High-fidelity Large-eddy Simulation Research Articles

Aeroacoustics of Twin Rectangular Jets Including Screech: Large-Eddy Simulations with Experimental Validation

High-fidelity large-eddy simulations (LESs) are performed to investigate aeroacoustic characteristics of jets issuing from twin rectangular nozzles with an aspect ratio of 2:1 at two overexpanded conditions and the design condition. For all three jet conditions simulated, LES predicts qualitatively similar near-field flow statistics to those measured at the University of Cincinnati. Using the Ffowcs Williams-Hawkings method, LES captures the fundamental screech tone and its harmonics fairly well at multiple observer locations in the far-field. Intense jet flapping motions in the near field along the minor axis, which are influenced by jet-to-jet interactions, are found to correspond to those frequencies. Moreover, the predicted overall sound pressure levels are within 1–2 dB of the experimental measurements. However, the screech tones appear to be intermittent, as the twin-jet interaction pattern varies irregularly. To extract dominant flow structures at the screech frequencies and identify the twin-jet coupling modes, spectral proper orthogonal decomposition (SPOD) analysis is used. SPOD analysis recovers energetic peaks at the screech frequencies, and the corresponding leading modes indicate strong upstream radiation originating from the fifth/sixth shock cells. For the two overexpanded conditions, the leading modes show antisymmetric coupling in the minor axis at the fundamental screech frequencies. In contrast, the two jets behave symmetrically with respect to each other in the major axis, in line with the absence of jet flapping in this direction. Furthermore, the leading SPOD eigenvalues turn out to be, at least, two orders of magnitude larger than higher-order eigenvalues, suggesting potential of reduced-order models for the twin-jet screech.

The signature of a propeller–rudder system: Acoustic analogy based on LES data

The acoustic analogy is utilized to analyze the sound from a propeller–rudder system, exploiting data from high-fidelity Large-Eddy Simulations, performed on a cylindrical grid consisting of 3.8 billion points. Simulations were conducted with the downstream hydrofoil at incidence angles of 0°, 5°, 10° and 15°. The analysis demonstrates the significant effect of the downstream hydrofoil in increasing the sound pressure levels, especially due to the loading noise from its surface, but also as a result of the enhanced complexity of the wake topology. For increasing angles of incidence, the wake experiences a growing elongation in the direction of the span of the hydrofoil and higher values of cross-stream velocity, reinforcing the shear between the wakes shed by the propeller and the hydrofoil, respectively. A very complex directivity of the acoustic signature develops, whose dependence on the orientation of the hydrofoil is variable across both the azimuthal and the streamwise directions. Separation on the suction side of the hydrofoil for large incidence angles has the effect of reducing the loading component of noise from its surface, which is the leading one, with the exception of the radial coordinates within a few diameters from the axis of the propeller and its wake.

Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal.

High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equationfor the mass-flux velocity, a_{j}, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the a_{j} transport equationis shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.

Numerical visualization of wind turbine wakes using passive scalar advection–diffusion equation and its application for wake management

To visualize and characterize the unsteady properties of the wake trailing behind a wind turbine, we propose a novel numerical methodology in this study. Through a wind-tunnel experiment using a smoke generator, we succeeded in visualizing a compact-type small-scale wind turbine wake using continuous scalar plumes from a single point source. Next, to simulate the above wind-tunnel experiment, we proposed a method using the passive scalar advection–diffusion equation based on a high-fidelity large-eddy simulation (LES). The actuator-line method (ALM) was adopted for the wind turbine model. We succeeded in qualitatively reproducing the wake visualization experiment in the wind tunnel described above and verified the effectiveness of the proposed numerical visualization method. To evaluate the characteristics of wakes generated by wind turbines in more detail, we conducted a quantitative comparison using a disk-shaped volume source with the same size as the swept area, set behind the wind turbine model. The results indicated that the non-dimensional time-averaged passive scalar profile in the near- and far-wake regions qualitatively matched the shape of the stream-wise velocity profile, despite having opposite signs. In other words, it was shown that if a disk-shaped volume source with the same size as the swept area is placed just behind the wind turbine, it is possible to accurately predict the behavior of the wind turbine wake. Finally, to validate the proposed method for wind farm wake management, we performed a visualization of wake flows in a virtual offshore wind farm consisting of 12 wind turbines with short separation distances. Through detailed comparison of two types of numerical results with different wind directions, we showed that the proposed method can effectively demonstrate the range of spatial influence of the wakes formed by the wind turbine with special attention.

