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| − | =2. Theory=
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| − | ==2.2 CFD-DEM coupled method==
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| − |
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| − | ''' ''' CFD-DEM coupling method is a numerical analysis method for multiphase flow problems of particles and fluids. It has been widely used in many fields. Its basic idea is to model the fluid as a continuous medium and calculate it in the CFD method，and DEM and Newton's second law are combined to calculate the motion of particles which are considered to be a discrete phase.
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| − | The flushing process of the toilet consists of two parts: one is the flow of water flow, the other is the movement of particles under the effect of water flow. In the process of the flow of water flow, water flow is considered to be a continuous phase, it can be calculated by solving the continuity equation and N-S equation. In the process of particle motion, particles are considered to be a discrete phase, the force and motion of particles can be calculated by Newton's second law. The data for the process of the flow of water flow and particle motion can be transmitted through the interface card.The coupling process for the flushing process of the toilet in FLUENT and EDEM is shown in Figure 1 [16-18].
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | [[Image:Draft_Li_649584643-image19.jpeg|600px]] </div>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | Figure 1 The calculation process of CFD-DEM coupled method</div>
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| − | According to Figure 1, in the calculation, FLUENT first calculates the flow field of an interpolation time period, and transmits the flow field information of the interpolation point to EDEM at an interpolation time interval. EDEM reads the flow field information from FLUENT, then adds various field forces to the motion equation of particles by the interface plug-in (API) and start to calculate the forces and motion of particles in the corresponding interpolation time interval. After EDEM completes the calculation in the interpolation time period, FLUENT starts to update the flow field in the next interpolation time period in circulation. The interpolation time period is the time interval of data transmission, and the value is taken the smaller and the calculation error is the smaller. The minimum interpolation time interval is a FLUENT calculation time step, that is the time step is the smaller, the calculation accuracy is the higher.
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| − |
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| − | The flow field information transmitted from FLUENT to EDEM includes velocity field, volume fraction field (or density field) and pressure-gradient field. The main reason why the volume fraction field or density field need to be transmitted is that the calculation domain contains two kinds of mediums: water flow and air in the flushing process of the toilet, the field forces (buoyancy force and drag force) of particles in different mediums are different. Therefore, it is necessary to distinguish the properties of mediums in various locations in fluid domain. The interface plug-in between FLUENT and EDEM is compiled by Visual Studio development tool through API. The contents of the interface plug-in include reading the flow field information, distinguishing the properties of mediums in calculation domain, calculating field forces and setting the interpolation time interval for a transient calculation. In this paper, the effect of water flow on particles is mainly considered, and it is a one-way coupling method.
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| − |
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| − | =3 Simulation and experimental conditions=
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| − | ==3.1 Simulation parameter settings==
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| − |
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| − | ===3.1.1 CFD parameter settings===
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| − | ''' '''In this paper, the flushing process of a siphon jet toilet with different structural parameters of siphon pipes is studied by CFD-DEM coupling method. According to the structural characteristics of the toilet model and considering the calculation time and accuracy, the hybrid grid is used to mesh, that is, the water tank part with regular structure is divided into structured grids to reduce the number of grids, and the unstructured grids are used to mesh in other areas to reduce the difficulty of meshing. The number of grids is about 2.3 million (Figure 2a).
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| − | In the CFD calculation of the flushing process, the pressure base solver is used for a transient solution. The VOF model is used to calculate the multiphase flow, and the air is setted as the first phase, water is setted as the second phase. The Realizable k-epsilon model is chosen for the turbulence model and the standard wall function is applied to deal with the near-wall. Pressure-velocity coupling method adopts SIMPLE algorithm, the momentum equation is discretized by second-order upwind, and turbulent kinetic energy, turbulent kinetic energy dissipation rate and transient equation are discretized by first-order upwind. According to the actual situation of the flushing process, a pressure inlet boundary condition and two pressure outlet boundary conditions are setted up, as shown in Figure 2b. In Figure 2b, the red part is water, the blue part is air, and the water in the water tank is 5.5 L. The computation''' '''time step of FLUENT is 0.0002 s, the computation time is 6.6 s, and the maximum iteration step is 20 steps.
