Second-order Response Surface Research Articles

Heat Transfer Analysis and Structural Optimization for Spiral Channel Regenerative Cooling Thrust Chamber

There is currently a lack of efficient heat transfer analysis methodologies for spiral channel regenerative cooling that has been increasingly applied in liquid rocket engines. To figure out the heat transfer characteristics of the spiral channel regenerative cooling thrust chamber, a simple 1D method based on the traditional semi-empirical formula after correcting the flow velocity is proposed. The accuracy of this approach is verified by the 3D numerical simulation. The verified method is further used to analyze the distribution of inner wall temperature in the test case and optimize the channel’s parameters. The research shows that the maximum inner wall temperature cooled by the spiral channel is 8.5% lower than that of the straight channel under the same channel size and boundary condition, indicating that the application of the spiral channel significantly improves the cooling effect. In addition, the 1D model combined with the second-order response surface model is employed to optimize the channel width, channel height, pitch, and inner wall thickness aiming for the best cooling effect. The calculated maximum temperature of the inner wall after the structure optimization is 586.6 K, which is 29.8% lower than the initial structure before optimization.

Optimization Method Based on Hybrid Surrogate Model for Pulse-Jet Cleaning Performance of Bag Filter

The pulse-jet cleaning process is a critical part of the bag filter workflow. The dust-cleaning effect has a significant impact on the operating stability of bag filters. Aiming at the multi-parameter optimization problem involved in the pulse-jet cleaning process of bag filters, the construction method of hybrid surrogate models based on second-order polynomial response surface models (PRSMs), radial basis functions (RBFs), and Kriging sub-surrogate models is investigated. With four sub-surrogate model hybrid modes, the corresponding hybrid surrogate models, namely PR-HSM, PK-HSM, RK-HSM, and PRK-HSM, are constructed for the multi-parameter optimization involved in the pulse-jet cleaning process of bag filters, and their objective function is the average pressure on the inner side wall of the filter bag at 1 m from the bag bottom. The genetic algorithm is applied to search for the optimal parameter combination of the pulse-jet cleaning process. The results of simulation experiments and optimization calculations show that compared with the sub-surrogate model PRSM, the evaluation indices RMSE, R2, and RAAE of the hybrid surrogate model RK-HSM are 9.91%, 4.41%, and 15.60% better, respectively, which greatly enhances the reliability and practicability of the hybrid surrogate model. After using the RK-HSM, the optimized average pressure F on the inner side wall of the filter bag at 1 m from the bag bottom is −1205.1605 Pa, which is 1321.4543 Pa higher than the average pressure value under the initial parameter condition set by experience, and 58.4012 Pa to 515.2836 Pa higher than using the three sub-surrogate models, verifying its usefulness.

Normative database of response surface method for human trunk extension in isometric mode.

Recent studies show that asymmetric movements are important Low Back Disorders risk factors. Measuring the trunk strength and identifying the coupling effects in different postures can provide an objective tool to assess one's task capacity. This paper estimates the maximum performance capacity for isometric trunk extension and accompanying torques. Thirty males performed maximum voluntary isometric extension in 33 trunk postures on Sharif Lumbar Isometric Strength Tester device. Corresponding moments and angular positions were collected. Second-order full response surface models (RSM) were exploited to formulate the relationship between strengths and three trunk angles. The results of correlation coefficient, percent of standard estimation error and lack of fit reflected the adequacy of models. In conclusion, the main torque was the extension, but at the same time lateral bending and rotation torques were observed. For predicting these three torques in a specific posture and injury prevention, the second order RSM is a useful tool. The presented models can be used in the fields of ergonomics, occupational biomechanics and sport.