Large eddy simulation of two separated hypersonic shock/turbulent boundary layer interactions

We present a detailed statistical description of turbulence in the high-fidelity Large Eddy Simulation (LES) of hypersonic shock-and-turbulent boundary layer interactions with strong separation. Our high-fidelity LES method uses a 4th-order, bandwidth-optimized Weighted Essentially Non-Oscillatory (WENO) scheme combined with a robust shock-capturing method and dynamic mixed model formulations for the closure of subgrid scale terms. Our mixed models, which contain a scale-similar term in addition to the purely dissipative one, are shown to accurately and significantly improve separation prediction compared to purely dissipative closures, such as the dynamic eddy viscosity formulation.

Vertical structure of conventionally neutral atmospheric boundary layers

SignificanceThe presented model describes the vertical structure of conventionally neutral atmospheric boundary layers. Due to the complicated interplay between buoyancy, shear, and Coriolis effects, analytical descriptions have been limited to the mean wind speed. We introduce an analytical approach based on the Ekman equations and the basis function of the universal potential temperature flux profile that allows one to describe the wind and turbulent shear stress profiles and hence capture features like the wind veer profile. The analytical profiles are validated against high-fidelity large-eddy simulations and atmospheric measurements. Our findings contribute to the scientific community's fundamental understanding of atmospheric turbulence with direct relevance for weather forecasting, climate modeling, and wind energy applications.

Evaluation of a lattice Boltzmann-based wind-turbine actuator line model against a Navier-Stokes approach

Due to the cost and difficulty to precisely measure aerodynamic quantities in onshore and offshore wind farms, researchers often rely on high-fidelity large eddy simulation, based on Navier-Stokes flow solvers. However, the cost of such simulation is very high and does not allow, in practice, extensive parametric studies for large wind farms. Among others, the lattice Boltzmann method is a good candidate for much faster, ExaScale wind farm flow simulations. The present paper aims to assess the validity of a lattice Boltzmann-based actuator line model and highlights its strengths and potential weaknesses. With this intent, comparisons against a Navier-Stokes approach commonly used in the wind energy community are performed. We assess the potential of the lattice Boltzmann method to reduce the computational cost of such simulations by analyzing the performance of the different solvers and their scalability. The lattice Boltzmann-based waLBerla solver reduces the computational costs significantly compared to SOWFA while maintaining the same accuracy as the Navier-Stokes-based method. Furthermore, we show that a multi-GPU implementation leads to an even more drastic reduction of the computational time, achieving faster-than-real-time simulations. This performance will allow extensive parametric studies over large wind farms in future studies.

Extension and validation of an operational dynamic wake model to yawed configurations

This work extends the capabilities of an operational dynamic wake model to yawed cases. The proposed framework brings together flow sensing and Lagrangian flow modeling into a unified framework: both the freestream flow field and the wake one are discretized as series of information-carrying particles. A source condition for these particles is thus obtained from the wind turbine measurements through flow sensing techniques. The estimated flow field state across the wind farm is finally reconstructed by propagating these particles downstream at their own characteristic velocity. The resulting framework is first presented and its extension to yawed turbine is then discussed. Comparison against high-fidelity Large Eddy Simulations of yawed wind turbines confirms the good potential of the approach: different yaw angles are considered and the performance of the model are evaluated. This study indicates that the proposed framework captures the relevant large scale wake features caused by the combined effect of yawing and wake meandering at a low computational cost thereby making it suitable for online model-based control.

Pitch/Plunge Equivalence for Dynamic Stall of Unswept Finite Wings

Pitch/plunge equivalence for deep dynamic stall of a straight finite wing is considered by employing large-eddy simulations. The flowfields are computed with a well-established time-implicit high-fidelity large-eddy simulation approach. The wing has a moderate aspect ratio of and a NACA 0012 section incorporating a rounded tip. The flow parameters are a freestream Mach number of and chord Reynolds numbers of . Pure pitching and equivalent plunging maneuvers are considered with a reduced frequency of and minimum and maximum effective angles of attack of 4 and 22 deg, respectively. The pitch and plunge dynamic stall cases are compared in detail in terms of the unsteady three-dimensional flow structure, surface pressure, and loading. Differences in the lift and moment coefficient are shown to be correctable, employing a steady thin-airfoil theory for a cambered airfoil that accounts for the rotation-induced apparent camber present in the pitching case. This pitch/plunge equivalence is extendable to the dynamic stall of a swept wing, as demonstrated in another paper by the authors [“Pitch–Plunge Equivalence for Dynamic Stall of Swept Finite Wings,” AIAA Journal (submitted for publication)].

A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct the flow field in large-scale numerically simulated wind farms by large-eddy simulations (LES). Different wind farm layouts are considered, and we find that a combination of horizontal and vertical staggering leads to improved wind farm performance compared to traditional horizontal staggering. We analyze the wind farm flows using the amplitude selection (AP) and sparsity-promoting (SP method) DMD approach. We find that the AP method tends to select modes with a small length scale and a high frequency, while the SP method selects large coherent structures with low frequency. The latter are somewhat reminiscent of modes obtained using proper orthogonal decomposition (POD). We find that a relatively limited number of SP-DMD modes is sufficient to accurately reconstruct the flow field in the entire wind farm, whereas the AP-DMD method requires more modes to achieve an accurate reconstruction. Thus, the SP-DMD method has a smaller performance loss compared to the AP-DMD method in terms of the reconstruction of the flow field.

Influence of an upstream hydrofoil on the acoustic signature of a propeller

The acoustic analogy is adopted to reconstruct the sound generated by a system consisting of a hydrofoil and a downstream propeller. The data from high-fidelity large-eddy simulations with the hydrofoil at angles of incidence of 0°, 10°, and 20° were generated using a cylindrical grid consisting of 1.7 × 109 points. The results of the analysis demonstrate the following: (i) the strong influence by the incidence of the hydrofoil on the acoustic signature of the system; (ii) the leading role of the non-linear component of sound at small radial coordinates in the vicinity of the wake, especially moving away from the propeller plane; (iii) the leading role of the linear component of sound from the surface of the propeller moving away along the radial direction; (iv) the importance of the shear between the wakes shed by the hydrofoil and the propeller in accelerating the process of instability of the coherent structures and reinforcing the non-linear sources of sound; and (v) the strong, complex directivity of sound at small radial coordinates, as a consequence of the interaction between the wakes from the hydrofoil and the propeller.

Interrogating common clarification models for unit operation systems with dynamic similitude

Surface overflow rate (SOR), plug flow reactor (PFR) and continuously stirred tank reactor (CSTR) are common models for clarification unit operations (UO). With wide deployment in engineering practice and regulation, through tools from spreadsheets to complex numerical codes, these models are formulated based upon conceptualized system geometry (e.g., rectangular channel) and idealized hydrodynamics (plug flow or well-mixed conditions). Yet the hydrodynamics and geometry of actual UO systems can be complex and substantially different from these assumptions. As a result, the applicability and generalizability of these models require critical and systematic interrogation. This study examines the predictive capability and generalizability of these common models for a hydrodynamic separator (HS), tanks, rectangular clarifiers and an urban drainage basin based on physical model data and high-fidelity large-eddy simulation (LES). Moreover, this study presents a novel application of dynamic similitude to developing a more generalized and physically interpretable model based on the hypothesis that PM and PM-partitioned constituent separation in a UO can be approximated solely through the dimensionless settling velocity W (Hazen number). Based on this hypothesis and dynamic similitude, a similarity modified gamma model (SMG) is proposed and tested. With dynamic similitude and W, results show common models are not robust and generalizable for predicting PM separation with error ranging from 30 to 50% and can significantly oversize a clarifier up to 904%. The non-linear characteristics of PM separation are shown to have a critical role in clarifications system design scalability and economics. In contrast, the SMG model is robust and generalizes the PM separation for geometrically similar systems, irrespective of particle density, particle size distribution (PSD), and loading conditions. The developed theory and proposed SMG model also can simplify and reduce the effort as well as expense of physical model testing while serving as an adjuvant for numerical simulations of clarification systems. Results also reveal commercial HS systems do not outperform simple plain tank geometries. The complex turbulence vortical structures pose significant challenges for UO system analysis and design.

