Simulation of the plasticizing behavior of composite modified doublebase (CMDB) propellant in grooved calendar based on adaptive grid technology

Su-wei Wng , Xiu-duo Song , Zong-ki Wu , Lei Xio , Gung-pu Zhng ,Yu-ing Hu , G-zi Ho ,*, Wei Jing ,**, Feng-qi Zho

a National Special Superfine Powder Engineering Research Center of China, School of Chemistry and Chemical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

b Xi'an Modern Chemistry Research Institute, Xi'an, 710065, China

Keywords:Composite modified double base propellant Calendering process Fluid simulation Vortex flow

ABSTRACT The frequent occurrence of safety accidents during the calendering process is caused by the flammable and explosive properties of composite modified double-base(CMDB)propellant.Optimization of process parameters with the aid of fluid simulation technology could effectively ensure the safety of the calendering process. To improve the accuracy of the simulation results, material parameters and model structure were corrected based on actual conditions, and adaptive grid technology was applied in the local mesh refinement. In addition, the rheological behavior, motion trajectories and heat transfer mechanisms of CMDB propellant slurry were studied with different gaps, rotational rates and temperatures of two rollers.The results indicated that the refined mesh could significantly improve the contour clarity of boundaries and simulate the characteristics of CMDB propellant slurry reflux movement caused by the convergent flow near the outlet. Compared with the gap, the increased rotational rate of roller could promote the reflux movement and intensify the shear flow of slurry inside the flow region by viscous shear dragging. Meanwhile, under the synergistic effect of contact heat transfer as well as convective heat exchange, heat accumulated near the outlet and diffused along the reflux movement,which led to the countercurrent heat dissipation behavior of CMDB propellant slurry. The plasticizing mechanism of slurry and the safety of calendering under different conditions were explored, which provided theoretical guidance and reference data for the optimization of calendering process conditions.Based on the simulation results, the safety of the CMDB propellant calendering process could be significantly improved with a few tests conducted during a short research and development cycle.

1. Introduction

Solid propellants are one of the most important power sources of modern weapon systems and aerospace technology and have received much research attention. They greatly affect the strike range of missiles as well as the propulsion of rockets.Depending on the feedstock components, solid propellants can be classified into double-base propellants, modified double-base propellants and composite modified double-base (CMDB) propellants. CMDB propellant is nitrocellulose(NG)plasticized with nitroglycerin(NC)as binder,which is spiked with ammonium nitramine explosives such as black hexogen (RDX), octogen (HMX), metallic fuel and other additives. The specific preparation of the model by the screw extrusion process is shown in Fig.1.

Compared with conventional double-base propellants as well as composite double-base propellants, modified double-base propellants have many advantages, such as high energy density, low characteristic signals, free filling and stable and continuous production of propellant products [1]. Thus, modified double-base propellants have become a priority for many tactical missiles versus solid rocket engines, which help meet the needs for the development of modern weapon technology characterized by“efficient damage and accurate attack” [2-5].

Fig.1. Schematic diagram of the preparation process of CMDB propellant [6,7].

As shown in Fig. 1, the screw extrusion process of modified double-base propellants can be divided into main six steps: preparation of NC/NG,water displacement,calendering and plasticizing,conveying and drying, screw extrusion and cutting charge [6,7].Relative to the other steps, the calendering process requires the application of large extrusion shear action to the propellant slurry in a high temperature environment with the aid of two heterorotating roller cylinders, thus achieving the dissolution (plasticization)of the propellant slurry[8],expulsion of adsorbed water[9]and homogeneous mixing of the components [10]. The plasticization, dehydration and mixing effect of the propellant slurry in the calendering process directly affect the final performance and quality consistency of propellant products [11]. Previous studies have shown that increasing the roller cylinder temperature is beneficial for enhancing molecular thermal mobility and improving the plasticity of propellant slurry. Reducing the roller cylinder gap can increase the propellant drug substance pressure and accelerate the diffusion speed of solvent molecules,and decreasing the roller cylinder rotation rate while increasing the roller cylinder diameter can prolong the thermal time of the propellant slurry and accelerate the progress of water evaporation and plasticization[8,12-14].

Previous studies have used the smooth roll calendering technique to achieve the continuity of the pressing process by opening grooves in the barrel wall as well as enlarge the shearing and extrusion effects of the roller cylinder on the propellant drug substance with the aid of grooves with different section shapes,thus effectively improving the plasticization effect of the propellant slurry and production efficiency [15,16]. However, the opening of grooves can not only improve the plasticizing effect of propellant but can also aggravate the friction and extrusion between propellant and metal wall and between propellant and propellant,resulting in the conversion of part of the mechanical energy to internal energy and the excessive accumulation of heat in propellant[17].This leads to increases in the frequency of safety accidents,such as burning explosions and sympathetic explosions of propellant, during calendering[18,19].

