2.1 Analysis tools

Gas turbines are complex machines with numerous dependencies between different components. Therefore, engine analysis tools are used. To limit the amount of input parameters needed, the engines are assessed by means of a parametric analysis. Various tools exist for this, and the following two are used: pyCycle and Gasturb.

pyCycle was created as an efficient engine analysis tool to be incorporated into multidisciplinary analysis and optimisation solutions and is based on NASA’s openMDAO framework [Reference Hendricks and Gray24–Reference Gray, Hwang, Martins, Moore and Naylor26]. The determination of the thermodynamic properties of the flow is done using an adaptation of NASA’s Chemical Equilibrium with Applications (CEA) method [Reference Gordon and McBride27–Reference Gray, Chin, Hearn, Hendricks, Lavelle and Martins29]. pyCycle is an open-source code and can thus easily be accessed and modified. The pyCycle models an engine by linking different components after each other and ensuring consistency between them in terms of mass and energy fluxes. This programme design allows the user to build their own architectures.

The other analysis tool used is Gasturb 12 [30], originally developed to automate parametric and performance cycle analyses and find optimal cycle parameters [Reference Kurzke31]. It can also assist in more detailed aspects of the engine, such as preliminary component sizing and mass estimation. The user can select from a number of predetermined engine cycles, which cannot be altered. This means that the SIR cycle cannot be modelled in Gasturb. However, the baseline APPU (a two-spool free power turbine turboshaft engine) is available and can be used to verify the pyCycle model.

Gasturb is also used for the (core) mass estimation. The total mass of the baseline APPU can be calculated by Gasturb. Equation (2) is used to estimate the mass of the SIR APPU. As the conventional parts of the SIR APPU are similar but slightly differently sized, the baseline mass is linearly scaled with the inlet mass flow rate to get the SIR APPU core mass. In order to do this, the mass of the new HEs is added. The determination of HE masses is explained in Subsection 3.3. The mass of the condenser and any additional ducting due to the two separate gas paths have not been included because an approximate method could not be found, and a detailed design is out of scope for this research.

(2) \begin{align} {m_{SIRAPPU}} = \frac{{{W_{SIR}}}}{{{W_{APPU}}}}{m_{APPU}} + {m_{HEs}}\end{align}

In their current state, both tools cannot yet model the SIR cycle. Because pyCycle can be enhanced with custom-built components, it is used for the main analyses. After adding the required components, both the baseline and SIR cycles are modelled and compared. Gasturb is used to verify the correct functioning of the baseline model in pyCycle. Additionally, Gasturb is used to estimate the motor mass.

2.2 Turbomachinery efficiencies

An important aspect of a gas turbine is the efficiency of the components of the turbomachinery. These have a significant impact on the performance of the engine. Therefore, it is important to establish and use the appropriate efficiency. These are influenced by the type of compressor or turbine, the size, the level of technology and the amount of turbine cooling air. To allow for later modifications and determinations of engine parameters, such as pressure ratios, turbine entry temperature (TET) and allowable material operating temperature (AMOT) of the turbines, a method was developed to determine the efficiency based on a few component parameters.

The efficiency of the baseline component was determined based on the corrected mass flow rate on the small side of the component (compressor exit and turbine inlet). For this, data from Snyder and Tong [Reference Snyder and Tong32] was used, which is shown in Fig. 3. This data includes the efficiency discrepancy between axial and centrifugal compressors and blends it into one continuous data set. The ‘Advanced’ technology level is used for the analyses, as the intended EIS is still some years away.

Figure 3.

Component efficiency as a function of corrected mass flow for different technology levels with their respective fitted curves (data from Ref. [Reference Snyder and Tong32]).

This base efficiency is used for compressors, but turbines require the determination of the cooling air requirement and its impact. The required cooling air fraction is determined with a method from Jonssen et al. [Reference Jonsson, Bolland, Bücker and Rost33]. This method requires only the temperature of the coolant, the incoming flow and the AMOT. The latter is set at 1450 K [Reference Yin and Rao3, Reference Yin, Tiemstra and Rao34]. According to Yin and Gangoli Rao [Reference Yin and Rao3], every 1% cooling air fraction lowers the turbine efficiency by 0.6%. These aspects are factored in to obtain the final turbine efficiency. More detailed information on this method and its implementation can be found in Ref. [Reference van Schie23].

