An Analytical Study on the Performance and Feasibility of Converting a Combined Gas or Gas Propulsion System to a Combined Gas Turbine–Electric and Steam System for a Type 22 Frigate

Abstract

A Type 22 Broadsword class of frigate uses a combined gas or gas (COGOG) propulsion system that utilizes four different gas turbines, depending on the mode of operation. Its twin ST40M cruise gas turbines are operational most frequently, and an increase in their efficiency would significantly impact fuel usage and ship range. This study evaluates the option to upgrade the cruise gas turbines to a combined gas turbine–electric and steam (COGES) system, which utilizes a steam Rankine cycle to recover energy from the exhaust gases of the gas turbine. An alternative system using hot air is also analyzed for performance comparison. The analysis contains calculations for the energy extraction and dimensions of heat exchangers, for the power extracted from the additional steam or air turbine and for pressure losses of the exhaust gas. Different configurations for the heat exchangers were investigated, as well as various parameters for the steam and hot air. The size and mass of the system were an important aspect of the analysis. It was concluded that an auxiliary system operating at a maximum steam pressure of 20 bar could generate an additional 771 kW of power while adding a mass of 7.4 tons to the frigate. These findings suggest that upgrading to a COGES system could cover the electricity needs of the entire ship and thus reduce the overall fuel consumption, resulting in lower operational costs and less emissions.

1. Introduction

The selection of propulsion systems constitutes a critical aspect within the domain of naval ship design. Historically, these systems have been tasked with meeting the requisite criteria of speed and power output for ship operation. However, contemporary considerations have shifted the focus towards solutions that offer enhanced fuel efficiency. Unlike their commercial counterparts, naval ships are characterized by diverse operational profiles involving a spectrum of speeds and electric loads, thereby complicating efforts to optimize fuel consumption. Consequently, the determination of propulsion system configurations for modern naval ships is contingent upon a set of discernible criteria [1]:

• Ship speed requirements;
• Noise reduction;
• Infrared signatures;
• A wide range of operating conditions;
• Better fuel efficiency;
• Cleaner emissions.

The Type 22 Broadsword class of frigate (Figure 1) was first built for the British Royal Navy. The shipbuilding began in 1984, and the first launch was in April 1986. A total of fourteen frigates were built with their production being divided into three batches. Two of these ships were sold to Romania and are now part of the Romanian Naval Forces [2].

The Type 22 frigate uses a COGOG (combined gas or gas) propulsion system, which consists of two high-efficiency and low-output gas turbines used for cruising speeds and another two high-output gas turbines used for operations that require high speeds [3] (Figure 2). The original ships used two Rolls-Royce Olympus TM3B gas turbines (used for high-speed operations) and two Rolls-Royce Tyne RM1C gas turbines (for cruising) [4]. Each set of turbines can be used independently with the help of a clutch. Since there is no gearbox, it is not possible to run all four turbines at the same time. One reason that smaller turbines are used for cruising is that it is more fuel-efficient to run them at 100% power than to run the bigger turbines at partial power. This system is also used in the Russian Navy’s Slava class cruisers and the Hatsuyuki class destroyers, which are part of the Japanese Maritime Self-Defense Forces and the Royal Netherlands Navy Kortenaer class frigate. Starting in 2003, the ships entered a modernization program [2], which consisted of changing its previous propulsion system with a newer system. The chosen system was the Pratt & Whitney ST40M gas turbine which is derived from the PW150A aviation turboprop gas turbine [4].

A more energy-efficient setup for each COGOG cruise gas turbine are the COGES (combined gas turbine–electric and steam) and COGAS (combined gas and steam) systems. These configurations allow for reclaiming some of the heat energy of the exhaust gases that leave the gas turbine and converting it using a closed steam circuit, similar to what is used inside a thermal power plant. It consists of a boiler that vaporizes the water intake, a turbine that extracts power from the resulting steam and a condenser and a feed pump, to liquify the water and send it through the boiler again, respectively [5,6]. The schematic for this system and its corresponding cycle diagram (a classic Rankine cycle) are shown in Figure 3. In a COGES configuration, the shaft of the steam turbine is connected to an electric generator, which produces an electric current similar to the diesel generators of the ship. Meanwhile, a COGAS configuration directly uses the shaft power produced by the steam turbine to drive an additional propeller, used for additional propulsion.

