Nozzle Model Research Articles

Numerical analysis of influence of cavitation characteristics in nozzle holes of curved diesel engines

By targeting at the high-pressure common rail nozzle of diesel engines, we put forward a curved nozzle structure, established six groups of nozzle models with different curvatures. By using the CFD software STAR-CCM+, based on the incompressible fluid volume function (VOF) multiphase flow model, applying the K-Epsilon two-layer turbulence model, combined with the Schnerr-Sauer cavitation model, we investigated the degree of influence of the curved nozzle on the cavitation characteristics in the nozzle hole. Cavitation at the inlet, middle and outlet of nozzles was observed under injection pressure of 50, 100 or 150 MPa. The effects of curvature on cavitation were analyzed in detail according to cavitation volume fraction, cavitation volume content, mass flow, turbulent kinetic energy and velocity coefficient. It was found the curved nozzle can significantly reduce the cavitation degree in the nozzle holes, and the larger nozzle bending led to a smaller cavitation degree in the holes. Meanwhile, the average turbulent kinetic energy increased obviously and the average velocity decreased in both the holes and outlet, but the mass flow did not change much.

Influence of nozzle clearance of VG turbocharger turbine on performance and internal flow

Abstract To realize a sustainable society, it is necessary to reduce exhaust gas from automobiles and improve fuel efficiency. Turbochargers are useful for the purpose and especially variable geometry (VG) turbochargers are often installed because their nozzle blade angle can be optimally changed according to the rotational speed of the engine. To change the angle, it is needed to provide the nozzle clearance on both hub and shroud sides. In this study, CFD (Computational Flow Dynamics) calculations of a turbocharger turbine were conducted. The rotational speed of the turbine was set to 10,000 rpm. The diameter of the wheel blade is 60 mm and the height of the nozzle blade was 9.71 mm. The following were mainly investigated: the effect of the nozzle clearance position or blade angle on turbine performance, and the effect of leakage vortex from nozzle clearance on the downstream flow in the wheel domain. First, the steady-state CFD analysis on the nozzle and wheel domain was conducted. Four models of nozzle clearance were used: No Clearance (NC), Hub Clearance (HC), Shroud Clearance (SC), and Hub and Shroud Clearance (HSC). And four nozzle blade angles were used. With the Shroud Clearance model, the torque efficiency was worst with every nozzle blade angle. It was also found that the leakage flow rate from the nozzle clearance affects the loss increase in the wheel domain. Second, the unsteady-state CFD analysis on the full domain (casing + nozzle + wheel +diffuser) was conducted to investigate the leakage flow from nozzle clearance. The turbulence model was DES (Detached Eddy Simulation). Hub Clearance model and Shroud clearance model were used. The leakage vortex generated from nozzle clearance was found to flow into the wheel domain. With each nozzle model, the rotating directions of those vortexes were opposite. By the rothalpy loss investigation with the Hub Clearance model, it was confirmed that the portions of wheel domain where two leakage vortexes flow into showed larger losses than other portions. Those portions were located diagonally in two places, and they rotated in the opposite direction to the wheel rotation. On the other hand, with the Shroud Clearance model, the portions where the rothalpy loss was large were not shown regularly.

Thermal stress analysis and structural optimization of ladle nozzle based on finite element simulation

The ladle nozzle is one of the most important components in metal smelting. The cracking phenomenon occurs due to excessive thermal stress, which seriously affects the performance and life of the ladle nozzle. In this paper, a new composite structure of ladle nozzle is proposed, which consists of two materials with different properties and costs. The thermal physical parameters of the material are measured by high temperature dynamic Young’s modulus test method, thermal expansion test and flashing method. Based on the new structural model of the composite ladle nozzle, finite element simulation is used to combine the material ontology model, contact mechanics model and heat transfer model to study the temperature and thermal stress distribution inside the composite structure of the ladle nozzle during the casting process by taking representative key points inside the ladle nozzle. There is a large temperature gradient in the area near the casting hole, and the farther away from the casting hole, the smaller the temperature change. The ladle nozzle structure was optimized and compared with the existing ladle nozzle structure. The results show that the optimized composite structure of the ladle nozzle has significantly lowered thermal stress extremes under thermal shock, while the thermal stress distribution tends to be more uniform, which can largely reduce the chance of crack generation. This study is of great significance for improving the reliability and service life of the ladle nozzle and reducing its production cost.

