Numerical optimization of an injection volumetric expander for use in waste heat recovery organic Rankine cycle

Numerical optimization of an injection volumetric expander for use in waste heat recovery organic Rankine cycle

Numerical optimization of an injection volumetric expander for use in waste heat recovery organic Rankine cycle S Declaye, S Quoilin, V Lemort Energy ...

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Numerical optimization of an injection volumetric expander for use in waste heat recovery organic Rankine cycle S Declaye, S Quoilin, V Lemort Energy Systems, University of Liège, Belgium

ABSTRACT Waste heat recovery organic Rankine cycle (ORC) systems allow generating mechanical or electrical power from local low grade heat sources. This paper shows how the power produced by the system can be increased by achieving several evaporating pressure levels and injecting low pressure flow during expansion. A numerical model of the vapour injection expansion is developed and different system configurations are compared. In comparison with a simple configuration of the cycle, vapour injection configuration yields a maximum increase of 16% of the power production. Moreover, the specific power can be increased by 26%, which would largely reduce the specific investment cost of the waste heat recovery system. NOMENCLATURE ‫ܥ‬ሶ cp h M ‫ܯ‬ሶ P ‫ݎ‬௩ T u V v w

Calorific capacity flow Specific heat Specific enthalpy Mass Mass flow rate Pressure Built-in volumetric ratio Temperature Specific intern energy Volume Specific volume Work

Greek symbols ߝ௦ Isentropic efficiency

1

[W/K] [W/(kg-K)] [J/kg] [kg] [kg/s] [bar] [-] [°C] [J/kg] [m³] [m³/kg] [J] [-]

subscript BP Low pressure cd Condenser ev Evaporator exh Exhaust exp Expander HP High pressure hs Heat source inj Injection oh Overheating ph Preheater pp Pump r Refrigerant s swept start start t total

INTRODUCTION

In the case of the traditional steam cycle, several enhancements are introduced in order to increase efficiency, specific power or life of components. In the case of organic Rankine cycle, many enhancements have also been proposed. The simplest one is to add a regenerator between the turbine and the condenser. Several

_________________ © The Authors, 2011

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authors investigated this option using different working fluids and showed that significant efficiency gains can be achieved with dry fluids. For instance, Mago et al. (1) obtain an efficiency improvement of 16% using R113 as working fluid. Woodland et al. (2) proposed to combine the use of a regenerator with a flooded expansion. Several working fluids and flooding media were investigated and a maximum cycle efficiency rise of 24% was found with ammonia as working fluid and water as the flooding media. Robbins et al. (3) studied the use of a binary mixture of CO2 and amyl acetate with separation of the less volatile component before expansion and obtained a maximum thermal efficiency of 14.2%. This paper aims at proposing a cycle enhancement that could yield a significant impact on the power output in waste heat recovery applications without the requirement of adding major components. This solution consists in using several evaporating pressure levels. This is currently used in traditional steam cycles in order to obtain a better match between the temperature profile of the cycle and the heat source and therefore reduce exergetic losses in the boiler. However, this configuration involves multi-stage expansion and therefore requires multiple turbines. In small scale organic Rankine cycles, the requirement of multiple turbines could be avoided by injecting the low pressure vapour during expansion in a volumetric expander. This paper investigates two configurations of a waste heat recovery organic Rankine cycle that have in common the use of two evaporating pressure levels and a vapour injection volumetric expander. 2

CONFIGURATION

The reference configuration (A) is shown in Figure 1. This simple configuration is commonly used in organic Rankine cycle.

Figure 1 : scheme of reference configuration of an organic Rankine cycle (configuration A) The first enhanced configuration (B) is shown in Figure 2. At the pump outlet, the refrigerant is split into two flows and one of them is throttled. The heat source is firstly used to evaporate the high pressure flow and then the remaining heat is used to evaporate the low pressure flow. The high pressure line is connected to the expander inlet while the low pressure flow is injected into the expander during expansion. At the expander outlet, the total flow is condensed by means of the heat sink and the liquid flows back to the pump inlet.

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Figure 2 : scheme of the first enhanced configuration of an organic Rankine cycle (configuration B) The second enhanced configuration (C) is shown in Figure 3. At the pump outlet, the refrigerant is split into two flows and one of them is throttled to an intermediate pressure. The heat source is firstly used to vaporize (form saturated liquid to saturated vapour) the high pressure flow. At the vaporizer exhaust, the heat source flow rate is split into two flows. One of them is used to evaporate the low pressure flow and the second one is dedicated to preheat (from pump outlet conditions to saturated liquid) the high pressure flow. The flow repartition is regulated in order to have the same calorific flow rate in the high pressure preheater. In this case, temperature profile of the heat source and the working fluid in the preheater are parallel and exergy destruction rate in this heat exchanger is the lowest: ,

,

,

,

,

,

Where , ,

is the constant pressure specific heat of the heat source is the constant pressure specific heat of the working fluid. is the mass flow rate of the heat source

, ,

is the mass flow rate of the working fluid

Figure 3 : scheme of the second enhanced configuration (configuration C)

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2.1 Modelling hypotheses Main hypotheses for modelling the pump, the condenser and the evaporators are displayed in Table 1. Table 1: main hypotheses for modelling the pump, the condenser and the evaporators Overheating at evaporator exhaust Pump isentropic efficiency Subcooling at condenser exhaust Condensing temperature Minimum temperature difference in all heat exchangers

0K 0.6 0K 30 °C 7.5 K

The heat source is chosen to be a 0.2 kg/s air flow at 175°C for all simulations. 3

EXPANDER INLET EXERGY FLOW RATE

The main purpose of both enhanced configurations is to reduced exergy destruction rate in the evaporator by reducing the mean temperature difference between heat source and working fluid. The lower the exergy destruction rate in the evaporator the higher the exergy flow rate available at expander inlet.

Exergy flow rate (kW)

Considering the main modelling hypotheses, the only remaining degrees of freedom are the evaporating temperature(s) (i.e evaporating pressure(s)). For each configuration, evaporating temperature(s) are optimized in order to maximize the exergy flow rate at the expander inlet (i.e. at the evaporator(s) outlet). This optimization is performed using the genetic algorithm available under the EES environment (4) for four working fluids (R123, R245fa, HFE7000 and n-pentane). 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Fluid (configuration) Figure 4 : exergy flow rate at expander inlet for three evaporator configurations and four working fluids Figure 4 shows the exergy flow rate at the expander inlet for the three configurations described in section 2 and four working fluids. The following observation can be deduced from this figure:

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• • • •

The highest exergy flow rate is obtained with the configuration “C” regardless of the working fluid. The best fluid remains R245fa whatever the configuration selected. The simple (A) configuration combined with R245fa shows higher exergy flow rate than the arrangement “B” with all other fluids. The configuration “C” with R245fa allows increasing the exergy flow rate by 24% compared to configuration “A” with the same working fluid. With configuration “B” the gain is limited to 4.8%. These gains are linked to the logarithmic mean temperature difference in the heat exchangers: temperature profiles between heat source and refrigerant are better adapted and exergy losses are reduced.

One can conclude that the evaporation under two pressure levels brings a clear reduction of exergy destruction rate in the boiler. In other words, if the isentropic efficiency of the expander remains constant, configuration B and C allow producing more mechanical power from the same heat source. However, since the goal is to use a single expander, the low pressure flow has to be injected during expansion. This injection process could have a significant effect on expander performance. 4

VAPOUR INJECTION EXPANDER

4.1 Model Description In order to predict, the performance of a vapour injection volumetric expander, a model is developed that accounts for injection pressure, injection port position and injection duration. This model is divided into five steps: admission, expansion before injection, injection itself, expansion after injection and exhaust. Pressure drops during admission, injection and exhaust being neglected, the P-V diagram is shown in Figure 5. The values of and depends on the position of , , the injection port while the ratio

(

,

is the built in volumetric ratio of the expander

).

Figure 5 : P-V diagram During admission phase, the suction pocket is filled with fluid flowing from high pressure evaporator while its volume grows form 0 to which is the swept volume of the machine. The work done during this phase is given by:

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The mass captured during this phase is equal to:

Where is the specific volume of the fluid at the high pressure evaporator outlet. Once the suction port is closed, the volume of the pocket starts to decrease. This expansion is supposed to be isentropic and the work done during this phase is given by:

When the volume reaches , the expansion pockets enter in communication , with the injection line. Pressure drops during injection being neglected, the pressure in the pocket instantaneously reaches the pressure of the injection line and this pressure is maintained during the whole injection process. The work produced during this phase is equal to: ,

,

The injected mass is obtained using the first law of thermodynamics between point 3 and 5:

Where is the specific enthalpy of the fluid at low pressure evaporator outlet. When the volume of the pocket reaches , the injection process ends. The , increase of volume then results in a decrease of pressure. This second expansion process is assumed to be isentropic and takes place until the pocket enter in communication with the outlet port. The work done during this phase is given by:

The total work produced during a machine cycle is then equal to

Where

is the exhaust work given by:

4.2 Optimization of the System The model of the expander is coupled to the model of the evaporator in order to obtain a model of the whole system (see Figure 6).

Figure 6

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The simulation model can be used to find evaporating temperatures ( , and ) and injection port position ( ) that maximize the net power produced , , by the system. This optimization is performed using the genetic algorithm available in EES for four working fluids (R245fa, R123, HFE7000 and n-pentane) and five built-in volumetric ratio (3, 4, 6, 8, 10). The most important results are displayed in Table 2. In this figure, it can be observed that: • •





The fluid that shows the maximum net output power is R245fa regardless of the configuration and the built-in volumetric ratio. For low built-in volumetric ratio, the benefit of both enhanced configuration is limited to a few percent. The built-in volume ratio of scroll and screw machines is usually lower than 4 which mean that for both types of expander, the investigated configurations wouldn’t bring a significant improvement. The maximum power increase using configuration C is 16.1% with R123 as the working fluid and a built-in volumetric ratio of 10. This configuration could then be used with machines that show a high built-in volumetric ratio such as piston expanders. Configuration C allows significantly decreasing the swept volume of the expander per unit of power for most of fluids and built-in volumetric ratio. According to Tchanche et al. (5), the cost of the expander is directly proportional to the swept volume and represents an important part of the total installed cost. Table 2: Global results Config. A