Ideally, in a Rankine cycle, the boiler raises the temperature of the steam to a superheated state (point 1 in the diagram) such that the pressure drop experienced in the turbine does not produce any liquid water pre-condenser. Otherwise, the formation of water droplets inside the turbine would reduce both its stage efficiency and overall performance, while also accelerating blade erosion [7]. However, in practice, this would require much higher heat extraction from the boiler, and thus real turbines usually expand the steam to a state that is on the saturation curves.

The most common equipment for boiling and condensing water, suitable for high pressures, is a shell and tube heat exchanger, shown in Figure 4. It uses a bundle of small tubes to carry fluid and create a very large contact surface area with a second fluid that passes through the shell. The flow of the shell-side fluid is usually delimited by baffles, which give it a desirable velocity for heat exchange, while also providing structural support and vibration stabilization for the small tubes [8]. For the proper functioning of the heat exchanger in this study, baffles are not needed or taken into consideration. In the case of a COGES/COGAS circuit boiler, the tube-side fluid is water/steam, and the shell-side fluid is the hot exhaust gas coming from the duct, while the condenser utilizes cold sea water in the tubes to liquefy the steam passing through the shell [9]. The latter heat exchanger also contains a hotwell at the bottom, which collects the condensed water and acts as a reservoir for the closed cycle. While these types of devices typically have sizeable weights and volumes, they are suitable for use on large marine vessels, where such parameters are not of immediate concern. Nevertheless, these parameters are analyzed and considered when choosing a balanced heat exchanger design.

This study investigates the conversion of one of the ST40M gas turbines into a COGES arrangement, such that the additional electrical energy generated can be used to power the auxiliary systems on the ship. This way, the diesel generators that traditionally supply that energy would be able to operate at a lower capacity and burn less fuel, thus reducing the overall fuel consumption of the frigate. Such methods and others have previously researched the possibility of further enhancing a ship’s fuel efficiency. For example, switching to another type of fuel like LNG (Liquified Natural Gas) would come with benefits in both the economical and the greenhouse emissions sector [10]. Investigations conducted on multi-nozzle ejectors with inclined nozzles [11] resulted in better fluid mixing, with a higher maximum velocity value, which can lead to better efficiency. Adopting this solution requires a lot of attention due to other critical parameters such as the entrainment coefficient and pressure loss coefficient that vary alongside the inclination angle [11]. Studies conducted by researchers from The Maritime Department at the University of Zadar and the Faculty of Mechanical Engineering and Naval Architecture at the University of Zagreb [12] showed that slow steaming and gasification is another short-term measure for fuel savings and reducing CO₂ emissions.

To evaluate the energy recovery performance of the steam turbine, a comparison is made with a recovery system that runs with hot air. This configuration would be similar to a turboshaft gas turbine, consisting of a compressor, a combustion chamber that is to be replaced by a heat exchanger, a turbine that spins the compressor and a second independent turbine, called a power turbine, which can be connected to a propeller for thrust or an electrical generator. This is an open cycle which would need a separate intake and exhaust for the working fluid (air). The advantage of this setup is that the compressor provides some of the temperature rise needed by the turbines, and thus the heat exchanger can operate at a higher mass flow, eliminating the need for a condenser or a pump.

The energy recovery is evaluated for a range of different pressure values for both steam and hot-air turbines, while also pre-dimensioning the boiler and the condenser in order to obtain an approximate value for the total weight of the system. A possible solution is then chosen based on the recovered energy, the weight and size of the heat exchangers and the induced backpressure. A possible installation configuration will be suggested.

2. Materials and Methods

To determine the power that can be extracted from the ST40M exhaust gas (with its properties fixed at nominal operation, listed in

Table 1. Exhaust gas properties at nominal operation.

Temperature [°C]	Mass Flow [kg/s]	Pressure [bar]
502	10.3	1.05

), some assumptions need to be made about the properties of the other fluids.