These accidents are caused by several factors. First, local hot spots can be easily formed during the mixing of hard impurities because of the crushing and extrusion during the plasticizing process, which induces increases in temperature and propellant degradation [16]. Second, molecules of water in propellant that have not been removed can easily foam under high temperature environments and cause the adiabatic compression of bubbles,thus accelerating the formation of hot spots [9]. Third, unreasonable roller structure parameters and groove cross-section size lead to propellant backflow and stagnation in the process of processing,thus prolonging the calendering process of propellant[12].Fourth,inappropriate process conditions, such as excessive wall temperature, roller speed and low twin-roll gap, strengthen the shear and extrusion effect of the roller on propellant slurry[15],which could result in the increased potential safety hazards of the propellant calendering process.

To solve these problems (both in China and abroad), hard impurities, such as metal and glass mixed in propellant before the calendering process,first need to be removed via manual screening,magnetic separation and impurity removal [20], which effectively prevents the local hot spot caused by the crushing of hard particles.Second, the air bubbles in propellant can be cut during the calendering process via a scraper mounted above the work roll to accelerate the escape of gas from the bubbles, thus significantly reducing the safety hazards caused by the adiabatic compression of gas [20]. Next, rollers with U-shaped or V-shaped cross-section grooves on the surface can increase the feed volume, improve the plasticizing effect and achieve continuous conveying, calendering and shear plasticizing of propellant under the synergy of automatic feeding and filtering cutting systems [8,15].

In addition, to weaken the accident hazards and the economic and personnel losses that they cause, the U.S. Army Defense Logistics Agency, Xi'an Modern Chemistry Research Institute and other domestic and foreign units have studied the theory and technology of fire extinguishing under the combustion environment of propellants and have successively developed fire extinguishing devices, such as the fast reaction ultra-high-speed spray fire extinguishing system [16] and the ultra-high-speed rain sprinkler system [21]. Li et al. [22] also adopted the linkage technology of far-infrared temperature measurement and spray cooling to monitor the propellant temperature in real time and spray cooling when it approached the critical temperature on fire.However, these safety measures, which were mainly used for remediation after accidents, could easily create a stagnation in production that not only extends the supply cycle of the products but also affects the stabilization of the quality of the propellant.

To effectively prevent and circumvent safety accidents such as implosions, the safety characteristics and plasticization quality of propellant under different calendering process conditions have been examined with the aim of safely preparing high-quality propellant products through parameter regulation. For example, Yue et al. [23] found that increasing roller cylinder temperature and decreasing the twin-roll gap both contributed to accelerating the diffusion rate of solvent molecules inside nitrocellulose and improving the plasticity of propellant slurry; decreasing the roller rotation rate could prolong the propellant thermal time and contribute to propellant plasticization and water evaporation.However, because of the properties of propellant slurry (namely flammability and explosivity), detection and observation of the pressure, temperature and shear stress of propellant slurry during the calendering process are challenging, which increases the difficulty of ascertaining the explosion mechanism, plasticization mechanism and safety thresholds as well as empirically setting current process parameters.

Computational fluid mechanics (CFD) has been used in China and abroad to aid the exploration of rheological behavior,the stress distribution and the mixing effects of propellant slurry during processing [24-26]. The goal of this approach is to provide reference data for the setting and optimization of process parameters and, in turn, to minimize injuries to personnel resulting from the high incidence of accidents and associated economic losses. S Luther et al. [27] found that viscous fluid would form a distinct vortex motion at the nip and continuously increase the flow rate along the exit direction during the calendering process. Furthermore, raising the nip leads to lower pressure, which can facilitate the mixture of gas bubbles in the product. N D Polychronopoulos et al.[28]used the fluid simulation software OpenFOAM to analyze the three-dimensional flow field characteristics of polymer fluids and found that the melt exhibits helical lateral flow behavior during the calendering process because of the extrusion effect of the roller cylinder.This approach thus determines the actual flow path of the calendering material in a non-intuitive way. Peng et al. [29] simulated the calendering and plasticizing process of typical energetic materials by Polyflow and found that the distribution and dispersive mixing effects of the drug substance under the twin-roll inter propellant were mainly affected by the dual action of shearing and stretching. The proximity of the spacing to the roller cylinder surface led to an increased shearing effect. Ying et al. [30] used simulations to show that the propellant slurry located at the gap of the twin-roll is subject to the highest shear rate, shear stress and viscous heat and is also most prone to ignition and explosion accidents.

Few simulation studies have been conducted on the calendering process of propellant slurry in China and abroad. The evolution rules of propellant slurry conveying, plasticizing and heat transfer during calendering have not yet been fully investigated.In addition,the rheological equation and model size selected by previous researchers in the simulation process still show some deviations from actual propellant slurry characteristics and equipment structure.As a result, accurately describing the calendering and plasticizing process of propellant slurry and providing effective guidance for adjusting process parameters remain difficult.

