Response time characterization of Organic Rankine Cycle evaporators for dynamic regime analysis with fluctuating load

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1 Available online at ScienceDirect Energy Procedia 00 (2017) IV International Seminar on ORC Power Systems, ORC September 2017, Milano, Italy Response time characterization of Organic Rankine Cycle evaporators for dynamic regime analysis with fluctuating load Manuel Jiménez-Arreola ab, Christoph Wieland c, Alessandro Romagnoli b* a Energy Research Interdisciplinary Graduate School, Nanyang Technological University, , Singapore b School of Mechanical and Aerospace Engineering, Nanyang Technological University, 63789, Singapore c Institute for Energy Systems, Technische Universität München (TUM), Garching b. München, Germany Abstract The Organic Rankine Cycle (ORC) is one of the main technologies for recovery of low grade heat. However, many of the applications, especially waste heat recovery, present the challenge of thermal power fluctuations of the heat carrier. These fluctuations result in sub-optimal component selection and poor cycle performance at off-design conditions. This study aims to characterize the dynamic behavior of an ORC evaporator under fluctuating load as a method for dynamic behavior optimization at the design stage. This is done by constructing response-time charts that highlight the dependence of the thermal inertia of the evaporator in three main design variables: heat exchanger geometry, heat exchanger wall material and working fluid thermal properties. The characterization can then be used at a particular application to choose the proper design parameters that can reduce some of the variability of the heat input. This is illustrated with a case study from an ORC evaporator recuperating waste heat from a billet reheating furnace The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. Keywords: ORC, WHR, dynamic modelling, transient analysis, time constant, thermal power fluctuations 1. Introduction Low grade heat is present in numerous renewable and low carbon energy sources such as geothermal, solar thermal and waste heat recovery (WHR). In particular, waste heat recovery has the enormous potential to increase the overall * Corresponding author. Tel.: address: a.romagnoli@ntu.edu.sg The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

2 2 Jimenez-Arreola, M./ Energy Procedia 00 (2017) energy efficiency of various energy-intensive sectors, and in this way mitigate carbon emissions, exploit new economic opportunities and reduce energy resources waste [1]. One of the most established and well suited technologies to recover low grade heat is the Organic Rankine Cycle (ORC) due to the lower evaporation temperatures of the organic fluids and its economic advantage at low power [2]. Some of the most promising sectors for WHR such as the heavy industry (i.e. steel manufacturing) and the transport sector (i.e. excess heat from vehicle engines) typically show fluctuations over time of both the thermal power content and temperature of the heat carriers. These fluctuations are intrinsic due to the batch or pulsating nature of some of the processes as well as irregularities of production or driving conditions. Although of a slower nature, other low-grade energy sources such as geothermal and solar-thermal also show daily or seasonal fluctuations. Fluctuations of load present many challenges. The ORC will operate most of the time at off-design condition and will require a suitable control design in order to operate within safe and acceptable ranges and reduce the deviations from design point. Off-design operation due to the fluctuation has a detrimental effect on the overall efficiency of the system and can lead to increased pay-back periods or economical unfeasibility. On the other hand, particularly in automotive applications, direct evaporation (direct heat exchange without an intermediary thermal oil loop between hot source and working fluid) is an attractive option due to constraints of space and mass of the equipment, but the high fluctuations of the load have hindered its application. When working under fluctuating input, ORCs will respond to the changes in load in a certain amount of time according to their thermal inertia. As transients are significantly slower in heat exchangers than the other ORC components [3,4], the system thermal inertia can be well represented by the evaporator response times. Consequently, one way to simplify the analysis of the ORC dynamic behavior is to isolate the evaporator. To some extent, the