2.1. Steam Cycle

Based on the academic literature, the steam condenses in a turbine down to a pressure between 0.03 and 0.08 bar [13]; thus, the condenser was chosen to operate at a saturated fluid temperature of 39 °C and pressure of 0.07 bar. To analyze a range of heat exchanger configurations and calculate efficiencies, the pressure that the feed pump produces is taken at 8 different values between 10 and 70 bar. As the pump would likely only slightly increase the temperature of the saturated water (due to inefficiencies), 40 °C is considered as the boiler water inlet temperature. Considering the mass flow of the exhaust gases in comparison with the study conducted by Muench et al. [14], it was concluded that a superheated vapor temperature of 400 °C is achievable. Following their method, the analysis of the heat exchanger is conducted by splitting it into four distinct regions shown in Figure 5, as follows: economizer, low-quality evaporator, high-quality evaporator and superheater. The characteristic parameters of the heat transfer are separately calculated for each section due to their different properties, in order to determine the necessary total heat transfer area.

The water/steam circuit starts at the inlet of the economizer and ends at the outlet of the superheater. As the water enters the low- and high-quality boiler, it can be observed that the temperature does not increase until the inlet of the superheater. Phase change takes place throughout this stage, and the energy required to transform the whole mass flow into steam is given by the latent heat of the vaporization of water. The split between the LQ and HQ boiler is taken at the point where the vapor fraction reaches 0.7, where heat transfer turns from being predominantly dictated by nucleate boiling to being driven by mist flow.

On the gas side of the heat exchanger, it is recommended to keep the temperatures above the sulfuric acid dew point, in order to avoid serious corrosion problems. Since the standard marine diesel fuel that is used for this type of gas turbine can contain a maximum sulfur content of 1% [15], that limit is taken as 135 °C. The location with the highest risk of reaching this dew point is the water inlet of the economizer, where both the water and the exhaust gases are at their lowest temperatures. There, the parameter that needs to be monitored is the outside wall temperature of the water tubes. This temperature tends to be significantly lower than that of the gas itself due to the high thermal conductivity of the cold water. It is a complex function of flow geometries, fluid thermal parameters and temperatures T1 and T8, but for the purposes of this paper, we proposed a minimum value for T8 of 250 °C to eliminate the possibility of sulfur dioxide formation. The discussed fluid properties are centralized in

Table 2. Working fluid properties at the inlet and outlet of the heat exchanger.

Properties	Water/Steam	Exhaust Gas
Inlet temperature [°C]	40 (liquid)	502
Outlet temperature [°C]	400 (superheated steam)	250
Mass flow [kg/s]	to be determined	10.3
Pressure [bar]	10–70	1.05

.

The required water mass flow can be easily determined by using the heat flux of the exhaust gas, given by its mass flow (${\dot{\mathrm{m}}}_{\mathrm{eg}}$), specific heat capacity (${\mathrm{c}}_{\mathrm{p}}$) and temperature difference through the boiler ($∆\mathrm{T}={\mathrm{T}}_4-{\mathrm{T}}_8$):

$${\dot{\mathrm{Q}}}_{\mathrm{b}}={\dot{\mathrm{m}}}_{\mathrm{eg}}{ \mathrm{c}}_{\mathrm{p}} ∆\mathrm{T}.$$

(1)

It is assumed there are no losses to the environment and the heat flux is fully absorbed by the water/steam. The required mass flow (${\dot{\mathrm{m}}}_{\mathrm{w}}$) can be calculated using a similar formula, while also considering that phase change occurs, dictated by the specific heat of vaporization (${\mathrm{h}}_{\mathrm{fg}}$) and the temperature at which vaporization starts (${\mathrm{T}}_2$), and considering the average heat capacities of the water (${\mathrm{c}}_{\mathrm{p} \mathrm{w}}$) and steam (${\mathrm{c}}_{\mathrm{p} \mathrm{s}}$) in the economizer and superheater, respectively:

$${\dot{\mathrm{m}}}_{\mathrm{w}}={\displaystyle \frac{{\dot{\mathrm{Q}}}_{\mathrm{b}}}{{\mathrm{c}}_{\mathrm{p} \mathrm{w}} ({\mathrm{T}}_2 - {\mathrm{T}}_1)+{\mathrm{h}}_{\mathrm{fg} }+{\mathrm{c}}_{\mathrm{p} \mathrm{s} }({\mathrm{T}}_{3 }-{\mathrm{T}}_2)}} .$$

(2)

For every heat exchanger configuration analyzed, is should be verified that the boiler can operate under the specified conditions: the temperature difference ${\mathrm{T}}_7-{\mathrm{T}}_2$ needs to be above zero at the “pinch point” at the outlet of the economizer, to ensure heat flow between the two fluids.

