report Nr. 00000
Literature Study
Convective heat transfer to fluid operating at a supercritical pressure
Author(s):Catternan Tom
University/department:Ghent University - Department of Flow, Heat and Combustion Mechanics
Address:Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
02/11/2018
Frame
This report is composed in the frame of the IWT SBO-110006 project The Next Generation Organic Rankine Cycles ( funded by the Institute for the Promotion and Innovation by Science and Technology in Flanders (IWT).
The presented work is part of WP4 ‘Development of supercritical technologies’. In particular a literature survey is made in agreement with subtask D4.2. In this report the possible benefits of using SC fluids in ORCs and acceptable ranges of the different operational parameters are presented.
The goal of this report is to communicate the advantages using supercritical fluids and recent progress in research about convective heat transfer to fluids working at a supercritical pressure towards the research partners and advisory board of the ORCNext project. As such, this work should not be considered a scientific article.
Content
Frame
Content
Chapter 1 Introduction
1.Supercritical state
2.Thermophysical fluid properties
Chapter 2 Forced convection heat transfer in supercritical fluids
1.Introduction
2.Literature review
3.Review of a selected group of experimental studies
4.Data presentation [4]
4.1Description in terms of local conditions only
4.2Presentation in terms of a heat transfer coefficient
4.3Presentation in terms of dimensionless groups
5.General characteristics for supercritical heat transfer – Heat transfer regimes
5.1Heat transfer enhancement
5.2Heat transfer deterioration
5.3Influence of the heat flux
5.4Influence of the mass flux
5.5Influence of the direction of flow
5.6Influence of the diameter of the pipe
5.7Influence of buoyancy
6.Summary and future experimental work
Chapter 3 Correlations for forced convection supercritical heat transfer
1.Introduction
2.Correlations
3.Conclusion
References
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Literature Study -Convective heat transfer to fluid operating at a supercritical pressure
Report no. 00000
Chapter 1
Introduction
Investigation of the heat transfer process and heat transfer coefficients are of major importance as it reflects to the efficiency and the cost of the heat exchanger design. The sizing of heat exchangers for supercritical fluid parameters with existing models for subcritical parameters can lead to inaccurate results and false conclusions.
Compared to a subcritical organic Rankine cycle, the temperature profiles of the heat source and the supercritical organic working fluid are closer to each other, resulting in a smaller logarithmic temperature difference (LMTD) and so a lower heat exchanger thermal efficiency is expected. In order to achieve the same efficiency, a much larger heat exchanger surface is needed. So, it is very important to study the relatively unknown heat transfer mechanisms around the critical point to improve the heat exchanger surface and the design algorithms.
Studies concerning heat transfer to supercritical fluids have been widely investigated since the 1950’s and have been practically used in the field of fossil-fired power plants, where supercritical water is used in steam generators to increase the thermal efficiency. At the beginning of the 1960s, the use of supercritical fluids as coolant in nuclear reactors has been broadly studied in the USA and the former USSR. This idea regained potential in the 1990s when the SCWRs (Supercritical Water Reactor) as the next generation nuclear reactors were developed. Superconductivity effects are achieved by cooling the conductor with fluids that are close to their critical points. Rockets and military aircraft are cooled using fuel at supercritical pressure as an on-board coolant. Highly charged machine elements such as gas turbine blades, supercomputer elements, magnets and power transmission cables are cooled with supercritical fluids.
The fluids used in all studies dealing with heat transfer and hydraulic resistance are water, carbon dioxide and cryogens like hydrogen and helium, and this almost only in circular tubes. Beside these commonly used fluids, there were also some experiments using liquefied gases (air, argon, hydrogen, nitrogen, nitrogen tetraoxide, oxygen, and sulphur hexafluoride), alcohols (ethanol and methanol), hydrocarbons (n-heptane, n-hexane, di-isopropyl-cyclohexane, n-octane, isobutane, isopentane, and n-pentane), aromatic hydrocarbons (benzene, toluene, and poly-methyl-phenyl-siloxane), hydrocarbon coolants (kerosene, TS-1, RG-1, and jet propulsion fuels RT and T-6) and refrigerants [1]. Only a few studies were done in annuli, rectangular channels and bundles.
Heat transfer experiments are complex due to the extreme variation of the thermo-physical properties with temperature, with as a result that theoretical and empirical models become useless. Also difficulties occur concerning high operating pressures, high compressibility which makes the density sensitive to relatively small pressure variations and the high specific heat which can prevent the achievement of a thermal equilibrium.