In order to improve the safety of actual production more effectively, the rheological equation of propellant slurry and simulation model size are modified in this paper according to actual calendering conditions of propellant slurry and device structure parameters, which is a more effective approach for aiding production.Besides,the adaptive grid technology is also applied in the local refinement of grids at grooves and roll gaps to improve the simulation accuracy, which provide more detailed parameter changes.Meanwhile,based on the previous studies,the rheological behavior, motion track and heat transfer mechanism of CMDB propellant slurry in groove calendering are further explored to reveal the plasticizing mechanism of propellant during calendering process.Generally,this work provides new theoretical insights into the determination of calendering process parameters and the achievement of highly efficient plasticization and safe production.

2. Numerical simulation

Fluid simulation of the CMDB propellant slurry calendering process can be classified into pre-procession, solution and postprocession. The pre-procession can be further subdivided into geometric modeling, grid division, material parameters, boundary conditions and solution settings.Compared with solution and postprocession, the model size constructed in the pre-procession and the input material parameters can affect the matching between simulation results and actual conditions, and the choices of flow boundary conditions and solution methods determine the solution accuracy of the simulated parameters. Therefore, the reliability of the simulation results was improved in this study by modifying the rheological model, refining the grid size and altering the solution method.

2.1. Rheological equation and material parameters

Before simulation, the apparent viscosity of CMDB propellant slurry should first be measured at different shear rates,followed by fitting with different constitutive models. After testing, the rheological model with the highest goodness of fit was achieved and used for subsequent material parameter setting[31].However,the viscosity of propellant slurry in previous studies has generally been tested at a low shear rate (<1 s-1), as it is difficult to accurately describe the rheological behavior of propellant slurry under high shear (25-30 s-1) during the calendering process, which caused the simulation results to deviate from the actual state [29,30].Therefore, the apparent viscosity of CMDB propellant slurry was characterized at a high shear rate in the range of 10-37 s-1and then was fitted by the least-squares method with a goodness of fit of 99.98% (Fig. 2). According to the rheological data and the fitted constitutive model, the apparent viscosity of the propellant slurry gradually decreased with the shear rate and showed clear pseudoplastic fluid characteristics [19,25]. Moreover, other material parameters listed in previous studies,such as density,specific heat capacity and thermal conductivity,were also retested and modified in pre-procession (Table 1).

2.2. Model construction and grid division

In addition to the rheological equation and other material parameters, the physical model of the flow region between the two grooved rollers needs to be constructed and then meshed by the finite element mesh generator before the process of solution. In previous studies, the three-dimensional (3D) model of the calendering machine was constructed and meshed for the subsequent simulation analysis, and the number of 3D grids was reduced to improve the simulation efficiency at the expense of simplicity of the physical model and increased grid size [27,29,30]. Although more detailed features of the flow domain can be obtained for the 3D model, the complicated surface structure of the grooved roller and the highly converged outlet size between the rollers make it difficult to achieve clear surface profiles during the simulation even with multiple grid refinement.As a result,the simulation of the 3D model not only failed to improve the accuracy of the solution but also created a large amount of mesh and reduced the operational efficiency of the server.

Fig. 2. Apparent viscosity and rheological equation of CMDB propellant slurry.

Table 1 Material parameters of CMDB propellant slurry.

In addition,the effect of process conditions on the flow state and characteristic parameters of propellant slurry between the two rollers has also been previously explored.Previous work has shown that the flow rate, temperature and pressure of propellant slurry remain nearly unchanged along the axial direction of the roller when the length of the roller is much higher than the diameter.To study the rheological behavior of propellant slurry, a twodimensional (2D) model was used for simulation, and the quadrilateral meshes near the boundaries of the flow region were refined by adaptive grid technology.Compared with the 3D grid model,the contour clarity of flow region boundaries and the simulation accuracy of grooves and other details can be significantly improved without affecting the calculation efficiency.Both the 3D grid model and the refined 2D grid model are shown in Fig. 3.

Furthermore,to further improve the accuracy of simulation,the calendering device in use was surveyed and drawn to achieve the detailed structural dimensions,which are listed in Table 2 and were used for the construction of the above model.

2.3. Setting of boundary conditions

During the simulation process, some reasonable basic assumptions were made to facilitate calculation and analysis without affecting the accuracy of the simulation: (1) the simulated propellant slurry was an incompressible fluid; (2) all of the solid surfaces satisfied the boundary conditions without slip;(3)the target fluid in the flow region was fully developed laminar flow; and (4)the viscous force was considered at high viscosity,and the effect of inertia force and gravity was ignored. Meanwhile, considering the rotational rate of rollers and the viscosity of slurry, the flow state was set as laminar flow for the small reynolds number with no slip on the wall, and heat transfer was mainly done by means of heat conduction in the laminar boundary layer.

