Reference Configuration Research Articles

A multiobjective optimization of 3D - slot jet configuration for enhancement of film cooling in an annular combustor liner

This study reports the results of a combined experimental and numerical investigation of the performance of a three-dimensional film cooling slot configuration and its optimization using an evolutionary-based genetic algorithm. The primary objective of the optimization is to maximize the area-averaged film cooling effectiveness (ηad.avg) and minimize its standard deviation (ση) at a fixed coolant mass flux for a single liner. The experimental study is conducted on flow and heat transfer characteristics to validate the numerical model under laboratory conditions (low temperature and pressure). A design space is created using the Latin hypercube sampling technique, and it is solved using steady-state RANS simulations with the validated numerical model to estimate the ηad.avg and ση under actual engine conditions (high temperature and pressure). A surrogate model is developed using the kriging technique to predict the objective functions with the geometrical parameters of the slot. Following this, the optimum configuration is identified using the genetic algorithm. The geometrical parameters are slot jet diameter (d), slot jet pitch (p), lip taper angle (α), and lip length (L). The numerical results show that the optimum configuration outperforms the two reference configurations of the baseline combustor. At a blowing ratio (BR) of 1, the optimum configuration enhances the ηad.avg by 8% and reduces the ση by 6.6% compared to reference -1 configuration. Similarly, compared to reference -2, the optimum configuration enhances the ηad.avg by 19.8% and reduces the ση by 5.2.%. Furthermore, under actual engine conditions, a numerical study is conducted on a subsequent row of liners to determine the optimum length of the cooling ring. The numerical results show that the optimum slot configuration cools an additional liner length (G/S) of 5.5 compared to the reference-1 slot and results in a reduction of one pair of cooling rings in the combustor, which contributes to a 16.6% less coolant mass flux.

Application of double-error correction codes to protect configuration programmable logic memory against space radiation

Objectives. Programmable logic integrated circuits of the field programmable gate array (FPGA) type based on static configuration memory are widely used in the electronics of onboard spacecraft systems. Under the influence of space radiation, errors may occur in the FPGA configuration memory. The main methods of protection against such errors involve various options for reservation triggers, as well as the use of error-correcting codes in special error detection and correction circuits. The purpose of the present work is to determine which error-correcting codes are best suited to the implementation of internal scrubbing of the FPGA configuration memory taking redundancy into account.Methods. The paper analyses various methods for scrubbing FPGA configuration memory, which are used to correct errors caused by the action of space radiation. It is proposed to increase the efficiency of internal scrubbing of the FPGA configuration memory using codes that correct both single- and double-adjacent SEC-DED-DAEC errors. In this case, the need to perform external scrubbing of the configuration memory is reduced by overwriting it with a reference configuration from non-volatile radiation-resistant memory; in this way, FPGA downtime caused by the external scrubbing procedure is reduced. Due to the known SEC-DED-DAEC codes having a non-zero probability of erroneous detection and subsequent erroneous correction of a double non-adjacent error, as well as various redundancy and implementation complexities, a study was made of the most efficient code for internal scrubbing.Results. The results showed that the Datta, Neale and Hoyoon–Yongsurk codes are optimal from the indicated positions. Recommendations are given for selecting a specific code depending on the specific requirements for a particular planned space mission.Conclusions. The study confirms the effectiveness of protecting the memory of programmable logic by using two-error-correcting codes.

