Gravity Effects during Mold Filling: Fluid Front Dynamics - American

Chapter 16

Gravity Effects during Mold Filling: Fluid Front Dynamics

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: August 14, 2001 | doi: 10.1021/bk-2001-0793.ch016

M.

C.

Altan andK.A.Olivero

School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman,OK73019

Gravity effects on free surface flows during mold filling are experimentally studied and found to be significant in some flow regimes. A n experimental disk-shaped mold cavity is constructed which allows for flow observation and measurement of spreading, the tendency for the bottom of the flow front to advance ahead of the top due to gravity. A method is developed in order to perform experiments to investigate the effect of pertinent non-dimensional parameters. Results are presented at three radial cavity locations isolating each of these non-dimensional parameters. Significant dependence of spreading on Bond number is observed.

Molding operations involving low viscosity polymers such as reaction injection molding (RIM) are commonly used to manufacture net-shape components quickly and inexpensively. These molding operations typically involve the displacement of air in a cavity by a polymeric resin, which is either cooled or cured to form the final solid part. The interface between the polymer and the air, referred to as the free surface, progresses through the cavity during filling and may be influenced by a variety of factors including viscous forces, surface forces, and gravity. In most reaction injection molding, curing starts during the filling and is usually completed within a minute. Therefore, the dynamics of the free surface could affect heat transfer as well as curing rate in

© 2001 American Chemical Society

Downey and Pojman; Polymer Research in Microgravity ACS Symposium Series; American Chemical Society: Washington, DC, 2001.

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228 the mold, and thus ultimately the mechanical properties of the molded part. Non-uniform curing can result in a variety of defects, including nonhomogenous mechanical properties, warping and void formation. A number of experimental and theoretical studies dealing with free surfaces are published in literature. The most common approach in determining free surface shapes with respect to molding processes is to assume the Capillary number is high, and thus viscous forces dominate surface forces. For example, in Behrens et al. (7), the fluid front shape is completely dictated by the flow kinematics and gravity effects are not considered. Other studies address the issue of the viscous stress singularity and so-called slip length used in analysis of moving contact lines (2,5). However, these do not address the free surface shape over the entirety of the free surface. Closely related are investigations to establish dynamic contact angles (4-6). In these studies, the focus is also on the flow dynamics near the contact point. Blake investigated gravity effects on free surface shape in mold filling (7,8); however this study involves a vertically aligned cavity in which gravity does not cause an asymmetric fluid front. Several studies have been performed which include gravity effects on the spreading of a liquid drop on a solid surface including gravity effects on the shape and motion of the free surface (e.g., Chen, et al. (9) and Hocking (10)). These studies tend to involve slow-moving, quasi-static free surfaces, and may not be directly applicable to forced flow in a mold cavity. A trend in molding processes is towards the use of lower viscosity resins. These resins allow for higher fill rates and lower injection pressures, thus leading to higher production rates and lower equipment cost. However, the use of low-viscosity polymers increases the complexity of flow dynamics. For example, Reynolds numbers governing the flow may become too large for Stokes flow assumptions to be valid. In addition, gravity effects on the free surface, which are usually neglected, can have pronounced effects on these flows, particularly on filling patterns and residence times. For planar mold cavities the flow is typically assumed to be symmetric about the midplane. However, i f gravity effects become important, the bottom of the flow front can advance well ahead of the top. In such cases, i f the gravity effects are neglected in numerical mold filling simulations, the shape and location of the weld lines (i.e., the lines at which the fluid front meet during filling) may be inaccurately predicted. Example fluid front shapes with and without sagging due to gravity are depicted in figure 1. The aim of the current study is to experimentally quantify the effect of gravity on the free surface shape during the filling of a mold cavity. It is of particular interest to isolate the important non-dimensional parameters governing the fluid front dynamics. Towards this end, mold filling experiments are performed to characterize the spreading of the fluid front during filling of a disk-shaped cavity. The independent effects of each of the Reynolds, Bond, and Capillary numbers on spreading are observed.



Figure 1: Representative fluid front shapes. Left: symmetric fluid front in the absence of gravity effects. Right: spreading of the bottom offluid front due to gravity.