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| − | | [[Image:Draft_Li_649584643-image20.png|264px]]
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| − | | [[Image:Draft_Li_649584643-image21.png|center|318px]]
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| − | |}
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| − | </div>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | Figure 2a The assembled grid model Figure2b The setting of boundary conditions</div>
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| − |
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| − | ===3.1.2 DEM parameter settings===
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| − | The solid medium in the flushing process is polypropylene spherical particles with a radius of 8.75 mm, a density of 890 kg/m<sup>3</sup>, a flushing quantity of 130, and the wall material of the toilet is ceramic. The formation of particles is set up by the secondary development of the granular factory, that is all water tested balls are generated at the water seal position of the toilet at the beginning of the calculation, and this ensures that the initial state of the water tested balls is the same in each test in order to avoid the influence of the randomness of particle formation on the flushing results. Considering that the contact force between particles and between particles and the inner walls of the toilet, it is necessary to determine the contact parameters between particles and between particles and the walls. In this paper, a high-speed camera is used to measure the contact parameters. Detailed parameter settings are shown in Table 1. The computation time step of''' '''EDEM is setted as 2Í10<sup>-6</sup> s.
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | '''Table 1 The setting of EDEM parameters'''</div>
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| − | {| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
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| − | | style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Material properties
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| − | | style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Poisson ratio
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| − | | style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Density（kg/m<sup>3</sup>）
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| − | | style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Shear modulus（Pa）
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| − | |-
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| − | | style="border-top: 1pt solid black;text-align: center;"|Particles
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| − | | style="border-top: 1pt solid black;text-align: center;"|0.41
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| − | | style="border-top: 1pt solid black;text-align: center;"|890
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| − | | style="border-top: 1pt solid black;text-align: center;"|3.2e+08
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| − | |-
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| − | | style="text-align: center;"|Pipe wall
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| − | | style="text-align: center;"|0.22
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| − | | style="text-align: center;"|2300
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| − | | style="text-align: center;"|9.06e+10Pa
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| − | | style="text-align: center;"|Collision attributes
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| − | | style="text-align: center;"|Restitution coefficie
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| − | | style="text-align: center;"|Static friction coefficient
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| − | | style="text-align: center;"|Rolling friction coefficient
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| − | | style="text-align: center;"|particles-particles
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| − | | style="text-align: center;"|0.6282
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| − | | style="text-align: center;"|0.12
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| − | | style="text-align: center;"|0.0486
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| − | | style="border-bottom: 2pt solid black;text-align: center;"|particles-walls
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| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.7823
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| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.2
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| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0306
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| − | |}
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| − |
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| − | ===3.1.3 Structure parameter setting of siphon pipes===
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| − | In this paper, the influence of structural parameters of siphon pipes on the flushing performance of the toilet is studied. In order to better analyze, the structures of siphon pipes is divided, which are shown in Figure 3.
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | ''' [[Image:Draft_Li_649584643-image22.png|246px]] '''</div>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | Figure 3 The division of structural parameters of siphon pipes</div>
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| − | In Figure 3, the structure size of siphon pipes is characterized by six parameters: R, L<sub>1</sub>, H<sub>1</sub>, L<sub>2</sub>, H<sub>2</sub> and D. R is the inclination angle of A-B section of siphon pipes, H<sub>0</sub> is the water seal height of of siphon pipes, L<sub>1</sub> is the length of radian change, H<sub>1 </sub>is the height of radian change, L<sub>2 </sub>is the length of E-F section of secondary water seal, H<sub>2 </sub>is the height of secondary water seal, and D is the diameter of siphon pipes. R, L<sub>1</sub>, H<sub>1</sub>, L<sub>2</sub>, H<sub>2</sub> and D are named as inclination angle, curvature width, curvature length, secondary water seal width, secondary water seal height and pipe diameter, respectively. All these parameters are both connected and independent, when one of them is changed, the other parameters remain unchanged. In order to explore the effect of six parameters on the flushing performance, six tests are carried out, and the detailed parameters are shown in Table 2.