2.3 Modelling in pyCycle

In its current publicly available version, pyCycle is not able to model the SIR cycle because it lacks the capability to model liquid water and the phase change, there are no HE and water collection components available, and a modified combustor that is able to inject (partial) steam needs to be implemented. The HRSG, condenser and collector are entirely new components added to pyCycle, and the combustor is an altered version of the original. The nature of pyCycle allows these new components to be linked to an engine of conventional components. This subsection describes the workings inside the new components, as well as the determination of the main HE parameters.

The CEA implementation in pyCycle is able to model water vapour at various pressures and temperatures, but not liquid water and its phase change. The thermodynamic properties of the pure water flow in HRSG, such as enthalpy, latent heat and boiling temperature, are determined using the IAPWS-97IF method [Reference Cooper and Dooley35]. The condensation process in the condenser is governed by the relative humidity method described by Sonntag [Reference Sonntag36], and the latent heat released is determined using the IAPWS-97IF method.

Two key components of the SIR cycle are the heat exchangers: the HRSG and the condenser. Both are envisioned to be counterflow heat exchangers. This means that theoretically, the hot-side outflow can be as cold as the cold-side inflow, and vice versa. The heat transferred is governed by Equation (3):

(3) \begin{align} E = \frac{{{W_h}( {{h_{in,h}} - {h_{out,h}}} )}}{{{Q_{max}}}} = \frac{{{W_c}( {{h_{out,c}} - {h_{in,c}}} )}}{{{Q_{max}}}}\end{align}

where

\begin{align*} \left. {\begin{array}{*{20}{l}}{{Q_h} = {W_h}( {{h_{in,h}} - {h_{h,{T_{in,c}}}}} )}\\{{Q_c} = {W_c}( {{h_{h,{T_{in,h}}}} - {h_{in,c}}} )}\end{array}} \right\}{Q_{max}} = MIN( {{Q_h},{Q_c}} )\end{align*}

Here, $E$ is the effectiveness of the heat exchanger, the fraction of the theoretical maximum heat transfer ${Q_{max}}$ that occurs. $W$ denotes the mass flow rate and $h$ is the specific enthalpy of the flow. The subscripts $h$ and $c$ indicate the hot and cold flow, respectively. The convenience of using the specific enthalpy over a specific heat and temperature is that any variation in specific heat is taken into account, as well as the latent heat of a phase change. The flow parameters on both sides are known, and $E$ is a design parameter set by the user, allowing quantification of the heat transfer rate and subsequently of the outflow parameters.

It is found that for the current HRSG application, there is not sufficient heat transfer to evaporate all the water, meaning that a mixture of water and steam is injected into the combustor, thereby creating the need to add a modified combustor.

The next heat exchanger in the SIR cycle is the condenser. This component further cools down the gas flow such that the water vapour condenses to liquid water, which subsequently can be collected. Liquid hydrogen (LH $_2$ ) fuel is used as the heat sink for this process and is therefore the limiting factor in heat extraction. Hydrogen is assumed to enter the condenser in the liquid state, at 4.00 MPa and 20 K, above the critical pressure of hydrogen. The thermodynamic properties are taken from McCarty et al. [Reference McCarty, Hord and Order37]. The enthalpy difference between 20 K and 300 K is taken, and any variation from 300 K in temperature is approximated using a constant specific heat capacity of 14.50 kJ/kg K.

The final temperature of the exhaust gases is determined iteratively as a consequence of cooling. The amount of water condensed depends on the final temperature, but that temperature depends on the amount of water condensed. The iteration is complete when the following equation is true:

(4) \begin{align} {Q_{h2}} = {Q_{cooling}} + {Q_{condensation}}\end{align}

where ${Q_{h2}}$ is the achievable heat flow rate in hydrogen, and ${Q_{cooling}}$ and ${Q_{condensation}}$ are the heat flow rates attributed to the cooling of the flow and the extraction of latent heat, respectively.

