THE 8TH ASIAN SYMPOSIUM ON VISUALIZATION, 2005

Paper number 71 71-1

A Three-Dimensional Simulation of Flow Mixing in a Mixing Head of an Injection Moulding Machine

K. Maneeratana, S. Putivisutisak, S. Sucharitpwatskul, T. Intarakumtornchai and S. Chaiyapinunt

Department of Mechanical Engineering, Chulalongkorn University, Bangkok, Thailand Phone: +66 (0)2218-6610, Fax: +66 (0)2252-2889, E-mail: fmespt@eng.chula.ac.th

Corresponding author S. Putivisutisak

Abstract The paper presents the numerical simulation of three-dimensional flow mixing in the head chamber of an injection moulding machine used in an automotive steering wheel factory. Two fluids, Polyol and Isocyanate, are injected into the mixing head through the flow passage of diameter D at a very high pressure. The mixed fluids are then driven into the mould to form the cover foam on the steering wheel. It is assumed that there is no chemical reaction occurs during the mixing in the head chamber since the time period is short. The commercial software, CFX, is employed to compute the flow mixing and the results are used to investigate the characteristics of the head. By varying the diameters φ and angles of the inlet ports, the optimised configuration of the mixing head is obtained at the diameter ratio /φ D of 0.54 and 90° inlet angles, which concurs with the operated machine. Keyword: Finite volume method, two phase, flow mixing, injection moulding 1. Introduction Reaction injection moulding is widely used to produce foam for automotive components. The chemicals are mixed in the mixing head set, which comprises of the head body and two moving pistons. As manufacturers in Thailand usually buy machines, chemicals and procedures directly from suppliers with very few knowledge transfer, the production process is very rigid; it is neither expedient to change suppliers nor to adapt the existing machinery to other tasks, etc.

A steering wheel manufacturer experienced such difficulties with shorten life cycle of the mixing head set and, thus, initiated a project to study the optimised design of the head of a reaction injection moulding machine. The study was divided into 4 parts: the chemical properties and reaction, flows in the head, effects of the flows and other loads upon the head material as well as the fracture of components [1].

It is the chemical fluid mixing in the head that is presented in this paper. First, the descriptions of the currently in-use mixing head and its operating conditions are outlined. Then, the problem is simulated and an acceptable model established using the CFX, followed by the model utilisation in finding the optimised design of head configurations. 2. Descriptions of the Mixing Head and its Operation By releasing the 1st piston, the two chemicals, Polyol and Isocyanate, are injected into the head of the reaction injection moulding at the temperature of 20° and the pressure of 180 20± and 170 20± bar, respectively. After 3 to 4 seconds in the mixing head, the mixed fluids undergoing reaction are pushed into the mould by the 2nd piston before setting around the steering wheel frame (Fig. 1). 3. Finite Volume Modelling by CFX As Isocyanate is volatile and highly toxic [2], it is expensive and dangerous to study the mixing in the head chamber experimentally. Hence, the finite volume method is used to simulate the process instead.

K. Maneeratana, S. Putivisutisak, S. Sucharitpwatskul, T. Intarakumtornchai and S. Chaiyapinunt

71-28th Asian Symposium on Visualization, Chiangmai,Thailand, 2005.

a) Mixing head and pistons b) Lower section of the mixing head

Fig. 1 Mixing head of the reaction injection moulding machine From experiments [1], the maximum amount of reaction occurs at around 220 seconds after the

impact mixing of the two chemicals. Therefore, it is assumed that there is no chemical reaction occurs in the head since the mixing time period is very short compared to the total reaction time duration. Additional assumptions are the inclusion of body force from gravity and the laminar flow.

The commercial software CFX [3] is used to model the problem. The mathematical model composes of the conservation of mass, conservation of momentum, transport equation of components, constraint equation for mass fraction and conservation of energy.