Next, the 2D grid model created in Gambit was imported into the fluid simulation software of Fluent for the boundary conditions setting.Considering the required production efficiency of 180 kg/h at 15 rpm, the volume flow was set as 2.94× 10-5m3/s at 15 rpm with different temperature and spacing, while the outlet pressure was set as 23.54 MPa at 2 mm with different speed according to the actual pressure of propellant slurry during calendaring. The other boundary conditions and related process parameters are shown in Fig. 4 and Table 3, respectively.

2.4. Choice of solution methods

In addition to the physical parameters and boundary conditions,the choice of solver also affects the efficiency of the solution and the accuracy of the results,as a suitable solver can effectively improve the convergence of the calculation. In previous studies, the segregated solver, including the SIMPLE, SIMPLEC and PISO algorithms,have frequently been used for calculation and solution in Fluent.In the process of solution, flow field parameters such as velocity and pressure were set independently and solved one by one;the other parameters were then modified according to the solution results.However, because of the oversimplified coupling term of the flow region in the continuous equation, the change in flow field parameters could not be accurately reflected in the modified equation.

Therefore,the coupled algorithm in the coupled solver was used as the pressure-speed coupling mode in the process of solution,which can simultaneously solve control equations such as the continuity equation,momentum equation and energy equation.In addition, the coupled algorithm can effectively improve the convergence rate of the solution by solving each variable in parallel,which is more suitable for fluids showing strong interaction dependence among various parameters.

The least-squares cell-based gradient discrete scheme was used to determine the grid surface,construct scalar values,calculate the diffusion term and discretize the velocity derivative, which could reduce the number of operations without loss of precision compared with the green-gauss cell-based and green-gauss nodebased gradient discrete scheme.As the decreased relaxation factor could improve the convergence rate and reduce the calculation efficiency,the relaxation factors for pressure and velocity were set to 0.5, while the under-relaxation factors for density, body forces and energy were set to 0.8. Laminar was selected as the viscous model for the high viscosity and low Reynolds number of propellant slurry after calculating the tangent velocity of the roller surface.

Fig. 3. 3D grid model (a) and refined 2D grid model (b).

Table 2 Structural dimensions of the calendering device.

3. Results and discussion

Fig. 4. Schematic of boundary conditions used for simulation.

Table 3 Technological parameters of the calendering process.

The plasticization of CMDB propellant mainly refers to the formation of a strong solution with plasticity by dissolving the linear nitrocotton(NC)macromolecules in the solvent nitroglycerin(NG),which could endow the propellant with great flowability and improve the quality of followed extrusion. During the process of dissolution, intermolecular forces such as hydrogen bonding were disrupted because of the formation of polar covalent bonds with the addition of NG solvents, which contributed to the transformation of NC rigid molecules into flexible molecular structures with high plasticity.

However, effectively promoting the penetration of NG solvent into the interior of NC molecules by molecular diffusion as well as stirring mixing is difficult. Therefore, the calendar was used to accelerate the plasticizing efficiency of CMDB propellant slurry,and the diffusion rate of solvent molecules during calendering was greatly affected by pressure and temperature,which were adjusted by technological conditions, such as the gap, rotational rate and temperature of the two rollers.To further improve the plasticizing effect of propellant, the flow field parameters, such as velocity,pressure, temperature and viscosity, were simulated under different calendering conditions to investigate the rheological behavior, motion trajectories and heat transfer mechanisms of CMDB propellant slurry.

3.1. Effect of roller gap on the calendering process of propellant slurry

During the calendering process, reducing the roller gap could endow the propellant slurry with high squeezing pressure, which not only increased the diffusion rate of NG molecules inside NC but also improved the plasticity of propellant slurry and the molding quality of propellant grain. However, the large squeezing effect of the roller also led to the occurrence of accidents, such as the ignition and explosion of propellant slurry [32].

Therefore, the simulation results of Case 1, 2, 3 and 4 were compared and analyzed to investigate the effect of roller gap on the calendering process of propellant slurry when the wall temperature and rotation speed of the roller were constant.

3.1.1. Effect of roller gap on the velocity of propellant slurry

The velocity cloud charts, statistical values and vector chart of CMDB propellant slurry simulated with different gaps are shown in Fig. 5. The maximum velocity was obtained in contact with the roller wall surface and decreased gradually along the normal direction (Fig. 5a-d). According to the cloud charts, the gap of two rollers had less of an effect on the velocity of propellant slurry in the flow region,and the data shown in Fig.5(e)also demonstrated that the average velocity (AV) around the centerline and maximum velocity (MV) in the flow region basically remained unchanged with different spacing.Compared with the propellant slurry around the centerline,the maximum flow velocity of the propellant slurry near the roller wall surface could reach about 42 cm/s, which was much higher than the 16 cm/s of the central propellant slurry.

