Optimal Runner Research Articles

Optimal runner design for balanced filling in a multi‐cavity mold using a two‐stage analytical approach

AbstractIn a multi‐cavity mold, parts from each cavity have consistent properties if the runner system ensures balanced melt‐front advancement. An unbalanced mold, however, narrows the processing window, complicating quality control and making it harder to maintain standards. Molds with an inherently balanced filling, such as the H‐type runner system, are preferred. However, as the number of cavities increases, improvements are needed to address the issues caused by shear heating. Additionally, the material waste in the H‐type runner system is significantly greater than in the fishbone runner system. Based on the rheological concept, a two‐stage analytical approach is established to optimize the fishbone runner system. The diameter of each runner in the fishbone runner system is optimized by controlling pressure drop and remaining time to achieve balanced filling. The impact of these factors is thoroughly examined, as well as why they must be controlled during optimization. The proposed work links the physical situation to its mathematical model, proving highly beneficial for new runner system designs, especially without commercial software assistance.Highlights A new approach to solving unbalanced filling in multi‐cavity molds. Pressure drop and remaining time are key factors for optimization. Two‐stage analytical approach ensures optimization accuracy. The optimal runner system reduces injection pressure for molding. An alternative method for designing fishbone runners without CAE assistance.

Theoretical calculation and simulation analysis of hydraulic joint pressure loss based on fluid dynamics

To study the pressure loss in the runner during the rotating transmission of the hydraulic joint, the local pressure loss of the hydraulic joint is simplified, and the theoretical estimation method of the pressure loss of the hydraulic joint is proposed. Based on the finite element software Comsol, the numerical analysis of the hydraulic joint is carried out to study the effect of the regularity of different fluid inlet and outlet angles and the width of the annular runner on the pressure loss of the runner. The results show that the relative numerical simulation result error of the theoretical calculation of fluid pressure loss is within 20%, and the theoretical calculation method proposed in this paper can guide the rapid evaluation of slip ring pressure loss. The pressure loss of the slip ring increases at first and then decreases gradually with the increase of the fluid inlet and outlet angle. When the angle of the fluid inlet and outlet is 30, the pressure loss of the hydraulic joint is the largest. The pressure loss of the hydraulic joint gradually decreases with the increase of the width coefficient of the runner. When the width coefficient increases to a certain value, the pressure loss reduction effect of the runner is weakened, and the optimal runner width is 0.8-1.2 times the design width of the equal section.

Optimization of Runner Balance for a Family Product of Injection Molding Process

A family mold is used in the injection molding process to produce components of different sizes that would normally be assembled into a single product assembly. The uniform quality of each injection molded part is strongly influenced by the filling balance of the mold cavity. The filling balance can be controlled by optimizing the dimensions of runners that are directed towards each cavity. In this paper, an optimization method is proposed that aims at balancing the filling time that maximizes the quality of a family mold cavity. There are two steps proposed in this research, namely theoretical calculations and simulation of runner balanced design using the software. The results of this study can be used as a practical reference in designing a mold for family products to avoid design errors as early as possible. The result obtained from an industrial case study highlighted the effectiveness of the proposed approach in finding the optimal runner dimension by a restricted number of simulations.

Numerical optimization and experimental validation of the runner of a gravitational water vortex hydraulic turbine with a spiral inlet channel and a conical basin

This paper describes the use of the response surface methodology for the numerical optimization of the runner of a gravitational water vortex hydraulic turbine with a conical basin and a spiral inlet channel. The effect of the relative position of the runner (p), the number of blades (n), and the relation between the mean diameter of the blades (Db), and the diameter of the basin (D), (Db/D) on the efficiency of the turbine was evaluated, and the optimum runner was determined. A second-order regression model representing the efficiency of the turbine was developed. From this model, it was found that the highest efficiency of 65.18% was reached when all the independent variables were set to their higher values, i.e., Db/D, n, and p equal to 0.45, 6, and 0.6, respectively. Experiments were performed using the optimal runner (Db/D=0.45, n=6) and four values for p (0.4, 0.45, 0.50, and 0.55). It was not possible to test the optimal condition with p=0.6, due to the final quality of the acrylic model, the runner collided with the walls of the cone. The experimental efficiencies for the p values were 30.13, 38.35, 53.19, and 60.77%, respectively. According to the response model, these efficiencies correspond to 28.84, 40.46, 50.80, and 59.99%, respectively.