Nonlinear mechanics of remodeling

In this paper, we present a large-deformation formulation of the mechanics of remodeling. Remodeling is anelasticity with an internal constraint—material evolutions that are mass and volume-preserving. In this special class of material evolutions, the explicit time dependence of the energy function is via one or more remodeling tensors that can be considered as internal variables of the theory. The governing equations of remodeling solids are derived using a two-potential approach and the Lagrange–d’Alembert principle. We consider both isotropic and anisotropic solids and derive their corresponding remodeling equations. We study a particular remodeling of fiber-reinforced solids in which the fiber orientation is time-dependent in the reference configuration—SO(3)-remodeling. We define an additional remodeling energy, which is motivated by the energy spent in collagen fiber-reinforced living systems to remodel to enhance stiffness or strength in the direction of loading. We consider the examples of a solid reinforced with either one or two families of reorienting fibers and derive their remodeling equations. This is a generalization of some of the proposed remodeling equations in the literature. We study three examples of material remodeling, namely finite extensions and torsion of solid circular cylinders, which are universal deformations for incompressible isotropic solids and certain anisotropic solids. We consider both displacement and force-control loadings. Detailed parametric studies are included for the effects of various material and loading parameters on fiber remodeling. It is observed that during remodeling, there is a competition between the action of the internal strain energy function and the remodeling energy. For a given material, a remodeling process dominated by strain energy works to align fibers in a direction that minimizes strain energy. On the other hand, a remodeling process dominated by the remodeling energy aligns fibers in the direction of the maximum principal strain according to a constitutive choice. We finally linearize the governing equations of the remodeling theory and derive those of linear remodeling mechanics.

Unstable flame structure adjacent to discrete wall with narrowly-ventilated air cavity

This paper investigates the interaction between a discrete non-reactive wall with a narrow ventilated cavity and a turbulent diffusion flame. The analysis is based on both experiments and large eddy simulations (LES). Firstly, the prediction is compared with experiments on two reference configurations: a continuous wall and a discrete system. The analysis was carried out to establish the validity of models to capture the boundary-layer flame and heat exchange. Overall, the predictions are in reasonable qualitative and quantitative agreement with experimental results. The article then examines the spacing effect of inert discrete elements on flame characteristics. The analysis is conducted for a vertical and horizontal layout. The orientation and spacing of the elements affect the stability of the flow structure and fire dynamics. It produces larger or smaller flames, which affect the flame-to-element heat transfer. Correlations were developed to predict flame height and heat flux. The study's findings can aid further fundamental studies to predict and mitigate the flame spread risk over such systems with combustible elements.

Large Interferometer For Exoplanets (LIFE)

Context. The next generation of space-based observatories will characterize the atmospheres of low-mass, temperate exoplanets with the direct-imaging technique. This will be a major step forward in our understanding of exoplanet diversity and the prevalence of potentially habitable conditions beyond the Earth. Aims. We compute a list of currently known exoplanets detectable with the mid-infrared Large Interferometer For Exoplanets (LIFE) in thermal emission. We also compute the list of known exoplanets accessible to a notional design of the future Habitable Worlds Observatory (HWO), observing in reflected starlight. Methods. With a pre-existing statistical methodology, we processed the NASA Exoplanet Archive and computed orbital realizations for each known exoplanet. We derived their mass, radius, equilibrium temperature, and planet-star angular separation. We used the LIFEsim simulator to compute the integration time (tint) required to detect each planet with LIFE. A planet is considered detectable if a broadband signal-to-noise ratio S/N = 7 is achieved over the spectral range 4–18.5 µm in tint < 100 h. We tested whether the planet is accessible to HWO in reflected starlight based on its notional inner and outer working angles, and minimum planet-to-star contrast. Results. LIFE's reference configuration (four 2-m telescopes with 5% throughput and a nulling baseline between 10–100 m) can detect 212 known exoplanets within 20 pc. Of these, 49 are also accessible to HWO in reflected starlight, offering a unique opportunity for synergies in atmospheric characterization. LIFE can also detect 32 known transiting exoplanets. Furthermore, we find 38 LIFE-detectable planets orbiting in the habitable zone, of which 13 have Mp < 5M⊕ and eight have 5M⊕ < Mp < 10M⊕. Conclusions. LIFE already has enough targets to perform ground-breaking analyses of low-mass, habitable-zone exoplanets, a fraction of which will also be accessible to other instruments.