The velocity vector chart shown in Fig. 5 (f) indicated that the trajectory of propellant slurry was distributed symmetrically along the central vertical line,and there was a vortex-like circumferential flow on the left and right sides of the flow region,which was mainly caused by the velocity difference in the propellant slurry near the outlet. In the convergent flow channel at the outlet site, the propellant slurry near the wall surface flowed out easily of the outlet because of its higher flow velocity, while propellant slurry with slower flow velocity around the centerline accumulated at the outlets and flowed upward under the strong extrusion of the rollers[33]. Along with the back-flow, the countercurrent propellant slurry bifurcated and turned over around the inlet, and the two vortex reflux movements were formed symmetrically in the flow region.

The cloud charts also illustrated that the reflux movement contributed to increasing the propellant slurry velocity in the interior of the flow region, and the velocity of fluid in the return path was significantly higher than the velocity of fluids near the routes.On the one hand,the formation of vortex reflux movement could effectively improve the convective mixing effect of propellant slurry in the flow region core and realize the uniform distribution of each component. On the other hand, the distribution of residence time between the rollers was greatly broadened, which often triggered the thermal degradation of propellant slurry.

3.1.2. Effect of roller gap on the temperature of propellant slurry

The temperature cloud charts and statistical values of CMDB propellant slurry simulated with different gaps are shown in Fig.6.Heat transfer behaviors,such as heat conduction between the roller wall and propellant slurry and heat convection between propellant slurry in the flow region, took place in the calendering process(Fig. 6a-d) [33]. The wall temperature of the working roller was 5°C higher than that of the idling roller in the simulation process to ensure that the propellant slurry was fully coated on the surface of the working roller. During plasticization, the heat on the wall surface of the roller was first absorbed by the propellant slurry near the wall surface by heat conduction and then transferred and diffused to the core of the flow region by convection heat transfer in the process of refluxing,which accelerated the uniform distribution of temperature in the flow region.In addition,the propellant slurry located inside the grooves took the lead in heating because of its large contact area with the roller wall and quickly achieved a uniform distribution of temperature within the grooves.However,the temperature difference around the centerline of flow region indicated that there was a large temperature gradient between the propellant slurry on both sides of the flow region, which was caused by the different setting temperature of the rollers and the independent reflux movement with little mass exchange and convective heat transfer.

Moreover, the temperature cloud charts in Fig. 6 also indicated that the high-temperature propellant slurry on the wall surface of the roller accumulated near the outlet before the backflow movement.As a result,the hot spot was formed because of the excessive accumulation of heat,which could trigger the localized degradation of propellant. Because of the temperature difference between the two rollers, the temperature of propellant slurry was significantly higher in the right side of the outlet convergent channel than in the left side.In addition,the enlarged roller gap also increased the heat dissipation area and improved the radiant heat dissipation efficiency of propellant slurry at the outlet.Therefore,both the average temperature around the centerline and the probability of hotspot formation decreased with the increase of roller gap.

3.1.3. Effect of roller gap on the viscosity of propellant slurry

The viscosity cloud charts of CMDB propellant slurry simulated with different gaps are shown in Fig.7.Because of the strong shear action of the rollers and the rheological characteristic,the viscosity of propellant slurry near the wall surface is much lower than that inside the flow region (Fig. 7). In addition, the red high-viscosity region, which resembled a triangle star shape in the cloud charts,coincided with the motion trajectory of the refluxing propellant slurry shown in Fig.5.This might be attributed to the fact that the slurry in the red high-viscosity region refluxed in the form of tensile flow because of the large negative pressure near the outlet of the flow region produced by the extrusion effect of rollers,whereas the slurry in the green area of cloud charts also moved in the form of shear flow under the viscous shear drag of the refluxing propellant slurry.

Fig. 5. Velocity cloud charts (a-d), statistical values (e) and vector chart (f) of CMDB propellant slurry with different gaps.

Fig. 6. Temperature cloud charts (a-d) and statistical values (e) of CMDB propellant slurry with different gaps.

Fig. 7. Viscosity cloud charts (a-d) of CMDB propellant slurry with different gaps.

Moreover, the increased gap between two rollers reduced the shear stress near the center of the outlet [34] and caused a slight increase in propellant slurry.In the calendering process,aluminum powder and other explosive particles in the form of ultrafine powder can easily agglomerate into large-size powder masses because of the high surface activity.Shear stress is one of the main mechanical external forces breaking up agglomerates.Therefore,in addition to the viscosity, the increased roller gap also reduced the mixing uniformity of each formula component in the flow region.3.1.4. Effect of roller gap on the reflux capacity of propellant slurry

The backflow of propellant slurry was found in previous studies[29],while the factors affecting the reflux efficiency were not clear and the reflux capacity was difficult to be analyzed intuitively.Thus,in view of the apparatus used for experimental verifications of the solids conveying properties of grooved screw extruder [35], the inlet pressure was applied to characterize the reflux capacity of slurry under the setting of inlet without outflow. And the higher pressure difference,the stronger reflux capacity of propellant slurry during calendering. Meanwhile, considering the free boundary of inlet in actual production, the simulated pressure of inlet was higher than actual pressure value.