1.Supercritical state
A supercritical fluid is a fluid at pressures and temperatures that are higher than the thermodynamic critical values. A fluid that is at a pressure above the critical pressure, but at a temperature below the critical temperature is also known as a “compressed fluid”. Mostly, the term “supercritical fluid” refers to both a supercritical fluid and a compressed fluid, which is also the case in this literature study (Figure 1).
Figure 1: Different fluid phases in p,T-diagram.
The critical point can be defined as the pressure and temperature at which no distinction between the liquid and the vapour phase of a fluid can be made (point c in Figure 1 and Figure 2). The supercritical state then can be defined as the region in which the fluid pressure is slightly above this critical value. The critical point is characterized by the state parameters Tcrit, Vcrit, and pcrit, which have unique values for each pure substance and must be determined experimentally. As there is no liquid-vapour phase transition, a critical heat flux[1] or dry-out does not occur. A decline in heat transfer does occur, but only in a limited range of parameters, also known as heat transfer deterioration. This is a steady deterioration and does not result in a drastic drop in heat transfer compared with the dry-out phenomenon.
Figure 2: Isothermal lines in a p,v-diagram
The major difference in behaviour between a subcritical and a supercritical fluid is shown in Figure 2. Below the critical temperature, Tcrit, the variation of pressure and volume along an isotherm shows discontinuities where the isotherm intersects the saturation line. At this line, phase-change occurs at a constant pressure and temperature. Along this isotherm the vapour and liquid fraction is changing from 100% vapour to 100% liquid. At the critical temperature the isotherm has a zero slope at only one point, there where the pressure is equal to the critical pressure. Above the critical temperature, the isotherms have no discontinuities anymore and there is a continuous transition from a liquid-like fluid to a gas-like fluid.
2.Thermophysical fluid properties
One of the challenges in the design process of a supercritical heat exchanger is to determine the value of the overall heat transfer coefficient U as well as the necessary heat exchanger area. As the value of the heat transfer coefficient depends on the thermophysical properties of the working fluid, it is important to study and understand the behaviour of these properties transferring from subcritical to supercritical state.
The thermophysical properties of a fluid going from subcritical to supercritical state are strongly dependent on temperature, especially in the critical and pseudo-critical temperature range where thermodynamic and transport properties show rapid variations [2]. For a supercritical pressure there is a temperature where the specific heat capacity cp rises to a peak and then falls steep. This temperature is the so-called pseudo-critical temperature, Tpc (Figure 3). Below the pseudo-critical temperature, the fluid has liquid-like properties while above, it resembles more to a vapour. As the pressure increases, the pseudo-critical temperature also increases (Figure 4), the maximum value of the specific heat cp becomes smaller and the variations of the other fluid properties are less severe.
When a fluid at supercritical pressure in a turbulent flow is heated from a subcritical to a supercritical temperature, it changes gradually from a liquid to a gaseous state. At positions further away from the critical and pseudo-critical region, the forced convection heat transfer is nearly the same, correlated by the usual single phase correlations.
As a result, the heat transfer coefficient cannot be considered constant through the complete heat transfer process.
Figure 3: The variation of specific volume v, specific heat cp, absolute viscosity η, thermal conductivity λ and specific enthalpy h for water at pressure of 245 bar.
At each pressure, a local maximum of the specific heat capacity occurs. The line connecting the maximum values (in the supercritical pressure range) is called the pseudo-critical line (Figure 4).
Figure 4: Pseudo-critical line of water in a p,T-diagram (left) and specific heat of water at the pseudo-critical line (right)[3].
Besides the specific heat capacity, other thermophysical and transport properties such as the density (), Prandtl number (Pr), the dynamic viscosity () and the thermal conductivity () also vary with the temperature and pressure (Figure 5).
Within a very narrow temperature range near the pseudo-critical line the density and the dynamic viscosity experience a significant drop. The Prandtl number shows the same behaviour as the specific heat capacity cp, having a large peak at the pseudo-critical point.The thermal conductivity λdecreases as the bulktemperature of the fluid rises, showing a local peak near the pseudo-critical point, therefore not at the pseudo-critical point. With temperatures above the pseudo-critical temperature, the thermal conductivity drops very fast.
As mentioned before, as the supercritical pressure increases, the pseudo-critical temperature rises and the variations of the thermophysical properties with the temperature are less severe and the existing theoretical and empirical methods become generally more acceptable. Severe property variations with significant heat transfer effects as a result occur in the pressure region from the critical up to about 1.2 times the critical pressure [4].
The strong dependence of the thermodynamic properties on temperature and pressure leads to different heat transfer regimes.
Figure 5: Variation of density, Prandtl number, dynamic viscosity and thermal conductivity in supercritical water with T and p (pcrit = 22.03 MPa, Tcrit =374°C)[3].
The latest versions of NIST software calculates the thermophysical properties of ammonia, argon, butane, carbon dioxide, ethane, isobutane, methane, nitrogen, oxygen, propane, propylene, refrigerants R-11–14, 22, 23, 32, 41, 113–116, 123–125, 134a, 141b, 142b, 143a, 152a, 218, 227ea, 236ea, 236fa, 245ca, 245fa and RC318, and water within wide ranges of pressures and temperatures.
Chapter 2
Forced convection heat transfer in supercritical fluids
1.Introduction
Forced convection heat transfer measurements in pipes to fluids at supercritical pressure have been made using a wide range of fluids (water, carbon dioxide, nitrogen, hydrogen, helium, ethane, R22 and R134a), with the majority of data for water and carbon dioxide. Carbon dioxide is an easier fluid to handle because of its lower critical temperature and pressure and so most of the experiments in literature are about supercritical CO2. Most of the data obtained for forced convection near the critical point has been obtained for pipes and channels with uniform cross section. In recent years also non-circular sections have been investigated, like triangular and square cross-sections. Mostly a uniform heat flux is used to heat the supercritical fluid.Even with these simplified conditions, the obtained experimental results are quite different even for the same sets of data and each set of data is matched with their own correlations.
2.Literature review
In literature more than one hundred papers are found about heat transfer at supercritical pressures. Several correlations have been proposed, but most of them are limited to a certain parameter range and working fluid.
Several review studies about forced convection heat transfer at supercritical pressure have been written. Petukhov[5] made in 1970 a review of experimental works and correlations for heat transfer and pressure drop for supercritical water and CO2. Jackson and Hall [6][7][8] (1975 and 1979) investigated the heat transfer phenomena at supercritical pressure, compared several correlations with test data and a semi-empirical correlation was proposed to account the effect of buoyancy on the heat transfer at supercritical pressure. Polyakov [9] updated this review in 1991 and added a numerical analysis. The heat transfer mechanism and the trigger of heat transfer deterioration were discussed in his review. In 2000, Kirillov [10] reviewed the researches done in Russia about heat and mass transfer at supercritical parameters of water and a new correlation was discussed. Prioro et al. [1] made a literature survey in 2004, giving an overview of almost all correlations.
Some experimental works carried out for supercritical water and carbon dioxide are summarized inTable 1 with their test conditions, this is not a complete list.
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Literature Study -Convective heat transfer to fluid operating at a supercritical pressure
Report no. 00000
Table 1: Summary of the test condition for supercritical water and CO2.
p (MPa) / G (Mg/m²s) / Q (MW/m²) / D (mm) / L (mm) / L/D / TB (°C) / (°C) / Remarks / SubjectDickinson (1958)[11] / 25,0-32,1 / 2,1-3,4 / 0,88-1,8 / 7,6 / 1600 / - / - / - / - / Heat transfer
Shitsman (1959, 1963) / 22,0-25,0 / 0,3-1,5 / <1,16 / 8 / 1500 / - / =<450 / - / - / Heat transfer, heat transfer deterioration, oscillation
Domin (1963)[12] / 22,0-26,0 / 0,6-5,1 / 0,58-4,5 / 2,0; 4,0 / 1075; 1233 / - / =<450 / - / - / Heat transfer, oscillation
Bishop (1962, 1965)[13] / 22,6-27,5 / 0,68-3,6 / 0,31-3,5 / 2,5-5,1 / - / 30-565 / 294-525 / 16-216 / - / Heat transfer
Swenson (1965)[14] / 22,7-41,3 / 0,2-2,0 / 0,2-2,0 / 9,4 / 1830 / - / 70-575 / 6,0-285 / - / Heat transfer, Heat transfer deterioration
Ackermann (1970)[15] / 22,7-44,1 / 0,135-2,17 / 0,12-1,7 / 9,4-24,4 / - / - / 77-482 / - / - / Heat transfer, pseudo-boiling phenomena
Yamagata (1972)[16] / 22,6-29,4 / 0,31-1,83 / 0,116-0,930 / 7,5; 10,0 / 1500-2000 / - / 230-540 / - / Vertical and horizontal / Heat transfer, Heat transfer deterioration
Griem (1999)[17] / 22,0-27,0 / 0,3-2,5 / 0,20-0,70 / 10-24 / - / - / - / - / - / Heat transfer
Sabersky (1967) [18] / 7.24-7.58-8.27 / - / 0,437 / - / - / - / 24.9- 25.6-40.5 / - / Horizontal / Visualisation, turbulence
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Literature Study -Convective heat transfer to fluid operating at a supercritical pressure
Report no. 00000
3.Review of a selected group of experimental studies
As can be seen, experimental studies have been performed since 50’s. The experiments of Dickinson (1958) [11], Ackermann (1970) [15], Yamagata (1972) [16] and Griem (1995) [17]were mainly related to the design of supercritical pressure fossil power plants. The tube diameter ranges from 7.5 mm up to 24 mm. A good agreement was obtained between the test data of Dickinson [11] and the Dittus-Boelter equation at a wall temperature below 350°C. Large deviation was obtained at a wall temperature between 350°C and 430°C. In both the experiments of Domin (1963) [12] and of Dickinson [11], no heat transfer deterioration was observed, whereas heat transfer deterioration occurs in the tests of Yamagata [16] and of Ackermann [15]. It was shown by Yamagata [16] that at low heat fluxes, heat transfer is enhanced near the pseudo-critical line. Heat transfer deterioration happened at high heat fluxes. Ackermann [15] observed boiling like noise at the onset of heat transfer deterioration, which was, therefore, treated as a similar phenomenon like boiling crisis under sub-critical pressures. The test data indicated that pseudo-critical heat flux (CHF), at which heat transfer deterioration occurs, increases by the increasing pressure, increasing mass flux and decreasing tube diameter.
The experimental works ofBishop (1964)[13] and Swenson (1965) [14]were performed in the frame of designing supercritical light water reactors. In the work of Bishop[13], small diameter tubes were used, whereas in the work of Swenson[14], circular tubes of a larger diameter 9.4 mm were applied. In addition to smooth circular tubes, whistled circular tubes and annular channels were also used by Bishop[13]. Nevertheless, no experimental data in annular channels are available in the open literature. Both tests showed the entrance effect on heat transfer coefficient. In the experiments of Swenson[14], no heat transfer deterioration was observed. Empirical correlations were derived based on the test data achieved.
Many tests were performed in former Soviet Union in supercritical water, carbon dioxide and Oxygen[19] [20]. The phenomenon of heat transfer deterioration was first observed by Shitsman et al. (1963)[19]at low mass fluxes. During the tests pressure pulsation took place, when the bulk temperature approached the pseudo-critical value. Based on the test data, several correlations were developed for predicting heat transfer coefficient, onset of heat transfer deterioration and friction pressure drop.
The main conclusions drawn from the experimental works mentioned above are summarized as follows:
- The experimental studies in the literature covers a large parameter range:
- P: 22.0 – 44.1 MPa
- G: 0.1 – 5.1 Mg/m²s
- Q: 0.0 – 4.5 MW/m²
- D: 2.0 – 32.0 mm
- TB: ≤ 575°C
However, it has to be kept in mind that this parameter matrix is not completely filled with test data. Further check is necessary to find out parameter combination at which no test data are still available.
- Heat transfer deterioration is only observed at low mass fluxes and high heat fluxes with the following temperature condition:
- At low heat fluxes a heat transfer enhancement was obtained as the bulk temperature approaching the pseudo-critical point.
- The experimental works are mainly restricted to circular tube geometry.
- Some special effect has been studies, i.e. entrance effect, channel inserts, flow channel orientation and heat flux distribution.
- Large deviation was obtained between the Dittus-Boelter equation and the test data with the bulk temperature or the wall temperature near the pseudo-critical value.
- Several empirical correlations have been derived based on the test data.
Due to its lower critical pressure (7.4 MPa) and critical temperature (31°C), experiments in supercritical carbon dioxide require much less technical expenditure. However, some results have been well extrapolated to water equivalent conditions. Based on the test data in CO2, Krasnoshchekov (1966)[21] proposed an empirical correlation of heat transfer, which was also successfully applied to heat transfer in supercritical water[6]. Several authors have performed tests with carbon dioxide studying systematically the effect of different parameters on heat transfer [6][8] and on the behaviour of heat transfer deterioration[22].