The power output of the steam turbine is obtained using the Rankine cycle characteristic to the calculated properties. Isentropic expansion is initially assumed for the calculation. The inlet enthalpy (${\mathrm{h}}_1$) and the theoretical outlet enthalpy (${\mathrm{h}}_2$) can thus be determined based on the pressure and temperature at those points. By correcting the theoretical enthalpy drop ($\mathrm{H}={\mathrm{h}}_1-{\mathrm{h}}_2$) with the internal efficiency factor ${\mathsf{\eta }}_{\mathrm{i}}$, which has the usual value of 0.8 for steam turbines, the real internal enthalpy drop (H′) is obtained. This can now be used to calculate the real power extracted by the turbine while taking into account mechanical efficiency ${\mathsf{\eta }}_{\mathrm{mech}}$ caused by small frictional losses:

$$\mathrm{P}={\dot{\mathrm{m}}}_{\mathrm{w}}\mathrm{H}’{ \mathsf{\eta }}_{\mathrm{mech}} .$$

(3)

The real enthalpy of the steam at the outlet of the turbine is determined as follows:

$${\mathrm{h}’}_2={\mathrm{h}}_1-\mathrm{H}’.$$

(4)

After leaving the turbine, the steam needs to be condensed, in order to be recycled through the pump, boiler and the turbine again. As previously mentioned, in real Rankine recuperation cycles, the turbine will partly condense the steam through expansion. The resulting mixture of liquid and gas is characterized by the vapor quality x, defined using the enthalpies of saturated steam (${\mathrm{h}}_{\mathrm{f}}$) and of vaporization (${\mathrm{h}}_{\mathrm{f}\mathrm{g}}$) as follows:

$$\mathrm{x}={\displaystyle \frac{{\mathrm{h}’}_2 - {\mathrm{h}}_{\mathrm{f}}}{{\mathrm{h}}_{\mathrm{fg}}}} .$$

(5)

As a result, the heat exchanger needs to condense the remaining steam, down to the saturated liquid point, which requires energy:

$${\dot{\mathrm{Q}}}_{\mathrm{C}}=\mathrm{x} {\dot{\mathrm{m}}}_{\mathrm{w}}{ \mathrm{h}}_{\mathrm{fg}}.$$

(6)

Assuming a mass flow of cooling sea water, with a fixed tube inlet temperature (${\mathrm{T}}_{\mathrm{sw}-\mathrm{in}}$), its outlet temperature (${\mathrm{T}}_{\mathrm{sw}-\mathrm{out}}$) can also be calculated. The shell-side wet steam mixture will remain at a constant temperature ${\mathrm{T}}_{\mathrm{sat}}$ throughout this whole process (Figure 6). To accommodate the regulations regarding the level of thermal pollution, the outlet temperature of the cooling sea water needs to be limited to 5 °C higher than the intake water temperature [16,17]. According to Tsimplis et al. [18], the average temperature of the Black Sea is around 13.5 °C, which gives a maximum outlet temperature of the cooling water of 18.5 °C. These temperatures set the intake and discharge conditions for the cooling side of the condenser.

2.2. Hot Air Cycle

In the case of the hot air—exhaust gas heat exchanger—it is similarly assumed that the air can only be heated up to 400 °C. In this case, however, the compressor is responsible for part of the air temperature increase. For example, for a compression ratio of 4 and assuming room temperature air at the inlet, the air leaves the compressor at 180 °C. That means that the heat exchanger only needs to provide a temperature increase of around 220 °C. The lower $∆\mathrm{T}$ inside the heat exchanger and the lower ${\mathrm{c}}_{\mathrm{p}}$ of the air allow for a higher mass flow to be heated and circulated through the auxiliary turbine system.

