Grid Arrangement Research Articles

Computational Prediction of Co-firing with Various Biomass Waste Using Turbulent Non-Premixed Combustion

Co-firing in coal power plants has limitations because the existing combustion systems are designed to provide optimal performance only with coal. Therefore, investigating the combustion aspects of co-firing by mixing coal with biomass before applying it to existing coal power plants is necessary. To address this, a new numerical model was developed to predict the co-firing behavior of coal with various types of biomass waste, specifically focusing on temperature and pollutant behavior. This study developed a co-firing model in a Drop Tube Furnace (DTF) using a composition of 25% Wood Chips (WC), 25% Solid Recovered Fuel (SRF), 25% Empty Fruit Bunch Fibers (EFFR), and 25% Rice Husk (RH). A structured grid arrangement and the Probability Density Function (PDF) were utilized to depict the relationship between chemical combustion and turbulence. The distributions of temperature and mass fractions of pollutants along the furnace axis were predicted. The highest temperature was observed with 25% EFFR, attributed to its highest volatile matter content. The simulation predicted that 25% RH would be the lowest SO2 emitter. However, it also showed a slight increase in NO and CO levels due to the increased oxygen content when coal was mixed with biomass. The simulation with 25% EFFR predicted a decrease in CO2 emissions compared to other biomass types. The results of this parametric investigation could support the implementation of biomass co-firing technology in existing coal-fired power plants.

Analysis of ansys fluent for Wall-Modeled Large-Eddy Simulation of Turbulent Channel Flow

Abstract This study assesses the accuracy of ansysfluent 19.2, a commonly employed general-purpose finite volume solver, in the context of wall-modeled large-eddy simulation for turbulent channel flow at a moderate Reynolds number, Reτ=2000. The sensitivity of the solution to variations in grid resolution, aspect ratio, grid arrangement (collocated versus staggered), and subgrid-scale (SGS) model is analyzed and contrasted to results from a corresponding direct numerical simulation (DNS) and a mixed pseudospectral and finite differences solver. Results indicate good convergence of first- and second-order statistics from the staggered grid setups as the grid is refined, whereas no clear trend is observed in cases with collocated grid setups. Velocity spectra show a lack of an apparent inertial range trend and rapid decay of energy density at high wavenumbers, with a spurious energy pile-up near the cutoff wavenumber indicating the presence of unphysical oscillations in the velocity fields. Grid refinement strengthens such oscillations in collocated grid setups and reduces them in staggered grid setups. Two-point streamwise velocity autocorrelation maps reveal an underprediction of turbulent structure size. In contrast, cross-stream autocorrelations agree with corresponding curves from direct numerical simulation, showing signatures of alternating high- and low-momentum streaks in the logarithmic layer.

Multigraphs from crossword puzzle grid designs

Abstract Crossword puzzles lend themselves to mathematical inquiry. Several authors have already described the arrangement of crossword grids and associated combinatorics of answer numbers [Fer14] [Fer20] [McS16]. In this paper, we present a new graph-theoretic representation of crossword puzzle grid designs and describe the mathematical conditions placed on these graphs by well-known crossword construction conventions.

Magnetohydrodynamic double diffusion natural convection of power-law Non-Newtonian Nano-Encapsulated phase change materials in a trapezoidal enclosure

PurposeThe present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.Design/methodology/approachThe governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (Th) left wall and a cold (Tc) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (104 ≤ Ra ≤ 105) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θf = 0.5) and volume fraction (ϕ = 0.04).FindingsThe findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 104 to 105, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.Research limitations/implicationsThis research is for two-dimensioal laminar flow only.Practical implicationsPCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.Originality/valueAs per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

Flexural behavior of RC beams strengthened with CFRP grid-reinforced engineering cementitious composite

Flexural strengthening of RC beams by replacing the tension part with carbon fiber reinforced polymer (CFRP) grid‐reinforced engineering cementitious composite (ECC) matrix has been proved to be a reliable way in the marine environments. However, few studies have been conducted on the arrangement of CFRP grids so far, which is supposed to be a possible way to deal with the premature fracture of CFRP grid and debonding of strengthening layer. In this paper, the flexural behavior of RC beams strengthened with CFRP grid‐reinforced ECC matrix is experimentally studied. The location of CFRP grid and the number of CFRP grid layers were specially discussed. Results from experiments indicated an improvement range of 66.67 %∼100 % in the peak load of strengthened RC beams, with a higher initial cracking load from 4.72 %∼20.47 % when compared to the reference beam. The generating of initial cracks was delayed with the CFRP grid close to the bottom, whereas the development of cracks was accelerated. The bearing capacity showed a nonlinear relationship with the distance from CFRP grid to the beam bottom, and a linear relationship with the number of CFRP grid layers. Finally, the formulas for the flexural capacity of strengthened beams were developed, considering the plasticity and cracking of concrete.