Fig.8. Inlet pressure and pressure difference of CMDB propellant slurry with different gaps.

The inlet pressure and pressure difference between the inlet and outlet of CMDB propellant slurry with different gaps are shown in Fig. 8. The inlet pressure and pressure difference increased exponentially as the roller gap decreased under the same outlet pressure. This stems from the fact that decreasing the roller gap could not only reduce the outlet size of the flow region and hinder the outflow of propellant slurry, but it could also increase the accumulation scale of propellant slurry near the outlet and the negative pressure value generated by calendar. Thus, a large pressure difference between the inlet and outlet is established in the flow region while the propellant slurry was pushed back, which also represented the enhanced reflux capacity of propellant slurry. In addition, the decrease in the gap also led to the interference collision between two rollers and aggravated the probability of ignition and explosion of propellant because of the high pressure. It was found after experimental verification that 2-mm roller spacing was appropriate and used in subsequent investigations of process parameters.

3.2. Effect of rotational rates on the calendering process of propellant slurry

During calendering, the high rotational rates of rollers could endow propellant slurry with great shearing action, which contributed to improving the dispersion uniformity and plasticizing quality of the propellant.Therefore,the simulation results of Case 5,6,2,7 and 8 were compared and analyzed to investigate the effect of rotational rates on the flow field parameters of propellant slurry with the same wall temperature and roller gap.

3.2.1. Effect of rotational rates on the velocity of propellant slurry

The velocity cloud charts,statistical values and flow diagram of CMDB propellant slurry with different rotational rates are shown in Fig.9.The flow velocity of propellant slurry in contact with the wall surface of rollers increased with the rotational speed; in addition,more peripheral propellant slurry was brought flowing toward the outlet. However, because the conveying capacity of the roller was proportional to the speed of the roller,the excessively high speed of the roller increased the outlet velocity of the propellant slurry and the counter-flow velocity of the refluxing propellant slurry, while the reverse flow and vortex reflux of propellant slurry in the flow region could not be formed at low roller speed. As the rotational speed of rollers increased from 5 rpm to 10 rpm, the original reverse flow movement of propellant slurry in the flow region gradually developed into the vortex backflow movement, which was improved along with the increased rotational speed of rollers.The data shown in Fig. 9 (f) also demonstrated that the small velocity of slurry and conveying capacity of the roller at 5 rpm made it difficult for the propellant slurry to be retained at the outlet and thus was hardly sufficient for backflow. Along with the increased rotational speed,both the conveying capacity of the rollers and the flow velocity of propellant slurry were improved, which indicated the higher volume flow under certain cross-section area of outlet.Meanwhile, the extensive slurry accumulated near the outlet because of the difficulty in timely outflow,which followed with the formation of reflux movement under the squeezing action of rollers. In addition, the increase in the average and maximum velocity of propellant slurry around the centerline of the flow region also demonstrated that the increase in the roller speed helped increase the countercurrent velocity and improve the dispersive mixing uniformity of different components inside the flow region.However, the excessive roller speed could not only promote the reflux movement and broaden the residence time distribution of propellant slurry,but it could also aggravate the internal friction of propellant slurry and produce much viscous dissipation heat,which increased the combustion-explosion hazard.

Fig. 9. Velocity cloud charts (a-e), statistical values (f) and flow diagram (g) of CMDB propellant slurry with different rotational rates.

3.2.2. Effect of rotational rates on the temperature of propellant slurry

The temperature cloud charts and statistical values of CMDB propellant slurry with different rotational rates are shown in Fig.10.As the roller speed increases, the heat of the roller wall gradually diffuses and transfers to the inlet of the flow region(Fig.10).This is mainly because the increase in the roller speed helps extend the return path of the propellant slurry, permitting it to carry out convective heat transfer with more slurry and promote the homogenization of temperature inside the flow region. At the rotational speed of 5 rpm,most of the propellant slurry that conducted heat conduction with the wall surface was transported by the rollers to the outlet and flowed out;only a small part of propellant slurry went against the current and conducted convection heat transfer with materials inside the flow region.In addition,the heat exchange materials were mainly concentrated in a small area in the lower part of the flow region. However, as the rotational speed increased and the backflow track improved, the boundary of convection in the flow region gradually expanded to the inlet, which also caused the decreased area of low-temperature area in blue.