High‐pressure under‐expanded hydrogen leakage model considering gas‐wall friction loss

AbstractThe integral model is used to predict the concentration field, only suitable for low‐pressure leakage, while the virtual nozzle model is widely used in high‐pressure leakage but ignores the friction between the hydrogen and the tube wall during the leakage. We modified the virtual nozzle model by adding the gas‐wall friction loss term to the momentum conservation equation. A theoretical model of a high‐pressure under‐expanded jet is proposed by combining the integral model with the improved virtual nozzle model, which was validated by a series of helium (instead of hydrogen) dispersion in an unenclosed environment. And then the high‐pressure hydrogen leakage system was set up to investigate hydrogen concentration along the centerline of the jet was measured under different pressures. Results show that the mole fractions along with the axial distance all comply with the hyperbolic decay law. Within the range of 40 cm < z < 100 cm, at other pressures of 1, 2, 4 MPa, the minimum deviations of high‐pressure under‐expanded hydrogen leakage prediction model and experiments are 1.67%, 1.37%, 1.33%, respectively. The study is adequately precise to predict high‐pressure leakage concentration and also gives ideas about the installation position of the hydrogen sensor in engineering.

Numerical research on influence of structural parameters of common-rail injector on injection rate of each nozzle hole

Performance of diesel engines are influenced by fuel spray distribution, fuel-air mixture formation and combustion, which are also influenced by hole-to-hole fuel injection rate from multi-hole injectors. In this study, a customized spray momentum flux experimental test rig was used to measure the transient injection rates from a two-layered 8-hole diesel injector. The results indicated that the fuel injection rate and the cycle fuel injection quantities of the lower-layered nozzle holes were 3–15% higher than the fuel injection rates and the cycle fuel injection quantities of the upper-layered nozzle holes. A three-dimensional (3D) computational fluid dynamics (CFD) model of the two-layered 8-hole diesel injection nozzle was developed and validated by analyzing the relative error between the numerical results obtained from the model and the experimental results measured with the test injector. The simulation results showed that the relative average deviation of hole-to-hole cycle injection quantities were less than ±1%, which is the result of 5% increment in the cross-sectional area of the upper-layered holes.

Analysis of droplet size uniformity and selection of spray parameters based on the biological optimum particle size theory.

Based on the theory of biological optimal particle size, the most easily attached droplets for different organisms have different particle sizes. To achieve the best average particle size, the droplet size in the atomization field must be more uniform and attain a high the adhesion rate. Therefore, during the application process, not only the average particle size of the droplets but also the influence of the uniformity of the droplets in the spray field must be considered. In this study, 20 small-angle fan nozzles ranging from 20° to 40° are used as the research objects. The droplet size information in the atomization field is obtained using a laser particle size analyzer, and the droplet uniformity under different parameters is calculated. The results showed that within the range of the parameters selected in the experiment, the droplet size increased with an increase in the flow rate, and decreased with an increase in the pressure. In addition, the angle had little effect on the droplet size. Increasing the spray height, spray angle, and pressure, while reducing the equivalent outlet diameter of the nozzle was beneficial to improve the uniformity of droplets. The order of the degree of influence of the four parameters on the uniformity of the droplets was height>equivalent outlet diameter (r)>pressure>spray angle, and the influence weights were 51.1%, 37.1%, 7.8%, 4.1%; 48.4%, 37.6%, 10%, and 4%. Under the condition of the parameter settings used in this experiment, the optimal atomization effect for the four intervals of 150-200 μm, 200-250 μm, 250-300 μm, and 300-400 μm was analyzed from the perspective of uniformity. The nozzle models with the best atomization effects in each interval were SS4003-0.3MPa, SS4006-0.3MPa, SS4008-0.3MPa, and 633.512.30.CC-0.1MPa.

Coupled Thermo-Structural Analysis Model of Solid Rocket Motor Nozzle considering the Variation of Friction Coefficient under Operating Conditions

Multi-interface is a typical feature of solid rocket motor nozzles, and the interface evolution law is an important aspect to analyze the thermo-structural response of solid rocket motor nozzles. In this paper, based on the friction coefficient test at different temperatures, a coupled thermo-structural analysis model of solid rocket motor nozzle considering the variation of friction coefficient under operating conditions was established. Firstly, the friction coefficient was tested to model the variation at different temperatures. Then, by adopting structure gap, variable friction coefficient, thermal contact resistance, and friction heat production, a strongly coupled non-linear model was established. Simulations using the non-linear model and traditional model were performed, in which the stress of the throat insert was within the required stress range of the material. The ground firing test result demonstrated the validity of the analysis model, and the non-linear model was in a better agreement with the firing test than the traditional model. Therefore, it can be concluded that with a more specific friction coefficient to represent the friction behaviour of the different parts of the nozzle, the strongly coupled non-linear model established in this paper can reflect the essence of thermo-structural response of solid rocket motor nozzle.

HOW DO THE DROPLET SPECTRUM UNIFORMITY AND SPRAY VOLUME OF FLAT-FAN NOZZLES INFLUENCE FUNGICIDE SPRAY DISTRIBUTION QUALITY IN SOYBEANS?

Droplet spectrum quality is essential to effectively control crop pests and diseases. This study aimed to characterize the droplet uniformity of the eight most popular flat-fan nozzles used by Brazilian farmers and relate it to their spraying quality. The method consisted of using a laser-diffraction-size analyser to determine droplet-size distribution for three fungicide spray solution compositions and at two flow rates. Our goal was to identify the nozzle models with the highest and lowest Span values for each fungicide spray solution. In the first stage, the results confirmed differences in uniformity and droplet size for both nozzle models and flow rates applied. However, these differences were not the same for both flow rates nor constant for all fungicide spray solution compositions. Through field experiments, we could understand how the combination of flow rate, nozzle model, and spray solution composition provides different results and application efficiencies. Based on our results, we can state that Span has an impact on the number of droplets prone to drift and quality of canopy coverage. Therefore, this droplet-quality parameter should be considered and displayed in nozzle catalogues to improve nozzle selection and sprayer configuration, thus enhancing application quality.

Numerical study of the effect of surface topography on atomization performance in geometrically sensitive areas of centrifugal nozzles

Integral three-dimensional printing of aeroengine fuel nozzles is an emerging trend. However, the large relative roughness of the internal flow paths created by this processing method is problematic. To study the influence of the rough surface morphology on atomization performance in geometrically sensitive areas of centrifugal nozzles, this paper describes numerical simulations of the atomization process of five nozzle models with rough orifice sections. The simulation framework considers a coupled internal and external flow in stages. The macroscopic morphology of the numerically calculated spray field is found to be consistent with experimental results, with maximum errors in the Sauter mean diameter, spray angle, and flow rate of just 8.7%, 3.7%, and 6.1%, respectively. The numerical results show that the nozzle's rough surface morphology in geometrically sensitive areas has a non-negligible impact on the liquid film velocity fluctuations, primary breakup, and secondary atomization characteristics. Indeed, the effect on primary breakup is large, with the maximum difference between the five rough-surface models reaching 22.9%. The effect on secondary atomization is small, with a maximum difference of just 5.7% except in the number of droplets, which has a maximum difference of 22.1%. Among the five rough-surface models, the atomization characteristics of the smooth model differ greatly from those of the real model, whereas a power-function model best reflects the real surface morphology. This study provides new ideas for nozzle performance prediction and optimization, and provides a reference for engineering applications of three-dimensional printed centrifugal nozzles.

Effect of turbulence models and cavitation intensity on the motive and suction nozzle mass flow rate prediction during a non-equilibrium expansion process in the CO2 ejector

A variety of ejector constructional concepts can be effectively examined by advanced numerical tools. The development of the modelling techniques of the two-phase meta-stable expansion process in the CO2 ejector motive nozzle provides the detailed flow data of the primary stream. However, the complexity of the entrainment processes in the mixing section still requires attention for the accurate prediction of the suction nozzle flow. Hence, in this paper, an analysis of four turbulence models and cavitation phenomena (four intensity levels) in the CO2 ejector was performed on the basis of the calibrated non-equilibrium expansion model of the ejector motive nozzle. Twenty-three motive nozzle points from the subcritical range (from 50 bar to 70 bar and 8 °C to 23 °C) were coupled with the evaporation temperature of -6 °C and two pressure lift levels (3 bar and 6 bar). Simulations of 460 cases were validated using data from the CO2 ejector refrigeration unit with a 50-kW cooling capacity. The vapour quality distribution in the motive nozzle with cavitating evaporation was described in terms of the primary pressures and the considered turbulence models. An influence of the turbulence formulation on the secondary stream behaviour in the mixing zone was also investigated regarding the suction nozzle mass flow rate. Finally, the proposed model of the CO2 ejector was characterised by the mass flow rate prediction discrepancy at an average level of 4.6% and 12.3% for the motive and suction nozzle, respectively.

Analysis of thruster nozzle in a high-temperature environment using partitioned coupling framework to combine a kinematic hardening plasticity model and a creep model

A framework based on a partitioned stress integration technique was proposed by the present authors for a general combined elastic-plastic and creep constitutive model. It was developed to analyze a structure used in a high temperature environment. In the present study, a thruster nozzle model subjected to thermal strain is analyzed using the framework to verify it. The Ohno-Wang model and the Norton-Bailey model are used for the elastic-plastic model and the creep model, respectively. This combined model is also verified..

The Pressure Peaking Phenomenon for Ignited Under-Expanded Hydrogen Jets in the Storage Enclosure: Experiments and Simulations for Release Rates of up to 11.5 g/s

This work focuses on the experimental and numerical investigation of maximum overpressure and pressure dynamics during ignited hydrogen releases in a storage enclosure, e.g., in marine vessel or rail carriage, with limited vent size area, i.e., the pressure peaking phenomenon (PPP) revealed theoretically at Ulster University in 2010. The CFD model previously validated against small scale experiments in a 1 m3 enclosure is employed here to simulate real-scale tests performed by the University of South-Eastern Norway (USN) in a chamber with a volume of 15 m3. The numerical study compares two approaches on how to model the ignited hydrogen release conditions for under-expanded jets: (1) notional nozzle concept model with inflow boundary condition, and (2) volumetric source model in the governing conservation equations. For the test with storage pressure of 11.78 MPa, both approaches reproduce the experimental pressure dynamics and the pressure peak with a maximum 3% deviation. However, the volumetric source approach reduces significantly the computational time by approximately 3 times (CFL = 0.75). The sensitivity analysis is performed to study the effect of CFL number, the size of the volumetric source and number of iterations per time step. An approach based on the use of a larger size volumetric source and uniform coarser grid with a mesh size of a vent of square size is demonstrated to reduce the duration of simulations by a factor of 7.5 compared to the approach with inflow boundary at the notional nozzle exit. The volumetric source model demonstrates good engineering accuracy in predicting experimental pressure peaks with deviation from −14% to +11% for various release and ventilation scenarios as well as different volumetric source sizes. After validation against experiments, the CFD model is employed to investigate the effect of cryogenic temperature in the storage on the overpressure dynamics in the enclosure. For a storage pressure equal to 11.78 MPa, it is found that a decrease of storage temperature from 277 K to 100 K causes a twice larger pressure peak in the enclosure due to the pressure peaking phenomenon.

Modeling the airflow field of vortex spinning

Vortex spinning technology adopts a high-speed swirling airflow to rotate the fibers with open-ends to form yarn with real twists. The airflow behavior within the nozzle has a great effect on the yarn-formation process. In this study, a three-dimensional calculation nozzle model and corresponding three-dimensional airflow region model were established to enable the numerical calculation; airflow behavior—pressure, velocity, and the turbulent airflow field, and the streamline of airflow—was investigated in the presence of fiber bundles within the vortex spinning nozzle. Hybrid hexahedral/tetrahedral control volumes were utilized to mesh the grids in the calculation region. To consider airflow diffusion and convection in the nozzle, the Realizable k- ε turbulence model with wall function was adopted to conduct the calculation. Dynamic and static pressure values were obtained by numerical analysis to predict the action of the inner surface of nozzle and the wall resistance on the high-speed swirling airflow. The numerical simulation of dynamic airflow behavior can generate great insight into the details of airflow behavior and its distribution characteristics, and is helpful for understanding the spinning mechanism and promoting optimization of the spinning process.

Secondary neutron dose contribution from pencil beam scanning, scattered and spatially fractionated proton therapy

The Orsay Proton therapy Center (ICPO) has a long history of intracranial radiotherapy using both double scattering (DS) and pencil beam scanning (PBS) techniques, and is actively investigating a promising modality of spatially fractionated radiotherapy using proton minibeams (pMBRT). This work provides a comprehensive comparison of the organ-specific secondary neutron dose due to each of these treatment modalities, assessed using Monte Carlo (MC) algorithms and measurements. A MC model of a universal nozzle was benchmarked by comparing the neutron ambient dose equivalent, H*(10), in the gantry room with measurements obtained using a WENDI-II counter. The secondary neutron dose was evaluated for clinically relevant intracranial treatments of patients of different ages, in which secondary neutron doses were scored in anthropomorphic phantoms merged with the patients’ images. The MC calculated H*(10) values showed a reasonable agreement with the measurements and followed the expected tendency, in which PBS yields the lowest dose, followed by pMBRT and DS. Our results for intracranial treatments show that pMBRT yielded a higher secondary neutron dose for organs closer to the target volume, while organs situated furthest from the target volume received a greater quantity of neutrons from the passive scattering beam line. To the best of our knowledge, this is the first study to compare MC secondary neutron dose estimates in clinical treatments between these various proton therapy modalities and to realistically quantify the secondary neutron dose contribution of clinical pMBRT treatments. The method established in this study will enable epidemiological studies of the long-term effects of intracranial treatments at ICPO, notably radiation-induced second malignancies.

THEORICAL STUDY ON PROPULSIVE PERFORMANCE OF OBLIQUE DETONATION ENGINE

Detonation combustion is characterized by the high thermodynamic efficiency and fast heat release. Benefitting from these potential advantages, an oblique detonation wave (ODW) is introduced into the combustion chamber and oblique detonation engine (ODE) plays an important role in hypersonic air-breathing propulsion systems. Previous studies mainly focused on the initiation structures, standing features and wave systems of oblique detonation, but the global analysis of ODE propulsive performance is still absent at the macro-level. In this paper, the flow and combustion processes of an ODE are decomposed into four basic modules, named as inlet model, mixing model, combustion mode and nozzle model, respectively. We solve these four basic flow processes using theoretical methods and propose a systematically theoretical approach that can be used to predict the ODE propulsion performance. On the basis of previous ODW initiation structures and waves systems, four different combustion modes, i.e., over-driven ODW, Chapman-Jouguet ODW, over-driven normal detonation wave and oblique shock-induced constant-volume combustion, are chosen to describe the heat release processes of combustible mixture in the ODE combustor. The effects of different combustion modes on fuel specific impulse of the ODE are also analyzed. In addition, the influence mechanisms of inflow parameters, combustor parameters and intake-exhaust parameters on the thrust performance of ODE are also obtained, and the results show that the major factor of fuel specific impulse of an ODE consists mainly of the inflow Mach number and the expansion ratio of engine nozzle. Finally, combined with precious detonation research results, such as the standing features and initiation structures of oblique detonation in a confined space, the preliminary design direction of oblique detonation engine are proposed, which mainly involve some constrained conditions, such as geometrical constraints, inflow velocity limitations and stability ranges of a detonation wave in ODE combustor.

Engineering Model of a Plug Nozzle for the Engine of a Prospective Supersonic Civilian Airplane

Engineering Model of a Plug Nozzle for the Engine of a Prospective Supersonic Civilian Airplane

Effect of working pressure and spacing of nozzles on the quality of spraying distribution

The correct placement of the crop protection product on the target depends on the adequate distribution provided by the spray nozzles. In this research, the objective was to verify the influence of the working pressure and spacing between nozzles on the quality of the spray distribution. It was analyzed the nozzles jets concerning symmetry, opening angle and flow rate. Two methodologies for determining the volumetric distribution were used, considering (1) the simultaneous collection of a set of nozzles arranged in a spray boom and (2) the volumetric distribution of each discrete sample of nozzle. Overlapping between spray jets was used to calculate the coefficient of variation (CV) due the nozzles spacing. Nine models of flat fan nozzles were used, at two nominal flow rates and four working pressures. The working pressure achieved a big effect on the quality of volumetric distribution. The pressure of 100 kPa produced the worse results of volumetric distribution, with CVs higher than 10% along the boom for all nozzle models, in both flow rates. Continuous improvements in the quality of distribution were observed with the increase in pressure until reaching 300 kPa, followed by a slight decrease in quality when reaching 400 kPa pressure. The spray nozzle model has also a big effect on the quality of distribution and there are no implied design characteristics that can turn easier a better choice of nozzles. Both methodologies for the determination of spray distribution achieved similar results and can be used for the nozzles spray distribution quality determination.

Quality Analysis of Some Spray Parameters When Performing Treatments in Vineyards in Order to Reduce Environment Pollution

There is a worldwide trend that supports the rational use of chemicals in agriculture. It has become common knowledge that irresponsible application of pesticides can cause food security issues, by endangering human and animal health while also having negative environmental consequences. The aim of this experiment was to assess the qualitative parameters of spraying treatments in vineyards. To achieve this, a vineyard and orchard sprayer machine was used for the application of treatments under a gradient of pressures (3, 5, 7, 9 bar). Water-sensitive collectors were placed at three heights (0.8 m, 1.5 m, 2.5 m). Following spraying was determined using DepositScan: the volume median diameter characterization of droplets (DV 1, DV 5, DV 9), and coverage degrees of sprayings. Results indicated that best coverage degree and larger droplets tend to be deposited 1.5 m from the ground, which corresponds with the highest proximity to the positioning of the nozzles of the machine during application, and lowest coverage is found at the top, where droplets deposited also tend to be smaller. For the anti-drift nozzle model used in the study, the best coverage was obtained at a pressure of 5 bar. For sustainability of agricultural practices and rational use of pesticides, more research is required for optimization of increased precision spraying that could ensure high coverage at lower doses of chemicals and coarse droplets. In this way the quantity of product sprayed is expected to be reduced, due to minimization of off-target losses and increased efficiency. This can ensure that negative environmental impacts are lowered. Improved treatment application at higher positioning of the canopy remains a challenge and shall receive more attention.

Research on Improving the Working Efficiency of Hydraulic Jet Submarine Cable Laying Machine

The anchoring and hooking of ships, bedrock friction and biological corrosion threaten the safety and stability of submarine cables. A hydraulic jet submarine cable laying machine manages to bury the submarine cables deep into the seabed, and effectively reduces the occurrence of external damage to the submarine cables. This machine uses a hydraulic jet system to realize trenching on the seabed. However, the hydraulic jet submarine cable laying machine has complicated operation and high power consumption with high requirements on the mother ship, and it is not yet the mainstream trenching method. In this paper, a mathematical model for the hydraulic jet nozzle of the submarine cable laying machine is established, and parameters that affect the trenching efficiency are studied. The effects of jet target distance, flow, angle and nozzle spacing on the working efficiency of the burying machine are analyzed by setting up a double-nozzle model. The results of the theory, numerical simulation and experiment show that the operational efficiency of the hydraulic jet submarine cable laying machine can be distinctly improved by setting proper jet conditions and parameters.

Visualization and measurement of turbulent flow inside a SEN and off the ports

This work describes a visualization technique that allows to register and analyze flow inside a Submerged Entry Nozzle (SEN) model. The internal flow has a swirling pattern that produces characteristic flow conditions that can be used in efficiently supplying liquid steel from the tundish to the mold in the continuous casting process. The visualization method is a first step in analyzing the characteristics of the internal flow and hence in designing new SENs. A LED light source is employed to illuminate the SEN which reduces the reflections in the images. To enhance visualizations and measurements, a transparent cell consisting of a cubic volume with reduced dimensions was used to capture images from the high-speed camera and to record the flow pattern within the SEN. The SEN model consists of a vertical, constant diameter tube with two rounded exit ports located at the bottom with a downward angle of 15° each. The working fluid is water and reaches Re=10,000 within the cell. We also use the laser illuminated Particle Imaging Velocimetry (PIV) to calculate the velocity of fluid within the SEN and close to the exit ports. We confirm previously reported formation of three vortexes that interact with each other altering the swirl motion of the exit flow. Experimental results were compared with numerical simulations. The comparisons contribute to the validation of findings of Computational Fluid Dynamics (CFD) and Smoothed-Particle Hydrodynamics (SPH) results. Qualitative and quantitative similarities were found. Both physical and numerical results display a high turbulent flow behavior at the lower zone of the SEN. Experimental and numerical methods may be used together as a development method to measure and evaluate the characteristics of the flow behavior inside and outside the SEN model in order to design a better SEN to increase the quality of the steel slab.