Quantifying local cardiac substrate heterogeneity from high density recordings: an experimental study

Abstract Background and Purpose High-density (HD) grid catheters offer enhanced local electrical conduction characterization, owing to their unique grid arrangement. This arrangement enables the generation of orientation-independent EGMs, termed omnipolar EGMs (oEGMs), overcoming limitations associated with traditional unipolar and bipolar EGMs. This innovation holds potential for differentiating healthy tissue from scarred or arrhythmogenic areas. In this study, we introduce a novel metric, the Vector Field Heterogeneity (VFH), designed to quantify the heterogeneity of propagation wavefronts in local vector maps derived from oEGMs. Methods We developed and validated the VFH metric through a combination of simulations and experiment conducted on Langendorff-perfused rabbit hearts. Simulations involved creating a model that generated 100,000 simulated maps exhibiting various levels of disorganization. For experimental data, 68 propagation maps were utilized, including 29 from basal recordings, 39 from recordings with stimulation (4 or 6Hz), from five Langendorff-perfused rabbit hearts at 37ºC, using a multielectrode mapping catheter with 128 electrodes spaced 1mm apart. The VFH metric, based on vector field theory (see figure 2), was computed and compared to the widely adopted the Spatial Inhomogeneity Index (SI) from Statistical analysis was then performed to assess the distribution of heterogeneity values. Results The analysis of the VFH metric through simulations revealed a linear increase in VFH values with disorganization up to a 45º angle, followed by a plateau. Different catheter grid sizes demonstrated that larger grids reduced the standard deviation, with the VFH metric converging to a lower value of approximately 0.62 for larger grids. Experimental data indicated that for a 4x4 grid, VFH values averaged 0.35 without stimulation and decreased to 0.11 with stimulation. The VFH metric consistently outperformed the SI index in binary classification of basal vs stimulated conditions, as evidenced by higher Area Under Curve (AUC) values in both Receiver Operating Characteristic (ROC) and Precision-Recall (PR) analyses across various catheter sizes. For example, in the 4x4 grid, the AUROC for the VFH metric was 0.9752 compared to 0.8311 for the SI index, showcasing the VFH metric’s superior accuracy in assessing cardiac wavefront heterogeneity (see figure 2). Conclusion Vector Field Heterogeneity (VFH) emerges as an effective tool for characterizing cardiac tissue. It successfully differentiates between stimulated and non-stimulated tissue, accurately representing progressive disorganization in simulated maps. The VFH metric demonstrates superiority over the established Spatial Inhomogeneity (SI) index, making it a reliable parameter for assessing cardiac heterogeneity, especially on small high-density grids. It holds promise for clinical use in studying and understanding the cardiac substrate during arrhythmic conditions.Figure 1.Abstract Figure.Figure 2.Methods and Results.

Generating grid maps via the snake model

Generating grid maps via the snake model

Implementation of a level-set-based volume penalization method for solving fluid flows around bluff bodies

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry.

Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions

Aiming towards a better understanding of the flow field around a fully appended Joubert BB2 submarine model, and in order to complement the experimental investigations of the wake of the hydroplanes and sail, large eddy simulation (LES) with the dynamic Smagorinsky model was conducted. Three sets of grids with a maximum grid number of up to 228 million were designed to perform the LES simulation for the Joubert BB2 under 10° yaw conditions, with a freestream Reynolds number based on the local freestream velocity and a hull length of ReL = 2.2 × 107. Comparisons of the wake of the cruciform appendage were made with experiments to verify the computational accuracy and to examine the influence of the spatial resolution. A satisfactory result was more representative of the experiments with the improvement in grid spatial resolution. The evolution characteristics of three co-rotating vortices originating from the cruciform appendage under the most refined grid arrangement are further described in detail under straight-ahead and 10° yaw conditions. The comparison results show that, in the core-flow region, the resultant velocity, vorticity magnitude, and TKE were stronger and the wake was more complicated under 10° yaw conditions. Tip vortex tracking under 10° yaw conditions exhibited significant three-dimensional characteristics as the wake developed downstream.

Pressure gradient and an upstream cylinder on nanofluid flow around a heated cylinder: Heat transfer and entropy analysis

This study numerically investigates the nanofluid flow around a long heated cylinder of square cross-section (DSC) with height placed parallel to a cold wall at a fixed gap height The incident flow is Couette–Poiseuille (C–P) flow. Another cylinder of rectangular cross section (UREP) is placed on the upstream side in an inline arrangement with different gap spacings between the cylinders. The base fluid is chosen as the water and ethylene glycol–water mixture. Numerical experiments are made using staggered grid arrangement on non–uniform grid, finite volume methods, and Semi–Implicit Method for Pressure Linked Equations algorithm. Impact of pressure gradient at the inlet (due to C–P flow), position and shape (square/rectangular) of the UREP, nanoparticle concentration, and base fluid on the crowding of isotherms around edges of the DSC and hence to the heat transfer characteristics (Nusselt number and entropy generation rate density) is investigated. Bejan number is used to ratify that the irreversibility due to heat transfer is the major constituent of the total system irreversibility here. A reduction of heat transfer and entropy generation from the values of an isolated DSC is natural here due to the inline arrangement. An effort is made to improve the heat transfer by reducing the height of the UREP or/and by generating unsteadiness in the incoming flow to the DSC using a bluffer UREP or/and an increased pressure gradient. Finally, some scenarios are reported where the heat transfer decrement is less in comparison to that of the total system irreversibility.

The Options in Decarbonization Pathways for Malaysia

Abstract Two activities in Malaysia that emit large amounts of CO2 are electricity generation, and iron and steel production. To decarbonize the former, Malaysia should invest in a flexible energy system to overcome the intermittent characteristic of solar energy by influencing the pattern of demand with peak load pricing, increasing energy storage capability, and entering into a regional electricity grid arrangement. Malaysia should respond to the recent large capacity expansion in iron and steel production with blast furnace-basic oxygen furnace (BF-BOF) technology by ending immediately the issuance of new licenses for facilities that use this BF-BOF technology, and speed up the process of adopting advanced green, near-zero emission technologies (e.g., Hydrogen Breakthrough Ironmaking Technology [HYBRIT]), by applying for foreign technical assistance (e.g., the United Nations Climate Technology Center and Networks [UN-CTCN]) and for concessionary climate finance under the Paris Agreement. Finally, to be consistent with the 1.5°C pathway for the world, Malaysia should aim to commit to achieve peak carbon emissions by 2030 and net zero emissions by 2050.

Analytical Study on Yield Resistance for Staggered Arranged High Strength Bolted Frictional Joints

AbstractThe yield resistance of a high strength bolted frictional joint is evaluated based on the designed net cross‐section area. The Japanese Specifications for Highway Bridges specifies a designed net cross‐section area could be increased by a factor of 1.1 in the verification of the net cross‐section yield resistance at Serviceability Limit State in high strength bolted frictional joint where the bolts are placed in grid arrangement. In the design of a staggered arranged high strength bolted frictional joint, the width of strip to be deducted from the transverse section on account of a staggered arrangement w is used. And the width of strip w is negative when p2/(4g) is larger than d0. However, the designed net cross‐section area of a staggered arranged high strength bolted frictional joint is unclear. In this study, FE analysis of staggered arranged high strength bolted frictional joint was carried out by varying the number of bolts in the top column k and the gauge distance transverse to the loading g as parameters. The results indicated that in some cases, the ratio of the net cross‐section yield resistance predicted by FE analysis to the designed net cross‐section yield resistance may be less than 1.1, but a factor of 1.1 can be applied with a suitable arrangement.

Collocated Finite Difference Method in General Coordinates for Simulation of Flow Over Arbitrary Geometry

A finite difference method to be used in simulations of turbulent flows such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) has been developed and verified for basic benchmark flows. The method is constructed using the general curvilinear coordinate system with the collocated grid arrangement of the variables so that it can be easily applied to various engineering flows including hydraulic applications involving complex geometry and moving boundary. The computer code is verified by test calculation of steady laminar internal flow in a curved cavity and an external flow above a curved hill. Furthermore the same code is used to conduct a DNS of fully-developed turbulent flow in a two-dimensional open channel and a LES of flow over curved hill. All results indicate that the method is sound with sufficient accuracy for the intended applications.

Transonic Flow Computation Over A Heat Shield Using Three Dimensional Finite Element Method

A three dimensional finite element method is employed for solution of the transonic full potential equation in mass conservation form. The finite element analysis allows the boundary conditions to be treated in simple and exact manner, without the use of a mapping scheme. The full potential equation is based on the assumption of irrotational flow and density of the fluid is calculated using isentropic relation and it is applicable for upstream local Mach number upto 1.6. The nonlinear full potential equation is reduced to a set of nonlinear algebraic equation using Galerkin’s formulation. An iterative scheme in conjunction with the artificial viscosity term is used to solve the set of algebraic equations. The artificial viscosity term stabilizes the numerical scheme and captures the shock very well. An appropriate grid arrangement is selected in the algorithm to maintain proper and continuous linkage between upstream and downstream of the flow at the centroid of the hexahedral element. The surface pressure distribution in the freestream Mach number range 0.80 - 0.95 and at an angle of incidence 5 degree shows a fairly good agreement with the experimental data. The present finite element discretization can be coupled with the commercially available software.

Lightweight and Flexible 3D ERGO@Cu/PA Mesh Current Collector of Li Metal Battery for Dendrite Suppression

The utilization of 3D Cu current collectors has been approved to be an efficient design to suppress the uncontrolled dendrite growth of Li metal anodes. However, the widely used 3D metallic Cu often has high self-weight and impaired mechanical properties and cannot meet the requirements of high energy density and industrial production. Here, we developed a lightweight, malleable, lithiophilic, and reticular composite Cu-based current collector using a nylon (PA) framework as the 3D substrate, by a synergized approach of combining the conductive Cu/PA with lithiophilic reducing graphene oxide (ERGO) coating. The 3D grid arrangement lowered the regional current density, and the lithiophilic ERGO layer induced Li nucleation, all of which endowed the ERGO@Cu/PA mesh as an anode current collector with attractive performance. The ERGO@Cu/PA composite was applied to display the necessary dendrite-free Li deposition behavior. It delivered an impressive Li plating/stripping behavior and electrochemical performance in half cells and Li/Li symmetric battery tests. The full cell using the ERGO@Cu/PA composite with predeposited Li as the anode and LiFePO4 as the cathode achieved stable cycling and excellent rate performance. Notably, the synergistic combination of light and flexible 3D Cu/PA mesh with lithiophilic ERGO coating proved a valid path to adjust Li anodes in the fields such as flexible wearable devices.

Studies on ion flow dynamics in a disk-shaped inertial electrostatic confinement fusion device under the influence of a triple grid arrangement

The basic interest of studying the ion flow dynamics in a disk-shaped inertial electrostatic confinement fusion (IECF) device is to achieve an explicit condition where large fusion products are possible from such a portable device, and then, it can be used for a wide range of applications. We modified the existing IECF device by introducing two external grids along with the central grid and investigated the plasma properties using the Langmuir probe technique at different operating voltages in this new configuration of the device. By taking measurements of the plasma properties throughout the chamber, the device is optimized for better ion confinement and ion flow behavior. A well-established comparison of plasma properties, such as ion density and potential in this new arrangement, has been carried out with the single-gridded IECF system. The triple grid arrangement switches to a lower working pressure region, and hence high energetic ion beams are procured. Because of the different discharge mechanisms, variations in plasma potential profile and ion confinement processes are observed when compared to the single-gridded IECF device.

Design, implementation and performance analysis of an off- grid solar powered system for a Nigerian household

Solar panel converts direct current obtained from the sun into an alternating current which is often used in various applications. Photovoltaic (PV) power generation technology is used as a stand-alone system to bridge the power demand requirement due to increasing energy consumption. This paper aimed at presenting the design, implementation, and performance analysis of an off- grid solar power system for a Nigerian household. A comprehensive design was done on Solar PV systems, parts and components, and the principle of operation. Average solar irradiance of the location was obtained from data collation center at Nigerian Meteorological Agency (NiMet). The method utilizes the development of block diagram which shows the component layout and their connections and a flowchart which shows the procedure of achieving the objectives of the research. Battery efficiency, PV current measurement, current profile display and commissioning of the installed PV system formed the results. Thereafter, Implementation and performance analysis was carried out. The load demand assessment shows that power required was 23,820 Wh per day at maximum and 11,260 Wh per day when diversity factor was applied (Table 1). Consequently, a 3500VA inverter was selected with a battery size of 800AH.The test result showed that with a load of 11,260 Wh the device supplied energy for about 24hours uninterrupted. Therefore, off grid arrangement reduces the dependency on grid and allows users to derive maximum satisfaction without having relied on public power utilities.•Obtaining annual solar radiation data from NiMet and determine the load estimation.•Set up experiment that determine; Battery efficiency, solar panel required and connection mode suitable to achieve the desired current rating, Inverter rating, Charge controller as well appropriate protective devices.•Installation of project compartments and the commissioning tests by categories of load injection.

Scaffold-Free Tracheal Engineering via a Modular Strategy Based on Cartilage and Epithelium Sheets.

Tracheal defects lead to devastating problems, and practical clinical substitutes that have complex functional structures and can avoid adverse influences from exogenous bioscaffolds are lacking. Herein, a modular strategy for scaffold-free tracheal engineering is developed. A cartilage sheet (Cart-S) prepared by high-density culture is laminated and reshaped to construct a cartilage tube as the main load-bearing structure in which the chondrocytes exhibit a stable phenotype and secreted considerable cartilage-specific matrix, presenting a native-like grid arrangement. To further build a tracheal epithelial barrier, a temperature-sensitive technique is used to construct the monolayer epithelium sheet (Epi-S), in which the airway epithelial cells present integrated tight junctions, good transepithelial electrical resistance, and favorable ciliary differentiation capability. Epi-S can be integrally transferred to inner wall of cartilage tube, forming a scaffold-free complex tracheal substitute (SC-trachea). Interestingly, when Epi-S is attached to the cartilage surface, epithelium-specific gene expression is significantly enhanced. SC-trachea establishes abundant blood supply via heterotopic vascularization and then is pedicle transplanted for tracheal reconstruction, achieving 83.3% survival outcomes in rabbit models. Notably, the scaffold-free engineered trachea simultaneously satisfies sufficient mechanical properties and barrier function due to its matrix-rich cartilage structure and well-differentiated ciliated epithelium, demonstrating great clinical potential for long-segmental tracheal reconstruction.

The Impact of Furniture Arrangement upon Experiential Learning in Architectural Design Studios, with Reference to Cairo, Egypt

Architectural education is one of the most special and complex disciplines that need specific spatial requirements. Architectural design studio is the backbone of architectural education for that the setting of the studio affects the students' productivity; it should suit the learning process and activities to help the students. Yet, many studios follow the traditional grid setting. The experiential learning cycle developed by Kolb is known to be an effective educational strategy in architecture and consists of four stages which are concrete experience, reflective observation, abstract conceptualization, and active experimentation that balance input and output data through learning activities. In order to fully acquire the requirements of the experiential learning cycle, there are spatial requirements that should be taken into consideration, one of which a seating arrangement is a common factor that can balance the tangible and non-tangible factors. The aim of the study is to test the impact of the four seating arrangements on Kolb's learning activities to figure out the most appropriate arrangement for each activity to realize the highest levels of productivity in the studio. The study was carried out at four universities in Cairo, Egypt (two private-two public). An online survey was completed by 322 participants from 3rd, 4th, and 5th year undergraduate students and staff members. The results were analyzed quantitatively using SPSS software. They suggest that the seating arrangement can be easily changed to suit the users' needs that a centralized/u-shaped arrangement is best for eight activities. The radial arrangement was best for four activities, while clustered arrangement was best for two activities, and a grid arrangement was best for four activities. There are some limitations of this study, as the study was done with the existing physical factors: if there was the possibility to change some of the physical factors, it may have affected some of the results according to the participants' preferences. It is hoped that the findings of the study may help architecture educators and administrators take more appropriate decisions regarding the seating arrangement in architectural design studios, in relation to different learning activities towards realizing more desirable outcomes.

Pelatihan Model Discovery Learning Untuk Meningkatkan Kemampuan Guru Menyusun Kisi dan Soal Hots

This school action study aims to improve teacher skills in compiling grids and questions at level 3 (based on HOTS). The results of the analysis of academic supervision in 2019 showed that 60% of the teachers in the cluster did not understand well the grid arrangement and level 3 questions to solve problems at school through training with the discovery learning model to be able to manage grids and questions. The research design is School Action Research (PTS). Increased teacher activity in observing the six stages of discovery learning, namely: a) Stage 1 Stimulation; b) Phase 2 Problem Formulation 3 Data Collection; d) Data Processing Stage 4 e) Stage 5 Verification; and f) Stage 6 Generalization. As a result, teacher training activities have increased from cycle I to cycle II as much as 11.34 (11.34%), for the cognitive aspect of teachers who got an A grade as many as 6 teachers (25%), class B as many as 15 teachers (62.5% ), and class C as many as 3 teachers (12,5%). The conclusion is that the use of the Discovery Learning model training can improve teacher training activities and skills in compiling grids and level 3 questions (HOTS) independently.