How do water and CO2 impact the stability and emissions of the combustion in a micro gas turbine? — A Large Eddy Simulations comparison

Micro Gas Turbines have to become more operational and fuel flexible, and carbon clean. Applying cycle humidification and Exhaust Gas Recirculation (EGR) in combination with Carbon Capture offers a solution. However, current advanced mGT cycle development is limited by the combustor. To improve the cycle performance further, stable and complete combustion has to be achieved under unconventional diluted conditions. Accurate data predicting the stability and performance of specific mGT combustors under these diluted conditions are still missing. A comparison between classic natural gas combustion in an mGT and three diluted cases with water and/or CO2 using Large Eddy Simulations (LES) is presented in this paper. Results show that complete and stable combustion was reached for all cases. Although the flow dynamics are identical, diluted operating conditions lead to a wider reaction zone. An outlet temperature reduction could be observed in the water diluted cases due to the higher specific heat of the humidified combustion air. Regarding CO emissions, the humidified case presents slightly lower concentrations (25 ppm) compared to the reference case (32 ppm), while the dry EGR case shows the highest values (50 ppm). Based on high fidelity LES results, the feasibility of mGT combustor operating under diluted conditions has been proven.

Prediction of Wall Heat Fluxes in a Rocket Engine with Conjugate Heat Transfer Based on Large-Eddy Simulation.

Although a lot of research and development has been done to understand and master the major physics involved in cryogenic rocket engines (combustion, feeding systems, heat transfer, stability, efficiency, etc.), the injection system and wall heat transfer remain critical issues due to complex physics, leading to atomization in the subcritical regime and the interactions of hot gases with walls. In such regimes, the fuel is usually injected through a coaxial annulus and triggers the atomization of the central liquid oxidizer jet. This type of injector is often referred to as air-assisted, or coaxial shear, injector, and has been extensively studied experimentally. Including such injection in numerical simulations requires specific models as simulating the atomization process is still out of reach in practical industrial systems. The effect of the injection model on the flame stabilization process and thus on wall heat fluxes is of critical importance when it comes to the design of wall-cooling systems. Indeed, maximizing the heat flux extracted from the chamber can lead to serious gain for the cooling and feeding systems for expander-type feeding cycles where the thermal energy absorbed by the coolant is converted into kinetic energy to drive the turbo-pumps of the feeding system. The methodology proposed in this work to numerically predict the flame topology and associated heat fluxes is based on state-of-the-art methods for turbulent reactive flow field predictions for rocket engines, including liquid injection, combustion model, and wall treatment. For this purpose, high-fidelity Large Eddy Simulation Conjugate Heat Transfer, along with a reduced kinetic mechanism for the prediction of chemistry, liquid injection model LOx sprays, and the use of a specific wall modeling to correctly predict heat flux for large temperature ratio between the bulk flow and the chamber walls, is used. A smooth and a longitudinally ribbed combustor configuration from JAXA are simulated. The coupling strategy ensures a rapid convergence for a limited additional cost compared to a fluid-only simulation, and the wall heat fluxes display a healthy trend compared to the experimental measurements. An increase of heat transfer coherent with the literature is observed when walls are equipped with ribs, compared to smooth walls. The heat transfer enhancement of the ribbed configuration with respect to the smooth walls is coherent with results from the literature, with an increase of around of wall heat flux extracted for the same chamber diameter.