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | '''Table 2 The structure parameters of siphon pipes'''</div>
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|NO.
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| − | | colspan='2' style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''R''（°）
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''L<sub>1</sub>''（mm）
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''H<sub>1</sub>''（mm）
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''L<sub>2</sub>''（mm）
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''H<sub>2</sub>''（mm）
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| − | | style="border-top: 2pt solid black;border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|''D''（mm）
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| − | |-
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|1
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| − | | colspan='2' style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|36,40,44,48,52,56
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|55
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|210
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|90
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|30
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| − | | style="border-top: 2pt solid black;text-align: center;vertical-align: top;"|50
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| − | |-
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| − | | style="text-align: center;vertical-align: top;"|2
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| − | | style="text-align: center;vertical-align: top;"|48
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| − | | colspan='2' style="text-align: center;vertical-align: top;"|45,50,55,60,65,70
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| − | | style="text-align: center;vertical-align: top;"|210
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| − | | style="text-align: center;vertical-align: top;"|90
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| − | | style="text-align: center;vertical-align: top;"|30
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| − | | style="text-align: center;vertical-align: top;"|50
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| − | |-
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| − | | style="text-align: center;vertical-align: top;"|3
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| − | | colspan='2' style="text-align: center;vertical-align: top;"|48
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| − | | style="text-align: center;vertical-align: top;"|65
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| − | | style="text-align: center;vertical-align: top;"|170,190,210,230,250
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| − | | style="text-align: center;vertical-align: top;"|90
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| − | | style="text-align: center;vertical-align: top;"|30
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| − | | style="text-align: center;vertical-align: top;"|50
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| − | |-
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| − | | style="text-align: center;vertical-align: top;"|4
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| − | | colspan='2' style="text-align: center;vertical-align: top;"|48
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| − | | style="text-align: center;vertical-align: top;"|65
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| − | | style="text-align: center;vertical-align: top;"|210
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| − | | style="text-align: center;vertical-align: top;"|60,70,80,90,100,110
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| − | | style="text-align: center;vertical-align: top;"|30
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| − | | style="text-align: center;vertical-align: top;"|50
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| − | |-
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| − | | style="text-align: center;vertical-align: top;"|5
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| − | | colspan='2' style="text-align: center;vertical-align: top;"|48
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| − | | style="text-align: center;vertical-align: top;"|65
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| − | | style="text-align: center;vertical-align: top;"|210
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| − | | style="text-align: center;vertical-align: top;"|90
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| − | | style="text-align: center;vertical-align: top;"|10,20,30,40,50,60
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| − | | style="text-align: center;vertical-align: top;"|50
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| − | |-
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|6
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| − | | colspan='2' style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|48
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|65
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|210
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|90
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|30
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| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|44,47,50,53,56,59
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| − | |}
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| − |
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| − | ==3.2 Experimental platform==
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| − | ''' ''' In order to study the influence of structural parameters of siphon pipes on the flushing performance, a set of experimental platform with adjustable structural parameters of siphon pipes need to be builded. The simulation model used in the numerical calculation is based on a siphon jet toilet. Therefore, the building of the physical experimental platform is also based on it, and the improved toilet model is shown in Figure 4. In this experimental platform, the shape of siphon pipes can be adjusted arbitrarily within a certain range, and the water volume in the water tank can be controlled automatically through a flowmeter. The structural parameters of the siphon pipes are consistent with the parameters in the simulation experiment, and the water volume in the water tank is 5.5 L. It should be noted that the influence of siphon pipe diameter on the flushing performance has not been studied in the experiment, this is because the siphon pipe diameter is related to the basin structure of the toilet, when the basin structure is determined, the pipe diameter is also determined, and the siphon pipe diameter is 50 mm in this experiment. In addition, because of the size limitation of the toilet model, there are only three values of the curvature length parameters are studied. In the experiment, the material properties and quantity of solid granular medium are the same as those in the simulation, and each experiment is carried out six times, then the average value is taken as the quantity of flushing balls.