SO

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Experimental Setup A n experimental molding setup is constructed to observe and measure the features induced by gravity during the filling of a mold cavity. The setup consists of a disk-shaped mold cavity containing various embedded sensors, a peristaltic pump to inject the fluid, and a P C based data acquisition system for monitoring the flow. The mold cavity is formed by placing aluminum spacer plates between one-inch-thick Plexiglas sheets. A circular section with a 9-inch radius is cut out from the center of each spacer plate. Various gap-widths ranging from 0.0625 to 1.0 inch are attainable by using different combinations of these plates. Shim steel spacers having thicknesses 0.004, 0.008, and 0.012 inch are inserted between the spacer plates and Plexiglas to achieve more precise gap-width control. Inlet gate diameters of 0.125, 0.250, and 0.375 in. can be selected by inserting one of three available inlet gates fabricated from Plexiglas. In addition, the mold can be turned over to allow the inlet to be placed on either the top or bottom mold wall. Pressure transducers and fluid front sensors for flow measurements are mounted in both the top and bottom Plexiglas sheets along radial lines as illustrated in figure 2. The advancing fluid front is sensitive to the surface quality of the mold walls, thus, the Plexiglas mold walls are sanded at the sensor locations by a series of 400, 600, 1000, and 4000 grit sandpaper, followed by polishing with a buffing wheel and polishing compound. This greatly reduces perturbations to the fluid front shape as the front passes the sensor locations. Glycerol diluted with water is selected as the filling fluid. Fluid properties can be varied easily by changing the volume fraction of water in the mixture. The mixture behaves as a Newtonian fluid and viscosities ranging from 1 to 1200 cP can be obtained. Most experiments in this study utilize viscosities between 50 and 400 cP, which are similar to the viscosities observed during reaction injection molding process (11). It should be noted that non-Newtonian effects are shown to be small for some polymers used in reaction injection molding (77). The fluid is injected at constant flow rate by a Masterflex IP73 microprocessor controlled peristaltic pump. Two pump heads can be configured in a parallel arrangement to yield flow rates for water ranging from 4x10~ m /s to 2.7X10" m /s at a maximum pressure of 40 psi. For higher viscosity fluids, the flow rates are somewhat reduced. The pump and controller are labeled on the photograph of the experimental setup shown in figure 3. A n inline pulse dampener, not visible in figure 3, minimizes flow fluctuations which are common to peristaltic pumps. Figure 4 is a close up diagram of one of the three fluid front sensors mounted in the mold walls at 7?=2, 4, and 6 in. Each sensor consists of one power terminal and three sensing terminals as shown in figure 4. A sensing 6

4

3


3


Figure 2: Experimental mold cavity diagram: cross section and dimensions.



Figure 3: Setup for mold filling experiments. The mold is shown with three pairs offluid front sensors and two pressure transducers placed on the top wall.



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Figure 4: Schematic cross section of probe wiring depicting the advancement of fluid front through a probe location.



234 circuit connected to a data acquisition system measures contact times based on the corresponding resistance drop when the fluid contacts each of the three sensing terminals. The circuit operates by monitoring the voltage across a reference resistor in series with the sensing terminal. A change in voltage indicates a resistance change across one of the sensing terminals due to fluid contact. A n op amp in the circuit amplifies the voltage reading and conditions the signal, significantly lowering its output impedance (the data acquisition system has a maximum input impedance of 1000 ohms.) A total of nine such circuits are attached to each of the sensing terminals. The three contact times are clearly identifiable in the raw voltage data obtained from each of the three fluid front probes. The spreading at each radial location is calculated from the times at which the fluid front contacts terminals 1, 2 and 3 of a given fluid front probe (i.e., t t , and £?), and the two radial locations of these terminals, R and R (all labeled in figure 4) It is assumed that each point on the fluid front travels at uniform velocity at a given radius. The equation for spreading is derived in ref. (12) based on the contact times and terminal radii as, h

2

a

b

Isolating Non-Dimensional Parameters The experimental setup is designed to simulate mold filling operations over a wide range of flow parameters. Dependence of spreading on these physical filling parameters, such as flow rate and gap-width, can be easily ascertained by varying the individual parameters independently. However, it is useful to obtain the dependence of flow dynamics on the pertinent non-dimensional parameters. This is difficult to achieve by arbitrarily selected fill conditions, as changing a single parameter, such as the volume flow rate, can result in different values for all the non-dimensional parameters. There are three non-dimensional parameters expected to affect spreading and flow characteristics during an isothermal, Newtonian filling: the Reynolds, Bond, and Capillary numbers. A fourth non-dimensional value, the contact angle, is a characteristic of the experimental apparatus (i.e., the contact angle depends on the fluid injected and the mold surface.) Thus, a method needs to be developed to determine the experimental parameters; i.e., the gap-width, L, the volume flow rate, Q, and the properties of the filling fluid, to achieve a prescribed set of non-dimensional parameters. To obtain this solution, the Reynolds, Bond, and Capillary numbers are defined as


235


R e =

EiL.,

Bo

=

^ L . C a ^ ,

(2)

where g is the acceleration due to gravity, and ρ, σ, and μ are the fluid's density, surface tension, and viscosity, respectively. It is clear from eqs 2 that as gravity goes to zero, Bond number will be zero and the other non-dimensional parameters, Re and Ca, remain unaffected. Thus, experiments in microgravity could be utilized to further investigate the effects of Reynolds and Capillary numbers in the absence of gravity (i.e., Bo=0). Non-dimensional parameters are defined at the location of the first fluid front probe (#=2.0 in.), and thus the velocity, u, represents the average velocity at R=2.0 in. The velocity, u, scales linearly with die volume flow rate, Q, and represents a characteristic velocity scale. These expressions are rearranged and combined to eliminate two of the physical experimental parameters, u and L as, 1/4

r

0=

pBc>

S )

ψ\

v

(*Γ-Κ·

Rej

(3)

In eq 3, gravity is a known constant and Re, Ca, and Bo are constant parameters, leaving three unknowns. It is observed that all unknown parameters in eq 3 (i.e., μ, ρ, and σ) are properties of the filling fluid. Glycerol diluted with distilled water is selected as the filling fluid, and the fluid properties are obtained experimentally based on the volume fraction of glycerol in the mixture, /as,

P = P„Q-f)

+ P f,

(4)

e

σ = 72.3-8.3/, 3

2

μ = 134.67/' - 60.238/ + 8.4509/ +1 0

Gravity Effects during Mold Filling: Fluid Front Dynamics - American

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