2.1 Configuration 1: reference – ram air

The reference thermal management system, irrespective of its installation, features an air inlet for essential mass flow, converting incoming fluid kinetic energy to augment static pressure and minimise losses. A diffuser in the system enlarges the channel cross-section, reducing flow velocity and increasing static pressure, guided by the area ratio. The pressure coefficient of the diffuser is influenced by static pressure and dynamic pressure. Ensuring a half-opening angle between 7 and 14 degrees in diffuser design, as investigated by Refs [Reference Idelcik12, Reference Bräunling13], mitigates separation phenomena near the wall, sustaining efficient pressure increase without compromising system stability. After the diffuser, the air enters the heat exchanger with the air mass flow and air temperature depending on the operating condition, experiencing a heat transfer from the hotter cooling fluid flow with a prescribed inlet temperature and a cooling fluid mass flow that results in the desired exit cooling flow temperature. The cooling fluid mass flow is controlled so that the inlet temperature of the heat exchanger is kept constant. The cold air flow undergoes a temperature rise due to the absorbed heat output. Furthermore, the heated air is expanded to ambient pressure through a variable nozzle. The reference TMS is shown in Fig. 1.

Figure 1.

Ram air-based configuration, which is used as the reference TMS.

2.2 Configuration 2: upstream fan

In the configuration shown in Fig. 2, a fan stage is positioned before the heat exchanger, allowing for reduced flow velocity and influencing entry conditions and pressure losses. This configuration will be called “pushing fan”. The fan is driven by an electric motor to increase the mass flow. Due to the increased pressure and reduced velocity resulting from the fan installed in the TMS, the diffuser in front of the HEX can be made shorter in this configuration. The shortened diffuser is a benefit, but the energy input raises air temperature, diminishing the entry temperature gradient of the heat exchanger. Consequently, higher air mass flow is required for the required heat dissipation. This variant requires higher mass flows and compressor power compared to the prior configuration, where no compressor is installed, resulting in increased heat dissipation by the TMS at constant propulsion power. The larger system, increased TMS mass, and higher aerodynamic drag contribute to an overall higher propulsion power.

Figure 2.

Configuration with an upstream fan, here called pusher fan.

2.3 Configuration 3: downstream fan

The configuration in Fig. 3 introduces a fan stage behind the heat exchanger, here called “pulling fan”. The compressor compensates pressure losses caused by the heat exchanger and enables mass flow adjustments, allowing for higher mass flows at lower flight velocities and anticipating a more compact TMS. Similar to the fanless variant, there is no temperature rise caused by the compressor before entering the heat exchanger, resulting in lower air inlet temperatures and maintaining a significant temperature gradient to the hot fluid side. Significant temperature differences between the fluids reduce mass flow requirements. However, the upstream diffuser must be designed for minimal pressure loss. This requires an extended diffuser with low pressure loss for efficient entry into the heat exchanger. Since there is no fan installed between diffuser and HEX, which reduces the velocity, the diffuser is longer than the upstream fan configuration. Crucially, the fan stage is electrically driven and contributes directly to the overall power requirements of the aircraft. This increases the heat dissipation requirements at constant propulsion power, potentially requiring an increase in overall TMS size.

Figure 3.

Configuration with a downstream fan, here called pulling fan.

2.4 Configuration 4: dual fan

Figure 4 examines a TMS configuration with two compressors. This design includes a front fan to condition the heat exchanger and a rear fan to compensate for pressure drop. The goal is to combine the benefits of the previous configurations while mitigating the negative effects. The first fan reduces the inlet velocity, minimises pressure losses and builds up pressure. However, controlling the temperature rise is critical to maintain a significant temperature gradient. The results of mission and performance calculations will determine whether this configuration, with its increased complexity, has any drawbacks, including the potential effects of its length and the increased control effort required to coordinate the two compressors.

Figure 4.

Configuration with a down- and upstream fan, here called dual fan.