evaporator will act as a buffer between the thermal load and the downstream components, specifically the expander. Because of the afore-mentioned challenges, it is important to understand and characterize the dynamic behavior of the system in a systematic and simple way in order to design the system and control from not just the steady-state thermodynamic optimization perspective but also from an operational optimization point of view. For instance, it may be preferred to design an evaporator that can effectively filter out some of the large amplitude fluctuations in order to have a more robust system to the variability of the load. One way to characterize the dynamic behavior of the system under a particular load is to compare the response time of the ORC evaporator to the rate of change of the fluctuations and identify different dynamic regimes of response: behavior close to a quasi-steady state, response transient dominated or fluctuations effectively filtered out. The present work aims to characterize the dynamic behavior of ORC evaporators under fluctuating load in a systematic way, by examination of the evaporator response times as a function of the fluid properties and heat exchanger design parameters and compare it to the frequencies of load fluctuation. This can help as a tool for the design of evaporator heat exchanger for optimized dynamic operation. Nomenclature Γ Dynamic regime number, - Subscripts τ ev Evaporator response time, s w Metal wall (heat exchanger) Τ load Characteristic period of load fluctuation, s f Working fluid D Diameter, m avg Average value L Length, m sat Saturation state CapR Capacity ratio, dimensionless parameter, - l Sub-cooled liquid state Ja lv Jakob number, dimensionless parameter, - v Super-heated vapor state ρ Density, kg/m 3 C Specific heat capacity, solid, J/(kg K) Acronyms T Temperature, K WHR Waste heat recovery H vap Spec. enthalpy of vaporization, J/kg ORC Organic Rankine Cycle Specific heat capacity, working fluid, J/(kg K) C p

3 Jimenez-Arreola, M./ Energy Procedia 00 (2017) Fluctuating thermal load and evaporator dynamic regime number For the sake of simplicity a fluctuating thermal power load can be described as a sinusoidal with a certain frequency and amplitude of oscillation. This approach can be extended in the case of real irregular load profiles by performing Fourier analysis to extract the main frequency components of the profile. In the case of an ORC once-through evaporator, because of a certain thermal inertia the changes of the thermal power will not be instantaneously reflected in the state of the working fluid in the evaporator. This transient time is due to the non-negligible heat capacity of the heat exchanger wall as well as the heat transfer characteristics dependent on the flow regime and fluid properties. For a simplified sinusoidal profile according to the frequency of fluctuation and the thermal inertia of the evaporator, the response state of the fluid at the outlet of the evaporator (enthalpy gained by the fluid), will not follow the whole amplitude of fluctuation unless the changes are slow enough. A dynamic regime number Γ, can be defined as: Γ = τ ev Τ load (1) Where, τ ev is a characteristic response time of the evaporator, and Τ load is the period of fluctuation of the load (i.e. a half-way period of a sinusoidal or the pulse time of a pulse-like profile). The magnitude of this number will give us an indication of the percentage of the load amplitude that the evaporator can follow due to its intrinsic inertia. Three different extreme cases can be identified and will be called dynamic regimes. Quasi-steady. (Figure 1a). The response reaches almost the full amplitude of variation, with a certain time lag. Transient (Figure 1b). The response reaches a significant amplitude change but does not reach the full amplitude of the load. The response is dominated by transients. Quasi-constant (Figure 1c). The amplitude of response does not change significantly. It stays approximately constant in an average value (or trend) of the fluctuation. (a) (b) (c) Figure 1: Dynamic regimes according to thermal inertia and load frequency: a) Quasi-steady, b) Transient, c) Quasi-constant 3. Response time characterization of ORC evaporator The response times of ORC evaporator depend on several parameters. However, the objective of this work is to have an approach showing in a more systematic and intuitive way the dependence of the thermal inertia of the ORC evaporator in three main areas of design: geometry, wall material and fluid thermal characteristics.