Computational Modeling of an Aortic Medial Wall: Effect of Residual Stresses on a Mechanical Behavior of the Aortic Ring

Abstract The aorta is the largest artery in an animal body and is an important organ in the pulsatile flow regulation from the left ventricle. The mechanical and structural characteristics of the aortic media, which are primarily composed of smooth muscle cell layers and elastic laminae (ELs), have profound effects on the physiology and pathophysiology of the aorta. However, many aspects of the aortic tissue remain unknown due to the inherent layered wall structure and the regionally varying residual stresses. This study aimed to computationally represent EL buckling in the aortic medial ring at the unloaded state and reproduce the transmural variation in residual stresses and EL waviness across the vascular wall. A multi-objective optimization technique was applied to a series of simulations with the “unit” structure to obtain an idealized stress distribution throughout the aortic wall thickness. Hence, an appropriate boundary condition given to an initial reference configuration of the aortic ring was successfully identified. As a result, the average “idealized” residual stresses of smooth muscle cell layer and EL were on the order of 20 and −80 kPa, respectively, while EL waviness was ∼1.01 in the unloaded state. Further, it was verified that the ring model with a radial cut will open spontaneously when the inner and outer layers of the medial wall are subjected to relative compressive and tensile residual stresses, respectively, in the unloaded state.

Optimization Effect of the Improved Power System Integrating Composite Motors on the Energy Consumption of Electric Vehicles

The multi-power source coupled transmission system is a high-performance and energy-saving potential power transmission system, and most of the commonly used pure electric vehicles in the market that use multi-power source coupled drive adopt the motor dual-axis distributed independent drive scheme. The configuration design method for multi-power source fusion hybrid systems mainly focuses on the search and selection of power split hybrid systems based on planetary gear mechanisms. But it has not yet covered the configuration design of transmission systems, resulting in a lack of universal expression and generation methods for the configuration of multi-power source fusion hybrid systems in pure electric vehicles. Therefore, to solve the configuration optimization design problem of a dual-motor single-planetary-array power system, an improved general matrix topology design method is proposed to generate all feasible topology structures. And energy consumption, economy, and the dynamic performance of alternative configurations are optimized and simulated through the control strategy based on a dynamic programming algorithm. Under comprehensive testing conditions, 25 alternative options that met the screening criteria were selected, and, ultimately, five optimized configuration options were obtained. Configuration 1 has the best economy, reducing energy consumption by about 6.3%and increasing driving range by about 6.7%. Its 0–100 km/h acceleration time is about 31.4% faster than the reference configuration. In addition, the energy consumption economy during actual driving is almost the same as the theoretical optimal energy consumption economy, with a difference of only 0.3%. The success of this study not only provides an innovative method for optimizing the configuration of dual-motor single-row star train power systems, but also has a positive impact on improving energy utilization efficiency, reducing energy consumption, and improving the overall performance of electric vehicles.

A coupled model of transport-reaction-mechanics with trapping, Part II: Large strain analysis

A coupled finite strain chemo-transport-mechanical formulation with trapping is here proposed to extend a previous work set in the realm of small strain theory in continuum mechanics. The theory is rooted in non-equilibrium rational thermodynamics. The kinematics is based on a multiplicative decomposition of the deformation gradient to account for swelling and shrinking, thermal, elastic and inelastic contributions. Mass balance laws and balance of linear and angular momentum, as well as the laws of thermodynamics for a convecting body, are directly formulated in their material description, after specifications of some standard transformation rules between current and reference configuration. Thermodynamic restrictions are identified based on the functional dependence of the referential Helmholtz free energy density, which is chosen as the thermodynamic potential, and further subjected to a constitutive additive decomposition. Constitutive prescriptions for the chemical potentials, referential heat and mass fluxes, chemical kinetics and the generalized heat equation lead to the establishment of the governing equations. The theoretical framework is complemented by numerical simulations, highlighting the potential of the proposed formulation in multi-physics applications.