3.1 Multidisciplinary design technique

In order to evaluate a TMS in its entirety, it is not always possible to estimate which operating point has to be chosen as the design point. During the MCL, which is the top of climb, the maximum corrected mass flows are reached, which define the fan cross sections. The ram air configuration has its maximum corrected mass flow during take-off. The maximum heat load may occur at different operating points. The electrical components are sized at the point of maximum power demand. Therefore, a multi-design point approach is applied. Crucial performance variables, for example the nozzle pressure ratio or the maximum corrected mass flow, in the fictitious design point are automatically set accordingly. This ensures that all dimensioning operating points are considered, allowing the integration of any component into any propulsion system model independent of its design point. A loop over all operating conditions is used to determine the maximum heat to be dissipated based on the maximum power required and transferred to the fictitious design point. Together with the component geometry, the TMS is then designed, and all other operating points and disciplines are calculated again.

The investigations are performed using the numerical propulsion simulation software (NPSS), which allows the implementation of the design logic presented here, however, this logic can be applied to any performance tool [14].

3.2 Designing thermal management systems with installed fans

An initial study analyses the effectiveness $\varepsilon $ , which is defined according to Equation (1) and the relative pressure losses in the heat exchanger for different heat exchanger types. It is essential to distinguish effectiveness from efficiency, as effectiveness relates solely to the transferred heat flux $\dot Q$ to the maximum possible heat flux, excluding additional losses such as fluid pressure losses, which can impact the quality of a heat exchanger. Therefore, the optimum design for a heat exchanger is one that minimises pressure losses while maximising efficiency. The use of the smaller capacitance flow ${\dot C_{min}}$ follows from the first law of thermodynamics, since two unequal capacities on the hot and cold sides imply that only the smaller capacitance flow can reach the inlet temperature of the other fluid. To calculate the heat transfer, the epsilon-NTU method is applied using NPSS. Within NPSS a plate offset strip fin heat exchanger can be designed with the correlations described in Refs [Reference Shah15–Reference Schlünder18].

(1) \begin{equation}\varepsilon = \frac{{\dot Q}}{{{{\dot C}_{min}}\left( {{T_{hot,in}} - {T_{cold,in}}} \right)}}\end{equation}

The brief study uses a generic plate heat exchanger with a constant geometry as an example to show that the pressure losses within the heat exchanger rise as the inlet Mach number in the heat exchanger matrix increases. At higher Mach numbers, the flow is more likely to transition from laminar to turbulent. Turbulent flow typically has higher skin friction and viscous effects, contributing to increased pressure losses along the pipes. Therefore, low inlet Mach numbers are set to determine the length of the cooling fluid flow within the heat exchanger.

3.2.1 TMS design

To size the heat exchanger the maximum transferred heat needs to be prescribed. The heat exchanger entry air mass flow is set accordingly. It is assumed that a reasonably low maximum cooling fluid exit temperature also is prescribed, allowing to generate a desired temperature delta to cool the propulsion system components. The air mass flow is defined as the cold flow and the cooling fluid is defined as the hot flow. Here the heat exchanger is assumed as a plate heat exchanger and simplified as a cuboid, see Fig. 5. The no-flow length is defined as the length perpendicular to the hot and cold flow. It is assumed that the ratio of hot-flow length and no-flow length is given, since the modeled heat exchanger is a given industry product and was scaled. The inlet area of the heat exchanger air side is a result of the selected optimal inlet Mach number according to Fig. 6 and the heat exchanger entry conditions. In this study, it was found that the optimal Mach number for this example is around 0.065 regarding effectiveness and pressure loss not taking masses into account. The inlet area of the heat exchanger cooling fluid side is a result of the necessary airflow to transfer the desired heat and the entry conditions (temperature and pressure) of the cooling fluid. The diffuser, which is in front of the heat exchanger, needs to be sized so that the desired heat exchanger entry Mach number is ensured. The cone angle for the diffuser is limited to 12 degrees to avoid excessive pressure losses [Reference Idelcik12, Reference Bräunling13]. The diffuser is designed with the methods described in Ref. [Reference Idelcik12]. Given the cone angle and the diffuser entry conditions the diffuser length is a result. The configurations shown in section 2.0 have one or two fans installed. The task of the fan is to provide enough mass flow at operating points with low flight velocities to ensure enough cooling. The fan pressure ratio is sized to provide a nozzle pressure ratio not lower than 1 plus a safety margin. The relative rotational fan speed is determined with methods described in Ref. [Reference Grieb19]. It is important to notice that the fan pressure ratio and the nozzle pressure ratio are adapted to the specific conditions of the flight envelope by the electric motor. A low fan power is aimed for to minimise size and mass of the fan and electric motor and also overall mission energy. With the help of an electric motor, the fan operating point can be chosen independently within its operational range. Too low fan pressure ratios are prevented by closing the variable nozzle. It is assumed that the electric motor is able to deliver the required power at any operating point.