A computational examination of large-scale pool fires: variations in crosswind velocity and pool shape

A high-fidelity large-eddy simulation and unsteady flamelet combustion model construct is deployed to numerically investigate the effects of crosswind magnitude and pool fire shape on large-scale pool fire attributes. These include general flame dynamics, flame shape and radiative flux magnitude in and around the fire. Three pool fire shapes at a nominal length scale of 10 m are subjected to four crosswind magnitudes between 0 and 20 m s $^{-1}$ . The pool shapes studied are circular, square and rectangular. The study includes the sensitivity of parameters to mesh and time step refinement. Results demonstrate that the rectangular shape, under crosswind, has low-levels of vertical velocity induction, resulting in a plume that is closer to the ground. In the quiescent regime, under-resolved meshes provide a higher radiative heat flux prediction compared with the most refined mesh. However, as crosswind increases, low mesh resolutions underpredicted radiative flux. This is due to the coarse mesh resolution not capturing small-scale vortical features that increased mixing and combustion efficiency. A transition of peak radiative flux with respect to crosswind occurs from the leeward- to windward-side of the pool, while sharp pool features result in larger radiative heat fluxes concentrated in regions of high scalar dissipation rate.

Investigation of wet ammonia combustion characteristics using LES with finite-rate chemistry

The interest in climate action and building sustainable energy system, has highlighted electricity derived fuels (eFuels) and has promoted studies considering ammonia as a eFuel for sustainable transportation and as a mean of energy storage. Ammonia combustion, however, poses several challenges due to the low reactivity and potential high NOx emissions. A promising solution is to add hydrogen and steam into the fuel/air mixture. Steam contributes to the enhancement of specific power output and efficiency in humidified gas turbine cycle, and hydrogen promotes reactivity of the eFuel and can be obtained by ammonia decomposition on-site. In the present study, wet combustion of ammonia/hydrogen blends is systematic studied using one-dimensional flame analysis and Large eddy simulation (LES) to understand the flame stabilisation and NOx formation mechanisms. When hydrogen content is low (H2%<30%vol) and Tad = 1750 K, flame speed is nearly independent while flame thickness is significantly dependent on the equivalence ratio Φ due to the steam dilution. At high hydrogen content, the reverse applies. The impact of the H2% on the emission is non-monotonic, peaking between 60%∼70% at various Φ. Rich and stoichiometric combustion benefits NO reduction at a balance of H2% and steam dilution. High fidelity LES demonstrates that the steam diluted hydrogen/ammonia blends can be stably burnt in a swirl burner in a MILD regime. The wet combustion distributes the flame at low H2% and reduces local NO emission. In rich conditions, low NO emission attributes to the activation of NO reburning progress. Compared to dry condition, low steam addition (Ω=0.1) in the reactant lifts the flame and enlarges the opening angle of the swirling flow. When flame speed is low, POD analysis shows two PVC related structures - a single and a double helix, which dominate the flow and flame dynamics. While when flame speed is high, quick combustion process damps the precessing motion.

Aerodynamic noise characteristics of airfoils with morphed trailing edges

Numerical investigation of the aerodynamic and aeroacoustic characteristics of a symmetrical NACA 0012 airfoil developed by National Advisory Committee for Aeronautics (NACA) with a conventional hinged flap and a morphed flap has been carried out. The unsteady flow characteristics over the airfoil surface and at the airfoil wake are captured using high-fidelity Large Eddy Simulations. The tests were carried out for a freestream velocity of U∞=20 m/s, corresponding to a chord-based Reynolds number of Rc=2×105, at angles of attack α=0° and 4°. The results of the airfoil static pressure distribution show that the airfoil with morphed trailing edge produces higher values of lift coefficient than the airfoil with hinged trailing edge due to its higher suction peak resulting in larger pressure difference between the suction and pressure sides. Furthermore, from the wake-flow measurements, boundary-layer analysis, wall-pressure spectra, space–time correlation, it is concluded that the Morphed airfoil produces higher values of surface pressure fluctuations near the trailing edge which extend farther into the wake of the trailing edge compared to the Hinged airfoil. Consequently, the increased pressure fluctuations at the vicinity of the trailing edge results in a higher values of radiated far-field noise for the airfoil with morphed trailing edge flap.

