Reference Only” experiments were performed to determine whether the trendline for the primary condition tests would continue. The trend line for the primary condition experiments, shown in Table 6 as tests 5–11, is shown in Fig. 12. The average deviation of the trendline in Fig. 13 from Fig. 12 is 11%. Between a Reynolds number of 2 × 105–106, the deviation ranged from 8% and 12%. Table 6 shows relevant test conditions for all the conducted tests.

Fig. 13
Complete sCO2 experimental dataset: reference-only points are shown to evaluate the impact on the trend
Fig. 13
Complete sCO2 experimental dataset: reference-only points are shown to evaluate the impact on the trend
Close modal
Given air correlations cannot be used to quantify sCO2 heat transfer, a correlation that can do so is necessary. Using the test at target conditions and manipulating the Martin correlation, a new correlation can be derived, fitting the data. The adjusted Martin correlation is provided below:
(10)

When Tj400°C,95<P(bar)<210,HD2.8.

The parameter n is determined by setting all other variables at the test condition values conducted in this study. Nusselt number is a range of values; thus, a range of n-values will be provided. Averaging the n-values for the Reynolds numbers between 105,000 and 401,000 provided the n-value for fitting the adjusted Martin for Reynolds numbers between 100,000 and 360,000. Averaging the n-values for the Reynolds numbers ranging between 470,000 and 601,000 provided the n-value for fitting the adjusted Martin for Reynolds numbers between 360,000 and 601,000. The deviation of the sCO2 dataset at the specified Reynolds numbers from the adjusted Martin correlation is shown in Table 9. Figure 14 displays the adjusted Martin correlation and the trendline for the sCO2 target conditions dataset [29].

Fig. 14
Adjusted Martin correlation with sCO2 target data and air correlations
Fig. 14
Adjusted Martin correlation with sCO2 target data and air correlations
Close modal
Table 9

Adjusted Martin correlation deviation from sCO2 target data set

Reynolds numberDeviation from sCO2
105,0923%
197,39312%
249,9843%
401,1037%
470,1121%
583,4436%
601,5309%
Reynolds numberDeviation from sCO2
105,0923%
197,39312%
249,9843%
401,1037%
470,1121%
583,4436%
601,5309%

Figure 15 shows the same data as Fig. 13 but with the uncertainty bands at a 95% confidence interval. As discussed earlier in the ‘Uncertainty Analysis’ section, the uncertainty of the thermocouples is 1.2 °C. The extremely large uncertainty values for Reynolds numbers greater than 600,000 is due to the temperature difference between the jet and the surface being too small to establish a more accurate certainty for the Nusselt number. Thus, as mentioned earlier, data points higher than 600,000 are shown for reference only. Table 10 shows the temperature difference per test and the total percent contribution to the total error. As the temperature difference increases, the total contribution of its error is minimized. Unfortunately, the maximum supply voltage at test conditions is approximately 17 V, given the rating of available mica heating elements. Even with this limiting factor, a number of tests were performed slightly past this value, as shown in Table 11, although this did not greatly improve the temperature difference. Due to the very large heat transfer rates of these exceedingly high-Reynolds number impinging jets, the heating method was unable to maintain a high block-to-jet temperature difference.

Fig. 15
sCO2 data with uncertainty
Fig. 15
sCO2 data with uncertainty
Close modal
Table 10

dT—between the jet and surface—contribution to the total Nu error decreases with increasing dT

P (bar), T (°C)Reynolds numberdT (°C)% dT is of total uncertainty% Nu uncertainty
197, 2251,157,3802.699.8%62%
203, 320638,9933.299.8%64%
202, 400601,5304.099.8%51%
191, 405583,4434.295.5%50%
179, 413470,1124.999.7%43%
197, 415401,1035.299.7%44%
209, 416249,9847.799.4%29%
95, 412197,39310.692.2%21%
203, 204256,14715.095.6%10%
117, 15482,93253.557.8%4%
P (bar), T (°C)Reynolds numberdT (°C)% dT is of total uncertainty% Nu uncertainty
197, 2251,157,3802.699.8%62%
203, 320638,9933.299.8%64%
202, 400601,5304.099.8%51%
191, 405583,4434.295.5%50%
179, 413470,1124.999.7%43%
197, 415401,1035.299.7%44%
209, 416249,9847.799.4%29%
95, 412197,39310.692.2%21%
203, 204256,14715.095.6%10%
117, 15482,93253.557.8%4%
Table 11

Test conducted around maximum voltage

Tests at target conditions
Reynolds number601,531583,444470,113401,104249,985105,092197,393
dT (° C)4.04.24.95.27.78.510.6
Voltage18.9419.0418.5617.0516.9712.5616.73
Tests at target conditions
Reynolds number601,531583,444470,113401,104249,985105,092197,393
dT (° C)4.04.24.95.27.78.510.6
Voltage18.9419.0418.5617.0516.9712.5616.73

Conclusion

The experiments performed in this study investigate the heat transfer capability of supercritical CO2 (sCO2) for single-jet impingement. The heat transfer data collected is the first available for sCO2 impingement studies and design at elevated pressure and temperature. A benchtop test is first performed to validate the heat transfer methodology, data reduction, and data acquisition systems. Then, the second set of tests is performed within the rig to validate the experimental apparatus and the procedures of concern in the benchtop test. The experimental air Nusselt numbers for the benchtop and rig tests show good agreement with the correlation and CFD. The primary conditions for the sCO2 experiments were to maintain a jet temperature of 400 °C at a pressure of 200 bar. However, for a number of tests, these conditions varied due to an assortment of factors. Reynolds number was varied between 80,000 and 600,000 to quantify how the heat transfer would change with increasing flowrate. As expected, the Nusselt number linearly increased with the Reynolds number.

Two commercial CFD solvers, star-ccm+, and ansysfluent were both used to provide pretest predictions and to assess their performance in this unique application. Utilizing CO2 thermophysical property tables, and the SST turbulence model, both solvers were run with identical boundary conditions and meshes. Both solvers showed excellent performance in predicting sCO2 impingement heat transfer in the evaluated Reynolds Number range.

The collected results show that sCO2 jet impingement provides substantially more heat transfer than predicted by air-derived correlations. As experimental air data is used to derive the air correlations; thus, capturing the heat transfer capability of CO2 would be outside of their abilities. Therefore, a sCO2 correlation is derived using the experimental data from the test condition of this study. The sCO2 correlation is obtained by modifying the Martin correlation. The modified correlation is limited to the primary conditions of this study shown in Eq. (10).

Acknowledgment

This paper was prepared as a part of work sponsored by an agency of the United States Government in partnership with Southwest Research Institute, General Electric Global Research Center, 8 Rivers Capital LLC, Air Liquide, the Electric Power Research Institute, the University of Central Florida, and Purdue University. Finally, the authors acknowledge the University of Central Florida Advanced Research Computing Center for providing computational resources and support that have contributed to the results reported herein.1

Funding Data

  • Department of Energy, United States of America (Award No. DE-FE0031929; Funder ID: 10.13039/100000015).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Disclaimer

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Footnotes

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