Compressible Layer Research Articles

Beryllium–tungsten graded density inner shells in double shell capsules for improved hydrodynamic stability

The outer surface of the high-Z inner shell in the double shell configuration of inertial confinement fusion experiments experiences Rayleigh–Taylor instability growth during the implosion process due to inverted density and pressure gradients between a highly compressed foam interstitial layer and the accelerating dense inner shell. Graded density layers have long been known to reduce instability growth rates. In this study, we employ high-fidelity radiation hydrodynamic simulations to demonstrate this improved stability when grading beryllium into tungsten. We first characterize the response to L-band preheat of these layers using a newly calibrated radiation drive. While graded layer capsules suffer reduced performance (here, measured as DD neutron yield from a CD foam fuel) in 1D simulations due to reduced kinetic energy coupling and reduced fuel compression, they suffer less of a performance drop when 2D instabilities are accounted for. With the improved stability of graded layers, we explore the performance of capsules with larger fuel radii and thinner shells as a preliminary study to find new designs in which graded layers produce the highest yields.

Improving contact damage resistance of spinel translucent ceramics through a multi-layer design

The brittle response of transparent spinel ceramics to contact damage is limiting their application as an alternative to glasses and single crystals. In this work, we explore a strategy to enhance the contact damage resistance of spinel ceramics by embedding alumina layers in a multi-layer architecture. Crack initiation upon Hertzian indentation was investigated in MgAl2O4 – Al2O3 laminates and compared to their corresponding monoliths. Contact stresses during loading were analyzed using finite element simulations by considering the elastic properties of the layers and contact non-linearities. Results were analyzed using Weibull statistics. It was found that the effect of in-plane residual stresses on crack formation in the laminate depends on the disposition of the compressive spinel layers, either at the surface or embedded in the structure. Embedding alumina between spinel layers increased the load-bearing capability before crack initiation by ~70% compared to spinel, offering a promising approach to enhance contact damage resistance.

Extension of the local domain-free discretization method to large eddy simulation of compressible flows

Most of the flow problems encountered in practical engineering are wall-bounded turbulent flows at high Reynolds numbers. Wall-modeled large eddy simulation (WMLES) is one of the most viable approaches for predicting these realistic flows. Immersed boundary (IB) approach is an efficient computational technique to solve flow problems involving complex and/or moving geometries. This work extends a sharp-interface IB method, named the local domain-free discretion (DFD), to WMLES of compressible flows at high Reynolds numbers. An equilibrium wall model based on solving the simplified compressible turbulent boundary layer equations is utilized to alleviate the requirement of high near-wall mesh resolution. In conjunction with the approximate boundary conditions prescribed by the modeled wall shear stress and wall heat flux, the tangential velocity and temperature at an exterior dependent node are evaluated. Then, the closure of the discrete form of governing equations at an interior node in the immediate vicinity of the immersed wall is accomplished. A simple non-equilibrium correction of the wall shear stress provided by the equilibrium wall model is introduced explicitly. The WMLES/DFD method is applied to a supersonic zero-pressure-gradient turbulent boundary layer flow, a shock wave/flat-plate boundary layer interaction, a supersonic compression ramp flow and high-speed turbulent Couette flows with various thermal boundary conditions. The influence of grid resolution is investigated in the simulation of zero-pressure-gradient turbulent boundary layer flow. By comparing the computed results with the referenced experimental data and/or numerical results, the accuracy and ability of the WMLES/DFD method to simulate compressible turbulent flows are verified.

Numerical Simulation of the Hysteresis Phenomenon and Asymmetrical Configuration of Turbulent Gas Flow in an Over-Expanded Nozzle Flows

The turbulent flow within Over-Expanded Nozzles is characterized by shock waves inducing unsteady separation of the boundary layer, which can exhibit both free and restricted detachment. This study investigates various physical phenomena encountered during the expansion regime, including supersonic jet formation, jet separation, adverse pressure gradients, shockwave interactions, turbulent boundary layers, compressible mixture layers, and large-scale turbulence. These complex phenomena significantly influence nozzle performance. Utilizing numerical simulations based on the resolution of Navier-Stokes equations via finite volume methods and employing the CFD-FASTRAN code, this research analyzes detachment characteristics, transition phenomena, and the predictive accuracy of different turbulence models. A test case from the ATAC project CNES-ONERA (Aerodynamics of Hoses and Back-bodies), is examined to elucidate the hysteresis phenomenon and asymmetrical configurations resulting from boundary layer detachment.

Contact damage response of alumina-based layered architectures under different loading configurations

Hertzian contact damage upon spherical indentation is investigated in alumina-based ceramics designed with embedded textured compressive layers. The effect of the location of the embedded layer and the testing configuration (parallel or normal to the layer orientation) on the sub-surface damage evolution is explored. An acoustic emission system for crack detection and post-mortem cross sectioning are employed to evaluate the onset and extension of damage in the different samples. Distinct acoustic signals detected at different contact loads are correlated with the onset of the ring crack, cone crack propagation and quasi-plastic deformation within the textured layer. The distinct damage mechanisms are influenced by the location of the embedded textured compressive layer and the loading orientation with respect to the layers. The design of layered ceramics for contact applications should consider the loading orientation as well as the contact stress field with respect to the “protective” layer to enhance damage tolerance.

Cloud–Cloud Collision: Formation of Hub-filament Systems and Associated Gas Kinematics. Mass-collecting Cone—A New Signature of Cloud–Cloud Collision

Massive star-forming regions (MSFRs) are commonly associated with hub-filament systems (HFSs) and sites of cloud–cloud collision (CCC). Recent observational studies of some MSFRs suggest a possible connection between CCC and the formation of HFSs. To understand this connection, we analyzed the magnetohydrodynamic simulation data from Inoue et al. This simulation involves the collision of a spherical turbulent molecular cloud with a plane-parallel sea of dense molecular gas at a relative velocity of about 10 km s−1. Following the collision, the turbulent and nonuniform cloud undergoes shock compression, rapidly developing filamentary structures within the compressed layer. We found that CCC can lead to the formation of HFSs, which is the combined effect of turbulence, shock compression, magnetic field, and gravity. The collision between the cloud components shapes the filaments into a cone and drives inward flows among them. These inward flows merge at the vertex of the cone, rapidly accumulating high-density gas, which can lead to the formation of massive star(s). The cone acts as a mass-collecting machine, involving a nongravitational early process of filament formation, followed by gravitational gas attraction to finalize the HFS. The gas distribution in the position–velocity (PV) and position–position spaces highlights the challenges in detecting two cloud components and confirming their complementary distribution if the colliding clouds have a large size difference. However, such CCC events can be confirmed by the PV diagrams presenting gas flow toward the vertex of the cone, which hosts gravitationally collapsing high-density objects, and by the magnetic field morphology curved toward the direction of the collision.

Analysis of Saturated Impulse for Square Plates under Flat Slamming Impact: Experimental and Numerical Investigation

The saturated impulse is a special phenomenon in the dynamic plastic behavior of engineering structures under intensive pulse loading, such as slamming loading. In this study, slamming experiments were performed on steel plates to investigate their slamming pressure and dynamic plastic responses, as well as the saturation phenomenon, and elucidate the effect of the plate thickness and material properties on the dimensionless saturated deflection and saturated impulse in combination with the published test data. The results show that the dimensionless saturated deflection and saturated impulse of the test plates gradually increased as the dimensionless stiffness decreased. After being validated against the experimental results, a numerical method that considered the fluid–structure interaction (FSI) effect was then employed to provide comprehensive insight into the transient plastic responses and saturated impulse of the flat plates under slamming impact. Numerical simulations revealed that the compressed air layer always existed during the effective process of the flat slamming impact. Through the numerical prediction of the dynamic plastic deflection and slamming pulse loading, it was observed that the saturated impulse phenomenon always took place after the time instant of the peak value of the pressure pulse. Furthermore, the analysis of the saturated impulse based on the numerical simulations indicated that the saturation phenomenon was more likely to be achieved as the water impact velocity increased.

Improved JPEG Lossless Compression for Compression of Intermediate Layers in Neural Networks Based on Compute-In-Memory

With the development of Convolutional Neural Networks (CNNs), there is a growing requirement for their deployment on edge devices. At the same time, Compute-In-Memory (CIM) technology has gained significant attention in edge CNN applications due to its ability to minimize data movement between memory and computing units. However, the deployment of complex deep neural network models on edge devices with restricted hardware resources continues to be challenged by a lack of adequate storage for intermediate layer data. In this article, we propose an optimized JPEG Lossless Compression (JPEG-LS) algorithm that implements serial context parameter updating alongside parallel encoding. This method is designed for the global prediction and efficient compression of intermediate data layers in neural networks employing CIM techniques. The results indicate average compression ratios of 6.44× for VGG16, 3.62× for ResNet34, 1.67× for MobileNetV2, and 2.31× for InceptionV3. Moreover, the implementation achieves a data throughput of 32 bits per cycle at 600 MHz on the TSMC 28 nm, with a hardware cost of 122 K Gate Count.

Effect of shot peening equivalent impact force on fatigue crack growth behavior and fatigue life prediction of train brake discs

Brake discs, vital rail components, are subjected to intense friction and thermal cycling during braking, leading to surface cracking and fatigue failure. To address these issues, a novel equivalent impact force model for shot peening is proposed in this paper, with the aim of measuring the efficacy of shot peening and predicting the fatigue crack propagation life of brake discs with the assistance of an enhanced SSO algorithm. A finite element model of a cast steel brake disc simulated fatigue crack propagation under sinusoidal cyclic loading. The validity of the multiple projectile random impact model was experimentally confirmed by introducing a residual stress field into the disc surface using equivalent impact forces of 0.3, 0.4 and 0.5 MPa. This stress field was incorporated into the cyclic fatigue crack propagation model and compared with the FCGR results. Shot peening produced a compressive residual stress layer which increased in thickness with increasing impact force. The fatigue crack propagation rate was highly sensitive to the equivalent impact force, decreasing between 0.3 and 0.4 MPa and increasing from 0.4 to 0.5 MPa. Optimal crack propagation inhibition was at 0.4 MPa, which increased fatigue life by 457 % compared to non-peened discs. The improved SSO algorithm also achieved a 6 % increase in prediction accuracy.

Microstructure and mechanical properties of wire and arc additive manufactured 2319 aluminum alloy treated by laser shock peening

The components manufactured by Wire and Arc Additive Manufacturing (WAAM) have some problems to be solved urgently, such as uneven microstructure, numerous pore defects, and residual tensile stress. Laser Shock Peening (LSP) is an innovative and advanced surface modification technology that improves mechanical characteristics by inducing significant plastic deformation and high compressive residual stress on metal surfaces. Therefore, combining LSP with WAAM is expected to solve its existing problems. In this work, LSP with different energy parameters was used to post-process the WAAM 2319 aluminum alloy. The results indicated that LSP could improve the microstructure, eliminate near-surface pores, harden the surface layer, and induce a residual compressive stress layer, and the effect was more effective with the increase of laser energy applied. The yield strength of the peened specimens significantly increased by 60.73 %, and the ultimate tensile strength also increased by 16.03 %. The hole fatigue life of the peened specimens was significantly improved, increasing by 179.8 % and 261.7 %, respectively, applying laser energies of 5 J and 10 J. Therefore, the engineering industry may benefit from a combination of LSP and WAAM technology.

Experimental investigation on the failure characteristic and synergistic load-bearing mechanism of multi-layer linings for deep soft rock tunnels

Multi-layer linings have been widely used in deep rheological soft rock tunnels for the excellent performance in preventing large-deformation hazards. Previous studies have focused on the bearing capability of multi-layer lining, however, its failure characteristics and synergistic load-bearing mechanisms under high geo-stress are still unclear. To fill the gap, three-dimensional geomechanical model tests were conducted and synergistic mechanisms were analysed in this study. The model test was divided into normal loading, excavating, and overloading stages. The surrounding rock deformation was monitored by using an improved high-precise extensometer measurement system. Results show that the largest radial deformation appears on the sidewall, followed by the floor and vault during the excavating stage. The relative convergence deformation of sidewalls springing reaches 1.32 mm. The failure characteristics of the multi-layer linings during the overloading stage undergo an evolution of stability, crack initiation, local failure, and collapse, with a safety factor of 1.0–1.6, 1.6–2.0, and 2.0–2.2, respectively. The synergistic load-bearing mechanism analysis results suggest that the early stiffness and late yielding deformation capacity of large deformation support measures play important roles in stability maintenance both in the construction and operation of deep soft rock tunnels. Therefore, the combination of yielding support or a compressible layer with reinforced support is recommended to mitigate the effect of the high geo-stress.