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| − | | [[Image:Draft_Li_649584643-image25.jpeg|center|264px]]
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| − | |}
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| − | </div>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | Figure 4 Experimental platform of toilet</div>
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| − |
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| − | ==3.3 Definition of flushing capacity==
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| − | <span id='OLE_LINK2'></span><span id='OLE_LINK3'></span>''' ''' In order to analyze quantitatively the flushing performance of the toilet and consider synthetically the relationship between the quantity of flushing balls and the amount of water in the flushing process, the flushing capacity is defined as the evaluation index of the flushing performance of the toilet, and the flushing capacity can be expressed by the following formula:
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| − | <math>P=\frac{V_B}{V_W}</math> （16）
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| − | Where V<sub>B</sub> is the volume of all tested water balls that are washed away, V<sub>W</sub> is the volume of water used in the flushing process. According to the formula of the flushing capacity, the flushing capacity can be understood as the volume of tested water balls that are washed away by a unit volume of water.
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| − | =4 The discussion of flushing performance =
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| − | <span id='dttl'></span>
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| − |
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| − | ====4.1 Verification of simulation law====
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| − | The relationship between the flushing capacity of the toilet and structural parameters of siphon pipes can be obtained by studying the flushing process of different siphon pipe structural parameters using CFD-DEM coupling method. In order to verify the reliability of the simulation law, the experiments under the same structural parameters are carried out, and the simulation law is compared with the experimental law, the results are shown from Figure 5 to Figure 9.
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| − | {|
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| − | | [[Image:Draft_Li_649584643-image27-c.png|294px]]
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| − | | [[Image:Draft_Li_649584643-image28-c.png|center|288px]]
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| − | |}
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| − | Figure 5 Comparison of inclination angle Figure 6 Comparison of curvature width
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| − | {|
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| − | | [[Image:Draft_Li_649584643-image29-c.png|288px]]
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| − | | [[Image:Draft_Li_649584643-image30-c.png|center|300px]]
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| − | |}
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| − |
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| − | Figure 7 Comparison of curvature length Figure 8 Comparison of secondary water seal width
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| − | [[Image:Draft_Li_649584643-image31-c.png|306px]]
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| − | Figure 9 Comparison of secondary water seal height
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| − | As are shown from Figure 5 to Figure 9, the experimental results and the simulation results have the same change rule, and only the absolute values are different. And the difference are mainly reflected in the value of the flushing capacity in the simulation, which is larger than that in the experiment. On the one hand, it is caused by the inconsistency of physical experiment model and simulation calculation model, on the other hand, it is also affected by the accuracy of coupling algorithm in simulation calculation. Although the simulation law and the experimental law are different in the absolute value, the factors that cause the difference all have the same effect on the absolute value of flushing capacity under all parameters, and as a whole, it can reflect the range of structural parameters with better flushing performance. Therefore, it is practicable to study the regularity of the flushing performance of structural parameters of different siphon pipes. The numerical simulation method is not limited by the fixed size of model, it can study the flushing process in a wider range of structural parameters. And it is also convenient to obtain data which is not easy to get in physical experiments, and it is helpful to further study the flushing mechanism and reduce the development cycle and cost.
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| − | Because of the size limitation of experimental platform, there is no study about the effect of diameter change of siphon pipes on the flushing performance. Therefore, we can use CFD-DEM method to simulate the flushing process under different diameters. The simulation results are shown in Figure 10.
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| − |
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | [[Image:Draft_Li_649584643-image32-c.png|336px]] </div>
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| − |
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | Figure 10 The influence of siphon pipe diameter on the flushing performance</div>
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| − | According to Figure 10，the flushing capacity increases gradually and the flushing performance of the toilet increases gradually with the pipe diameter increases from 44 mm to 53 mm. When the pipe diameter increases from 53 mm to 56 mm, the flushing performance of the toilet remains unchanged, it is mainly because all the tested water balls are washed out under the diameters of these two pipes. When the pipe diameter is increased to 59 mm, the flushing capacity begins to decline. It is mainly because the pipe diameter is the larger, the siphon strength is the lower and the flushing force is the smaller under the same water consumption condition, which also shows that the bigger is not the better under the same flushing water consumption condition, and the reasonable pipe diameter is helpful to get better flushing and water-saving comprehensive properties. When the diameters of the pipe are 53mm and 56mm, the flushing performance of the toilet is better. In addition, the diameter of the siphon pipe is the smaller, the velocity of water flow is the higher in the pipe, and the siphon negative pressure is the lower, but the flushing capacity is lower, which also shows that the flushing performance can not be judged directly by the velocity and the negative pressure in the pipe under the condition of the pipe diameter changes, and it is necessary to combine the punching balls test.
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| − |
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| − | ==4.2 The study of orthogonal experiment==
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| − |
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| − | ''' '''In order to explore the influence of the structural parameters of each siphon pipe on the flushing performance, and to find a better combination of the structural parameters of siphon pipes, an orthogonal test was carried out in this paper. According to the experimental part, the pipe diameter of the toilet is related to the structure of the basin wall. When the diameter of siphon pipes changes, the model of the basin wall also changes. If the orthogonal experiment is carried out, many different models of the toilet need to be made, which greatly increases the development cycle and cost. According to the above research, CFD-DEM coupling method can better reflect the change rule of the flushing capacity of the toilet, and we can use the simulation method to carry out the numerical analysis when it is not easy to carry out an experimental research. Therefore, we can use the simulation method to carry out the orthogonal test.
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| − | There are six parameters to be considered in the structure of siphon pipes, each parameter is taken at three levels, and the L<sub>18</sub>（3<sup>7</sup>）orthogonal table is selected for the test, a total of 18 experiments are required. The parameter settings and results of orthogonal test are shown in Table 3.
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| − |
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | '''Table 3 The parameter settings of orthogonal test'''</div>
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| − |
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| − | {| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
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| − | |-
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| − | | rowspan='3' style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Test number
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| − | | colspan='6' style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Factors
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| − | | rowspan='3' style="border-top: 2pt solid black;text-align: center;vertical-align: bottom;"|Flushing capacity
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| − | |-
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|A
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|B
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|C
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|D
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|E
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| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|F
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| − | |-
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''R''（°）
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''L<sub>1</sub>''（mm）
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''H<sub>1</sub>''（mm）
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''L<sub>2</sub>''（mm）
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''H<sub>2</sub>''（mm）
| |
| − | | style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|''D''（mm）
| |
| − | |-
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|1
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|48
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|45
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|200
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|90
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|20
| |
| − | | style="border-top: 1pt solid black;text-align: center;"|47
| |
| − | | style="border-top: 1pt solid black;text-align: center;vertical-align: top;"|0.0561
| |
| − | |-
| |
| − | | style="text-align: center;"|2
| |
| − | | style="text-align: center;"|48
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0648
| |
| − | |-
| |
| − | | style="text-align: center;"|3
| |
| − | | style="text-align: center;"|48
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0628
| |
| − | |-
| |
| − | | style="text-align: center;"|4
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|45
| |
| − | | style="text-align: center;"|200
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0663
| |
| − | |-
| |
| − | | style="text-align: center;"|5
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|47
| |
| − | | style="text-align: center;vertical-align: top;"|0.0434
| |
| − | |-
| |
| − | | style="text-align: center;"|6
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|90
| |
| − | | style="text-align: center;"|20
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0526
| |
| − | |-
| |
| − | | style="text-align: center;"|7
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|45
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|90
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0413
| |
| − | |-
| |
| − | | style="text-align: center;"|8
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|20
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0663
| |
| − | |-
| |
| − | | style="text-align: center;"|9
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|200
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|47
| |
| − | | style="text-align: center;vertical-align: top;"|0.0439
| |
| − | |-
| |
| − | | style="text-align: center;"|10
| |
| − | | style="text-align: center;"|48
| |
| − | | style="text-align: center;"|45
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0622
| |
| − | |-
| |
| − | | style="text-align: center;"|11
| |
| − | | style="text-align: center;"|48
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|200
| |
| − | | style="text-align: center;"|90
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0510
| |
| − | |-
| |
| − | | style="text-align: center;"|12
| |
| − | | style="text-align: center;"|48
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|20
| |
| − | | style="text-align: center;"|47
| |
| − | | style="text-align: center;vertical-align: top;"|0.0434
| |
| − | |-
| |
| − | | style="text-align: center;"|13
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|45
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|20
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0653
| |
| − | |-
| |
| − | | style="text-align: center;"|14
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|90
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|47
| |
| − | | style="text-align: center;vertical-align: top;"|0.0582
| |
| − | |-
| |
| − | | style="text-align: center;"|15
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|200
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0633
| |
| − | |-
| |
| − | | style="text-align: center;"|16
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|45
| |
| − | | style="text-align: center;"|220
| |
| − | | style="text-align: center;"|100
| |
| − | | style="text-align: center;"|30
| |
| − | | style="text-align: center;"|47
| |
| − | | style="text-align: center;vertical-align: top;"|0.0515
| |
| − | |-
| |
| − | | style="text-align: center;"|17
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;"|200
| |
| − | | style="text-align: center;"|110
| |
| − | | style="text-align: center;"|20
| |
| − | | style="text-align: center;"|50
| |
| − | | style="text-align: center;vertical-align: top;"|0.0663
| |
| − | |-
| |
| − | | style="text-align: center;"|18
| |
| − | | style="text-align: center;"|52
| |
| − | | style="text-align: center;"|65
| |
| − | | style="text-align: center;"|210
| |
| − | | style="text-align: center;"|90
| |
| − | | style="text-align: center;"|25
| |
| − | | style="text-align: center;"|53
| |
| − | | style="text-align: center;vertical-align: top;"|0.0663
| |
| − | |-
| |
| − | | style="text-align: center;"|Average value 1
| |
| − | | style="text-align: center;"|0.0567
| |
| − | | style="text-align: center;"|0.0571
| |
| − | | style="text-align: center;"|0.0578
| |
| − | | style="text-align: center;"|0.0543
| |
| − | | style="text-align: center;"|0.0583
| |
| − | | style="text-align: center;"|0.0494
| |
| − | | style="text-align: center;vertical-align: top;"|
| |
| − | |-
| |
| − | | style="text-align: center;"|Average value 2
| |
| − | | style="text-align: center;"|0.0582
| |
| − | | style="text-align: center;"|0.0583
| |
| − | | style="text-align: center;"|0.0541
| |
| − | | style="text-align: center;"|0.0593
| |
| − | | style="text-align: center;"|0.0603
| |
| − | | style="text-align: center;"|0.0584
| |
| − | | style="text-align: center;vertical-align: top;"|
| |
| − | |-
| |
| − | | style="text-align: center;"|Average value 3
| |
| − | | style="text-align: center;"|0.0560
| |
| − | | style="text-align: center;"|0.0554
| |
| − | | style="text-align: center;"|0.0589
| |
| − | | style="text-align: center;"|0.0573
| |
| − | | style="text-align: center;"|0.0522
| |
| − | | style="text-align: center;"|0.0630
| |
| − | | style="text-align: center;vertical-align: top;"|
| |
| − | |-
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|Range
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0022
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0030
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0048
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0050
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0081
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;"|0.0136
| |
| − | | style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|
| |
| − | |}
| |
| − |
| |
| − |
| |
| − | The range reflects the influence of each structural parameter change of siphon pipes on the flushing capacity, and the bigger range indicates that the structural parameters will cause a bigger change on the flushing capacity in the experiment, so the maximum row of range indicates that the level of its structural parameters is the most important factor affecting the flushing performance of the toilet. According to Table 3, the size relation of range is F>E>D>C>B>A, therefore, the order of the influence of the structural parameters of siphon pipes on the flushing capacity is from primary to secondary is pipe diameter, secondary water seal height, secondary water seal width, curvature length, curvature width and inclination angle. The optimized combination parameter of orthogonal test is A<sub>2</sub>B<sub>2</sub>C<sub>3</sub>D<sub>2</sub>E<sub>2</sub>F<sub>3, </sub>but the parameter combination don’t contain that one in the orthogonal test table. Therefore, it needs to be verified by experiments. The flushing capacity of the optimized combination scheme obtained by simulation method is 0.0663. Compared with the results of the orthogonal test, the flushing capacity of the fourth, eighth, seventeenth and eighteenth groups are all 0.0663, which is the same as that one in the optimized scheme. That is, all the solid particles are flushed out. Therefore, it is not yet able to determine whether the flushing capacity under the optimized parameters of the scheme is the optimal. In order to further determine the flushing performance between the optimized scheme and the fourth, eighth, seventeenth and eighteenth groups, the quantity of flushing balls is increased from 130 to 150, then the above five combination parameters are re-tested, and the results of the experiments are shown in Figure 11.
| |
| − |
| |
| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
| |
| − | [[Image:Draft_Li_649584643-image33-c.png|336px]] </div>
| |
| − |
| |
| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
| |
| − | Figure 11 The flushing capacity under different groups</div>
| |
| − |
| |
| − | ''' '''According to Figure 11, the flushing capacity is the biggest under the optimized scheme, this indicates that the best flushing capacity can be obtained when the inclination angle is 50°, the curvature width is 50 mm, the curvature length is 220 mm, the secondary water seal width is 100 mm, the secondary water seal height is 25 mm and the pipe diameter is 53 mm.
| |
| − |
| |
| − | =5 Conclusions=
| |
| − |
| |
| − | According to the above analysis, the following conclusions can be obtained:
| |
| − |
| |
| − | 1. CFD-DEM coupling method can be used to reflect the overall changing tendency of the flushing performance of the toilet, but the absolute value is different. Therefore, CFD-DEM coupling method can be used to study the regularity of the flushing performance of the toilet. When the experimental method is not easy, the simulation method can be used to analyze qualitatively the flushing performance of the toilet.
| |
| − |
| |
| − | 2. Better flushing performance of the toilet can be obtained when the inclination angle is 50°, the curvature width is 50 mm, the curvature length is 220 mm, the secondary water seal width is 100 mm, the secondary water seal height is 25 mm and the pipe diameter is 53 mm.
| |
| − |
| |
| − | 3. It is worth to further study about how to use CFD-DEM coupling method for quantitative analysis of the toilet flushing performance.
| |
| − |
| |
| − | ==Acknowledgement ==
| |
| − |
| |
| − | The authors gratefully acknowledged the support from the Program for scientific and technological innovation flats of Fujian Province (2014H2002). Fujian university-industry cooperation project (2017H6002). Fujian Natural Science Foundation (2017J01675). Key projects of Fujian provincial youth natural fund (JZ160460). No part of this paper has published or submitted elsewhere. The authors declared that they have no conflicts of interest to this work. All authors have seen the manuscript and approved to submit to your journal.
| |
| − |
| |
| − | ==References==
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| − |
| |
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| − | 2. Y. Wang, G. Xiu, and H. Tan, "Cad and Cae Analysis for Siphon Jet Toilet," in ''International Conference on Optics in Precision Engineering and Nanotechnology, ICOPEN 2011, March 23, 2011 - March 25, 2011'', Ed. by (Elsevier, Singapore, Singapore, 2011), p. 472.
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| |
