High-fidelity Computational Fluid Dynamics Research Articles

Performance Characterization of a Slotted Wind Turbine Airfoil Featuring Passive Blowing

Renewable energy is crucial for a sustainable future, and wind energy holds significant potential as a viable solution to meet global demands. The current study employs high-fidelity Computational Fluid Dynamics (CFD) simulations to investigate the unsteady aerodynamics of an S809 wind turbine airfoil carved with an inclined contracting curved slot at the mid-chord location. The numerical analyses cover a wide range of angles of attack, α = 0°-20°, at a chord-based Reynolds number of Rec = 5×105. The slotted airfoil exhibits superior aerodynamic performance over moderate-to-high angles of attack (α > 6°), with increased lift, reduced drag, and enhanced glide ratio of up to 1.3x, 0.5x, and 3.7x respectively, compared to the baseline. The slot-induced flow control significantly suppresses flow transition and separation across the airfoil surfaces. The attached-flow regime impedes the formation of flow anomalies, resulting in enhanced aerodynamic performance. Comparative analyses reveal significant reductions in velocity fluctuations, Reynolds shear, vorticity, and turbulent kinetic energy, across the slotted airfoil surface and wake region. The aeroacoustic analysis of the slotted airfoil exhibits substantial reduction in the far-field noise over moderate-high angles of attack, with an overall noise level reduction of approximately 14 decibels recorded at α = 17°. Overall, this study highlights the potential of slot-induced flow control as an effective strategy for enhancing the aerodynamic performance of wind turbines.

Verification and Validation of Spectral Element Code for Supercritical CO2 Flow in Vertical Heated Tubes

The investigation of heat transfer in supercritical CO2 (sCO2) has garnered considerable attention in recent decades, given sCO2’s potential as a promising working fluid for advanced power conversion cycles. Despite previous research efforts, there are still gaps in our understanding of sCO2 heat transfer, particularly in conditions associated with heat transfer deterioration. To delve into sCO2 heat transfer more comprehensively, we propose employing the high-fidelity computational fluid dynamics code NekRS to simulate sCO2 flow using the large eddy simulation technique. Through graphics processing unit acceleration, NekRS achieves a higher computational speed than traditional CPU-based systems. However, before using NekRS in practical applications involving sCO2, it is imperative to perform verification and validation. This paper presents our efforts to verify and validate the NekRS code’s capability for simulating sCO2 using heated vertical tubes, where heat transfer deterioration usually happens. To accommodate the unique properties of sCO2, we have modified the NekRS code by integrating third-party property modules, such as REFPROP and PROPATH. Our simulations are compared with experimental and numerical data from the literature, instilling confidence in leveraging NekRS for future engineering applications. Our simulations also reveal that the accuracy of the property module significantly impacts the results, with REFPROP outperforming PROPATH for sCO2 properties. Additionally, we observed that, depending on the flow direction, buoyancy can either enhance or suppress turbulence in sCO2 flow. In upward flow, under certain conditions, the suppressed turbulence leads to heat transfer deterioration, resulting in elevated wall temperatures.

Determination of Maneuvering Force Coefficients for a Destroyer Model with OpenFOAM

_ Ship maneuvering performance can be predicted using various methods, including physical model tests, rapid simulations using coefficient-based forces, and high-fidelity computational fluid dynamics. This article considers the application of computational fluid dynamics for the prediction of hull force coefficients to be used as inputs to rapid maneuvering simulations. The open-source software OpenFOAM was used to simulate forces on the destroyer model DTMB 5415 for steady drift, oscillatory pure sway motion, and oscillatory yaw motion. Recommendations are provided regarding best practices in a number of areas, including domain size, mesh refinement, time step size, and turbulent modeling. Predicted forces for steady drift angles up to 12 degrees are typically within 10%of experimental values. For oscillatory sway and yaw motions, predicted forces are typically within 25%of experimental values. Keywords maneuvering; OpenFOAM; best modeling practices

Sensitivity of Post-TAVR Hemodynamics to the Distal Aortic Arch Anatomy: A High-Fidelity CFD Study.

Patient-specific simulations of transcatheter aortic valve (TAV) using computational fluid dynamics (CFD) often rely on assumptions regarding proximal and distal anatomy due to the limited availability of high-resolution imaging away from the TAV site and the primary research focus being near the TAV. However, the influence of these anatomical assumptions on computational efficiency and resulting flow characteristics remains uncertain. This study aimed to investigate the impact of different distal aortic arch anatomies-some of them commonly used in literature-on flow and hemodynamics in the vicinity of the TAV using large eddy simulations (LES). Three aortic root anatomical configurations with four representative distal aortic arch types were considered in this study. The arch types included a 90-degree bend, an idealized distal aortic arch anatomy, a clipped version of the idealized distal aortic arch, and an anatomy extruded along the normal of segmented anatomical boundary. Hemodynamic parameters both instantaneous and time-averaged such as Wall Shear Stress (WSS), and Oscillatory Shear Index (OSI) were derived and compared from high-fidelity CFD data. While there were minor differences in flow and hemodynamics across the configurations examined, they were generally not significant within our region of interest i.e., the aortic root. The choice of extension type had a modest impact on TAV hemodynamics, especially in the vicinity of the TAV with variations observed in local flow patterns and parameters near the TAV. However, these differences were not substantial enough to cause significant deviations in the overall flow and hemodynamic characteristics. The results suggest that under the given configuration and boundary conditions, the type of outflow extension had a modest impact on hemodynamics proximal to the TAV. The findings contribute to a better understanding of flow dynamics in TAV configurations, providing insights for future studies in TAV-related experiments as well as numerical simulations. Additionally, they help mitigate the uncertainties associated with patient-specific geometries, offering increased flexibility in computational modeling.

Numerical investigation of aerodynamic interactions for the coaxial rotor system in low-speed forward flight

This study is conducted to investigate the aerodynamic characteristics of a coaxial rotor in low-speed forward flight using a high-fidelity computational fluid dynamics (CFD) solver. Numerical simulations are performed on the coaxial rotor and its isolated upper and lower rotors at two small advance ratios, 0.12 and 0.24. Interaction events in the flowfield, especially blade-vortex-interaction (BVI), are studied in detail. As the forward speed increases, the airload distributions become concentrated on the front part of the disk. Fluctuations in the loading indicate self-BVIs within each rotor, and blade-crossover events and rotor-to-rotor BVIs between the coaxial upper and lower rotors. Principal BVI events are identified in the well-captured wake structures by the 8th-order TENO reconstruction scheme. Self-BVIs on all rotors reduce in strength as the forward speed increases, while rotor-to-rotor BVIs on the coaxial lower rotor increase in strength with the increasing forward speed. In the coaxial configuration, the wake of the upper rotor is induced to move backwards and downwards due to the exertion of the lower rotor wake. The wake of the coaxial lower rotor features the most complex flow nature among all rotors. At both advance ratios, the coaxial lower rotor experiences a parallel rotor-to-rotor BVI, causing highly impulsive loading fluctuations along the blade span.

Optimizing Ship Airwake Database for Predicting Autospectra Using Deep Learning

Airwakes are shed behind a ship’s superstructure, and they represent a highly turbulent and rapidly distorting flow field. Because of this complexity, they require a baseline: A database of flow velocity points, preferably through experiments and also through high-fidelity computational fluid dynamics simulations. However the database is prohibitively costly, and in situ measurements, at a constant wind angle, are often affected by the weather. A previously developed perturbation scheme helps to generate the autospectrum in closed form from a given wind database, specifically, from the numerically extracted autospectrum for this database. The primary objective of this paper is to demonstrate how deep neural networks can be fruitfully exploited to reduce the dependence on a database of flow velocity points in generating the autospectra, by reducing the amount of in situ data required to achieve the same accuracy as established methods. Two machine learning approaches are developed to predict the autospectrum for a data set when provided with a subset of the wind data set at the input and are assessed using cross-validation. In the first, a neural network is applied to predict the perturbation scheme. Though this method did not predict the autospectrum better than the previously developed perturbation scheme, it laid the foundation for the second method. In the second, a neural network is applied to the autospectra which can be numerically extracted from a database. An improvement is found in the average error computed over all data sets for the model-predicted autospectrum compared to the average error in the autospectrum predicted using the conventional method. The model provided better results for 51.4% of the data sets compared to the conventional method, with many data sets showing marked improvement. The database measured from the Naval Academy YP676 training vessel is used for training and testing the neural network.

The construction of a neural network proxy model for ship hull design based on multi-fidelity datasets and the parameter freezing strategy

Designing a ship hull to keep the hydrodynamic performance meet the requirements is an indispensable step in the ship's preliminary design. However, in the traditional design process, the design workload is labor-intensive and time-consuming due to the need to estimate a large number of design schemes. To address this issue, this work developed a Neural Network Proxy Model (NNPM) to assist the hydrodynamic resistance prediction for the ship hull design process. The data used in the NNPM construction was supported by two Computational Fluid Dynamic (CFD) methods with different fidelity where the low-fidelity one for tuning and pre-training, and the high-fidelity one for fine-training. To mitigate the risk of overfitting stemming from disparities in data volumes, the parameter freezing strategy is adopted during the high-fidelity dataset-based fine-training. The results obtained from validation numerical experiments indicated that the NNPM exhibited a forecast error of less than 1% when compared to the high-fidelity CFD method. Importantly, this high accuracy is achieved while maintaining a low construction workload, demonstrating the potential of Artificial Intelligence (AI) to predict the hydrodynamic load of hulls in the ship's preliminary design, which can further advance the artificial intelligence-assisted design (AIAD) technology for various marine structures.

Neko: A modern, portable, and scalable framework for high-fidelity computational fluid dynamics

Computational fluid dynamics (CFD), in particular applied to turbulent flows, is a research area with great engineering and fundamental physical interest. However, already at moderately high Reynolds numbers the computational cost becomes prohibitive as the range of active spatial and temporal scales is quickly widening. Specifically scale-resolving simulations, including large-eddy simulation (LES) and direct numerical simulations (DNS), thus need to rely on modern efficient numerical methods and corresponding software implementations. Recent trends and advancements, including more diverse and heterogeneous hardware in High-Performance Computing (HPC), are challenging software developers in their pursuit for good performance and numerical stability. The well-known maxim “software outlives hardware” may no longer necessarily hold true, and developers are today forced to re-factor their codebases to leverage these powerful new systems. In this paper, we present Neko, a new portable framework for high-order spectral element discretization, targeting turbulent flows in moderately complex geometries. Neko is fully available as open software. Unlike prior works, Neko adopts a modern object-oriented approach in Fortran 2008, allowing multi-tier abstractions of the solver stack and facilitating hardware backends ranging from general-purpose processors (CPUs) down to exotic vector processors and FPGAs. We show that Neko’s performance and accuracy are comparable to NekRS, and thus on-par with Nek5000’s successor on modern CPU machines. Furthermore, we develop a performance model, which we use to discuss challenges and opportunities for high-order solvers on emerging hardware.

Investigation of Surface-Catalycity Effects on Hypersonic Glide Vehicle Trajectory Optimization

The optimization of a hypersonic glide vehicle’s reachable domain is studied using different models to constrain the stagnation-point heat transfer. The vehicle is modeled as a high-lift common aero vehicle that uses bank-angle modulation for crossrange maneuvering with a leading-edge thermal protection system made of an ultra-high-temperature ceramic. A constrained nonlinear optimization problem is formulated to determine the range of feasible trajectories that satisfy aerodynamic heating and loading constraints. The optimal control profile is determined using a modified particle swarm optimization routine that employs a penalty function approach to handle path and terminal constraints. Baseline trajectories are determined using an existing convective heat-flux correlation, and the effect of surface catalycity on the optimized trajectories is investigated by applying a correction factor, derived from high-fidelity computational fluid dynamics simulations, to the heat-flux correlation. Results demonstrate a high sensitivity of the optimized trajectories to the underlying aerothermodynamics model such that accounting for surface catalycity expands the reachability by an order of magnitude.

Experimental quantification of inward Marangoni convection and its impact on keyhole threshold in laser powder bed fusion of stainless steel

Laser metal additive manufacturing has the potential to revolutionize the production of complex geometries with high precision across various industrial applications. To optimize the reliability of the process, a detailed understanding of the melt pool dynamics during the process is essential, particularly in the nearly pore-free regimes. In this study, the melt pool dynamics across conduction mode to keyhole mode in laser powder bed fusion processing of stainless steel 316 L have been investigated by means of in-situ synchrotron X-ray imaging utilizing tungsten particles as tracers. The spatial distribution of the fluid flow in the melt pool has been quantified with a resolution of ∼10 µm through automatic tracing all moving particles in the melt pool. The results identified the influence of the interplay between laser power and scanning speed on melt flow velocities. The measurements also revealed a pronounced impact of the inward Marangoni convection on the conduction-keyhole threshold, offering a new degree of freedom to broaden the pore-free process window of laser-based additive manufacturing. These findings contribute to a more comprehensive understanding of the melt pool dynamics during laser metal additive manufacturing and provide a valuable reference for calibrating high-fidelity computational fluid dynamics models.

Data-driven identification and pressure fields prediction for parallel twin cylinders based on POD and DMD method

The mode analysis of parallel twin cylinders is conducted in this paper using two data-driven methods: proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). First, a high-fidelity computational fluid dynamics (CFD) model of parallel twin cylinders is established, and numerical simulations of the model are carried out. Subsequently, the fundamental principles of the POD and DMD algorithms are systematically introduced. Utilizing snapshots obtained from the high-fidelity CFD model, the POD and DMD methods are employed to extract the dominant flow structures. Furthermore, a comparison between the two data-driven methods is conducted by analyzing modal frequencies, pressure distribution, and the reconstruction errors of pressure fields. Finally, the pressure fields of non-sample points are predicted based on the POD–backpropagation neural network (BPNN) surrogate model and the DMD method, and the predicted results are compared with the CFD simulation results. It found that (i) the DMD method is capable of extracting the main coherent structures of the pressure fields, directly obtaining flow modes and their corresponding frequencies, and assessing the stability of flow modes; (ii) the DMD method can capture the main flow features of the pressure fields in both spatial and temporal dimensions, while the POD method is primarily efficient at capturing the spatial features of the pressure fields; (iii) in contrast to the frequency-ranked DMD method, the energy-ranked POD method can reconstruct the pressure fields using a smaller number of modes, indicating that the POD method has an advantage in terms of mode reduction; (iv) in contrast to the energy-ranked POD method, the frequency-ranked DMD method has a wider applicability to the range of flow types and has more advantages in stability analysis of complex dynamic systems; (v) the predicted pressure fields around the cylinder using the first five-order POD modes or DMD modes closely align with CFD calculation results. Additionally, the evolution of pressure fields predicted by the POD–BPNN surrogate model with the first five-order POD modes or the DMD method with the first 200-order DMD modes significantly agrees with CFD simulation results; (vi) the combined use of the POD–BPNN surrogate model and DMD methods allows efficient interpolation and extrapolation of samples, delivering exceptional predictive performance. This study offers insight into the coherent structures in parallel twin cylinders.

Influence of rotor blade flexibility on the near-wake behavior of the NREL 5 MW wind turbine

Abstract. High-fidelity computational fluid dynamics (CFD) simulations of the National Renewable Energy Laboratory (NREL) 5 MW wind turbine rotor are performed, comparing the aerodynamic behavior of flexible and rigid blades with respect to local blade quantities as well as the wake properties. The main focus has been set on rotational periodic quantities of blade loading and fluid velocity magnitudes in relation with the blade tip vortex trajectories describing the development of those quantities in the near wake. The results show that the turbine loading in a quasi-steady flow field is mainly influenced by blade deflections due to gravitation. Deforming blades change the aerodynamic behavior, which in turn influences the surrounding flow field, leading to non-uniform wake characteristics with respect to speed and shape.

Reliability assessment of off-policy deep reinforcement learning: A benchmark for aerodynamics

Abstract Deep reinforcement learning (DRL) is promising for solving control problems in fluid mechanics, but it is a new field with many open questions. Possibilities are numerous and guidelines are rare concerning the choice of algorithms or best formulations for a given problem. Besides, DRL algorithms learn a control policy by collecting samples from an environment, which may be very costly when used with Computational Fluid Dynamics (CFD) solvers. Algorithms must therefore minimize the number of samples required for learning (sample efficiency) and generate a usable policy from each training (reliability). This paper aims to (a) evaluate three existing algorithms (DDPG, TD3, and SAC) on a fluid mechanics problem with respect to reliability and sample efficiency across a range of training configurations, (b) establish a fluid mechanics benchmark of increasing data collection cost, and (c) provide practical guidelines and insights for the fluid dynamics practitioner. The benchmark consists in controlling an airfoil to reach a target. The problem is solved with either a low-cost low-order model or with a high-fidelity CFD approach. The study found that DDPG and TD3 have learning stability issues highly dependent on DRL hyperparameters and reward formulation, requiring therefore significant tuning. In contrast, SAC is shown to be both reliable and sample efficient across a wide range of parameter setups, making it well suited to solve fluid mechanics problems and set up new cases without tremendous effort. In particular, SAC is resistant to small replay buffers, which could be critical if full-flow fields were to be stored.

Multi-Objective Bayesian Optimization Design of Elliptical Double Serpentine Nozzle

The use of traditional optimization methods in engineering design problems, specifically in aerodynamic and infrared stealth optimization for engine nozzles, requires a large number of objective function evaluations, therefore introducing a considerable challenge in terms of time constraints. In this paper, this limitation is addressed by using a sample-efficient multi-objective Bayesian optimization that takes Kriging as a surrogate model and Expected Hypervolume Improvement as the infill criterion. Using this approach, the probabilistic model is continuously established and updated, and the approximate Pareto front is obtained at a relatively small computational budget. The objective of this work is to evaluate the applicability of employing a multi-objective Bayesian optimization framework for the aerodynamic-infrared shape optimization of an elliptical double serpentine nozzle at 6 km flight condition, where the objective functions are evaluated by means of high-fidelity computational fluid dynamics and reversed Monte Carlo ray tracing simulations. We achieve good results in both infrared radiation signature reduction and aerodynamic performance improvement with a reasonable number of evaluations, indicating that the proposed method is effective and efficient for tackling the computationally intensive optimization challenges in the aircraft design.

High Throughflow StreamVane Swirl Distortion Generators: Design and Analysis

Abstract In recent years, the StreamVane technology has developed into a mature and streamlined process that can reproduce swirl distortion for ground-test evaluation of fan and compressor performance and durability. A StreamVane device consists of complex turning vanes that accurately output a distorted secondary velocity field at a defined distance downstream. To further advance the applications and conditions in which these devices operate, a research effort was developed and completed to investigate methods to increase critical Mach numbers. The effort was split into three separate stages: (1) Perform high fidelity computational fluid dynamics (CFD) to identify peak Mach number locations within twin and quad swirl vane pack designs; (2) conduct thorough literature reviews on relevant high throughflow techniques; and (3) design and implement selected techniques to evaluate improvements using the same high-fidelity CFD methods. It was predicted that employing blade lean within high-speed vane junctions increased critical Mach numbers by 6.6%, while blade sweep resulted in a 3.5% increase. The results and conclusions from this effort are presented throughout this paper with a primary focus on comparing Mach numbers and swirl profiles between vane packs with and without high throughflow designs.

Enhancing Airfoil Performance through Artificial Neural Networks and Genetic Algorithm Optimization

As airfoil design plays a crucial role in achieving superior aerodynamic performances, optimization has become an essential part in various engineering applications, including aeronautics and wind energy production. Airfoil optimization using high-fidelity CFD, although highly effective, has proven itself to be time-consuming and computationally expensive. This paper proposes an alternative approach to airfoil performance assessment, through the integration of a deep learning algorithm and a stochastic optimization method. NACA 4-digit parametrization was used for airfoil geometry generation, to ensure feasibility and to reduce the number of input variables. An extensive dataset of airfoil performance parameters has been obtained using an automated CFD solver, laying the foundation for the training of an accurate and robust Artificial Neural Network, capable of accurately predicting aerodynamic coefficients and significantly reducing computational time. Due to the ANN’s predictive capabilities of efficiently navigating vast search spaces, it has been employed as the fitness evaluation method of a multi-objective Genetic Algorithm. Following the optimization process, the resulting airfoils demonstrate significant enhancements in aerodynamic performance and notable improvements in stall behavior. To validate their increased capabilities, a high-fidelity Computational Fluid Dynamics (CFD) validation was conducted. Simulation results demonstrate the approach’s efficacy in finding the optimum airfoil shape for the given conditions and respecting the imposed constraints.

Acoustic Metamaterials for Electronics Cooling Fan Noise Reduction

Acoustic noise is a significant obstacle that limits the performance of data centre Hard Disk Drive (HDD) storage systems. The primary noise source of these systems has been identified as cooling fans that are used for their thermal management. New acoustic metamaterial (AM) designs can be used as a solution to this problem. AMs can be custom-designed to address specific tonal frequencies that HDD servo systems show high sensitivity to. This paper focuses on developing a 3D-printed annular AM treatment that can be easily attached to the inlet or outlet of an axial fan. Initial design optimization was conducted using the Finite Element Method (FEM). Further FEM simulations were carried out using more realistic fan sources from high-fidelity Computational Fluid Dynamics (CFD) simulations. The AM geometry was tested experimentally with a fan that is commonly used in a data centre storage system, where the fan speed was set to induce an acoustic tone that negatively affects the performance of HDDs. Then a full scale Finite Element Method simulation was ran using fan acoustic source data extracted from a high fidelity CFD simulation. Results indicate significant noise reduction at the targeted frequency.

A general FSI framework for an effective stress analysis on composite wind turbine blades

The fluid-structure interaction (FSI) technique has been extensively used and developed in the past decades. Commonly, the reduced-order models are used in FSI analyses to assure the numerical robustness and efficiency. However, due to the increasing demand for higher numerical resolutions in modern wind turbine composite blade applications, intrinsic limitations of reduced-order models, such as their inability to account for complex aerodynamic flow interactions, multi-motion couplings, and sophisticated composite properties, have become the weaknesses in existing reduced-order FSI approaches. In this study, we propose a general FSI framework, which combines the advantages of high-fidelity Computational Fluid Dynamics (CFD) and robust Multi-Body Dynamics (MBD) methods, and detailed Finite Element Analysis (FEA) for analysing the detailed stress distributions on the composite structures. The results of predicted dynamics and the Von Mises stress on the composite blade structures under given operation condition are compared and reasonably agreed with the literature results, with a significant computational cost reduction by nearly 25% is achieved. The proposed FSI framework can be a general approach to investigate the multi-physical interactions where the composite structure specifications are involved, coupling with complex dynamic motions in three-dimensional space.

Numerical analysis of fluid force on orifice structure of valve disc for nuclear globe valve

The globe valve fails to open completely sometimes due to insufficient lifting of the valve disc during the operation of the nuclear power plant. The main reason is the inadequate understanding of changes in fluid force. Therefore, conducting research on the fluid force of the globe valve is crucial. In this study, we establish a high-fidelity computational fluid dynamics (CFD) numerical model to investigate the flow characteristics of a novel balanced globe valve. Based on the analysis results, we concluded that the size of the throttle orifice is an essential factor affecting fluid force. Therefore, the impact of the throttle orifice sizes on the fluid force is studied. Meanwhile, the coupling influence of different valve disc displacements and inlet pressures on fluid force is quantitatively analyzed. This study provides a basis for the design of globe valves and has potential value for the dynamic control and energy utilization.

Leading-Edge Vortex Controller (LEVCON) Influence on the Aerodynamic Characteristics of a Modern Fighter Jet

The purpose of this paper is to assess the influence of a novel type of vortex creation device called the leading-edge vortex controller (LEVCON) on the aerodynamic characteristics of a fighter jet. LEVCON has become a trending term in modern military aircraft in recent years and is a continuation of an existing and widely used aerodynamic solution called the leading-edge root extension (LERX). LEVCON is designed to operate on the same principles as LERX, but its aim is to generate lift-augmenting vortices, i.e., vortex lift, at higher angles of attack than LERX. To demonstrate the methodology, a custom delta wing fighter aircraft is introduced, and details about its aerodynamic configuration are provided. The LEVCON geometry is designed and then incorporated into an existing three-dimensional (3D) model of the aircraft in question. The research is conducted using OpenFOAM 8, a high-fidelity computational fluid dynamics (CFD) open-source software. The computational cases are designed to simulate the aircraft’s flight at stall velocities within a high range of angles of attack. The results are assessed and discussed in terms of aerodynamic characteristics. A conclusion is drawn from the analysis regarding the perceived improvements in fighter jet aerodynamics. The analysis reveals that both lift and critical angle of attack can be manipulated positively. With the addition of LEVCON, the average lift gain in the high angle of attack (α) range is between 8.5% and 10%, while the peak gain reaches 19.4%. The critical angle of attack has also increased by 2°, and a flatter stall characteristic has been achieved.