EVALUATION OF DEFORMATION PARAMETERS OF SILO FOUNDATIONS REINFORCED WITH SOIL-CEMENT ELEMENTS

The mandatory controlled criterion for steel silos is the limitation of foundation settlement and tilting, which is regulated by DBN V.2.6-221:2021. The threshold value of silo settlement is Smax,u = 150 mm. The most economical foundation solution is a large-sized slab on a natural base or a soil cushion. It is possible to stabilise the weak base by reinforcing it with vertical soil-cement elements (SCE). In Ukraine, most foundations have an underground gallery or silo floor. When the silos are first loaded, there is geodetic monitoring of the vertical settlement of the silo base and comparison of its data with the threshold values of settlement and tilting. The objective is to investigate the effect of limited-depth soil reinforcement on the stabilisation of the soil base and the average total foundation settlement. The task of the study is to create a methodology for predicting the impact of reinforcement with soil-cement elements on the parameters of the soil base general stiffness for a silo foundation. The research methods are geodetic monitoring of settlements around the perimeter of silo foundations during initial loading at four different elevators with different geological conditions. Thus, the predicting method of the impact while reinforcing with soil-cement elements on the general stiffness parameters of the soil base for the silo foundation was tested on the bases of silos for four elevators. These elevators represent different engineering and geological conditions. The proof of the methodology’s validity is the coincidence with the results of geodetic subsidence monitoring along the perimeter of silo foundations. According to the research results, it is possible to state that the reinforcement of the foundation base with vertical soil-cement elements allows for the effective stabilisation of soil parameters. We propose an evaluation method of the reinforcement effect with soil-cement elements in the form of the stabilisation coefficient for the soil base, kEi. We further prove the primary role of the soil-cement reinforcing elements operation and their length while stabilising the base. The base stiffness is stabilised at the compressible stratum depth and beyond the foundation boundaries. It is possible to use the method of reinforcement influence evaluation to determine the actual parameters of the stabilised soil base, n, according to geodetic monitoring data. The authors have studied the effect of limited depth reinforcement for stabilising the foundation. The research obtained the empirical dependence of the reinforcement required depth at given depth values for the base compressible layer. The authors proposed using the linearly deformed layer method, considering the operation of soil-cement elements as discrete soil reinforcement. The numerous experiments with the Finite Element Method confirm the high convergence of the calculated results with those obtained analytically. Keywords: foundation settlement, soil-cement element, geodetic monitoring, steel silo, foundation stiffness.

Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations, such as the root mean square, skewness and flatness factors, probability density function, and frequency spectrum, are assessed to be very weak. Regarding the space-time characteristics, the convection velocity Uc determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. At Mach 0.5, the peaks of the fast (Uc+c) and slow (Uc−c) acoustic waves are unattached to others with c denoting acoustic speed, while only the peak of the fast acoustic wave is distinguishable from the convective peak at Mach 1.2 and 2.0. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.

Effect of laser shock peening on tribological properties of 55SiMoVA bearing steel

Wear is an important factor limiting the service life of 55SiMoVA bearing steel. In this work, laser shock peening (LSP) technology is used to improve the tribological properties of 55SiMoVA bearing steel, and the corresponding underlying mechanism is systematically discussed. After LSP, the kurtosis (Sku) of surface roughness asperities reduced from 10.355 to 5.488, and no new phase was generated. Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) analysis suggested LSP induced the generation of dislocation structures and deformation twins, leading to a decrease in the average grain size and an increase in the fraction of high-angle grain boundaries. Due to the work-hardening and fine-grain strengthening, the microhardness increased by 16.6 %, the maximum residual compressive stress amounted to −793.1 MPa, and the coefficient of friction (COF) and wear volume were significantly reduced. Scanning electron microscopy (SEM) results indicated that the wear mechanism of 55SiMoVA bearing steel before and after LSP was not transformed. However, the abrasive wear and delamination wear of the LSPed specimens were significantly improved, which was mainly attributed to grain refinement, increasing microhardness and constructing a residual compressive stress layer in the subsurface layer of 55SiMoVA bearing steel. During the sliding process, the increase in microhardness limits micro-plowing on the wear surface, and the residual compressive stress inhibits the crack formation and expansion, improving the wear resistance of 55SiMoVA bearing steel.

The intrinsic scaling relation between pressure fluctuations and Mach number in compressible turbulent boundary layers

The intrinsic scaling relation between pressure fluctuations and Mach number in compressible turbulent boundary layers

Molecular dynamics characterization of the interfacial structure and forces of the methane-ethane sII gas hydrate interface

The nucleation of gas hydrates is of great interest in flow assurance, global energy demand, and carbon capture and storage. A complex molecular understanding is critical to control hydrate nucleation and growth in potential applications. Molecular dynamics is employed combined with the mechanical definition of surface tension to assess the surface stresses controlling interfacial behavior. We characterize the interfacial tension for sII methane/ethane hydrate and gas mixtures for different temperatures and pressures. We find that the surface tension trends positively with temperature in a balance of water-solid and water-gas interactions. The molecular dipole shows the complexities of water molecule behavior in small, compressed pre-melting layer that emerges as a quasi-liquid. These behaviors contribute to the developing knowledge base surrounding practical applications of this interface.

Using Micrometer Scale X-Ray CT and Pore Network Modeling to Assess High-Energy Bi-Layer Li-Ion Battery Cathode Structures

The optimization of cathode pore space is pivotal for enhancing the rate capability of lithium-ion battery electrodes. Previous studies on simulated cathodes have highlighted the importance of achieving an optimal porosity gradient, with a gradual increase from the current collector side to the separator side to accommodate the growing demand for ion transport in that direction [1]–[3]. In this research, we address this requirement by introducing and investigating bi-layer NCM 811 cathodes. These cathodes consist of a slurry-coated dense bottom layer and a spray-coated highly porous top layer with varying relative thickness to approximate the desired porosity gradient. Employing Micrometer-scale X-ray CT characterization and pore network modeling, we evaluate the structural features, demonstrating the effectiveness of the design, and quantify essential parameters such as porosity and tortuosity. Furthermore, the cathodes are integrated into lithium anode half-cells and subjected to electrochemical cycling at different rates to assess ion transport and rate capability. Our findings reveal that to achieve the highest discharge spatial energy density above 1C for cathodes approximately 100μm thick, the compressed bottom layer with 30% porosity should have a thickness of 60μm, while the highly porous top layer with around 47% porosity should be 40μm thick.Reference:[1] A. Shodiev et al., “Deconvoluting the benefits of porosity distribution in layered electrodes on the electrochemical performance of Li-ion batteries,” Energy Storage Mater., vol. 47, pp. 462–471, May 2022, doi: 10.1016/j.ensm.2022.01.058.[2] X. Lu et al., “3D microstructure design of lithium-ion battery electrodes assisted by X-ray nano-computed tomography and modelling,” Nat. Commun., vol. 11, no. 1, p. 2079, Apr. 2020, doi: 10.1038/s41467-020-15811-x.[3] K. Song, C. Zhang, N. Hu, X. Wu, and L. Zhang, “High performance thick cathodes enabled by gradient porosity,” Electrochimica Acta, vol. 377, p. 138105, May 2021, doi: 10.1016/j.electacta.2021.138105.

Dual skin effect and deep heterostructure of titanium alloy subjected to high-frequency electropulsing-assisted laser shock peening

Laser shock peening, an advanced technology for severe surface plasticity peening, encounters challenges such as shallow hardened layers and surface spalling when dealing with difficult-to-machine materials. In this study, we introduced a high-frequency electropulsing-assisted laser shock peening (HFEP-LSP) technique that coupled laser shock peening with high-frequency electric pulses to achieve a significant and deeper plastic deformation layer. In the HFEP-LSP technique, we first considered the dual “skin effect”, which coupled the skin effect of high-frequency electric pulses with the “skin effect” of the mechanical effect induced by the laser shock wave. An integrated experimental platform comprising an electric pulse generator, laser shock peening equipment, and a control system was built. A >1.6 mm deep compressive residual stress layer was obtained, and the depth of the plastic deformation layer increased by 83.3 %. Furthermore, we elucidated the dual “skin effect”-induced complex heterostructure and βm phase transition. A comprehensive analysis revealed the factors contributing to the deeper strengthening layer induced by HFEP-LSP, including the compressive residual stress and plastic deformation layers. In addition, the effects of laser shock peening and HFEP-LSP on the mechanical properties were investigated. Compared to the annealed samples, the ultimate tensile strength and elongation of the HFEP-LSP-treated samples were increased by 12.3 % and 57.1 %, respectively, with a fatigue life improvement of 176.4 %. The mechanism of synergistic improvement in strength and ductility was demonstrated.

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

Adjoint-based optimisation of time- and span-periodic flow fields with Space–Time Spectral Method: Application to non-linear instabilities in compressible boundary layer flows

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.