Performance Evaluation of the Basic Glaciothermal Engine

This chapter explains the exceptional performance of the basic glaciothermal fluid cycle and provides a detailed parametric analysis in order to optimise operation of the tube-fin condenser and glaciothermal boiler. Device dimensions and overall engine performance curves are generated. The combined results of this analysis determine the site requirements for installing a basic engine.

3.1 Introduction

Numerous parameters affect the performance of the basic glaciothermal engine described in Chapter 2. Ambient environmental conditions, configuration of engine components and operational settings all affect power output and efficiency.

Potential performance of the concept engine is analysed by reviewing the thermodynamic cycle and modelling the different input parameters for each engine component in turn. Performance curves are constructed for engines running both ethane and CO2 and plotted across the full operating

temperature domain. This facilitates subsequent analysis of year-round performance under ambient polar conditions. Critical operating points and engine management under extreme cold are discussed.

3.2 The working fluid cycle

3.2.1 Thermodynamic efficiency of glaciothermal cycles

The basic glaciothermal working fluid cycle achieves very high thermal efficiency relative to the Carnot limit. Absolute thermal efficiency is modest due to the meager temperature dipole between cold air and freezing water, but the amount of heat generated upon freezing of water is substantial (~335 kJ/kg). Thus the power output per litre of seawater feed is considerable – and the water is free.

We employ a variant Rankine cycle that has no superheat stage, and refer to it as a basic glaciothermal cycle, Fig. 3.1. This is equivalent to an Organic Rankine Cycle with no superheat. Operators familiar with the relative thermal efficiencies of geothermal ORC’s might be surprised at the optimistic efficiencies plotted for the basic glaciothermal engine cycle in Fig. 3.2.

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Fig. 3.1. T-S diagram of basic glaciothermal cycle (A-B-C-F-A) compared to an ORC Rankine cycle (A-B-C-D-E-F-A) with 50 °C superheat. Both run ethane: ; TBOIL -5 °C and TCOND -55 °C.

Remarkable overall glaciothermal power efficiencies are due to the following fortuitous circumstances:

1. Boiler MTD’s are very modest (~5 °C) due to latent heat transfer on both sides

2. Condenser MTD’s are also very modest (~5 °C) due to over-sized condensers (affordable because of the premium value of reliable cold climate RAPS’s)

3. Wet expansion of ethane or CO2 in two phase saturated region involves no superheat

4. High speed twin screw expanders (TSE’s) require no gearbox or converter electronics 5. Fixed volume ratios of dual phase TSE’s closely match ethane-CO2 density ratios

6. Extreme conditions (100 °C colder than normal) reduce denominator of Carnot equation

All these factors combine to produce thermal efficiencies relative to Carnot that are better than typical geothermal ORC cycles and much better than superheated steam cycles operating across similar heat source-sink temperature differences. Industry experience holds that standard superheat Rankine Cycles cannot achieve thermal efficiencies higher than 30—40% of Carnot. It is clear from Fig. 3.3 (a) that this is also true for low temperature working fluid cycles. Relative efficiency drops substantially with increasing superheat. Power cycles operating entirely within the two phase saturation dome, however, achieve fluid efficiencies around 90% of Carnot without superheating, Fig. 3.3 (b). Power cycles are also possible that employ quasi-isothermal reheat or heat recuperation,

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but for small scale devices the minor efficiency gains do not justify the added complexity.

Fig. 3.2. Performance curves for nominal basic glaciothermal engine as a function of ambient air temperature for various working fluids (at 70% isentropic efficiency and 80% mechanical to electrical conversion efficiency).

Fig. 3.3. Theoretical performance of natural refrigerant working fluids. Ideal isentropic efficiencies for (a) Rankine cycles of varying superheat, and (b) basic glaciothermal cycles (both _ 𝑎 𝑑 =100%).

3.2.2 Selection of working fluid species

Various physical properties of working fluids affect their ability to absorb and release heat and to generate motive power. Latent heat of vaporisation, heat capacity, density, thermal conductivity, viscosity, surface tension, and saturation pressure range all affect the performance of engine

components in different ways. Characteristic properties may be beneficial in some parts of the engine cycle and detrimental in others. High fluid density aids compression, but hinders power output for

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example. With all the permutations of inter-relating properties and processes it is necessary to plot the total engine performance in order to choose between competing fluids.

In the main region of interest for glaciothermal power generation between -40 and -60 °C the contrast between high and low performing fluids in terms of comparative nett engine thermal efficiency is around 40%, Fig. 3.2. Clearly hydrogen sulphide is very efficient, but may not be appropriate for other reasons, including corrosiveness. Carbon dioxide and ethane share very similar mid-range performance characteristics. A nett engine thermal efficiency of around 10% at an ambient air temperature of -60 °C is exceptional. Operational properties such as thermal stability, non-toxicity, and safe handling lead us to choose either ethane, CO2 or a mixture of both as our preferred working

fluid. Xenon permits very compact condensers but overall engine thermal efficiency is low.

3.3 Parametric analysis

This section explores the parametric relationships that affect the performance of individual heat transfer components. MATLAB device models calculate temperature glide along the full length of boiler and condenser tubes. This provides detailed quantitative estimates of heat and mass flows and permits an in depth analysis of the effects of competing input parameters.

3.3.1 Tube-fin condenser configuration

The tube-fin condenser comprises a condensing film heat source within the condenser tube and a forced convective air flow heat sink through external fins. Key variables affecting condensing film HTC include: condenser tube diameter and spacing, working fluid mass flux, and nominated

condensate outlet temperature gap relative to ambient air. Tube thickness and thermal conductivity are also important, but for this study we only consider copper tubes of proportional thickness.

Variables affecting the air fin HTC include fin spacing and thickness, and condenser tube diameter and spacing. Typical air flow velocities fall within the laminar flow regime so heat transfer is purely by conduction and fan speed has no effect on the HTC within the normal fan working range.

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Condenser tube diameter and spacing

The effect of condenser tube diameter and tube spacing on the heat transfer performance of our tube-fin condenser is depicted in Fig. 3.4. For each given set of input parameters our model calculates the required condenser tube lengths and number of tubes required to achieve the required heat sink capacity. These dimensions are used to estimate the total tonnes of copper needed by the tubes and fins per MW of engine nett power output. Small 3 mm diameter tubing permits the construction of very compact condensers across a range of tube spacings, Fig. 3.4 (a). Larger 12 mm tubing results in bulkier condensers for the same nett engine output, Fig. 3.4 (b). In each case, tube spacing of around 20 mm is optimal for the given 2.0 mm fin spacing.

(a) (b)

Fig. 3.4. Tonnes of copper per MW nett power for (a) 3 and (b) 12 mm condenser tubes versus tube spacing.

A large number of similar plots were constructed to find the most practical tube-fin condenser geometry. 12 mm tubes need much thicker walls to deal with the high pressure working fluid vapor. Although needing less Cu, 3 mm tubes become quite fragile and very many need to be constructed.