To determine the output of the power turbine in the air cycle, it is first necessary to establish the thermodynamic cycle corresponding to the specific parameters. It is first assumed that the air at the outlet of the gas generator turbine (with pressure ${\mathrm{p}}_1$ and temperature ${\mathrm{T}}_1$) is iso-entropically expanded through the power turbine down to atmospheric pressure (${\mathrm{p}}_0$) according to the following:

$${\mathrm{p}}_1^{1-\mathsf{\gamma }}{ \mathrm{T}}_1^{\mathsf{\gamma }}={\mathrm{p}}_0^{1-\mathsf{\gamma }} {\mathrm{T}}_{\mathrm{is}}^{\mathsf{\gamma }}.$$

(7)

The outlet temperature ${\mathrm{T}}_{\mathrm{i}\mathrm{s}}$ is used to find the real enthalpy difference extracted by the turbine, by considering again the internal efficiency factor ${\mathsf{\eta }}_{\mathrm{i}}$:

$${\mathrm{h}}_{\mathrm{is}}={\mathrm{T}}_{\mathrm{is}} {\mathrm{c}}_{\mathrm{p}},$$

(8)

$$\mathrm{H}=\left({\mathrm{h}}_1-{\mathrm{h}}_{\mathrm{is}}\right){ \mathsf{\eta }}_{\mathrm{i}}.$$

(9)

The mass flow of the hot air and the power output of the turbine were determined in the same way as for the steam turbine. This analytical analysis was performed for a range of pressure ratings between 10 and 70 bar for steam and 2.25 and 4 bar for air. The upper limit of 4 bar for air was chosen because, for higher compression ratios, a two-stage compressor is needed and that implies higher costs and a more complex geometry for the entire assembly.

2.3. Heat Exchanger Dimensioning

The next objective is to determine the approximate weight and size of the equipment that would be needed to convert each gas turbine to a COGES configuration. To that extent, the ε-NTU method described by Shah and Sekulić [19] is used to first calculate the surface areas necessary for heat transfer.

Starting with the boiler, the energy transferred between the fluids is calculated separately in each four-section split (see Figure 5). For the economizer and superheater, that energy is the product of the tube-side mass flow (${\dot{\mathrm{m}}}_{\mathrm{w}}$), temperature difference and the average specific heat capacity of the water or steam, according to Equation (1). Meanwhile, for the vaporization process, the low- and high-quality boiler energies can be calculated, respectively, as

$${\dot{\mathrm{Q}}}_{\mathrm{LQB}}=0.7{\dot{ \mathrm{m}}}_{\mathrm{w}}{ \mathrm{h}}_{\mathrm{fg}} \mathrm{and} {\dot{\mathrm{Q}}}_{\mathrm{HQB}}=0.3{\dot{ \mathrm{m}}}_{\mathrm{w}} {\mathrm{h}}_{\mathrm{fg}}$$

(10)

where each fraction is given by the percentage of steam evaporated. The effectiveness of heat transfer (ε) of each section is then calculated as follows:

$$\mathsf{\epsilon }={\displaystyle \frac{\dot{\mathrm{Q}}}{{\mathrm{C}}_{\min } {\mathsf{\Delta }\mathrm{T}}_{\max }}} .$$

(11)

${\mathrm{C}}_{\min }$ is the lower value from the two rate capacities of the fluids ($\mathrm{C}=\dot{\mathrm{m}}{\mathrm{c}}_{\mathrm{p}}$) and ${\mathsf{\Delta }\mathrm{T}}_{\max }$ is the difference between the maximum temperature of the hot fluid and the minimum temperature of the cold fluid. The rate capacity ratio (CR) is defined as follows:

$$\mathrm{CR}={\displaystyle \frac{{\mathrm{C}}_{\min }}{{\mathrm{C}}_{\max }}} .$$

(12)

In the LQ and HQ boilers, the specific heat capacity of the wet steam is considered infinite, since its temperature does not change; therefore, CR = 0.

The number of transfer units (NTU) is a nondimensional parameter that can be defined based on ε, CR and the heat exchanger flow arrangement. The formula for the NTU is based on a crossflow heat exchanger (single pass), for which the fluid with the higher rate capacity is mixed, while the other is unmixed:

$$\mathrm{NTU}= - \ln \left[1+{\displaystyle \frac{1}{\mathrm{CR}}}\ln \left(1 - \mathrm{CR} \mathsf{\epsilon }\right)\right].$$

(13)