Numerical Study on the Heating Effect of a Spring-Loaded Actuator—Part II: Optimization Design of Heater Parameters

Unfavorable temperatures and humidity will cause the failure of spring actuators. In order to ensure the safe operation of the actuator, it is necessary to optimize the design of the built-in heater system of the actuator itself. In this study, an experimental design and a response surface model were used to fit the empirical formulas for the minimum temperature, maximum humidity, and maximum temperature on the heater surface. On this basis, a genetic algorithm was used to establish the optimal size of the heater in the chamber of the spring actuator. The study results show that the air inside the actuator shows a trend of a decrease in temperature and an increase in relative humidity from top to bottom. The empirical equation obtained by fitting the second-order response surface model has high accuracy, and the maximum prediction errors for the minimum temperature, maximum relative humidity, and maximum temperature of the heater surface of the spring actuator are −0.5%, 11.7%, and 4.7%, respectively. When the environmental temperature reduces from 313 K to 233 K, the optimal heating power of the heater increases from 10 W to 490 W, the optimal relative length increases from 3.57 to 6, and the optimal relative width increases from 1 to 5.3. Therefore, the study can act as a reference for the temperature and humidity control system of future actuators.

Optimization and Prediction of Process Parameters during Abrasive Water Jet Machining of Hybrid Rice Straw and Furcraea foetida Fiber Reinforced Polymer Composite

In the last few decades, natural composite materials have been considered one of the highly sustainable ecological alternatives for reducing the consumption of synthetic materials. Today, research on natural fiber composites is the main thrust for their use in various industrial applications. Further, continuous research works are being carried out to utilize natural composites as an alternative to synthetic materials. However, the inhomogeneity of composites, delamination, fiber pullout, higher surface roughness (SR) and dimensional inaccuracy under traditional machining have led the attention towards non-traditional machining, such as abrasive water jet machining, to achieve high-quality components. Hence, in this study, an experimental analysis based on the design of experiments is conducted on the machinability of a hybrid rice straw/Furcraea foetida composite under abrasive water jet machining (AWJM). Further, the concentration of the rice straw and the AWJ process parameters are varied, and their effects on the quality of machining is evaluated. The experimental trials are designed based on the Taguchi L27 orthogonal array, followed by an analysis of variance (ANOVA). From extensive experimentations, the concentration of rice straw is observed to be the most contributing (93.5%) factor to the SR. The traverse speed (TS) shows the highest percentage contributions of 93.13%, 55.50 and 55.70% to the material removal rate (MRR) and the top (TKW) and bottom kerf widths (BKW), respectively. However, the interaction between the fiber concentration and traverse speed gives the maximum contribution (35.04%) to the kerf taper (KT). A second-order response surface model is generated to study the effects of the process parameters on the SR, MRR, TKW, BKW and KT in any experimental domain. Finally, the microstructural characteristics of the machined surfaces, such as micro-cracks, debonding, and fiber pullout, are discussed.

Further considerations in A-optimal second-order response surface designs

Second-order design of experiments over hypercubic regions is under consideration for the set -up in which the experimenters’ main interest is in estimation of parameters corresponding to higher-order terms of the model. The designs optimal under A-optimality criterion for the situation are obtained. Performances of the derived designs and the designs A-optimal for full model relative to each other are investigated. The derived A-optimal designs are found to have very high efficiency and, for all practical purposes, may be equally good for the full model. Under the set-up the best designs are also derived within the class of symmetric product designs and the class of central composite designs. AMS Subject Classification62K99, 62K05.

A calibration method of discrete element contact model parameters for bulk materials based on experimental design method

This study proposes a method to address the issues of large amount of calculation and low efficiency in the calibration of discrete element method (DEM) contact model parameters for rockfill, which is based on the experimental design method. Plackett-Burman design method was used to analyze the significance of each contact model parameter to the macro-mechanical parameters. Second-order response surface regression models were developed to analyze the relationship between macro-mechanical parameters and contact model parameters that have significant impact on them. The contact model parameters in the rockfill DEM were calibrated using a multi-objective optimization method based on laboratory triaxial tests. The calibrated parameters were then used to simulate discrete element triaxial tests of the rockfill under varying pressure conditions. The study demonstrates that calibrated parameters can accurately predict the macroscopic behavior of rockfill under different confining pressures. Additionally, the calibration method has good applicability and effectiveness.