Evaluation of an Improved AROME Configuration for Fog Forecasts during the SOFOG3D Campaign

Abstract This paper evaluates fog forecasts of a new AROME configuration dedicated to fog thanks to observations of the recent field campaign SOuth westFOGs 3Dimensions (SOFOG3D). This new configuration takes advantage of an upgraded horizontal and vertical resolution of a two-moment microphysical scheme [Liquid Ice Multiple Aerosols (LIMA)], and of the inclusion of a parameterization of the droplet’s deposition onto vegetation. A statistical study conducted over the 6 months of the SOFOG3D field campaign allowed the evaluation of the quality of fog forecasts produced by this new configuration to compare it to the current operational configuration of AROME. The main findings are as follows: the new configuration forecasts more fog events, with a few more false alarms, but improved the amount of fog events with low top height and with a low water content, underestimated by the reference configuration. The importance of the first level height for a good representation of the first few meters above the ground is crucial to improve the fog formation forecast. A delay of fog dissipation in the morning was highlighted in operational simulations and slightly reduced thanks to LIMA. This two-moment scheme produced thinner fogs, with less water content. These are more realistic, compared with observations, and thinner fog is also easier for solar radiation to dissipate.

Custom Transient Finite Element for the Modelling of Ultrasonic Control Methods for Downhole Well Integrity

The transient spectral element method can be understood as a specific high-order finite element method that is particularly accurate and fast with a low memory footprint, hence enabling 3D ultrasonic testing simulations on a standard PC. However, particular care must be taken in its settings when seeking both practicality and performance. In comparison, fast semi-analytical simulation using ray tracing is easily accessible to nondestructive testing experts, through the CIVA simulation software. Although this approximate model effectively deals with a wide range of industrial applications, it reaches its limits in certain cases, particularly at relatively low frequencies involving resonance phenomena. To deal with these challenging inspection configurations, CEA-List is working on dedicated finite element models in the CIVA framework to meet specific needs in a compromise between efficiency and accuracy. The case study considered in partnership with SLB perfectly illustrates the benefits of developing such a modelling approach. SLB provides cased-well imaging services using ultrasonic resonance methods to evaluate oil and gas well integrity. Defective cased wells have irregularities, such as corroded casings with pitting, localized cement debonding and channelings. Simulated ultrasonic signals of the actual wells are useful to understand the measurements and are available by finite element modelling with sufficient accuracy. However, the associated computational costs for numerous model cases limit the building of the model database as the digital twin of the actual well logging. The development strategy of dedicated hybrid finite element applications adopted by CEA-List is presented in broad outline. Cross-model comparisons on a reference configuration of pristine cases are presented, highlighting the effective limits of standard CIVA ray models. The contribution offered by the new hybrid finite element approach is then discussed. We discuss the evolution of model functionalities to handle geometries that differ from the canonical case (interface defects, loss of thickness in arbitrary geometries, etc.) from the perspective of a digital twin of this control.

A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements

We investigate discretizations of a geometrically nonlinear elastic Cosserat shell with nonplanar reference configuration originally introduced by Bîrsan, Ghiba, Martin, and Neff in 2019. The shell model includes curvature terms up to order 5 in the shell thickness, which are crucial to reliably simulate high-curvature deformations such as near-folds or creases. The original model is generalized to shells that are not homeomorphic to a subset of R2. For this, we replace the originally planar parameter domain by an abstract two-dimensional manifold, and verify that the hyperelastic shell energy and three-dimensional reconstruction are invariant under changes of the local coordinate systems. This general approach allows to determine the elastic response for even non-orientable surfaces like the Möbius strip and the Klein bottle. We discretize the model with a geometric finite element method and, using that geometric finite elements are H1-conforming, prove that the discrete shell model has a solution. Numerical tests then show the general performance and versatility of the model and discretization method.

Effects of localized application of porous material on trailing-edge noise of a circulation-controlled wing