The data shown in Fig. 10 (f) also indicated that the average temperature around the flow region increased with the rotational speed,and a small decrease occurred in the maximum temperature of the propellant slurry around the centerline. This mainly stems from the fact that more thermal energy was absorbed by the slurry and diffused in the convective heat transfer process because of the improved conveying capacity.In addition,more mechanical energy was converted into thermal energy by viscous dissipation for the enhanced shear rate,which led to an increase in the average temperature around the flow region. In addition, the heat transfer efficiency inside the flow region was also improved by strengthening the tumbling and stirring action of propellant slurry,which caused a slight decrease in temperature around the centerline. The local agglomeration of thermal energy and the emergence of hot spots were avoided for the intensified heat diffusion [36,37].

Fig.10. Temperature cloud charts (a-e) and statistical values (f) of CMDB propellant slurry with different rotational rates.

3.2.3. Effect of rotational rates on the viscosity of propellant slurry

The viscosity cloud charts of CMDB propellant slurry with different rotational rates are shown in Fig. 11. The viscosity of propellant slurry inside the flow region tended to be consistent at the speed of 5 rpm and much higher than that in contact with the wall surface of the rollers(Fig.11).Nevertheless,a great decrease in the viscosity was caused by the increased rotational speed. The low-viscosity area in blue near the wall surface of the rollers gradually expanded to the core;in addition,the high-viscosity area in red around the center of flow region was translated into the middle-viscosity area in green.This is mainly because the increase in the rotational speed enhanced the shear action of rollers on the propellant slurry near the wall surface,which could not only extend the backflow path and augment the backflow rate of propellant slurry but could also decrease the viscosity significantly and increase the low-viscosity area in blue. Meanwhile, the perfected reflux movement promoted the reflux velocity and its shear action on the surrounding fluid,which exacerbated the internal friction of propellant slurry.Furthermore,the decreased viscosity also reflects the high shear rate and stress inside the flow region, which was conducive to improving the dispersion and mixing uniformity of aluminum powder and other powder fillers. However, as the rotational speed exceeded 15 rpm, further increases in speed did not greatly affect the viscosity of propellant slurry in the flow region.

3.2.4. Effect of rotational rates on the reflux capacity of propellant slurry

The effect of rotational rates on the reflux capacity of propellant slurry was also characterized by the inlet pressure under the setting of inlet without outflow. And the inlet pressure and pressure difference between the inlet and outlet of CMDB propellant slurry with different rotational rates are shown in Fig.12.Along with the increased rotational speed,the linear increase in the inlet pressure and the absolute value of the pressure difference were calculated and listed below under the same outlet pressure, which indicated the stronger reflux capacity.This is mainly because more propellant slurry was delivered towards the outlet for the enhanced conveying capacity of the rollers,which accumulated because of the difficulty of timely outflow. Greater driving force was generated under the squeezing action of calendar to promote the countercurrent and rolling of the piled propellant slurry.

Fig.11. Viscosity cloud charts (a-e) of CMDB propellant slurry with different rotational rates.

Fig.12. Inlet pressure and pressure difference of CMDB propellant slurry with different rotational rates.

According to the experimental and simulation results, 15 rpm was used as the optimal roller speed in the actual processing. On the one hand, the high value of viscosity at low rotational speed was not conducive to the even mixing of propellant slurry during the calendering process.On the other hand,safety hazards,such as combustion and explosion, were frequently triggered by adiabatic compression and appeared at high speed.

3.3. Effect of wall temperature on the calendering process of propellant slurry

During calendering, the high temperature of rollers could promote the motion of molecular chains and accelerate the dissolution of solvent, which contributed to improving the plasticity of propellant slurry.Therefore,the simulation results of Case 2,9,10 and 11 were compared and analyzed to investigate the effect of roller temperature on the flow field parameters of propellant slurry with the same wall rotational speed and gap.

The temperature cloud charts and statistical values of CMDB propellant slurry with different roller temperatures are shown in Fig.13.The temperature around the flow region increased gradually with the roller wall temperature (Fig. 13a-d), which mainly stemmed from the fact that the enlarged temperature difference between the roller wall and propellant slurry enhanced the heat transfer efficiency in the calendering process. In addition, more thermal energy participated in the convection heat exchange process and increased the temperature of propellant slurry by heat diffusion. The data shown in Fig.13 (e) also indicated that as the temperature of the work roller and idling roller increased to 100°C and 95°C, respectively, the average temperature of propellant slurry around the flow region and its maximum temperature around centerline also increased from 77.7°C to 94.9°C and from 90.0°C to 98.7°C,respectively.Moreover,the comparison between Fig. 13 (c) and (d) also illustrated that greater wall temperature differences between the work roller and idling roller led to more pronounced temperature gradients of the propellant slurry around the centerline of the flow region.In addition,the steep drop in the average temperature around the centerline also indicated that the reduced temperature difference of the two rollers was conducive to promoting the heat transfer between the left and right sides of the flow region, which helped realize the uniform distribution of temperature in the flow region.