Optimization Design and Fatigue Lifetime Analysis for Elastic Wheel of Low-floor Trams Using in Urban Rail Transit

Elastic wheel is an important component of the low floor tram using in urban rail transit, so it is of significance to optimize its structure and predict its service lifetime. Firstly, the fatigue characteristics of rubber material are studied based on the crack energy theory, and a finite element model of an elastic wheel for fatigue lifetime prediction is constructed. The numerical simulation results show that the fatigue lifetime of such a elastic wheel does not match with the expected one. Secondly, based on the orthogonal numerical test and the Sobol model, an improved sensitivity analysis method is proposed. Taking the minimum strain as an optimization objective, and selecting the structural parameters determined by the sensitivity analysis method as the design variables, the second-order response surface model is established, and the multi-island genetic algorithm is used to carry out the single objective and multi-factor optimization design of the rubber bodies of elastic wheel under the condition of stiffness constraint. The simulation results of the elastic wheel show that the fatigue lifetime of the optimized structure is 30% higher than that of the original one. Finally, the optimized elastic wheel is tested, and the results show that the stiffness coefficient, and the fatigue lifetime as well, are all satisfy with the design requirements.

Lightweight Optimization Design and Fatigue Lifetime Analysis for Anti-rolling Torsion Bar of Rail Vehicle

Based on the fatigue strength assessment method in the FKM standard, the lightweight design of a type of anti-rolling torsion bar is studied by using the finite element method. Firstly, the finite element model of the torsion bar structure is constructed by using the Creo software and the HyperMesh software, and then the finite element analysis is carried out by using the ABAQUS software. The numerical simulation results indicate that under the condition of ultimate load 29.2kN, the static strength, anti-rolling stiffness and fatigue strength of the torsion bar are all satisfy with the design requirements. Secondly, the orthogonal numerical test method is utilized to investigate the influence of geometric parameters on the anti-rolling stiffness and Factor of Strength (FOS) value of the torsion bar. Taking the structural geometric parameters as variables and the FOS value as the objective function, a second-order response surface model is established. The single objective and multi-factor optimization design for the torsion bar under the condition of stiffness constraint is conducted by using the Isight software and multi-island genetic algorithm. The results show that, comparing with the original structure, the weight of the optimized structure is reduced by 20.89%, and the static and dynamic strength, and anti-rolling stiffness of the optimized structure are match with the design requirements. Finally, the static and dynamic strength tests for the optimized torsion bar are individually operated at the ultimate load and under two-stage cyclic loading with amplitude 18.0kN and 29.2kN. the results show that the calculated stiffness coefficient is consistent with the test one, and the service lifetime of the torsion bar is satisfy with the design requirement.

Optimization and Prediction of Thermal Conductivity and Electrical Conductivity of Vacuum Sintered Ti-6Al-4V-SiC(15 Wt.%) Using Soft Computing Techniques

Titanium silicon carbide (Ti3SiC2) is a novel composite material that has found a multitude of uses in the aerodynamics, automobile, and marine industries due to its excellent properties such as high strength and modulus, high thermal and electrical conductivity, high melting point, excellent corrosion resistance, and high-temperature oxidation resistance. These properties are strongly associated with physical properties and microstructural features. Due to difficulties in the synthesis of this material, there have been very few investigations on the relationship between microstructure and physical characteristics of titanium silicon carbide composites processed through powder metallurgical process. However, the importance of thermal conductivity and electrical conductivity of titanium silicon carbide composites in various potential applications has led to keen attention from several researchers. Hence, in this paper, optimization, and prediction of process input parameters during processing under vacuum sintering for achieving maximum electrical and thermal conductivity of Ti-6Al-4V-SiC(15 Wt.%) has been presented. Using Taguchi’s L9 Orthogonal Array, it has been observed that aging temperature (1150 °C), aging time (four hours), heating rate (25 °C/min), and cooling rate (5 °C/min) result in optimum input parameters for achieving the highest electrical conductivity values during the processing of Ti-6Al-4V-SiCp composites. Further, for maximum thermal conductivity values during the processing of Ti-6Al-4V-SiCp composites, aging temperature (1150 °C), aging time (four hours), heating rate (5 °C/min), and cooling rate (5 °C/min) are preferred. A second-order response surface model generated can be effectively used for predicting the electrical conductivity and thermal conductivity during the processing of Ti-6Al-4V-SiCp composites with an accuracy of 99.28% (electrical conductivity) and 99.14% (thermal conductivity). By comparing the experimental results along with the results of the mathematical model and the BPANN model results for nine trials, it was observed that the estimated value is accurate for all tests with an error of 0.39% (electrical conductivity) and 0.48% (thermal conductivity). Further, from X-ray diffraction studies and microstructural analysis, it has been observed that aging at 1150 °C for four hours resulted in the formation of a ternary carbide phase of titanium silicon carbide (Ti3SiC2), which resulted in maximum electrical conductivity (4,260,000 Ω−1 m−1) and thermal conductivity (36.42 W/m·K) of the Ti-6Al-4V-SiC (15 Wt.%) composite specimen.

The construction stability of large section tunnel considering the deterioration of clay mechanical properties

The stability of large-section clay tunnels is closely related to the mechanical behavior of the surrounding rock. The mechanical behavior of the surrounding rock is characterized by the coupled response of the physico-mechanical properties of the clay material and the tunnel construction conditions. Therefore, this paper proposes a numerical experimental study based on the response surface method to quantitatively link the stability of large-section clay tunnels with construction factors. It will provide a basis for quantitatively guiding the tunnel construction plan adjustment to ensure its stability. Firstly, the tunnel stability reserve is evaluated by considering the deterioration of physico-mechanical properties of clay surrounding rocks, and the relationship between the tunnel stability index and construction factors is established according to Taylor’s theorem. Secondly, the response surface method and the steepest ascent method are used to find the optimal fitting relationship between the tunnel stability reserve factor and tunnel construction factors. Finally, the analysis of a tunnel application shows that (a) the stability evaluation considering the deterioration of physical and mechanical properties of clay is well representative; (b) the “curved” region of the response of the tunnel stability reserve factor can be effectively determined by the steepest slope method; (c) for the “curved” region, a second-order response surface is more appropriate. This research will reveal the coupling relationship between tunnel stability, physico-mechanical properties of clay, and tunnel construction conditions, which will contribute to the development of intelligent tunnel construction.

Study on micro-forming taps with unequal fluteless spacing

Tools with unequal fluteless spacing (UFS) feature are used to cut different materials. The UFS tool and a traditional tool differ in terms of the angle between the two cutting edges. The UFS tool experiences smaller axial and radial cutting forces than the traditional tool so cutting vibration is reduced, tool life is increased, and the surface roughness of the workpiece increases. This study uses the smaller hole diameter (D), spindle speed (N), and cutting fluid concentration (C) for the central composite design (CCD). Minitab statistical software is used for the second-order response surface modeling of the maximum thread-filling rate (f) and the minimum torque (T) for micro-forming M1.2 mm taps using UFS on AL-7075 aluminum alloy. The analysis of variance (ANOVA) results for f and T show that D and C are the important parameters that affect f, and D, N, and C significantly affect T. Compared with the predicted conditions, the errors in f and T for the experiment are 2.51% and 2.25%, respectively. This study shows that the two second-order mathematical models that are derived using CCD and the response surface method (RSM) feature good prediction accuracy.

Multi-objective performance optimization of target surface of bionic blue whale-skin impinged by array jet

Jet impingement cooling technology is usually applied to combustor liner with large heat load. With the continuous improvement of high capacity and low emission of heavy-duty gas turbines,the research on low resistance and high cooling efficiency cooling technology is particularly important. To meet these urgent needs, based on the blue whale skin structure, a new array impingement target surface cooling structure was proposed from the perspective of bionics. The flow and heat transfer characteristics of the array impingement bionic target surface cooling structure were numerically simulated under high Reynolds number (Re) and high Heat flux density (q) conditions. The influence of groove depth (H, 1 to 3 mm), radius ratio (R/H, 1 to 3) and spacing ratio (P/H, 10 to 20) on the cooling performance of impingement target surface was analyzed. Multi-objective performance optimization of the bionic structure was carried out by using the second-order response surface approximation model (RSM) and the second-generation non-inferior sequencing genetic algorithm (NSGA-II), and the performance of the optimized structure was tested. The results show that the above optimization method is accurate and effective, and the optimal bionic structure is H = 1.212 mm, R/H = 1.132, P/H = 12.078. Compared with the plane target surface, the average Nusselt number (Nuave), flow friction factor (f), and comprehensive thermal coefficient (F) of the optimal bionic groove structure increased by 14.5%, 1.1% and 14.1%，respectively. The structure and multi-objective optimization method proposed in this paper can provide a certain reference for the design of new efficient cooling structure of heavy-duty gas turbines combustor liner.

System reliability-based design optimization of flexible pavements using adaptive meta-modelling techniques

Recognizing the need for sustainable and long-lasting structures, reliability-based designs have been gaining acceptance in the pavement engineering community. The Reliability Based Design Optimization (RBDO) is formulated to design cost-effective flexible pavements in the presence of uncertainties. Two meta-modelling approaches are considered in this study, the second-order adaptive Response Surface Model (RSM) and the adaptive Polynomial-Chaos based Kriging (PC-Kriging) meta-model. The study highlights the need for adaptive meta-modelling techniques in the reliability-based design of pavement structures, through the quantification of the epistemic uncertainty. For the numerical examples considered in this study, the model uncertainty was found to be around 1% for three-layer sections and below 2.5% for four-layer pavements. To address the correlation between the pavement failure modes, a System Reliability Based Design Optimization (SRBDO) approach is proposed in this paper. The SRBDO methodology is further adapted to design the optimum combination of pavement layer thicknesses and moduli, to meet the target levels of reliability, given the expected traffic demand and subgrade strength at a pavement site. Thus, the SRBDO formulation using adaptive meta-models, presented in this study, efficiently integrates the economic analysis of various pavement design alternatives with the Mechanistic-Empirical procedure in a system reliability framework.

Requirement of digestible calcium at different dietary concentrations of digestible phosphorus for broiler chickens 3. Broiler finishers (d 25 to 35 post-hatch)

An experiment was conducted to determine the digestible calcium (Ca) and digestible phosphorous (P) requirements of 25 to 35-day-old broiler chickens. Fifteen corn-soybean meal-based diets containing 2.0, 2.5, 3.0, 3.5, and 4.0 g/kg standardized ileal digestible (SID) Ca and 2.5, 3.5, and 4.5 g/kg SID P were fed to broilers from d 25 to 35 post-hatch. Each experimental diet was randomly allocated to 6 replicate cages (8 birds per cage). Body weight and feed intake were recorded, and the feed conversion ratio was calculated. On d 35, birds were euthanized to collect the ileal digesta, tibia, and carcass for the determination of ileal Ca, and P digestibility, concentrations of ash, Ca, and P in tibia and the retention of Ca and P in the carcass. Titanium dioxide (5.0 g/kg) was included in all diets as an indigestible indicator for the ileal digestibility measurement. Feed intake and total excreta output were measured during the last 4 d of the experimental period for the measurement of apparent total tract retention of Ca and P. Fixed effects of the experiment were dietary concentrations of SID Ca and SID P and their interaction. If the interaction or main effects were significant (P < 0.05), the parameter estimates for second-order response surface model (RSM) were determined using General Linear Model procedure of SAS. The maximum response was not predicted for most of the parameters (including growth performance and tibia) as the Ca effect was linear which indicated that the highest level of Ca employed in the study may have not been high enough. The requirement of dietary SID Ca for maximization of these parameters, therefore, depends on the dietary SID P concentration when the dietary SID Ca is within 2.0 to 4.0 g/kg. However, based on the factorial analysis, the highest weight gain was observed at 3.5 g/kg SID P and 3.5 g/kg SID Ca concentrations. Tibia ash was higher in birds fed 4.5 g/kg SID P and was unaffected by dietary SID Ca concentrations. However, based on overall findings, a combination of 3.5 g/kg SID P and 3.0-3.5 g/kg SID Ca may be recommended for the optimum tibia ash. The recommended SID Ca requirements (at 3.5 g/kg SID P) for weight gain (3.5 g/kg or 6.4 g/kg total Ca) and tibia ash (3.0-3.5 g/kg or 5.5-6.4 g/kg total Ca) are lower than the current Ca recommendations (7.8 g/kg total Ca equivalent to 4.25 g/kg SID Ca; Ross, 2019) for broiler finishers, suggesting possible excess of Ca in diets formulated based on the current recommendation.

Response Surface Methodology (RSM) Approach for Optimization of Parameters for Synthesis of Organic Compounds and Evaluation of Biological Activity with Molecular Docking

The triazolidine derivatives were synthesized by green and sustainable chemistry approach. The response surface methodology (RSM) was applied to optimize the reaction parameters during the synthesis. Reaction parameter which affect the yield of product were studied, which includes the temperature and time of the reaction. Various statistical RSM with different central composite designs (CCD) such as circumscribed (CCC), face-centered (CCF) and inscribed (CCI) were used to find the maximum yield of the product (%) of reaction at the given parameters and selected, which gave the maximum possible yield. The relationship between reaction parameters (temperature and time) and the yield of product modeled using second-order response surface model. The optimum reaction parameters given by CCI were 80.8 ºC reaction temperature and 15.03 min reaction time with yield of product is up to 94.57%. The adequacy and reliability of the predicted model was checked by ANOVA, R-square and adjusted R-square and revealed the good agreement between predicted model and actual experimental data. The study described here can be efficiently applied for the optimization of parameters in the synthesis of any organic compound. The molecular docking was carried out by using AutoDock vina 1.2.0 on (CYP51) [PDBID: 1EA1] and (DprE1) [PDBID: 4FDO] for target anti-tuberculosis activity while (FabH) [PDBID: 1HNJ] for target antimicrobial activity. There was better interaction within receptor amino acids compound 3d and 3b with FabH and CYP51 enzyme, respectively for anti-tuberculosis activity and compound 3d with DprE1 enzyme for antimicrobial activity observed very good docking score among all compounds.

Augmenting definitive screening designs: Going outside the box

Definitive screening designs (DSDs) have grown rapidly in popularity since their introduction by Jones and Nachtsheim (2011). Their appeal is that the second-order response surface (RS) model can be estimated in any subset of three factors, without having to perform a follow-up experiment. However, their usefulness as a one-step RS modeling strategy depends heavily on the sparsity of second-order effects and the dominance of first-order terms over pure quadratic terms. To address these limitations, we show how viewing a projection of the design region as spherical and augmenting the DSD with axial points in factors found to involve second-order effects remedies the deficiencies of a stand-alone DSD. We show that augmentation with a second design consisting of axial points is often the D s -optimal augmentation, as well as minimizing the average prediction variance. Supplemented by this strategy, DSDs are highly effective initial screening designs that support estimation of the second-order RS model in three or four factors.

Design and Optimization of Negative Poisson Ratio Thin-Walled Tube Using Sensitivity-Based Response Surface Model Methodology

Under low-speed collision conditions, the thin-walled structures located at the forepart of passenger car act as a significant energy absorber, which can reduce the injury degree of passengers in collision accidents. Therefore, the design of thin-walled structures is particularly important in automobile body development. High stiffness and strength contribute to structural integrity, but the resulting large collision force will be detrimental to occupant safety. To address this issue, the paper proposed a novel negative Poisson ratio thin-walled tube (NPR-TWT). In addition, the second-order sensitivity-based response surface models (SB-RSMs) were established to improve the efficiency of design optimization. Furthermore, the NPR-TWT was optimized by using the non-dominated sorting genetic algorithm (NSGA-II) to enhance its comprehensive performance. The results showed that the optimized NPR-TWT could absorb collision energy by sufficient displacement deformation and reduce the peak impact force. It can provide theoretical and practical guidance for the application of thin-walled structures in automobile body safety.

Requirement of digestible calcium at different dietary concentrations of digestible phosphorus for broiler chickens. 2. Broiler growers (d 11 to 24 post-hatch)

An experiment was conducted to determine the digestible calcium (Ca) and digestible phosphorous (P) requirements of 11 to 24 d old broiler chickens. Eighteen corn-soybean meal-based diets containing 1.80, 2.35, 2.90, 3.45, 4.00, and 4.55 g/kg standardized ileal digestible (SID) Ca and 3.5, 4.5, and 5.5 g/kg SID P were fed to broilers from d 11 to 24. Each experimental diet was randomly allocated to six replicate cages (8 birds per cage). Body weight and feed amount were recorded at the start and end of the experiment and the feed conversion ratio was calculated. On d 24, birds were euthanized to collect ileal digesta, tibia, and carcass for the determination of digestible Ca and P, the concentration of ash, Ca and P in tibia and the retention of Ca and P in the carcass, respectively. Titanium dioxide (5 g/kg) was included in all diets as an indigestible indicator for apparent ileal digestibility measurement. Total excreta output was measured during the last 4 d of the experimental period for the measurement of apparent total tract retention of Ca and P. Fixed effects of the experiment were dietary concentrations of SID Ca and SID P and their interaction. If the interaction or main effect was significant (P < 0.05), the parameter estimate for second-order response surface model was determined using General Linear Model procedure of SAS. The weight gain of broiler growers was optimized at the SID P concentration of 3.5 g/kg and SID Ca concentrations between 2.35 and 4.00 g/kg. At 3.5 g/kg SID P concentration, the required SID Ca for maximum weight gain was determined to be 3.05 g/kg, which corresponded to SID Ca to SID P ratios of 0.87. The concentration of SID Ca that maximized tibia ash at 3.5 g/kg SID P was 3.69 g/kg, which corresponded to SID Ca to SID P ratio of 1.05. Maximizing bone ash requires more Ca than maximizing weight gain. Carcass Ca and P retention were reflective of total tract Ca and P retention values. The estimated SID Ca requirements (at 3.5 g/kg SID P) for both maximized weight gain (3.05 g/kg or 6.11 g/kg total Ca) and bone ash (3.69 g/kg or 7.28 g/kg total Ca) are lower than the current Ca recommendation (8.70 g/kg total Ca equivalent to 4.03 g/kg SID Ca; Ross, 2019) for broiler growers, indicating possible oversupply of Ca in diets formulated based on the current recommendation.

Energy loss caused by the elbow of stiff shotcrete pneumatic conveying based on response surface method and CFD-DEM

To explore the energy loss caused by the elbow in the pneumatic transportation of stiff shotcrete, the numerical simulation of the gas-solid flow of stiff shotcrete was carried out based on CFD-DEM. The accuracy of the simulation results was verified by on-site test and parameter calibration. The relationship between air velocity, feed rate, R/D ratio, energy loss caused by elbow and maximum wear rate was studied by response surface methodology. A second-order response surface model between the energy loss caused by elbow and each factor was established. The relationship between the maximum wear rate and each factor was obtained. The effects of air velocity, feeding rate, and R/D ratio on the spatial position and velocity distribution of particles were revealed. This paper can provide a reference for the pneumatic conveying of shotcrete. • The effects of the solid-gas ratio on the energy loss caused by the elbow are studied. • Energy loss caused by the elbow shows a quadratic perturbation with the change of factors. • The maximum wear has a linear relationship with the factors. • The spatial and velocity distributions of particles at different positions are revealed.