Optimization of geometric parameters of hydraulic turbine runner in turbine mode based on ISMA and BPNN

AbstractThe hydraulic turbine in turbine mode (TMHT) has significant advantages in residual energy recovery, but rapid optimization of its runner parameters has always been a challenge. To address this issue, the optimization algorithm ISMA‐BPNN is proposed based on the improved slime mold algorithm (ISMA) and back propagation neural network (BPNN). First, an efficiency characteristic neural network (ECNN) and a water head characteristic neural network (HCNN), which take the geometric parameters of the runner as input, and the efficiency and water head as outputs, respectively, are constructed by combining the orthogonal test‐based sample data, computational fluid dynamics (CFD), and BPNN. Then, the slime mold algorithm is improved and the optimal runner geometric parameters are obtained based on the ISMA, ECNN, and HCNN, to achieve rapid optimization of the TMHT runner. Finally, the CFD‐based numerical calculation accuracy is verified through real machine tests, and the feasibility of the ISMA‐BPNN‐based rapid optimization strategy for TMHT performance is further verified through CFD numerical simulation.

Design and optimization of a runner for a gravitational vortex turbine using the response surface methodology and experimental tests

In this work, four runners for a gravitational vortex turbine (GVT) were initially analyzed numerically with the aim of selecting the one with the best efficiency (η). The selected rotor was optimized using the response surface methodology (RSM). Four design factors were considered: the number of blades (M), the twist angle (λ), the relationships between the runner upper (D) and lower (d) diameters, and the upper chamber diameter (Dcd); i.e., D/Dcd and d/Dcd, respectively. For the numerical analysis, a three-dimensional (3D) computational domain in ANSYS Fluent software with the K−ϵ RNG turbulence model and the six degrees of freedom (6-DoF) user defined function (UDF) method was utilized for the unsteady flow simulations. The η versus (vs.) the angular velocity (ω) curve was monitored during the CCD for all the treatments tested. The highest η was 0.522 under optimal design conditions; i.e., for M, λ, D/Dcd and d/Dcd equal to 6, 55°, 0.5 and 0.23, respectively. The optimal runner was built using a 3D printing and was experimentally tested utilizing a hydraulic bench. The experimental and numerical η vs. ω curves were compared. A difference of 5.1% between the maximum values of η was found.

Design and optimization of a bidirectional rim-generator turbine runner: Hydraulic performance optimization and structure strength evaluation

As a type of reliable renewable energy, tidal energy has great potential for development. But its technology is behind other renewable energy sources. One of the constraints is the efficiency and stability of tidal turbine. The objective of the present work is to optimize a rim-generator turbine runner by improving hydraulic performance and stress level. A multi-objective optimization based on the response surface methodology is adopted during the optimization process so that an optimal runner blade can be identified. Both the blade shape and the number of the blade are determined. The numerical method is verified by comparing with the experimental test, and the numerical results show good agreement with the experimental results. The hydraulic losses in the ebb generation mode and the flood generation mode are compared, and the mechanism of the difference of the hydraulic losses between the two modes are analyzed, especially the hydraulic losses in the guide vanes. The stress analysis based on the fluid-structure interaction theory shows the optimized rim-generator turbine runner has good structural strength. This work could contribute to the development of the rim-generator turbine, and further to the utilization of the tidal energy.

Analysis of the thermal effect of a lithium iron phosphate battery cell and module

AbstractBased on the theory of porous electrodes and the properties of lithium iron batteries, an electrochemical‐thermal coupling model of a single cell was established. The model was mainly used to study the temperature rise and temperature distribution characteristics in different regions of lithium iron batteries under different working conditions. In addition, a heat dissipation comparison analysis was carried out for different types of liquid cold runners, the optimal runner scheme was selected, and a structural optimization analysis was carried out. The simulation results show that the lithium iron battery discharges under the same ambient temperature and different C rates, and the battery temperature continuously increases with C. The temperature rise is mainly affected by Joule heat, and when the lithium iron battery is discharged at the same C but different ambient temperatures, the temperature rise of the lithium iron battery shows a decreasing trend with the increase in ambient temperature in a certain temperature range. The serial flow channel solution induces the best thermal behavior. Using the response surface optimization analysis, the three independent variable factors at which the temperature equilibrium R reaches the largest value under the liquid cooling module model are the rectangular flow channel length‐to‐width ratio, flow rate, and thermal conductivity.