4 4 Jimenez-Arreola, M./ Energy Procedia 00 (2017) Methodology and model Phase change phenomena in heat exchangers is a highly non-linear phenomena and so finding a time constant for the response time of ORC evaporators in an analytical way is not practical due to the complexity and non-linearity of the two-phase heat transfer correlations. For this reason, a pragmatic approach to find the characteristic response time of ORC evaporator is proposed. For this characterization, a dynamic model of a heat exchanger is needed. A finite-volume dynamic model of the evaporator has been built in the Modelica language, using ThermoCycle library [5] components and the External Media fluid properties library [6] coupled with CoolProp [7]. The model was simulated in the commercial software Dymola. As a simplification, the model disregards the secondary fluid flow and only considers the working fluid side and the metal wall. It also assumes the evaporator as a double pipe cylindrical exchanger where the fluid flows in the inner tube. It consists of a discretized 1-D fluid flow model of the working fluid side governed by time dependent mass and energy balance differential equations. Pressure losses are neglected. The fluid flow module is connected to a metal wall component that neglects thermal resistance and longitudinal conduction but considers thermal energy capacity. The heat coming from the secondary fluid is only considered as a homogenous heat flux source in the outer part of the metal wall. The heat transfer between the inner part of the wall and the working fluid is calculated based on the Gnielinski heat transfer correlation [8] for the liquid (sub-cooled) and vapor (super-heated) single phases and the Shah correlation [9] for the two-phase region. Having this dynamic model of a simplified ORC evaporator the following approach is followed for the characterization of the response time in the simulation environment. The evaporator simulation starts at time zero at steady state condition with a prescribed degree of super-heating. Then a step change of the homogenous heat flux is applied in the outer part of the heat exchanger wall while keeping all other boundary conditions fixed. The free response of the evaporator is then observed and recorded in the simulation environment. Since the outlet enthalpy is the property more representative of the thermal response of the evaporator it has been chosen as the parameter giving us the response time. The outlet enthalpy will gradually increment asymptotically from the initial steady state to a new steady state value after the transient is over. The time when the outlet enthalpy reaches 95% of the new steady state is defined as the response time τ ev. Figure 2 summarizes the model and dynamic characterization technique Dimensionless parameters Figure 2: Evaporator response time characterization model The thermal inertia or response time of an ORC evaporator depends on various different parameters. However three main aspects that depend on the decision variables of heat exchanger design and fluid selection can be identified: 1) geometry of the heat exchanger, 2) heat exchanger wall material and 3) thermal properties of the working fluid. By lumping some of the model parameters we construct dimensionless numbers effectively representing these three aspects in a generalized way. The proposed groups are as follows:

5 Jimenez-Arreola, M./ Energy Procedia 00 (2017) ) Geometric ratio D/L (Geometry). Defined as the diameter to length ratio of the flow pipe, it is related to the geometry of the evaporator. 2) Capacity Ratio (Wall material). It represents the relative heat capacity of the wall material to a relative heat capacity of the fluid during evaporation. Defined as: CapR = ρ w C w ρ f,avg ( H vap T sat ) (2) Where ρ w and C w are the density and heat capacity of the wall, ρ f,avg is the average density of the fluid in the evaporator, T sat is its saturation temperature and H vap is its enthalpy of vaporization. 3) Jakob number (Fluid thermal state). The ratio of sensible to latent heat gained by the fluid in the evaporator. Defined as: Ja lv = C p,v(t v T sat ) + C p,l (T sat T l ) H vap (3) Where C p,v and C p,l are the specific heat capacities of the fluid at vapor and liquid phases respectively and T v and T l are the initial outlet (super-heated vapor) and inlet (sub-cooled liquid) temperatures. Figure 3 shows how these dimensionless groups along with other fixed parameters completely define the dynamic model. The fixed parameters are those that will be defined by the static thermodynamic design requirements (i.e. heat transfer area) and the characteristics of the secondary fluid (temperature and heat flux available). The working fluid and thickness of the wall are also fixed to make the results comparable. In order to make the Jakob number unambiguous the initial super-heated value is also kept fixed. The response time for a given set of parameters can then be obtained by simulating the model with a step input change of the thermal load as described in section 3.1. Figure 3: Summary of parameters and methodology for obtaining one response time (dynamic characterization of ORC evaporator) 3.3. Response time charts In order to illustrate the dependence on the aforementioned decision variables of the evaporator design and fluid properties on the thermal inertia, constant response time curves charts are constructed as function of the three dimensionless parameters. An example of such charts is shown in Figure 4. These charts are created by interpolating several simulation points with varying values of the dimensionless parameters. The corresponding fixed parameters are listed in Table 1 and have been selected as to correspond with realistic tube geometry. The working fluid is selected as it has appropriate properties for the temperature (~ 650 K) and heat content (1-2 MW) encountered in a waste heat application from a billet reheating furnace of a steel industry.