For the boiler section, where the NTU is calculated at the limit CR $\to$ 0, the square bracket becomes 1 − ε. It should be remarked that the chosen boiler configuration is not necessarily a single pass; however, formulas for more complex geometries were tried, and similar results were obtained for the NTU. Once this number is calculated, the value for the heat transfer area (A) is obtained from the following definition:

$$\mathrm{NTU}={\displaystyle \frac{\mathrm{U} \mathrm{A}}{{\mathrm{C}}_{\min }}} ,$$

(14)

where U is the overall heat transfer coefficient. For each section, the value of the area depends on whether the outside value (${\mathrm{U}}_{\mathrm{o}}$) or the inside value (${\mathrm{U}}_{\mathrm{i}}$) of the coefficient is used. In this paper, the outside areas of the tubes (${\mathrm{A}}_{\mathrm{o}}$) are calculated using the shell-side value of the heat transfer coefficients, ${\mathrm{U}}_{\mathrm{o}}$. These values were initially chosen based on empirical data of heat exchangers utilizing the same fluids as this paper, with values between 50 and 100 W/m²K for the boiler sections and 1000 W/m²K for the condenser. More accurate values for ${\mathrm{U}}_{\mathrm{o}}$ were subsequently calculated and utilized, based on the fluid temperatures and boiler areas obtained with the initial values, the method for which is explained in Appendix A. The total transfer area of the boiler is calculated as the sum of the areas for each section. The heat transfer area for the condenser was calculated in a similar manner, though it was taken as only one heat exchanging section.

The mass of the boiler is calculated as the sum of three components: the pipes, the pipe fins and the shell. The arrangement and sizes of the tubes and fins of the heat exchanger must be chosen, in order to calculate the component masses. The configuration CF-9.05-3/4 J(c) from Kays and London [20] was selected, as its dimensions are fitting for the counter-crossflow needed for the boiler, with large enough spacing between the pipes to allow for a high mass flow of hot gas. The metal thickness of the pipes was chosen based on industrial steel pipe schedule ratings, such that the boiler would withstand the chosen inlet pressure, given the diameter of the pipe. These thicknesses range from 2.11 mm for a 10-bar inlet to 2.77 mm for 70 bar [21]. The heat exchanger configuration chosen specifies the ratio of the transfer area of the fins to the total one. This allows us to calculate the pipe transfer area and fin transfer area separately. Multiplying these values with the thickness of the pipes and of the fins (also given in the configuration), respectively, and further by a chosen density of steel, the inside mass of the boiler is calculated. Assuming that the shell and other components of the boiler would make up a third of its total weight, the total mass can be obtained for any chosen pressure. While the configuration of the condenser would, in reality, differ slightly from the one for the boiler, it was assumed that their masses would be proportional to the transfer area. Moreover, the boiler inlet water pressure value has little impact on the condenser transfer area, and thus a fixed condenser mass was determined as suitably accurate for any steam cycle, for a chosen sea water temperature.

A possible installation location for the heat exchanger (explained further in the Conclusions section) and its shape are shown in Figure 7. Assuming a square cross-section of size W × W and a length L, the next step is to determine these lengths.

Before choosing the desired configuration for the boiler, another design aspect to consider is the backpressure added to the exhaust gases. This pressure is a result of losses created by friction, blockages or sudden bends that the gas turbine needs to overcome in order to discharge gases at atmospheric pressure. High backpressure reduces the extraction of energy by the turbine and can cause overheating, mechanical failures and overall reduced gas turbine efficiency [23]. Thus, losses induced by the boiler should be minimized. For the purposes of this paper, a pressure drop lower than 5% is considered acceptable and produces no significant effect on the energy extracted. The percentage pressure drop for the exhaust gas (Δp) can be calculated using the formula given in Kays and London [20]:

$$\mathsf{\Delta }\mathrm{p}={\displaystyle \frac{{\mathrm{G}}^2}{2}} {\displaystyle \frac{{\mathrm{v}}_{\mathrm{in}}}{{\mathrm{p}}_{\mathrm{in}}}}\left[\left(1+{\mathsf{\sigma }}^2\right)\left({\displaystyle \frac{{\mathrm{v}}_{\mathrm{out}}}{{\mathrm{v}}_{\mathrm{in}}}} - 1\right)+\mathrm{f} {\displaystyle \frac{\mathrm{L}}{{\mathrm{r}}_{\mathrm{h}}}}\left({\displaystyle \frac{{\mathrm{v}}_{\mathrm{m}}}{{\mathrm{v}}_{\mathrm{in}}}}\right)\right] ,$$

(15)

where G is the mass flow divided by the free-flow area, v is the specific volume at the inlet (_in), outlet (_out) and the mean value (_m), σ is the ratio of free flow to frontal area, ${\mathrm{r}}_{\mathrm{h}}$ is the mean hydraulic radius of the flow, L is the flow length through the boiler and f is the friction factor. The latter is obtained by using the average Reynolds number of the flow in the specific graph for the heat exchanger configuration, available for CF-9.05-3/4 in reference [14]. The only parameters in Equation (15) that vary with boiler size are G, dependent on the W $\times$ W area, and L. The latter value is tied to W, since the total boiler volume is fixed, determined by the ratio of total transfer area to total volume given by the heat exchanger configuration. As a result, the pressure drop can be calculated for a range of W values, aiming to keep it below 5%.

The lower bound for W was found by making sure that the free-flow area for the exhaust gas should not be reduced throughout the exhaust pipe—the heat exchanger configuration of the gas turbine—which would otherwise create significant backpressure. As these calculations are based on an ST40M turbine, the exhaust pipe diameter is predetermined, which sets a minimum free-flow area for the gas in the boiler, and thus a minimum size of W. It should be noted that, while large values of W give smaller pressure drops, these also result in small L values, which would alter the initial cross-counterflow assumption for the heat exchanger by modifying its length–width proportions. Thus, a balanced W value was selected and presented in the Results section.

For a W value greater than the diameter of the exhaust pipe, the flow path should be expanded using a diffuser, similar to the one illustrated in Figure 8. This is an important feature of the system, as angles 2θ larger than 15° result in flow separation (and thus large pressure losses) [24], but low angles increase the length L needed for the diffuser. Since both its inlet and outlet dimensions are known based on the exhaust and the boiler, the length of the diffuser can be calculated.

3. Results

The data obtained from the analysis of the steam cycle are presented in

Table 3. Steam cycle parameters of interest for different boiler steam pressures.

${\mathbf{p}}_{\mathbf{steam}}$ [bar]	${\dot{\mathbf{m}}}_{\mathbf{w}\mathbf{ater}}$ [kg/s]	${\mathbf{P}}_{\mathbf{steam} \mathbf{turbine}}$ [kW]	${\mathbf{m}}_{\mathbf{boiler}}$ [kg]
10	0.958	692	1820
15	0.966	741	1950
20	0.973	771	2060
25	0.981	795	2340
30	0.988	830	2450
40	1.000	864	2680
50	1.014	884	2930
70	1.040	930	3900

. For the studied range, a closed water/steam circuit operating with a mass flow of approximately 1 kg/s extracts between 692 and 930 kW of additional power from the gas turbine was examined. These are significant results when compared to the 1900 kW that an ST40M gas turbine produces (at 93% capacity) in the cruise mode of operation. This extra power can be converted into electricity using an electrical generator. Depending on the conversion efficiency of the generator, a single COGES system operating at 20 bar should supply enough power to cover the electricity needs of the entire frigate. It should be noted that there are diminishing returns for operating at higher maximum pressures, especially when factoring in the weight of the boiler and the safety concerns of operating at very high pressures. For example, increasing the pressure from 20 to 30 bar results in a boiler mass increase of 18%, with only a 7% increase in power production. As a result, the operating steam pressure of the COGES conversion suggested is 20 bar.

The power comparison of the steam turbine with the hot air turbine can be visualized in Figure 9. As expected, even with the high mass flow of the hot air obtained, of around 12 kg/s compared to 0.973 kg/s of steam, the performance of the gas turbine is inferior to its counterpart. The peak performance obtained is around 306 kW at 3.75 bar. Beyond this pressure, the power output of the turbine is limited, since the compressor would need proportionally greater power to achieve higher compression ratios.

System Weight and Size

The corresponding mass of the 20-bar boiler was calculated to be approximately 2060 kg (Table 3). For this configuration,

Table 4. Configurations and pressure drop values for a 20-bar boiler.

W [m] *	L [m] *	${\mathbf{L}}_{\mathbf{diffuser}}$ [m]	${\mathbf{L}}_{\mathbf{total}}$ [m]	${\mathbf{p}}_{\mathbf{loss}}$ [%]
0.74	2.73	0.66	3.40	10
0.80	2.34	0.89	3.23	6.2
0.90	1.85	1.27	3.12	3.1
1.00	1.50	1.65	3.15	1.6
1.25	0.96	2.60	3.56	0.4
1.50	0.67	3.55	4.22	0.1

* refer to Figure 7b for the labels.

was obtained using the calculation methods described in the previous section, for a range of W values of up to 1.5 m. The smallest value of 0.74 m represents the critical boiler width below which the free-flow area of the exhaust gas is reduced. The value of ${\mathrm{L}}_{\mathrm{total}}$ is the sum of the lengths of the boiler and the diffuser.

Based on the criteria of 5% maximum pressure loss, a steam boiler of 0.9 m width satisfies all requirements and would be a fair design to utilize on a real ST40M gas turbine. At first glance, the 1.5 m width configuration has a much lower loss; however, the proportion of dimensions would break the initial assumption of a cross-counterflow heat exchanger, and thus the result is likely largely inaccurate.

The installation location of the heat exchanger is dependent on the value of ${\mathrm{L}}_{\mathrm{total}}$, which is over 3 m for all the configurations. The constrained horizontal length of the exhaust pipe is 2 m (pictured in Figure 7a) which does not allow for the diffuser–boiler system to be fixed there. However, there is the option to set up the boiler vertically, going into the exhaust funnel of the ship, which is of large enough diameter and length.

In terms of the other components of the auxiliary system, their weights and sizes were taken as fixed. The condenser mass was estimated at around 800 kg. For the steam turbine, manufacturers like Howden (owned by Chart) and Siemens Energy deliver models that have similar characteristics to the needs of such a project, and they can be used as a reference for the size of the system, with examples shown in Figure 10. The BASE steam turbine which is delivered by Howden is designed to deliver between 75 and 1.000 kW, for a steam inlet pressure of up to 40 bar and an inlet temperature of up to 400 °C. This turbine is rated for waste-heat recovery from a gas turbine, with dimensions of 1.5 × 2.5 × 2 m and a total weight of 4500 kg [25]. This setup also includes a generator that converts the shaft power of the steam turbine into electricity, making it a compact option. Siemens Energy also has the D-R RLA/D-R RLVA line of steam turbines which are rated for up to 745 kW [26].

4. Conclusions

Overall, upgrading a 1900 kW naval gas turbine to a COGES configuration proved to produce a significant supply of excess power, while also being a better option than using an auxiliary hot air system. At the chosen operational steam pressure of 20 bar, the steam turbine of a COGES conversion was estimated to produce 771 kW of power. Converted into electrical power, this would be enough to cover the entire electrical load of an operational Type 22 frigate. As a result, while the ship is in cruise mode, a single converted gas turbine could replace the need for diesel generators that conventionally produce electricity on the frigate. This would significantly reduce fuel usage and thus improve the overall fuel efficiency of the ship, lowering operational costs and reducing CO₂ emissions. Nevertheless, the generators are still needed to supply the ship when it is in high-speed mode or whenever the ST40M gas turbines are not operational.

For upgrading one cruise engine, the components would add an approximate additional mass of 7360 kg: 2060 kg for the boiler, 4500 kg for the turbine and generator and 800 kg for the condenser. Components such as pumps, piping, stands and mounts are excluded from this mass calculation. Considering that the original displacement of the frigate is 4900 tons [2], this means a 0.15% mass increase, which would not significantly alter the range of the ship. Upgrading a second cruise engine would likely result in a lower percentage mass increase, as the steam turbine could be shared between the two auxiliary circuits. Such an upgrade could provide the electricity needed for future installations of auxiliary systems of the frigate, such as more performant sonar, radar and weapon systems.

While similar research has been conducted in the past for different ships and gas turbines, this investigation offers a specific solution to lower fuel consumption for operating a naval Pratt & Whitney ST40M and similar gas turbines. This follows the global trend to reduce carbon emissions from fossil fuel engines. The results of this analysis align with those of similar investigations by Muench et al. [14], if accounting for proportionality with the power output of the upgraded gas turbine. Future research could investigate how an increase in the mass of the frigate influences its range and maximum speed both in cruise and high-speed operation, as well as the costs that such an upgrade would necessitate.