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Imece2013-64947 Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition IMECE 2013 November 15-21, 2013, San Diego, CA, USA IMECE2013-64947 ISOBARIC, ISOCHORIC AND SUPERCRITICAL THERMAL ENERGY STORAGE IN R134a Benjamin I. Furst Adrienne S. Lavine Mechanical and Aerospace Engineering Dept. Mechanical and Aerospace Engineering Dept. University of California, Los Angeles University of California, Los Angeles Los Angeles, CA,USA Los Angeles, CA,USA Reza Baghaei Lakeh Richard E. Wirz Mechanical and Aerospace Engineering Dept. Mechanical and Aerospace Engineering Dept. University of California, Los Angeles University of California, Los Angeles Los Angeles, CA,USA Los Angeles, CA,USA ABSTRACT e enthalpy for CPTES or internal energy for CVTES The effective thermal energy density of R134a subjected to (kJ kg-1) an isobaric or isochoric process is determined and evaluated in the two-phase and supercritical regimes. The results are h enthalpy (kJ kg-1) qualitatively extended to other fluids via the principle of -1 corresponding states. It is shown that substantial increases in hfg enthalpy of vaporization (kJ kg ) volumetric energy density can be realized in the critical region -1 for isobaric processes. Also, for isobaric processes which utilize ufg,eff effective latent heat for an isochoric process (kJ kg ) the full enthalpy of vaporization at a given pressure, there exists a pressure at which the volumetric energy density is a T temperature (K) maximum. For isochoric processes (supercritical and two- phase), it is found that there is no appreciable increase in u internal energy (kJ kg-1) volumetric energy density over sensible liquid heat storage; the effective specific heat can be enhanced in the two-phase, ∆( ) signifies a change in quantity ( ) isochoric regime, but only with a significant reduction in volumetric energy density. average fluid density (kg m-3) NOMENCLATURE INTRODUCTION The goal of this paper is to explore and evaluate the CPTES constant pressure thermal energy storage Thermal Energy Storage (TES) potential of isobaric and isochoric processes, using R134a as an example fluid. The CVTES constant volume thermal energy storage focus is placed on the energy density that can be obtained in a TES system using these processes. The motivation for -1 -1 investigating isobaric and isochoric processes is twofold. cp specific heat at constant pressure (kJ kg K ) Firstly, by utilizing an isobaric or isochoric process, energy can -1 -1 be stored under the dome in the two-phase regime where the cv specific heat at constant volume (kJ kg K ) latent heat of vaporization is available. Secondly, these -1 -1 processes can both be used to store energy near the critical ceff effective specific heat (kJ kg K ) point, where large enhancements in specific heat have been -3 -1 measured [1]. Both of these regimes (under the dome and in the cvol,eff effective volumetric energy density (kJ m K ) 1 Copyright © 2013 by ASME critical region) have been identified as having potentially high each. For example, in a CVTES system the pressure can energy densities [2], which may offset their disadvantages. increase substantially with temperature, while a CPTES system Isobaric and isochoric TES under the dome and in the would likely require some sort of robust, distensible volume. critical region appears to not have been thoroughly studied in The larger optimization problem has been investigated the literature. In TES reviews, the liquid-vapor phase change is elsewhere for the case of a high temperature (~400°C) CVTES mentioned only in passing (if at all) when discussing latent heat system with encouraging results [7]. Here, the focus is purely TES [3]. This is understandable considering that isobaric on the energy density potential of different thermodynamic processes require possibly impractical changes in volume—as a regimes. fluid changes from liquid to vapor at constant pressure its volume can change by several orders of magnitude. Additionally, the pressure in such a system could be high, depending on where the dome is crossed. In principle isochoric systems have been studied, but not in the same way proposed here. The case often studied in literature is the one where a liquid (e.g. water) is contained in a pressurized vessel in order to enable the liquid to store sensible heat at elevated temperatures without completely vaporizing [4]. In this paper a more general analysis is done to see if the energy density of an isochoric TES system can be increased by using the latent heat of vaporization. The TES characteristics of R134a were investigated using the highly accessible and accurate data from NIST REFPROP [5]. This program facilitated a systematic graphical and numerical evaluation of pertinent thermodynamic data. All Figure 1 – P-v diagram for R134a with isotherms graphs and thermodynamic values in this paper were derived [5]. from NIST REFPROP unless otherwise