6 6 Jimenez-Arreola, M./ Energy Procedia 00 (2017) (a) (b) Figure 4: Constant response time diagrams as function of geometric ratio D/L and capacity ratio CapR for two different Jakob numbers a) Ja lv =0.400, b) Ja lv = Points labelled A and B correspond to evaporators A and B of section 4 analysis. Table 1. Fixed parameters for response time diagrams of Figure 4. Heat transfer Wall Working fluid area thickness Sat. temperature Heat flux Initial super-heating Hexamethyldisiloxane (MM) 4 m 2 2 mm 450 K 10 kw/m 2 5K These diagrams show how the following three ORC design aspects affect the response time of evaporators. Geometry - D/L. The response time is slower with an increasing value of this group. This is because for a cylindrical pipe with a larger diameter the velocity of the flow decreases (with fixed mass flow) and it results in an overall reduction of the Reynolds number and heat transfer coefficient. Wall material- CapR. The response time increases with an increasing value of the capacity ratio. As the thermal capacity of the wall increases, and more energy is being stored in the wall material, the heat transfer to the fluid is delayed. Fluid thermal state- Ja lv. The response time increases as well with a higher Jakob number. The heat transfer is more effective in the two-phase region than in the one phase region and as the relative length of one phase region is increased (i.e. more sub-cooling), the transient is increased. Working fluids that have smaller latent heat relative to its sensible heat will also have a larger response times. Furthermore the diagram shows the interaction between the groups on the response time. For instance, there is a higher increase of response time with CapR as D/L increases. 4. Dynamic regime analysis: Steel billet reheating furnace waste heat recovery For a given application, in order to understand the dynamic operation and delays due to thermal inertia of a candidate ORC evaporator operating under fluctuating load, we need to compare the response times depicted in the response time charts with the actual fluctuating load. Figure 5a shows a real fluctuating load profile in the case of a billet reheating furnace off-gases. The waste heat can be recovered with an ORC via direct heat transfer. The objective is to show here the potentiality of using the response time diagrams and the dynamic regime number to select the evaporator that achieves a desired dynamic behavior. In order to calculate the dynamic regime number Γ as defined in equation 1, it is required to extract the frequency components of the load in order to calculate the characteristic periods of fluctuation Τ load of the load. This is done by Fourier analysis with the help of the periodogram tool of Matlab as shown in Figure 5b. Figure 5a shows the load with its corresponding main characteristic periods of fluctuation for different zones.

7 Jimenez-Arreola, M./ Energy Procedia 00 (2017) (a) (b) Figure 5: a) Thermal power profile of off-gases from a steel billet reheating furnace during a given period of operation showing dominant characteristic periods of fluctuation, b) Matlab periodogram showing the frequency components of the profile and dominant frequencies. With assistance of the dynamic response charts shown in Figure 4, two different candidate evaporators are chosen corresponding to certain values of D/L, CapR and Ja lv. By comparing the characteristic periods of Figure 5a with the response times in Figure 4a, Evaporator A is chosen so that it has a Γ higher than unity for the high frequency zone and so it falls into a dynamic regime that filters out some of the amplitude of fluctuation in that zone. Evaporator B, on the other hand, is selected so that all Γs are below unity and so it will stay in the quasi-steady regime. The two evaporator details are shown in Table 2 and are labeled as A and B in the response time chart (Figure 4a). According to the response times and the period of fluctuation the dynamic regime numbers Γ in the different zones can be calculated as portrayed in Figure 6. The figure also shows the simulation of the evaporator response (enthalpy increase) carried out in Dymola for both cases. (a) (b) Figure 6:Dynamic regime numbers and simulation results showing the heat input profile and evaporator response (enthalpy increase of the fluid) in the case study of a steel billet reheating furnace for a) Evaporator A, b) Evaporator B Table 2. Evaporator parameters for case study. Fixed parameters as in Table 1. Charact. Wall Evaporator D/L CapR Ja Time τ lv Fluid ev material Sat. temperature Fluid mass flow Heat transf. area (1 tube) Evap. A s Steel MM 450 K 0.25 kg/s 4 m 2 25 Evap. B s Aluminum MM 450 K 0.25 kg/s 4 m 2 25 #of parallel tubes