Figure 5.

Sketch of a plate heat exchanger.

Figure 6.

Effectiveness and relative pressure loss as a function of the heat exchanger inlet Mach number on an exemplary, generic plate heat exchanger with constant geometry. The subtraction of effectiveness and pressure loss is done by subtracting the effectiveness by the relative pressure loss.

3.2.2 Calculation technique

For the design of a TMS with installed fan(s) on an aircraft level, the following design rules are explained in this work in the form of a system of equations with independent and dependent variables. A distinction is made among universal, design and off-design iterations. The universal iteration is defined as an iteration where the input parameter in one operating point is adjusted to the condition in another operating point. A design point is the operating point in which the individual component, e.g. turbomachinery, electric motor, heat exchanger, is sized. In an off-design point, the geometry of the component or entire system is already set and will generally not be changed. In a universal iteration, the maximum heat demand from an operating point is selected for the design process of the heat exchanger. Moreover, the universal iteration is used to adapt the required aircraft thrust and the delivered propulsion system thrust at the same time. The heat exchanger is designed based on the maximum heat to be transferred. In addition, the mass flow of the cooling medium is determined by the maximum output temperature of the cooling flow. The inlet temperature of the cooling medium into the heat exchanger is the temperature of the fluid after it has passed through the components to be cooled. The aim is to ensure that the outlet temperature of the coolant corresponds to the defined target value of the maximum output temperature of the cooling flow. The integrated fan stage needs to operate on its operating line; therefore, the nozzle throat area is adjusted. The fan assures that the nozzle pressure ratio greater one is achieved. In the overall design, there is a balance of power and shaft speed between the electric motor and the fan stage, which are connected via a shaft. The system has now been determined and the design is defined.

The efficiency of the overall system is an input parameter in this study for evaluating the influence of the heat dissipation rate on the overall system. The efficiency is defined as the ratio between the sum of the TMS and propulsion power ( ${P_{TMS}} + {P_{Propulsion}})\;$ and the sum of the power plus the power loss, which is expressed as heat ${Q_{TMS}}$ , see Equation (2).

(2) \begin{equation}{\eta _{overall,\;propulsion}} = \;\frac{{{P_{TMS}} + {P_{Propulsion}}}}{{{P_{TMS}} + {P_{Propulsion}} + {Q_{TMS}}}}\end{equation}

3.2.3 Anti-freeze mechanisms

One fundamental problem with the TMS featuring liquid cooling at high altitudes is the risk of freezing, due to the significantly higher delta temperature across the heat exchanger compared to sea level conditions. To prevent coolant freezing, a novel design approach is proposed. This approach involves installing identical TMS modules in separate nacelles. In the event of a freezing risk, individual TMS modules can be closed and shut off, resulting in a higher cooling fluid temperature in the remaining active modules since the cooling fluid runs through all modules. The following section describes the simulation of this system.

If the cooling medium temperature drops below its freezing point plus a safety margin of 10 Kelvin during the mission, the nozzle can be closed within the fan stage’s allowable operational range to maintain operational stability. Therefore, it is assumed that the fan can operate until a minimum pressure ratio of 1 plus a safety margin, and the nozzle can also operate to a pressure ratio of 1 plus a safety margin. These conditions ensure a secure operation controlled by a variable nozzle geometry.

In the following, a TMS with six nacelles is designed, reducing system size and the absolute mass flow per nacelle. The geometry of the nacelles will be set in the design point where the heat exchanger is sized to the maximum heat per nacelle, which needs to be dissipated. The maximum heat per nacelle is identical for each nacelle. The design procedure is the same as described in section 3.2.1. At operating points where the cooling medium would freeze, individual TMS modules can be shut off. The inlet and nozzle are completely closed by a closing mechanism, allowing the electric motor and fan stage to be switched off. This procedure also allows, for instance, to create a constant temperature condition for batteries during cruise flight. Distributing the TMS in different nacelles and providing sophisticated control of the flaps offers the following advantages: the nacelles can be aerodynamically optimised to reduce drag and increase overall system efficiency. Both the diffusers and heat exchangers are designed for greater effectiveness. The system is highly redundant, improving reliability. This allows for the design of different TMS systems for different operating points, enhancing operational capability. The cooling components are decentralised. The system can operate in both hot and cold conditions and at any operating point, including charging, allowing for fully self-sufficient operation. Preconditioning by ground-based systems is not required. A disadvantage of distributed TMS modules is the complex control of the system as well as possible aerodynamic influences along the wing. Figure 7 shows an example of a generic, distributed thermal management system installed on a wing.

Figure 7.

Illustrative draft of a generic, distributed TMS exemplary installed on a wing.

3.3 System scaling

In considering the effects of the TMS at the aircraft level, it becomes imperative for the aircraft system to compensate for the drag of the TMS and to dynamically adjust to the corresponding alterations in thrust requirements. This adaptive response ensures the continual successful execution of the required transportation task, even in the presence of elevated thrust demands. Within the scope of this investigation, a ‘re-engineered aircraft’ is defined by a constant wing loading and thrust-to-weight ratio while changing the propulsion system. So the aircraft mission task (range, payload, etc.) remains unchanged. As the system weight escalates, the aircraft’s thrust requirement increases, allowing for the exploration and analysis of consequential snowball effects. The determination of the accurate thrust requirement incorporates the influence of the thermal management system’s thrust. This net thrust is calculated as the difference between the gross thrust and the combined dynamic pressure (ram) drag and nacelle drag at the given operational point. The nacelle drag encompasses friction drag, profile pressure drag, and potential spillage drag.

(3) \begin{equation}{F_{net,TMS}} = {F_g} - \;{F_{ram}} - {F_d}\end{equation}

The net thrust of the aircraft is defined as the sum of the propulsion and TMS net thrust.

(4) \begin{equation}{F_{net,\;\;aircraft}} = {F_{net,TMS}} + {F_{net,Propulsion}}\;\end{equation}

If the net thrust of the thermal system is negative, because the thrust generated by the Meredith effect cannot compensate for the drag, then the propulsion system gets heavier, the thrust requirement increases, and the heat to be dissipated also increases. Conversely, if the TMS can generate a positive net thrust, the propulsion will become lighter, and the heat dissipation required will decrease.

The main propulsion system, which is marked with the subscript ‘propulsion’, does not include the TMS, but consists of the main propulsion system only. The thrust-to-weight ratios for the aircraft ${\frac{{Thrust}}{{Weight}}_{aircraft}}\;$ and the main propulsion system ${\frac{{Weight}}{{Thrust}}_{propulsion}}\;$ are assumed to remain constant. The mass of the TMS is calculated separately. The additional main propulsion weight ${\rm{\Delta }}{W_{propulsion}}$ is calculated and thus the influence of the aircraft on the TMS. ${\rm{\Delta }}{W_{propulsion}}$ represents the difference in the main propulsion weight due to a different thrust demand. Here, it is assumed that the required thrust can be determined by a constant thrust-to-weight ratio at aircraft level.

(5) \begin{equation}{F_{aircraft}} = MTO{W_{aircraft}}*{\frac{{Thrust}}{{Weight}}_{aircraft}}\;\end{equation}

The propulsion mass without a thermal system can be defined using a different thrust-to-weight ratio at propulsion level, depending on the type of propulsion (e.g., hybrid electric, turbofan, etc.). The thrust is multiplied by the inverse thrust-to-weight ratio to calculate the propulsion mass ${W_{propulsion}}$ , Equation (6).

(6) \begin{equation}{W_{turbofan}} = MTO{W_{aircraft}}*{\frac{{Thrust}}{{Weight}}_{aircraft}}*{\frac{{Weight}}{{Thrust}}_{propulsion}}\;\end{equation}

If a turboprop propulsion system is used, Equation (7) can be utilised.

(7) \begin{equation}{W_{turboprop}} = MTO{W_{aircraft}}{\rm{*}}{\frac{{Power}}{{Weight}}_{aircraft}}{\rm{*}}{\frac{{Weight}}{{Power}}_{propulsion}}{\rm{\;}}\end{equation}

The following equation can be iteratively solved to obtain the mass deltas and the additional thrust requirement, since the mass of the TMS is changed by higher system power demands. Possible increases in structural mass are neglected.

(8) \begin{equation}MTO{W_{new,aircraft}} = MTO{W_{aircraft}} + {W_{TMS}} + {\rm{\Delta }}{W_{propulsion}}\end{equation}

(9) \begin{align}{\rm{\Delta }}{W_{propulsion}} &= \left( {MTO{W_{aircraft,new}}*{{\frac{{Thrust}}{{Weight}}}_{aircraft}}*{{\frac{{Weight}}{{Thrust}}}_{propulsion}}\;} \right) \nonumber \\[5pt]& \quad- \;\left( {MTO{W_{aircraft}}*{{\frac{{Thrust}}{{Weight}}}_{aircraft}}*{{\frac{{Weight}}{{Thrust}}}_{propulsion}}\;\;} \right)\end{align}

The total mass of the TMS ${W_{TMS}}$ is considered within the design process and includes the mass of the heat exchanger, ducts, nacelle, fan stage and electric motor.

3.4 Methods to assess the thermal management system

For the comprehensive system evaluation, masses, drag and power requirements are assessed. The focus here is not on energy consumption but solely on power at each operating point, given that energy equals power multiplied by time. It is assumed that time is a constant for each mission and can be chosen individually. The power requirement pertains to the entire system and can be determined according to section 3.3. The masses of the turbo components are parametrically estimated from the resulting geometry derived from the thermodynamic parameters (Mach number, mass flow) of the cycle process. The weight of electric motors is estimated by a specific torque to weight ratio derived from [Reference Anton and Siemens20]. The size and volume of the fins and the plates separating the mass flows defines the overall mass of the plate heat exchanger with offset stripped fins, see Equation (10) [Reference Shah15].

(10) \begin{equation}{m_{{\rm{total}}}} = {m_{{\rm{Fins}},hot}} + {m_{{\rm{Fins}},{\rm{cold}}}} + {m_{{\rm{Plates}}}} + {m_{{\rm{Walls}},{\rm{hot}}}} + {m_{{\rm{Walls}},{\rm{cold}}}}\end{equation}

The nacelle’s geometry is determined using inlet areas, length and diameter of individual components, and nozzle areas. Care is taken to ensure that the angle of the afterbody does not exceed 20 degrees to avoid flow separation. Additionally, the nose radius of the inlet lip is dimensioned to minimise spillage drag. The nacelle drag is determined based on its geometry, with profile, frictional and spillage drag calculated according to ESDU 80124. ESDU 81024 provides a method for estimating the drag of axisymmetric cowls at subsonic speeds. The drag is categorised into profile, spillage and wave drag, with the method relying on correlations of experimental data [21]. The correlations are built on critical mass flows, lip radius, Reynolds number and Mach number. Therefore, only rotationally symmetrical nacelles are designed.

The weight of the fan and ducts are derived from the NASA methodology for estimating length and weight of axial flow components. The weights for compressors are estimated with the correlation variables: mean diameter, number of stages, length to inlet mean diameter ratio [Reference Sagerser, Lieblein and Krebs22]. It is assumed that the installed nozzles and diffusers can be handled analog to ducts regarding the weight estimation.