The fully open flow passage and mixing chamber before the 2nd piston pushes the mixed chemical into the mould is used as the flow domain (Fig. 2a). Even though the injecting pressures of the chemicals are specified in the operating conditions, it is more convenient to use the equivalent mass flow rate at the inlet ports while the outlet area is at the atmospheric pressure. All other boundaries are considered to be simple walls (Fig. 2b). Most of the domain is divided into tetrahedral elements except the triangular prism is used near the wall for better distributions. A typical model (Fig. 2c) contains in excess of 60,000 nodes and 240,000 elements.

a) Computational domain b) Boundary conditions c) Computational grid Fig. 2 Problem descriptions of the fluid mixing in the head

From literature surveys and experiments [1],[4], the density, dynamic viscosity, specific heat and

thermal conductivity of the employed Polyol and Isocyanate are found as follows: 31031 kg/mρ =P , 31220 kg/mρ =I , 1.060 Pa sν = ⋅P , 0.155 Pa sν = ⋅I , 4000 J/kg K= ⋅Pc , 4000 J/kg K= ⋅Ic ,

0.6 W/m K= ⋅Pk and 0.6 W/m K= ⋅Ik , respectively.

A Three-Dimensional Simulation of Flow Mixing in a Mixing Head of an Injection Moulding Machine

71-38th Asian Symposium on Visualization, Chiangmai, Thailand, 2005.

Of the computational simulations, the fluid velocities, mass fraction, density and temperatures are recorded and analysed. As the function of the head is to produce evenly mixed fluids at the outlet, the standard deviation, SD, of the stated quantities should be low. For better physical representations, the mean x and SD at the outlet are calculated from the nodal values that are normalised by the exposed surface area of each element iA as:

2( ) and SD

−= =∑ ∑∑ ∑

i i i i

i i

x A x x Ax

A A. (1)

4. Condition Approximations for the Model In this section, the simulation of the flows in the investigated head under true operation conditions is conducted. Due to highly complicated conditions, further approximations with acceptably accurate results are sorted to reduce the computational efforts in the configuration optimisation later.

In all, 5 test cases are considered: 1 Steady state model of the flow in the head under true operation conditions, excluding energy

equations. 2 Steady state model of the flow in the head under true operation conditions. 3 Transient model of the flow in the head under true operation conditions. The time step is

prescribed as 0.5 s and the profile of the mass flow rates of the chemical is assumed to be sinusoidal.

4 As in 1, but with pressure boundary condition for inlet ports. 5 As in 1, but with specification of the 1st piston velocity.

The results from the modeling of test case 1 are shown in Fig. 3. When the fluids flow into the mixing chamber, the Polyol, with higher momentum, pushes some Isocyanate to the top end of the chamber (Fig. 3a). Of all results, the most important is the density distribution at the outlet (Fig. 3B) which best measures the quality of the mixed fluids.

The first set of test cases investigates the modeling assumptions. For the test case 2 with conservation of thermal energy, even though the temperature profiles at the outlet has swirling characteristics, the density distributions are not much different from test case 1 (Fig. 4). due to the low level reactions during the short period in the mixing head. Besides, without accurate reaction data from the highly dangerous experiments, it is impossible to accurately model the temperature profiles. When the transient model is considered in test case 3, the solutions show variations as expected but at 5 second, the temperature and density profiles are similar to test case 1 (Fig. 5). Hence, energy equation and transient modelling are neglected from the final model to reduced computational efforts.

When the boundary condition is considered in test case 4, the use of pressure condition causes problems for steady state modelling as the higher inlet pressure of Polyol forcefully reduce the mass flow rate of the Isocyanate, rendering the steady state simulation less accurate and not similar to the transient results in test case 3. For demonstration of more advanced simulation in test case 5, the 1st piston can move into the flow passage and push the mixed fluids into the mixing chamber.