Although high temperature could enhance the thermal motion ability of solvent molecules and improve the dissolution and plasticization efficiency of NC molecules, the plasticity of propellant slurry can be improved by increasing the roller temperature,which likely caused the thermal degradation behavior of propellant and created the safety hazards of ignition and explosion[38].Based on the simulation results,the roller wall temperatures of the calendar were set as 95°C and 90°C and were used in the subsequent preparation of double-base modified propellant.

3.4. Exploration of the heat transfer mechanism during the calendering process

To further explore the heat transfer mechanism and temperature distribution rule of propellant slurry in the flow region, statistical analysis of temperature was carried out at different contour sections; the results are shown in Fig.14. The temperature of propellant on the left and right sides of the flow region at different contour sections all first decreased and then increased from the wall surface to the centerline. This is mainly because the temperature of propellant slurry near the wall surface of the rollers was basically equal to the wall temperature,which was heated by heat conduction. Nevertheless, because of the difficulty of the transfer and diffusion of thermal energy before outflow,the temperature of propellant near the wall surface of rollers plunged along the normal direction. As the distance from the wall surface increased, the temperature increased slowly because of the reflux heat transfer of high-temperature propellant slurry; heating rates were higher closer to the centerline. Because of the temperature of the roller wall, the temperature of propellant near the wall surface of work rollers was higher than that of the idling roller,and the temperature difference decreased gradually closer to the centerline.

The data shown in Fig.14(b)also indicated that the temperature of slurry around the centerline decreased with the test height.Compared with the temperature at the center of the 150-mm contour section, the temperature at the center of the 100-mm contour section increased by 1°C. This is mainly because the heat energy and temperature of reflow propellant decrease gradually by heat diffusion during the reflow heat transfer process. Therefore,the temperature of propellant slurry at the initial position of the countercurrent needs to be monitored,and the process parameters need to be adjusted based on the temperature variation to ensure the safety of the calendering process.

4. Conclusion

To improve the plasticity of slurry and prevent the frequent occurrence of combustion and explosion, the calendering process of composite modified double-base (CMDB) propellant was investigated by fluid simulation technology. In addition, the rheological behavior, motion trajectories and heat transfer mechanisms were explored and clarified under different process conditions, which provided reference data and theoretical guidance for the subsequent process optimization of propellant slurry. The specific conclusions are as follows:

(1) The modification of the rheological model and model size improved the match between simulation results and actual conditions. In addition, the application of adaptive grid technology permits the refinement of the grid size near the flow region boundary without reducing the computational efficiency of the software, and the clarity of the boundary contour in the simulation model was significantly improved by the refined grids. Therefore, the simulation accuracy of slurry in the grooves and the convergence outlet of the barrel was greatly improved, which could accurately reflect the flow and heat transfer behaviors in the calendering process.

Fig.13. Temperature cloud charts (a-d) and statistical values (e) of CMDB propellant slurry with different roller temperatures.

Fig.14. Temperature distribution of propellant at y = 100 mm and y = 150 mm.

(2) During the calendering process, the ability of the propellant slurry near the centerline to flow out rapidly was difficult because of its low flow rate,which often accumulated at the convergent outlet and refluxed under the squeezing action of rollers.Meanwhile,the reflux movement of propellant slurry facilitated the uniform distribution of temperature around the flow region by heat conduction and convection.

(3) Compared with the gap between two rollers,the increase in rotational speed can not only significantly increase the reflux velocity,but it can also enhance the viscous shear drag action of propellant slurry. As a result, the rapid decrease in viscosity and improvement in the convective mixing effect inside the flow region were also caused by the increased speed,which contributed to the fracture of aggregate and the uniform distribution of filler.

(4) Because of the reflux movement, the temperature of propellant slurry at different contour sections all showed a pattern of first decreasing and then increasing from the wall surface of the rollers to the centerline,which also decreased with the increased height of contour sections because of heat transfer and diffusion. In addition, a large temperature gradient around the centerline was caused by the temperature difference between roller walls and the rolling reflux movement; greater temperature differences led to a more pronounced temperature gradient.

(5) Both the decreased roller gap and the increased roller speed could result in the accumulation of CMDB propellant slurry near the outlet, which showed the difficulty in timely outflow. Meanwhile, the inlet negative pressure was caused by the back-flow of slurry.The increased pressure difference between the inlet and outlet indicated the enhanced reflux capacity of propellant slurry during calendering, and compared with roller speed,the decreased roller gap showed greater effect on the reflux capacity.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was financially supported by Basic Product Innovation Technology Research Project of Explosives.