Future aircraft may cut drag by tightly integrating propulsion with the airframe—but that integration makes ordinary thrust bookkeeping ambiguous. This paper shows that two powerful assessment methods are closely related, with one emerging as a restricted form of the other.

Future transport aircraft use Boundary Layer Ingestion, Distributed Propulsion, Open Rotor, and Ultra High Bypass Ratio engine configurations as advanced propulsion-airframe concepts. These concepts can reduce overall aerodynamic drag, but they also create strong coupling between thrust and drag, so comprehensive performance assessment methods such as Exergy Analysis and Power Balance become necessary.

Both methods eliminate the need to explicitly determine aerodynamic forces acting on the body and apply to steady-state compressible flows. The paper develops unified nomenclature for comparing the methods and clarifying which physical phenomena each can investigate.

Its central result is that Power Balance terms can be deduced from Exergy Analysis by omitting heat transfer and associated entropy generation, while the two methods provide complementary insight into system losses. Improving the overall efficiency of future commercial aircraft requires new configurations to be taken into account.

The SFB-TRR 364 SynTrac investigates synergistic effects from adapting the standard tube and wing configuration through an interdisciplinary team. SynTrac is a Collaborative Research Centre between TU Braunschweig, the University of Stuttgart, and the German Aerospace Center.

The Collaborative Research Centre started in 2023 and contains 19 individual projects. Boundary Layer Ingestion partly ingests the boundary layer formed on the aircraft surface by viscous effects into the engine. The ingested boundary layer is re-accelerated at the nozzle exit, reducing the total kinetic energy dissipation in the flow field.

But BLI makes engine flow conditions highly dependent on the airframe flow field, so separating thrust and drag becomes ambiguous and state-of-the-art thrust bookkeeping becomes challenging. Drela’s Power Balance is a control volume analysis that accounts for mechanical power and is particularly useful for optimizing aircraft configurations with highly integrated propulsion systems.

Miller’s mechanical work potential represents the mechanical component of a state’s exergy by assuming isentropic work extraction from a higher pressure to the reference pressure. As aircraft systems improve and partly electrical aircraft are considered, effective heat management becomes increasingly important.

Waste heat can be transferred to areas where it benefits overall performance, and Exergy Analysis assesses those benefits by balancing total energy through the concept of exergy. Exergy Analysis assesses a system’s potential to perform technical work and has undergone significant methodological advancements for aircraft flows.

These developments have enabled applications across the aerospace industry, including highly integrated aerodynamic and aero-thermal systems with open rotor, ultra-high-bypass-ratio, and heat exchanger devices. For these highly integrated concepts, aerodynamic losses, propulsive efficiency, and installation effects must be accurately quantified to meet future performance and environmental targets.

The paper outlines Arntz’s Exergy Analysis and compares it with Drela’s Power Balance using comprehensive nomenclature. It also compares the assumptions and simplifications required by both methods. That comparison helps identify the most suitable tool for highly integrated aircraft and evaluate accuracy for subsonic and transonic flow regimes.

The key contribution is a mathematical relation showing that Power Balance can be derived from Exergy Analysis under specific assumptions. Because both methods are derived for steady-state flow conditions, the comparison retains that restriction for consistency.

Many aircraft performance assessments use steady operating conditions such as cruise or climb. Depending on the propulsion-system representation in the CFD simulation, such as an actuator disc, the unsteady behavior of individual propulsion components may not be resolved.

Consequently, the comparison is limited to steady-state operating conditions. The analysis begins by defining a suitable control volume around the aircraft, because both methods have requirements for the control volume surrounding the aircraft.

Figure 1 shows a cutaway section through a three-dimensional control volume around an arbitrary aircraft with Boundary Layer Ingestion at the upper trailing edge and a propeller at the lower side. The section is a notional aircraft configuration used to illustrate different possible surface types across aircraft.

Both methods consider only the fluid domain around the aircraft and track added and removed powers in an aircraft-fixed coordinate system. The control-volume boundaries therefore keep the same relative position with respect to the aircraft. The aircraft surface is an inner control-volume boundary divided into solid walls, moving walls, and permeable surfaces at the propulsor entry and exit.

The permeable surfaces account for power sources that are not resolved in the flow simulations and are therefore excluded from the control volume. Exergy Analysis also detects shock waves inside the control volume by wrapping them in an additional surface.

The changes of state caused by shock waves are calculated from outflow and inflow through the shock-wave surfaces. This avoids non-physical viscous-loss contributions caused by strong gradients in the shock region. A Trefftz plane is located downstream of a body to analyze the wake, and in practical applications it should be close to the body so individual loss mechanisms remain distinct.

For the transonic flow conditions investigated for highly integrated transport aircraft within the SynTrac project, only shock waves close to the aircraft boundary occur, so the surface shape can be freely chosen. A cylindrical shape simplifies evaluation of the surface integrals because those integrals become zero.

Exergy and its counterpart anergy divide a system’s total energy into a part fully usable for technical purposes and an unusable part, with reference to specific environmental conditions. To determine a system’s exergy content, the analysis considers a theoretical change of state to environmental conditions.

The First Law balances total energy, while the Second Law describes entropy transport and flow; heat exchange with the environment links the two equations. Solving the resulting equation gives technical work, and setting entropy generation to zero in the control volume gives the maximum theoretical work of the system.

That maximum work is the work the system can perform on the environment, which is exactly the system’s exergy. Arntz and colleagues applied the concept of exergy to aircraft flows using the fluid volume defined around the aircraft. Conservation of total energy, formulated through total enthalpy, is the foundation of this analysis.

Because Exergy Analysis is designed for RANS simulations or wind-tunnel experiments, its equations are derived in time-averaged form using Favre decomposition. Favre decomposition is needed because compressibility effects must be considered in transonic aircraft flows.

The procedure introduces turbulent shear stress and turbulent heat flux as major unknowns, expressed as functions of mean quantities for mean steady flow; the Boussinesq approximation describes turbulent stresses for eddy-viscosity models. The decomposed terms capture thermal energy outflow, isobaric surrounding work, boundary pressure work, potential energy rate, viscous-force work at the outer boundary, and stream-wise and transverse kinetic-energy deposition.

Applying the Gauss divergence theorem to the combined equations produces the Exergy Analysis equation in short notation. Some terms become zero on certain surfaces, while others are negligible. Unlike Exergy Analysis, Power Balance is based only on the mechanical energy equation.

It has no input from the Second Law of Thermodynamics and is strictly a First Law analysis. The averaged mean kinetic-energy equation is obtained from the averaged mass-conservation and momentum equations. The last two terms are zero on the outer surface because that surface is at a large distance from the aircraft body.

The equation is then manipulated algebraically to derive meaningful physical processes and reduced to compact form. The left-hand terms represent total mechanical-power supply, production, and inflow of mechanical energy into the control volume. The right-hand terms represent power consumption or mechanical-energy outflow through various physical processes and dissipation.

The comparison is designed to show the relation between Power Balance and Exergy Analysis. Because Power Balance uses the mechanical-energy equation while Exergy Analysis uses the First and Second Laws, the Power Balance equation should follow from Exergy Analysis when thermal influences are neglected.

That requires neglecting heat transfer, heat conduction, and the associated generation and transport of entropy. The comparison is divided into three sections, beginning with terms that appear equally in both methods. The remaining terms require algebraic reformulations involving the decomposition of propulsive enthalpy and the contribution of pressure terms.

Power Balance can be derived from Exergy Analysis by neglecting the terms that account for heat transfer and entropy. Power Balance is therefore a subset of Exergy Analysis. The viscous-dissipation term in the mechanical-energy equation can be obtained through the combined analysis of the First and Second Laws of Thermodynamics.

Both methods are closely linked, and their relevance depends on the application. Power Balance is valid for steady and periodically unsteady computations and is not limited to a particular turbulence model or form of averaging.

When heat transfer is involved, Power Balance fails to capture the thermal losses incurred during those processes because it handles mechanical energy rather than total energy. When a significant amount of non-mechanical energy, such as thermal energy, is involved, Exergy Analysis is worth using.

In the formulation stated here, Exergy Analysis is limited to steady flows and eddy-viscosity turbulence models. A wake-reduced Exergy Analysis formulation by Aguirre and colleagues lies beyond the scope of this paper. The Power Balance is a subset of Exergy Analysis: remove heat-transfer and entropy terms, and the mechanical balance remains.

The choice therefore depends on whether thermal and other non-mechanical energy effects matter.