8 8 Jimenez-Arreola, M./ Energy Procedia 00 (2017) It can be seen for evaporator B that all the Γs are smaller than unity, whereas for evaporator A some Γs are also bellow but some are above unity. This means that evaporator B will follow closely the changes of the load in its whole amplitude, while evaporator A will follow closely only on zones with a dynamic regime less than one, and will reduce some of the amplitude variation for the rest of the zones. In particular Evaporator A, reduces, in average, the amplitude of variation in 48% for the fluctuations with characteristic period Τ load of 274 s. From the operation point of view the evaporation with higher inertia, evaporator A, may be preferred, since it can reduce some of the variations. The reduction of the variations is beneficial since the ORC can then operate closer to a potential design point that will increase the efficiency of the components, namely the expander. It can also make feasible a direct evaporation arrangement. Another advantage is the reduction of component wear and maintenance costs. On other cases, however, although not all of the variability could feasibly be reduced or filtered out, the mitigation of some of the frequency components of the load can lead to a more robust system and to a more effective dynamic control. In such cases the dynamic regime analysis is a simple way to recognize which frequency components of the load can be mitigated by the thermal inertia of a candidate evaporator. This case study shows how, with the knowledge of presumed periods of fluctuation for a given load, an evaporator with a required thermal inertia for operability optimization (i.e. reduce some of the fluctuations) can be designed. For this, the response time diagrams can be used as a tool to choose the best combination of decision variables (geometry, wall material and fluid thermal characteristics). 5. Conclusions The present work shows a method to characterize the dynamic behavior of ORC evaporators by means of response time charts as function of design decision variables. The application of this method on the waste heat profile of a billet reheating furnace shows how such charts can be used as a straightforward tool to choose evaporator parameters that can reduce the amplitude variability on thermal power. In this case the evaporator A reduces the amplitude change by 48% for a frequency of mhz of fluctuation of the source. This results in a dynamically more robust system that can lead to operation closer to a design point and an increase of overall efficiency. There are many simplifications done to the current model such as the assumption of homogenous heat flux instead of the secondary fluid as well as a simplified geometry. These results, therefore, are only representative for a true counter-current heat exchanger in which the secondary fluid has a very high heat capacity, and only an approximation of a more realistic case. The addressing of these shortcomings will be the focus of the future work, as well as the practical application to other real case scenarios and the inclusion of an economic analysis. References [1] US Department of Energy. Waste Heat Recovery: Technology and Opportunities in U.S. Industry [2] Colonna P, Casati E, Trapp C, Mathijssen T, Larjola J, Turunen-Saaresti T, et al. Organic Rankine Cycle Power Systems: From the Concept to Current Technology, Applications, and an Outlook to the Future. J Eng Gas Turbines Power 2015;137: doi: / [3] Wei D, Lu X, Lu Z, Gu J. Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Appl Therm Eng 2008;28: doi: /j.applthermaleng [4] Quoilin S, Aumann R, Grill A, Schuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl Energy 2011;88: doi: /j.apenergy [5] Quoilin S, Desideri A, Wronski J, Bell I, Lemort V. ThermoCycle: A Modelica library for the simulation of thermodynamic systems. Proc 10th Int Model Conf 2014: doi: /ecp [6] Casella F, Richter C. ExternalMedia: A Library for Easy Re-Use of External Fluid Property Code in Modelica. Proc 6th Int Model Conf 2008: [7] Bell IH, Wronski J, Quoilin S, Lemort V. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolprop. Ind Eng Chem Res 2014;53: doi: /ie [8] Gnielinksi V. Forced convection ducts. Heat Exch. Des. Handb., Washington, D.C.: Ed. Hemisphere; 1983, p [9] Shah MM. Chart Correlation for Saturated Boiling Heat Transfer: Equations and Further Study. ASHRAE Trans 1982;88: