1.

INTRODUCTION

As a typical polymer melt, solid propellant slurry exhibits strange rheological properties with both Hook elastomer and Newtonian adhesive fluid characteristics when subjected to external force or external moment. They can both flow and deform, and their mechanical response is very complex. Extrudate swelling is another special phenomenon caused by the normal stress difference in viscoelastic fluid flow (Figure 1). When the polymer or solution flows out of a larger container through the capillary, the diameter can be observed, sometimes 3-4 times larger. This is because the elastomer has a memory effect. When the fluid is forced out, it wants to restore its original state, thus swelling, the longer the extension ratio, the longer the time, the worse the memory, the smaller the expansion ratio, when the material is in a high elastic state, the extrusion expansion is more obvious^1-3.

Figure 1.

Extrusion swelling effect.

There is a recoverable elastic deformation of solid propellant slurry during the flow through the aperture of the flower plate, and the diameter of the extrude after the flow through the aperture is larger than the diameter of the aperture, which is called the extrusion swelling effect, and its size is expressed by the extrusion swelling ratio (B=D_max/D).

In order to accurately describe the flow behavior of the propellant slurry, adopting a viscoelastic constitutive model is imperative. In this paper, the FENE-P model is used for simulation calculation, which provides a new idea for solving the free-surface flow problem of viscoelastic fluid. It is of great significance to guide the project to establish the actual calculation model and to determine the appropriate process parameters.

2.

CALCULATION MODEL

Figure 2 is the calculation model of extrusion expansion. Considering the symmetry of the flow, the simulation study of the selected model implements the finite element method, which effectively reduces the number of grids, improves the grid quality, and saves the calculation time in the computer simulation process.

Figure 2.

Calculation of the model

3.

BOUNDARY CONDITIONS

The flow boundary conditions of the extrusion expansion model are set as follows:

Boundary 1(EF): Inlet. Given the volume flow rate of the fluid at the inlet, the assumed flow is Q=1 m³/s.

Boundary 2(DF): Rigid wall. In the case of the extrusion rate is low, the fluid will adhere to the flow channel wall, which the zero normal rate and the zero tangential rate are both 0;

Boundary 3(BD): Free surface. The normal velocity and stress of the fluid are both 0;

The free surface is known as the moving boundary problem, refers to the solution domain containing an unknown boundary.

Boundary 4(AB): Outlet. The normal force and tangential force of the outlet are 0, indicating that the shear stress and normal stress between the fluid and the mouth die all disappear;

Boundary 5(AE): Plane of symmetry.

In the process of simulation, when the elastic fluid flow outlet will no longer be constrained from the wall of the flow channel. The fluid will swell and deform at the outlet, which causes good grid unit distortion deformation. Therefore, in the boundary setting, the grid reset technology should be applied to the finite element grid area of the extrusion part of the drug slurry^4-6.

4.

CONSTITUTIVE MODEL AND MODEL PARAMETERS

The FENE-P model is based on molecular theory and appears as a series of dumbbell^7-9 connected by springs (Figure 3).

Figure 3.

Dumbell definition of the FENE-P model.

For the differential viscoelastic flow, the additional stress tensor T is the sum of the viscoelastic partial stress T₁ and the pure viscous stress T₂. The FENE-P model is calculated from a state tensor based on the algebraic equation, as follows^10-13:

where, A is calculated by the lower differential equation:

where, L is the ratio of the maximum length of the spring to the length at rest:

r_eis an equilibrium length corresponding to the rigid motion, r₀is the maximum allowable dumbbell length, λ is relaxation time, η₁is the elastic viscosity coefficient, η₂is pure viscosity coefficient, r is viscosity ratio, D is the rate of the deformation tensor, the tr(A) is the trace of the A. For the model parameters are set up as follows:

5.

CALCULATION RESULTS AND ANALYSIS

5.1

Speed cloud map

The velocity field can directly reflect the flow state of the slurry. Figure 4 shows the velocity cloud image of the fluid in the flow process.

Figure 4.

Velocity at different relaxation time. (a): Velocity cloud at relaxation time 2; (b): Velocity cloud at relaxation time 10; (c): Velocity cloud at relaxation time 100; (d): The velocity distribution curves along the central axis at different relaxation time.

It can be seen from the Figure 4 that the velocity contour of the slurry fluid in the flow channel is relatively dense, especially at the outlet of the flow channel, which indicates that the slurry fluid is in a convergence state before the flow outlet mode, while at the free surface, the contour becomes divergent, the fluid velocity gradient is small, and becomes uniform at the end of the fluid. As the relaxation time increases, the greater the elasticity of the fluid, the closer the maximum velocity of the fluid is to the center of the flow outlet, the more obvious the fluid velocity changes, and the fluctuation is larger.

5.2

Pressure cloud map

Figure 5 shows the pressure clouds of the fluid during the flow.

Figure 5.

Pressure at different relaxation time. (a): Relaxation time 2; (b): Relaxation time 10; (c): Relaxation time 100; (d): Pressure values along the central axis of different relaxation time.

As can be seen from the Figure 5, the pressure of the slurry fluid in the flow channel decreases uniformly along the flow direction of the fluid. After squeezing the outlet mold, the pressure is minimum and approximately 0, owing to the slurry will no longer be subject to the binding force from the wall. The maximum pressure value of the slurry fluid in the flow channel decreases with the relaxation time.

5.3

Calculation and analysis of extrusion swelling ratio

According to the material parameters set in the simulation, the extrusion swelling model is simulated and the smooth scatter plot of the freesurface segment under different relaxation time (Figure 6). It is obtained that the maximum value at different relaxation times is 1.14,1.25 and 1.57 respectively, and then the extrusion swelling ratio at different relaxation times is calculated by the B=D_max/D equation.

Figure 6.

Extrusion swelling ratio under different relaxation time.

The extrusion expansion ratio is as follows:

It can be seen from the above calculation results that the extrusion swelling ratio increases with the relaxation time.

6.

CONCLUSION