Study on the effects of runner geometries on the performance of inline cross-flow turbine used in water pipelines

To supply continuous and reliable power to the water monitoring systems and motorized control valves in urban water supply networks, the inline cross-flow turbine has been developed. This study aims to investigate the effects of different runner geometries on the performance of inline cross-flow turbines and to determine the optimal runner geometrical parameters. In this paper, a theoretical analysis of the working mechanism of a cross-flow runner is first performed to study the impacts of the runner geometry on turbine performance. Thereafter, several turbine models with different runner geometries are built and simulated to analyse the output power, water head reduction and torque generation at each runner stage. The results indicate that a good match between the flow inlet angle and blade outer angle notably enhances the turbine performance. Based on the results, the recommended optimal blade outer angle in this research is 30°. In addition, the results also show that the runner diameter ratio has a major impact on torque generation at the runner first stage. A lower runner diameter ratio leads to a higher output power, but the water head reduction is also higher. Based on the results, the suggested runner diameter ratio is 0.68. A numerical study on the number of blades indicates that when the number of blades increases from 20 to 24, the turbine output power considerably rises, and the maximum output power reaches 2285 W. However, if the blade number is further increased, the variation in output power is very slight. Thus, the proposed optimal blade number is 24. Based on the research results, the maximum turbine efficiency can reach 50.9% after runner optimization.

Optimal Design for an Extruder Head Runner Based on Response Surface Method and Simulated Annealing Algorithm

The head runner of a rubber extruder is important for controlling rubber flow and improving extrudate quality. To clarify the effect of the structure parameters of the head runner of a doubleplex tread extruder on extrudate quality and obtain high-quality rubber extrusions, a finite element model of the down head runner was established. The extrusion process was analyzed through numerical simulations, wherein the Bird–Carreau constitutive equation and Navier slip law were used along with some computational methods, such as quadratic interpolation of velocity and linear interpolation of pressure and viscosity. The Newton iteration algorithm was used for numerical calculations. The mean-square deviation of velocity (SDV) of rubber flow in the outlet cross section was selected as the evaluation objective. A Placket–Burman design was used to select three key factors—angles A and B and outlet width D—from among eight runner structure parameters affecting the velocity variance. By using central composite design (CCD), the quadratic response surface model using the three key factors was established, and the influence law of a combination of the three key factors on SDV was obtained. The response surface model was optimized using the simulated annealing (SA) algorithm, and the optimal key factors of the head runner were obtained. The optimal runner design realizes a more uniform velocity distribution in the outlet cross section. Furthermore, a comparison of the simulated flow velocities of the original and optimal head runners at different inlet flow ratios and temperatures indicates that the optimal head runner flow velocity improves the extrusion quality. Thus, an optimal runner with optimal key factors was manufactured. Test results of the rubber flow state indicated that the flow is regular and that warping disappears. The proposed optimization strategy can be used practically for improving the head runner design, shortening the product development cycle, and reducing the production cost.

The optimal runner on the royal road

Assuming a simple biophysical model and using the Carathéodory method, we find the optimal strategy to run or swim a race.

Hydraulic design of a low-specific speed Francis runner for a hydraulic cooling tower

The air blower in a cooling tower is normally driven by an electromotor, and the electric energy consumed by the electromotor is tremendous. The remaining energy at the outlet of the cooling cycle is considerable. This energy can be utilized to drive a hydraulic turbine and consequently to rotate the air blower. The purpose of this project is to recycle energy, lower energy consumption and reduce pollutant discharge. Firstly, a two-order polynomial is proposed to describe the blade setting angle distribution law along the meridional streamline in the streamline equation. The runner is designed by the point-to-point integration method with a specific blade setting angle distribution. Three different ultra-low-specificspeed Francis runners with different wrap angles are obtained in this method. Secondly, based on CFD numerical simulations, the effects of blade setting angle distribution on pressure coefficient distribution and relative efficiency have been analyzed. Finally, blade angles of inlet and outlet and control coefficients of blade setting angle distribution law are optimal variables, efficiency and minimum pressure are objective functions, adopting NSGA-II algorithm, a multi-objective optimization for ultra-low-specific speed Francis runner is carried out. The obtained results show that the optimal runner has higher efficiency and better cavitation performance.

Runner design to improve quality of plastic optical lens

Although the layout of multicavity molds is a geometrically balanced design, when the melt flows into the runner, the shear-induced partial changes in material properties will result in intracavity imbalance. This study placed a rectangular flow restrictor within the tertiary runner of a precision optical lens mold to create melt turbulence through flow blocking. Due to polymer rheological characteristics, uniform melt temperature distribution in the runner channel could be obtained, making the temperature distribution inside the cavity more uniform, and reducing the thermal residual stress and warpage of injection molded parts. The optimal runner restrictor design is placing 5 mm away from the secondary runner centerline, making both the depth and the width of the block 3 mm. A relatively uniform melt temperature distribution with a maximum temperature difference of 1.1 °C can be achieved. Injection molds were fabricated according to the optimized restrictor design, and experimental verification was performed. The contour accuracy of a lens parallel to injection direction was improved from 10.44 to 5.03 μm. Therefore, this runner restrictor design can be applied to high-precision optical molds due to the ease of machining and the capability of improving the quality of optical lens.

사출성형에서 런너 크기의 최적화를 위한 CAE 적용

【The delivery system such as sprue, runner and gate is a waste of resin in injection molding operation. In this study the reduction of runner size has been investigated using injection molding CAE softwares, Moldflow and Moldex3D, and commercial CFD Softwares, Fluent and Polyflow. To verify the computational results experiment was performed. There were three considerations in deciding optimal runner size in this study: minimum pressure at the gate that makes resin fully filled in the cavity, minimum runner size that compensates shrinkage of resin in the cavity, and frozen layer thickness formed in the runner during injection. Through the computer simulations the optimal runner size that satisfies those three considerations has been decided. Although the computational results among the softwares were slightly different, it was enough to predict the optimal runner size. The previous runner diameter was 8 mm and predicted optimal size was 5 mm. This was verified by injection molding experiment. Thus, the way of CAE application in deciding optimal runner size adapted in this study would be appropriated.】

Design of the runner and gating system parameters for a multi-cavity injection mould using FEM and neural network

The design of the runner and gating systems is of great importance to achieving a successful injection moulding process. The subjects of this study are the finite element and abductive neural network methods applied to the analysis of a multi-cavity injection mould. In order to select the optimal runner system parameters to minimize the warp of an injection mould, FEM, Taguchi’s method and an abductive network are used. These methods are applied to train the abductive neural network. Once the runner and gate system parameters are developed, this network can be used to accurately predict the warp of the multi-injection mould. A simulated annealing (SA) optimization algorithm with a performance index is then applied to the neural network in order to search the gate and runner system parameters. This method obtains a satisfactory result as compared with the corresponding finite element verification.

Runner Design with Minimum Volume for Multicavity Injection Molds: Part II. Runner Layout

Following the optimal runner sizing given in Part I, this paper establishes rules for runner layouts to minimize volume using a mathematical analysis. For four cavities with their centers forming a rectangle, the X layout gives the smallest runner volume unless the aspect ratio of the rectangle exceeds 1.305. In the latter case, a double Y shaped (>-<) layout is the optimal. This rule is extended to multiple-of-four cavities in a rectangle and circularly arranged cavities. Several examples of optimal and recommended simpler runner layouts illustrate that runner volume can be reduced by up to 39%. In addition, a procedure based on a "runner design invariant" concept has been developed for modifying an existing runner design to reduce runner volume without knowing the material and processing parameters other than the power-law index.

Fluid flow in casting rigging systems: Modeling, validation, and optimal design

In this work, a methodology for the optimal design of flow in foundry casting rigging systems is discussed. The methodology is based on a novel, fully analytical design sensitivity formulation for transient, turbulent, free-surface flows. The filling stage of the casting process is modeled by solving the time-averaged form of the Navier-Stokes equations via a turbulent mixing-length model, in conjunction with the volume-of-fluid (VOF) method for modeling the free surface. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The finite element model of the filling process is verified through physical experimentation. Solutions of glycerol and water are used to perform laminar and turbulent flow filling experiments, which are used to verify independently the VOF algorithm and the adequacy of the mixing-length model. The results show that the numerical model accurately reproduces the main features of the flow, and filling times agree with acceptable accuracy. Finally, the analytical techniques are used to obtain an optimal runner shape, which eliminates air entrainment, and the design is verified experimentally.

Observations on the preceding paper of C. Hamburger: The Optimal Runner: a Control Problem with Phase Constraint

Assuming a simple biophysical model and using the Pontryagin maximum principle, we find the optimal strategy to run a race.

The Optimal Runner: a Control Problem with Phase Constraint

Assuming a simple biophysical model and using the Pontryagin maximum principle, we find the optimal strategy to run a race.