The CEA model as implemented in pyCycle uses a lower temperature limit of 200 K, which is also enforced in the condenser to avoid numerical complications. This puts a limit on ${Q_{cooling}}$ and consequently on ${Q_{h2}}$ . The result is that the heat exchanger effectiveness of the condenser is reduced if there is too much cooling potential in the hydrogen. This would happen if too little exhaust flow is directed into the HE path.

The last component on the HE path is the collector, a component that simply collects the condensed water. The mass flow rate of the gas flow is updated, and an additional outflow is created with the properties of the liquid water. The numerical procedure for the condenser and collector component is shown in Fig. 4.

Figure 4.

Schematic representation of the calculation procedure in the condenser and collector component [Reference van Schie23].

This water flow is pressurised with an extra pump. The power required is calculated using Equation (5):

(5) \begin{align} P = \frac{{{\rm{\Delta }}p \cdot V}}{\eta }\end{align}

where $P$ is the power required in kW, ${\rm{\Delta }}p$ is the pressure increase in Pa, $V$ is the water flow rate in L/s and $\eta $ is efficiency. The power required is reflected in a slight increase in enthalpy.

Another important aspect regarding steam injection in the combustion chamber is the reduction in NO $_x$ emissions. This reduction is a function of the water-to-air ratio (WAR); more steam results in a larger reduction in NO $_x$ . The WAR is the result of the amount of water recovered in the condenser, which is mostly dependent on the SR and TET. This function is determined using data from Xue et al. [Reference Xue, Hu, Nikolaidis and Pilidis38]. They used computational fluid dynamics (CFD) to develop a chemical reactor network that could predict NO $_x$ emissions and used this to investigate the effect of steam injection on NO $_x$ emissions. This model was applied to a kerosene rich-burn quick-quench lean-burn (RQL) combustor. The result is shown in Fig. 5, and Equation (6) is derived from this graph. This equation is valid up to a WAR of 0.06 (6%) or an approximate relative NO $_x$ of 0.2.

(6) \begin{align} relative\_N{O_x} = 1 \cdot {10^6}{x^6} - 6 \cdot {10^5}{x^5} + 1.2 \cdot {10^5}{x^4} - 1.26 \cdot {10^4}{x^3} + 7.7 \cdot {10^2}{x^2} - 33.37x + 1\end{align}

where

\begin{align*} x = \frac{{{W_{steam}}}}{{{W_{air}} + {W_{steam}}}}\end{align*}

Figure 5.

Influence of steam dilution on the overall NO $_{\rm{x}}$ emission [Reference Xue, Hu, Nikolaidis and Pilidis38].

However, as mentioned, this research applies to a kerosene RQL combustor and might not be applicable to the current engine being analysed, but in the absence of a better model, the correlation is still used, assuming that the dominant path of NO $_x$ production is still thermal NO $_x$ . However, it should be noted that the combustion characteristics of hydrogen and kerosene are different and therefore the resulting NO $_x$ emissions will also be significantly different [Reference Funke, Beckmann and Abanteriba39]. Therefore, the NO $_x$ reduction estimations carried out using the above-mentioned method are uncertain.

Lastly, appropriate effectiveness, pressure losses and mass estimations must be made for heat exchangers. These three parameters heavily influence each other; for example, greater effectiveness increases pressure loss and mass. Multiphase-flow HEs have not yet been applied to aero engines [Reference Schmitz, Klingels and Kufner18, Reference Kaiser, Schmitz, Ziegler and Klingels19], which means that there is no real-world example to take data. Therefore, a pressure loss value of 5% for each HE is taken from comparative studies [Reference Schmitz, Klingels and Kufner18, Reference Andriani, Ghezzi, Ingenito and Gamma40]. The value for $E$ is assumed to be similarly 0.8. Using this and the extrapolation of the ‘Oval Tube’ line in Fig. 6 [Reference McDonald, Massardo, Rodgers and Stone41], an HE matrix specific mass of 30 kg/(kg/s) [Reference Andriani, Ghezzi, Ingenito and Gamma40] is determined. Note that this is only the weight of the HE matrix. Additional components, such as connecting tubes, add 25% to this [Reference McDonald and Rodgers42], giving an HE specific mass of 37.5 kg/(kg/s).

Figure 6.

Relations between heat exchanger effectiveness and specific matrix mass [Reference Funke, Beckmann and Abanteriba39].

Figure 6 Long description

A line graph titled KEY TO TUBULAR RECUPERATORS. The horizontal axis represents recuperator effectiveness ranging from 0.60 to 0.90. The vertical axis represents recuperator matrix specific weight in pounds per pound per second, ranging from 5 to 400. The graph includes three data points labeled 1, 2, and 3, representing different studies and configurations of tubular recuperators. Data point 1 represents a recuperator for a 280 horsepower helicopter turboshaft engine tested in 1967. Data point 2 represents an estimated recuperator weight from a study of a 1000 horsepower helicopter engine done in 1970. Data point 3 represents an estimated recuperator weight from a study of a 500 horsepower helicopter engine done in 1980. The graph shows trends for different types of tubular recuperators, including circular tube, oval tube, plate fin, and primary surface configurations. The effectiveness regime for light weight recuperated propulsion gas turbines ranges from 0.60 to 0.75, while the effectiveness regime for recuperated gas turbines for power generation ranges from 0.80 to 0.90.

2.4 Fuel temperature

A limitation in the implementation of the engine model is that the fuel temperature cannot be specified directly, causing the combustion model to assume zero enthalpy relative to a reference state of 288.15 K at 1 bar (101.3 kPa) for all conditions. However, the energy required to heat H $_2$ from the tank state at 20 K to the combustor inlet temperature of 700 K corresponds to more than 9% of LHV, so the fuel temperature has a significant influence on the fuel consumption of the engine.

To account for the fact that the fuel temperature varies significantly between the different engine versions, an after-the-fact correction was applied to the SFC values obtained for the H $_2$ operations. The correction is shown in Equation (7) and calculates the relative fuel flow needed to inject a given amount of heat into the combustor, taking into account the difference in specific enthalpy ( $h$ ) with respect to the reference state in addition to LHV. Although this calculation neglects second-order effects such as the amount of water in the exhaust, this simplification has little impact since the corrections are on the order of single-digit percentages.

(7) \begin{align} SF{C_{corr}} = SFC\frac{{LH{V_{{H_2}}}}}{{LH{V_{H2}} + {h_{{H_2}}} - {h_{ref}}}}\end{align}

where ${h_{{H_2},condenser\_exit}}$ is the specific enthalpy of the fuel at the exit of the condenser and ${h_{{H_2},ref}}$ is the specific enthalpy of hydrogen at the reference state of 288.15 K and 1 bar. The corrected values are reported separately as SFC $_{corr}$ in the results tables. Interpreting the uncorrected and corrected SFC values requires some explanation. Since the baseline engine does not provide a clear means of heating the fuel prior to injection, the uncorrected SFC value is equivalent to assuming that an unspecified external heat source is used to heat the fuel to the reference temperature. The corrected value, on the other hand, is equivalent to injecting the fuel at the temperature at which it leaves the tank, 20K, which is technically inadvisable. The corrected SFC value for the baseline engine can therefore be interpreted as a worst-case scenario in which part of the fuel is burnt to produce the heat required to condition the remaining fuel for injection at reference temperature. In practice, this is likely unnecessary, since simply allowing the fuel to absorb some ambient heat would notably improve the situation. A practical implementation of the baseline engine would probably achieve an SFC somewhere in between the uncorrected and corrected estimates, depending on the available sources of heat.

In the SIR APPU, the fuel is heated in the condenser, above the reference temperature in cruise and take-off conditions. The corrected SFC value is therefore lower than the uncorrected value and closer to the real value that the engine cycle would achieve. By comparison, the uncorrected SIR value is of little significance, in addition to indicating how large the impact of fuel temperature can be when using H $_2$ as fuel. Because the heat capacity of kerosene is much lower for a given heating value, and the range of fuel temperatures is also significantly more limited, fuel temperature effects were not regarded for kerosene.