noted. R134a has a critical temperature, pressure and density of 101°C, 4.06 MPa and 512 kg/m3 respectively. RESULTS The evaluation of isobaric and isochoric TES with a There are a few subtleties involved in quantifying TES. particular fluid (R134a) has been done with the idea that using Generally the quantities of interest are the energy stored per real properties for an actual fluid would elucidate the TES degree temperature change per unit mass or unit volume. potential of these thermodynamic regimes in general, via the Temperature change is not a pertinent parameter for a purely well-established principle of corresponding states, which latent heat process. When there is a change in temperature (∆T) somewhat unifies the thermodynamic behavior of all fluids [6]. involved, it is useful to use an effective specific heat value (ceff) The trends seen for this particular fluid would then qualitatively defined as the change in specific energy (∆e) that occurs over apply to other fluids as well. the change in temperature divided by that change in In a Constant Volume Thermal Energy Storage (CVTES) temperature: or isochoric system, a fixed mass of fluid would be loaded into a fixed volume (container). With the addition of heat, the ∆푒 푘퐽 푐 = [ ] temperature and pressure of the fluid would increase while the 푒푓푓 ∆푇 푘푔 퐾 average density would remain constant and would depend on the initial quantity of mass and container size. Such a system Note that ∆e is enthalpy for a CPTES and internal energy for would follow a vertical line on a P-v diagram, and fluid could CVTES. Another useful quantity is the effective volumetric exist as a liquid, vapor or two-phase mixture (Figure 1). To pass energy density, defined as: through the critical point the fluid needs to be loaded at its critical density. ∆푒 ∙ 휌푚푖푛 푘퐽 In a Constant Pressure Thermal Energy Storage (CPTES) 푐푣표푙,푒푓푓 = [ ] ∆푇 푚3 퐾 or isobaric system, a fixed mass of fluid would be loaded into a distensible volume. As heat was added to the fluid, the where 휌푚푖푛 is the minimum density that occurs in the process-- container would adjust its size such that the pressure would this is appropriate when dealing with CPTES systems where the remain constant. Perhaps the simplest version of such a system volume (and thus average density) changes, as it corresponds to would be the prototypical, vertical piston/cylinder configuration the largest volume of the system. where the pressure exerted on the fluid in the cylinder is due to These quantities facilitate convenient comparisons between the force acting on the piston (its weight and the surrounding TES in different regimes and other materials, but must be used pressure). The piston would be allowed to move and thus with care. The effective values are only valid for the specific accommodate the changes in volume of the fluid while conditions under which they were derived, namely the specified maintaining a constant pressure. Such a system would traverse change in energy and temperature. They should not be a horizontal line on the P-v diagram (Figure 1). extrapolated to use with another ∆T without great care. For The overall optimization and feasibility of both a CPTES example, in a CPTES system an extremely high effective and CVTES system are beyond the scope of this paper, specific heat can be calculated along the critical isobar if ∆T is although there are clearly important implementation issues for made small enough, however this value of ceff is only valid for 2 Copyright © 2013 by ASME the given ∆T and the given enthalpy change, and using a different ∆T with that ceff would not make sense. (See the section on supercritical CPTES). This is emphasized since it contrasts with the familiar case of the specific heat being relatively independent of temperature (e.g. for liquids and solids). CPTES An overview of CPTES in R134a is given by the h-T diagram in Figure 2. This graph suggests that there are 3 main CPTES regions: 1) under the two-phase dome where a large change in enthalpy occurs at a fixed temperature (the enthalpy of vaporization); 2) outside the dome far from the critical region where enthalpy is approximately linearly dependent on temperature; and 3) in the critical region where enthalpy is non- Figure 3 – The enthalpy of vaporization, saturated vapor linearly related to temperature. From a TES perspective the density and volumetric energy density versus pressure for regions of interest are the critical region and under the dome, R134a. where there are relatively large changes in enthalpy over small (or no) changes in temperature. These two regions are discussed SUPERCRITICAL CPTES in more detail below. A CPTES system has the potential to exploit the large increase in cp that occurs near the critical point. Figure 4 shows these spikes in cp for several pressures in the supercritical region. The critical temperature and pressure of R134a are 101°C and 4.06 MPa.
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