By combining the results from these test cases, the final model chosen is the model of steady state simulation of the fluid flow without using the energy equation while using the mass flow rate to specify boundary condition at the inlet ports. 5. Configuration Optimisation After the acceptable model is obtained, it is used to study the mixing effects of the head parameters: the inlet port angles θ and diameters φ. First, the inlet port angle θ is varied while the diameters of the flow passage and the ports are kept constant. Six angles are modeled with 15° increment (Fig. 6). At the minimum angle of 45°, the chemicals are injected into the chamber at right angle to each other and slants towards the mixing chamber. On the other end at 120°, most fluids flow towards the end of the 1st piston before reverses back into the mixing chamber. When the density profiles and corresponding SD are compared in Fig. 6,

K. Maneeratana, S. Putivisutisak, S. Sucharitpwatskul, T. Intarakumtornchai and S. Chaiyapinunt

71-48th Asian Symposium on Visualization, Chiangmai,Thailand, 2005.

it is found that the most even mixing occurs at the port angle of 90° with the average density of 31,095 kg/m and SD of 1.79, compared to the SD of 6.86 at 45θ = ° and 5.15 at 120θ = ° .

a) Flow direction of the mixed fluids b) Density of the mixed fluids

c) Velocity vector of the fluids b) Velocity distribution in the mixing head

e) Mass fraction of Isocyanate f) Mass fraction of Polyol

Fig. 3 Results from test case 1: the steady state modelling without energy equation Then, the inlet port angle is kept constant at 90θ = ° . The diameter D of the flow passage, which is equal to the diameter of the 1st piston, remains the same while the diameter φ of the inlet port is increased from the original /φ D ratio of 0.543 to 0.829 (Fig. 7). As in the angle study, the mixing with lowest SD occurs at the original /φ D ratio of 0.543 in comparison with the SD of 10.68 at

/ 0.829φ =D .

A Three-Dimensional Simulation of Flow Mixing in a Mixing Head of an Injection Moulding Machine

71-58th Asian Symposium on Visualization, Chiangmai, Thailand, 2005.

a) Density of the mixed fluids b) Temperature distribution of the mixed fluids Fig. 4 Results from test case 2: the steady state modelling with energy equation

Fig. 5 Results from test case 3: the mass fraction of Polyol

Fig. 6 Standard deviation of flow mixing at different inlet port angles

K. Maneeratana, S. Putivisutisak, S. Sucharitpwatskul, T. Intarakumtornchai and S. Chaiyapinunt

71-68th Asian Symposium on Visualization, Chiangmai,Thailand, 2005.

Fig. 7 Standard deviation of flow mixing at different inlet port diameters

6. Conclusions This works aim to find the reasons behind design parameters of the head of the reaction injection moulding machine, namely the inlet diameters and angles. The low level reaction and its associated temperature rise in the mixing head do not significantly effects the flow characteristics. Moreover, results from the steady-state and transient simulations do not differ much with the use of mass flow rates for inlet boundary condition. Hence, the use of steady-state, two-phase flow mixing in the head is acceptable for the configuration analyses.

The optimised values of inlet port diameters and angles concur with those of the operating head under investigation. With this study, the database of the particular mixing head and procedures of analyses are established. If the operating conditions or chemicals are changed, the most suitable operating conditions can be found and, if necessary, the head configuration may be re-designed to accommodate these changes accordingly. Acknowledgements This paper was supported by the State and Industrial Cooperation on Commercial Research Project, Ministry of University Affairs, Federation of Thai Industries and the Summit Steering Wheel, Co. Ltd. Special thanks are due to Dr. S. Covavisaruch, Prof. P. Dechaumphai, Lect. N. Wansophark, Asst. Prof. K. Boonchukosol, Mr. V Rerkchavee and Mr. S. Ratanaporn. References [1] Chaiyapinunt, S., Covavisaruch, S., Dechaumphai, P., Wansophark, N., Putivisutisak, S., Maneeratana, K.

and Boonchukosol, K. “Development and Analysis of a Mixing Head with Displacement Piston Model for a Reaction Injection Mounding Machine for an Automotive Steering Wheel Industry”, Report submitted to Ministry of University Affairs, Royal Thai Government, (2004).

[2] ICI Polyurethanes, “Product Safety Data Sheets (MDI-based compositions: Hazards and Safe-Handling Procedures”, Belgium, (1997).

[3] AEA Technology Engineering Software Limited, “CFX User Documentation”, Ontario, Canada, (1999). [4] Klempner, D. and Frisch, K.C., “Handbook of Polymeric Foams and Foam Technology”, Hanser, (1991).