High-fidelity simulation of a hydraulic jump around a surface-piercing hydrofoil

For a surface-piercing hydrofoil traveling at high speed, a turbulent hydraulic jump may arise at the intersection of the body with the free surface. This hydrodynamic phenomenon involves violent wave breaking, bringing great challenges for experimental analysis. In this work, a high-fidelity large eddy simulation is performed to study the turbulent air-entraining flow near foil. One advantage of the present simulation is that a quantitative analysis can be implemented even in the turbulent two-phase mixing region containing a large amount of entrained air, which is difficult for traditional experimental and theoretical approaches. We employ a conservative coupled level set/volume-of-fluid scheme to capture the free surface. A highly robust scheme is introduced to guarantee stability in simulating large density ratio two-phase flows. The present method is implemented based on a block-structured adaptive mesh, by which the efficiency of the high-fidelity simulation can be improved. The main flow features of the wedge-shaped hydraulic jump, including the wave patterns, free surface elevation, and frequency spectra, are compared with experimental data. We find that the flow structures show clear differences from those found in the canonical hydraulic jump, owing to the presence of the foil surface. Shoulder wave breaking starts at the trough of the mid-body, develops in a wedge shape, depends strongly on Froude number, and is responsible for most of the large-scale air entrainment. The properties of the turbulent hydraulic jump and some of the key quantities characterizing the air-entraining flow, including the spatial distribution of the bubble cloud, the void fraction, and the bubble/droplet size spectrum, are fully investigated for typical Froude numbers.

Turbulent jet ignition of ultra-lean methane/air mixture under engine-like condition

Turbulent jet ignition (TJI) is a promising technology that enables engines to operate stably at ultra-lean-burn conditions for improved thermal efficiency. In the present work, TJI of an ultra-lean methane/air mixture (excessive air ratio λ = 2.0) under an engine-like condition (temperature of 900 K and pressure of 5.8 MPa) was numerically studied, with particular interest on the ignition patterns and the critical/favorable conditions for successful ignition/rapid combustion. A high-fidelity large eddy simulation was performed, with the linear eddy model being incorporated to account for turbulence–chemistry interaction. To represent the different amount/state of energy released from a pre-chamber, a variety of turbulent jet temperatures, inlet velocities, and orifice diameters were covered. The results identified two successful ignition patterns, including a flame propagation pattern and a jet re-ignition pattern. An ignition regime was also established, with the boundary between ignition success/failure identified by a global Damköhler number (Da) of 0.1. In terms of the combustion rate, heat release in the propagative flame is governed by the growth of the flame surface, which is primarily controlled by stretch and enlarges with the jet Reynolds number (Re). The present results suggest that, for low-reactivity fuels such as methane, the pre-chamber combustion in a TJI system should pursue complete heat release and increase Re and Da simultaneously for the injected turbulent jet into the main combustion chamber.

Large-eddy simulation and Co-Design strategy for a drag-type vertical axis hydrokinetic turbine in open channel flows

A drag-type, vertical axis hydrokinetic turbine, partially embedded in a relatively shallow channel streambank, has been introduced to mitigate side wall erosion while producing energy [1,2]. The turbine is deployed at river mid-depth to minimize the interaction with erodible bed and biota, floating debris, ice and logs, and it operates at low tip speed ratio, which is relatively safe for fish. To quantify the turbine performance and wake characteristics and to improve its design, we conduct high fidelity large-eddy simulations (LES) in an open channel flow under different operating conditions and blade geometry. The complex turbine geometry, including the rotor and housing structure, are captured by the immersed boundary method, while the coupled level-set and volume-of-fluid method is used to compute the free surface. The resulting power coefficients at different tip speed ratios are compared against results obtained in a reduced scale prototype experiment, carried out at the St. Anthony Falls Laboratory, for validation. Quantifying the near wake flow structures generated by the turbine and their contribution to the side wall shear stresses, responsible for potential streambank erosion, has become a critical design component. Blade geometry is indeed improved through multiple iterations using the reduced shear stress at the stream bank and the increased power coefficient as a combined metric in our co-design strategy. We believe such a procedure is essential to pursue diffused renewable energy extraction with positive environmental impacts.