Config. B

Config. C

rv,in

Fluid

Wnet

Vs

Wnet

Vs

Wnet

Vs

[-]

[-]

[W]

[cm³]

[W]

[cm³]

[W]

[cm³]

3

4

6

8

10

HFE7000 n-pentane R123 R245fa HFE7000 n-pentane R123 R245fa HFE7000 n-pentane R123 R245fa HFE7000 n-pentane R123 R245fa HFE7000 n-pentane R123 R245fa

2841 2865 2900 2969 3086 3074 3115 3222 3330 3249 3295 3470 3426 3281 3330 3566 3455 3252 3302 3590

76.4 83.3 62.7 38.7 65.9 72.4 55.3 33.4 52.3 58.0 43.2 26.5 43.9 47.9 36.7 22.0 38.0 42.8 31.5 19.1

2841 2865 2903 2969 3086 3085 3138 3222 3337 3329 3389 3492 3457 3442 3505 3624 3517 3492 3562 3666

76.4 83.3 62.9 38.7 65.9 71.8 52.8 33.4 52.8 56.7 44.4 27.2 44.2 48.3 36.4 22.8 38.1 42.2 31.2 18.5

2875 2950 2989 3024 3148 3201 3271 3316 3458 3520 3582 3609 3625 3673 3741 3836 3726 3733 3833 3946

74.1 77.4 56.8 37.6 63.3 77.4 51.3 30.9 48.7 54.6 40.7 30.5 40.3 44.2 34.8 20.6 34.3 44.2 29.8 17.4

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4.3 Injection port position In scroll and screw expanders, the position of the injection port imposes the time when the expansion pockets enter in communication with the injection line. The closer the port is to the exhaust of the machine, the lower the pressure in the pocket before injection. The shape and the area of the injection port influences the duration of injection and therefore the injected mass. The bigger the injection port, the longer the contact with the injection line and the higher the mass injected. In piston machines, injection start and duration are rather imposed by the control of the injection valve. In this case, a late opening of the injection valve leads to the injection of the fluid near the end of expansion process. Moreover, longer the opening of the injection valve, higher the mass flow injected. Figure 7 shows the P-V diagram of expansion for R245fa, a built-in volumetric ratio of 10 in configuration C. In this case the optimum evaporating temperatures are respectively 114.4 and 79.1 °C while the volumes of the expansion pocket at start and end of injection are respectively 43 and 50.4 cm³. It can be observed that the injection port has to be located in such a way that pressures in expansion pocket and injection line are equal at the beginning of injection. Unfortunately, these conditions seem to be difficult to realize in practice since a minimum pressure drop is required to efficiently fill up the expansion pocket. It can be noted that the main shape of P-V diagram is similar for all other fluids, configuration and built-in volumetric ratio combinations and conclusion remains therefore similar. 20 18 16 14

P [bar]

12 10 8 6 4 2 0

2. 0E -4

V [m³]

1. 6E -4

1. 2E -4

8. 0E -5

0. 0

4. 0E -5

E0

-2

Figure 7 : P-V diagram of expansion 5

CONCLUSION

First of all, two enhanced configurations with two pressure levels were compared to the simplest ORC configuration in terms of exergy available at the turbine inlet. This comparison shows that the exergy flow rate at the turbine inlet is increased by 4.8% with one configuration and by 24% with the second one. Second, a model of volumetric expander taking account for injection of the low pressure flow during expansion was developed and integrated into the cycle model. In comparison with a simple configuration of the cycle, vapour injection configuration yields a maximum increase of 16% of the power production for high built-in volumetric ratio machines.

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Last, the specific power can be increased by 26%, which would largely reduce the specific investment cost of the waste heat recovery system. REFERENCE LIST (1) (2)

(3) (4) (5)

J. Mago, M. Chamra, K. Srinivasan, C. Somayaji, An examination of regenerative organic Rankine cycles using dry fluids, Applied Thermal Engineering 28 (2008) 998–1007 B. Woodland, J. Braun, E. Groll, W. Horton, Performance benefits of organic Rankine cycles with flooded expansion and internal regeneration, In proceedings of international refrigeration and air conditioning conference at Purdue, 2010 T. Robbins, S. Garimella, Low-grade waste heat recovery for power producing using an absorption Rankine cycle, In proceedings of international refrigeration and air conditioning conference at Purdue, 2010 Klein S.A., Engineering Equation Solver, F-Chart Software, Middleton, WI, 2010 B. Tchanche, S. Quoilin, S. Declaye, G. Papadakis, V. Lemort, Economic feasibility study of a small scale Organic Rankine Cycle system in waste heat recovery applications, In proceedings of International Conference on efficiency, cost, optimization, simulation and environmental impact of energy systems, 2010

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