This manuscript reports on the effects of localized application of porous material on trailing-edge noise of a circulation-controlled wing. This circulation-controlled configuration consists of a main wing with a droop-nose and a highly deflected flap, where the flow on the flap is attached due to the Coanda effect. The rear 10% of the flap consists of porous material. The numerical investigation was mainly carried out with a High fidelity Zonal Overset-LES method. Due to the strong pressure difference between the pressure and suction side, the flap’s porous inset experiences an enhanced flow through the porous medium as compared to the reference configuration with a non-porous flap. As a result, the boundary layer on the flap’s suction side was considerably thickened. Upon analysing the turbulent sound sources, it became evident that the application of porous material resulted in higher levels of the power spectral density of surface pressure fluctuations across the complete spectrum, related to the aforementioned strong flow through the porous material. However, the turbulent eddies traversing on the porous material were slowed down (observation based on stream-wise correlations), which was a noise reduction mechanism observed in the current study. The far-field sound characteristics revealed that a noise reduction could be seen for certain radiation directions when considering only the flap’s trailing-edge noise as a sound source. Even when the full flap noise is considered, the noise reduction effect of the porous material is evident for frequencies f between 500 Hz and 10 kHz in the forward-downward radiation direction (as defined by the polar angle θ∈ [180∘, 270∘]). To conclude, this study provides novel insights regarding the importance of the flow-through aspect of porous material and the subsequent boundary layer thickening and argues that this phenomenon needs to be kept moderate in order to achieve noise reduction. Furthermore, the study emphasizes on the importance of curvature noise which needs to be the focal point of noise reduction in such circulation-controlled wings.

Modelling intralaminar damage mechanisms in fibre reinforced polymers at finite strains

An approach to predict intralaminar failure mechanisms in laminate fibre-reinforced composites, at finite strains, is proposed. Transverse matrix cracking is described by a smeared crack model, activated by an invariant-based failure criterion, where an embedded cohesive crack is considered in the continuum description. A deformation gradient decomposition based on homogenisation considerations is developed for a more objective finite strain kinematic description of transverse cracks. The local equilibrium problem is established in the reference configuration to naturally include re-orientation of the fracture plane, and the employed cohesive law is able to deal with non-monotonic loading. Moreover, a continuum damage model formulated in terms of the Green–Lagrange strain tensor is used for longitudinal failure. The simulation of an open-hole multi-directional specimen subjected to tension illustrates the ability of the proposed constitutive equations to capture experimental observations.

Ergodic Archimedean dimers

We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling.

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

Evaluation of the MACE force field architecture: From medicinal chemistry to materials science.

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation, and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems, from amorphous carbon, universal materials modeling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimization to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal.

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

Deformation-dependent permeability of fibrous materials

Fluid flow in fibrous materials depends on volumetric deformation, distortional deformation and fibre reorientation. The latter two effects introduce anisotropy in the hydraulic permeability. Motivated by the study of biological tissues, this work aims to develop an analytical model for evaluating the deformation-dependent permeability of fibrous materials. The material consists of a three-dimensional assembly of long fibres of a single type, with the fluid flowing through the interstices between the fibres. The macroscopic deformations are related to the deformation of a cylindrical representative element of volume (REV), comprised of a fibre surrounded by a cylindrical jacket of fluid. The effect of fibre orientation is modelled using an orientational probability distribution function (OPDF), and the REV permeability tensor is then evaluated using previously developed methods, accounting for the macroscopic deformation. Finally, the overall permeability tensor is calculated via directional averaging of the REV permeability tensor, in which the fibre OPDF serves as the weighing function. The model is validated numerically via a uniaxial contraction (confined compression) test performed for the case of an OPDF that is isotropic in the reference (undeformed) configuration, and is found to qualitatively reproduce experimental findings. The proposed model offers an analytical tool for evaluating the permeability of fibrous materials under large deformations, based on structural information such as fibre volumetric fraction, diameter and spatial orientation.

Mesoscale DVC analyses and parameter calibration for pantographic block in 3-point flexure

In the present work, the mechanical response of a fiber network metamaterial was studied when subjected to 3-point flexure. To account for the initial deformation of the sample due to the fabrication process, backtracking (i.e., the nominal mesh was accurately repositioned in the reference configuration) was implemented in the Digital Volume Correlation (DVC) procedure. Kinematic fields were then measured via DVC at two different scales. Finite element based DVC was validated thanks to a series of initialization steps. The displacement fields were successfully measured and a peculiar deformation mechanism was observed. These measurements were employed to calibrate the constitutive parameters of a second gradient continuum model introduced for modeling this type of metamaterial. Numerical simulations are shown to be in good agreement with experimental measurements at the macroscopic scale.

Science with the Einstein Telescope: a comparison of different designs

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where each detector has a 'xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple 'metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives.