Numerical simulation of cook-off characteristics for AP/HTPB

Qing Ye,Yong-gang Yu

School of Energy and Power Engineering,Nanjing University of Science and Technology,Nanjing,210094,China

Keywords:Cook-off Numerical simulation AP/HTPB

ABSTRACT The present study is devoted to researching the thermal security problems of large-scale solid rocket motor with Ammonium perchlorate/Hydroxyl-terminated polybutadiene(AP/HTPB).A two-dimensional axisymmetric model for the cook-off of solid rocket motor is established.The reaction kinetics for the cook-off process of AP/HTPB is described by the two-step global chemical mechanism.Numerical predictions of the cook-off behavior for the propellant are conducted at fast heating rate of 1.45-2.45 K/s,and slow heating rate of 0.001-0.003 K/s,respectively.The results show that in the fast cook-off condition,the initial ignition position of AP/HTPB occurs in the annular region of the outer wall of propellant without exception,and the center point in the region is(889.1,149.5).For the region,the axial width is 1.8 mm and radial thickness is 0.8 mm.However,in the slow cook-off condition,the ignition center position is shifted along the axial direction toward the right end face of the propellant with the increase of heating rate.Therefore,the influence of heating rate on ignition temperature and ignition delay time is nonnegligible within a certain range.

1.Introduction

Solid rocket motors are powerful devices of rockets and other missiles,which continuously increase the energy requirements of composite propellants with the rapid development of high technology.The high energy of solid propellants significantly reduces the thermal safety of rocket motors during transportation,storage,and use,which creates hidden danger.The cook-off test and cook-off numerical simulation are common methods to explore and assess the thermal safety of ammunition and high energy materials.Many scholars have carried out a large number of experimental studies for the thermal safety of energetic materials such as explosives and propellants.A 2D numerical code was developed to simulate the fast and slow cook-off heating conditions of confined munitions and to obtain the response of the energetic materials[1].Thermal analysis methods and slow cook-off tests are utilized for analyze the thermal decomposition characteristics of HTPB propellants[2,3].The porous morphology formed by the thermal decomposition process is a major factor that causes the slow cook-off violent response of HTPB propellants.A slow-cook-off test is conducted to study the influence factors of the cook-off characteristics of HTPE(Hydroxyl-terminated polyether)and GAP(Glycidyl azide polymer)solid propellants[4].The results demonstrate that the response of slow cook-off of HTPE propellants increase by adding 10% HMX (cyclotetramethylenetetranitramine).However,impact on GAP propellant cook-off response is small;and splint constraint will increase the response of two propellants.Yang Hou-wen et al.[5,6]establish a two-dimensional simplified model for a small solid rocket motor loaded with AP/HTPB propellant.Li Wen-feng[7]investigate the effect of charge size on the cook-off characteristics of AP/HTPB base bleed propellant,and the results show that the cook-off time is shortened with the increase in the grain diameter of charge The calculation results are shown that as the flame temperature increases,the ignition delay time decreases and the ignition temperature increases.The adiabatic effect of the thermal insulation grows with increasing flame temperature.Hedmanetal.[8]experimentally investingte the decomposition preceding autoignition of an ammonium-perchlorate-based composite propellant.

At present,the research of cook-off is based primarily on the combination of numeric simulation and test,because of the cookoff test is expensive,time-consuming,high risky and has many uncertainties.However,the numeric simulation method can be used to study the cook-off characteristics more safely and cheaply,and predictive research can be conducted.Experimental research for large solid rocket motor is rarely reported,as a result of precise control of the temperature field is difficult due to the enormous heating volume,and the risk is high.Under this background,this paper establishes a two-dimension cook-off model for a certain type of rocket motor,and calculates the ignition temperature,ignition position and delay time of the solid propellant during fast cook-off at three heating rates.

2.Theroretical models

2.1.Physical model

The simplified structure model of solid rocket motor[9]consists of shell,insulation,propellant,nozzle,an epoxy resin baffle,as shown in Fig.1.The 2-D simplified model is adopted here by five assumptions:

(1)The auto thermic reaction of AP/HTPB propellant abides by first order and second order Arrhenius laws related to pressure;

(2)The thermal contact resistance between shell and insulation,insulation and propellant is ignored;

(3)AP/HTPB propellant is assumed to be homogeneous and isotropic material,maintains solid phase in the whole simulation process;

(4)The physical parameters and chemical kinetic parameters of each material are constant;

(5)The gas flow rate is slightly in the motor due to the cook-off conditions.Convective heat transfer is ignored and only the heat transfer between the gas and the propellant is considered.

2.2.Governing equations

A two-step global chemical reaction kinetic,including thermolysis of AP and final exothermal reaction,is established,which includes the AP decomposition and one exothermic binder(HTPB)reaction:

The physical significances of symbols in formulas are shown in Table 1.The chemical reaction rates[11]R1and R2in reaction(1)and(2)are given:

Pressure is calculated by ideal gas state equation of P=ρRT/M.

The shell of solid rocket motor is heated.The heat is transferred to the internal system,which makes the temperature of AP/HTPB rise and ignite.Heat transfer and heat exchange between case,insulation and propellant are described by following unsteady 2-D axisymmetric equations[10,12]:

2.3.Boundary and initial conditions

According to the temperature change of the heated surface during the cook off test,boundary condition is applied to simulate the external thermal stimulion solid rocket motor.Temperature boundary condition of the shell is described by heating rate:

The interface between two kinds of solid materials,such as case,insulation and propellant,sat is fies temperature continuity and heat flux continuity condition:

a,b represent different kinds of solid materials.

The end face of case and nozzle is adiabatic boundary:

The initial conditions are as follows:

2.4.Grid independence

The numerical simulation of solid rocket motor is performed.The size of the solid rocket motor is shown in Fig.2 and Table 2.Structured quadrangular mesh is applied to mesh the motor structure model.Three meshes are taken to verify the grid independence,and the grid numbers are 326390,634900 and 1291890,named Node 1,2 and 3.Temperature of shell is calculated through the heating rate of 2.45 K/s.Temperature distribution curves for the nozzle throat section at a certain time is shown in Fig.3.The temperature of Node 3 is 369.5 K aty=0mm,and the temperature of Node 1 and Node 2 are 365 K and 369 K,respectively.Errors of Node 1 and 2 are 1.22%and 0.13%.Node 2 is selected because the result is consistent with which the grid number double refined.

Table 1 Physical significance of notations.

2.5.Calculation method and parameters

Based on the finite volume method,the Fluent software was used for a solid rocket motor fast cook-off numerical calculation.Solid propellant auto thermic reaction and rocket motor temperature boundary condition were loaded by user defined function to calculate.The discrete method was pressure-based implicit operator segmentation algorithm(PISO),and the density,energy and component equations were all discrete in the second-order upwind scheme.Numerical simulations of cook-off processes of the motor are performed under two groups,six kinds of heating rate of 1.45 K/s,1.95K/s,2.45K/s,and 0.001 K/s,0.002 K/s,0.003 K/s until the ignition reaction of propellant occurred.The material properties and reaction kinetic parameters of the solid rocket motor cook-off numerical simulations[11,13]are shown in Tables 3 and 4.

3.Results and discussion

3.1.Fast cook-off characteristics

The numerical simulation of fast cook-off of a rocket motorloaded with AP/HTPB propellant was carried out.The shell is heated at the rate of.45 K/s,1.95 K/s and 2.45K/s.The temperature distribution at different time is shown in Fig.4.The external heat transferred to the rocket motor,through the wall of the shell.The temperature of shell increased quickly,while the internal temperature of the propellant almost remains constant,throughout the process because the heat conductivity capacity of the insulating and the propellant is less than that of the shell.At the outlet of the nozzle,the nitrogen in the cavity was in direct contact with the high-temperature shell,so the temperature of the nitrogen in the nozzle was higher than that near the propellant.

Table 2 Size of solid rocket motor.

Table 3 Parameters of materials[11].

Table 4 Chemical reaction kinetic parameters of AP/HTPB propellant[13].

Fig.5(a)and(b)are ignition positions inside the motor of heating rates 1.95K/s and 2.45 K/s respectively.As can be seen from Figs.4 and 5,ignition positions of three heating rates firstly occur in the outer circular region of AP/HTPB near the nozzle without exception.The center points are(889.1,149.6)mm,for the axial length 1.8 mm,radial thickness 0.8mm.Combined with the ignition delay and temperature corresponding to the three heating rates(shown in Table 4),it was found that within a certain range,the heating rate has a little effect on ignition temperature,and the ignition delay period decreases with the increase of heating rate.

The temperature of four typical points such as external point A and middle point B in insulation,outside point C and inner point D of the propellant,is monitored in the calculation,and the coordinates of points were shown in Fig.2.Results of temperature measurement are given in Fig.6,and trends of temperature profile are same as three heating rates.Heating rates of two points are different in insulation.Temperature of outside propellant rise slowly at the initial stage,and rise faster after 320 K due to thermal decomposition and release heat of AP.AP reacted rapidly and released a lot of heat when the temperature reaches the ignition temperature.The inside of propellant was contacted directly with nitrogen.Nitrogen failed to transfer heat to the propellant due to slight heat conduction,so the temperature of inside propellant changed slightly.The ignition temperature,delay time and position at different heating rates were shown in Table 5.Combined with ignition delay periods and ignition temperatures corresponding to three heating rates,it was found that the heating rate has little effect on ignition temperature within a certain range,and the ignition delay period decreased in the increase of heating rate.

3.2.Slow cook-off characteristics

In the numerical simulation of slow cook-off of a rocket motor loaded with AP/HTPB propellant,the case was heated at the rate of 0.001K/s,0.002 K/s and 0.003 K/s.Temperature distribution in motor before and after ignition at a heating rate of 0.001K/s is illustrated in Fig.7.In Fig.7,the radial temperature distribution of the propellant is no uniform before and after ignition.This is explained by the fact that the heat is transferred radially from the outside to the inside.The ignition delay period is 158927s,and ignition temperature is 524.2045.The ignition position is a ring on the propellant shoulder.The axial length is 4 mm,and radial thickness is 2 mm,and the center is(880,148)mm.

Table 5 The ignition temperature,time and position at different heating rates.

Fig.8 is temperature distribution of ignition time in the motor at the heating rates,0.002 K/s and 0.003 K/s.In comparison,it can be seen that in three different slow-burning operating conditions,the temperature distribution of the engine at the time of ignition is approximately the same,and the ignition position is on the shoulder of the propellant,but there is a slight difference in the center of the ignition position.The ignition delay period,ignition temperature and position corresponding to different slow heating rates are listed in Table 6.

As shown in Table 6,it can be seen that in the case of slow cookoff,the center of the ignition position of the propellant shifts along the axial direction toward the right end face of the propellant with an increase in the heating rate,but the change in the radial direction is not significant.The area of the ignition position shrank as the heating rate increases.The increasing temperature around the region hinders heat transfer to the contiguous area,and is conducive to the accumulation of heat at ignition position.

The average temperature of Table 5 is slightly exceeded than that in Table 4,which is due to the difference of heat conduction in the motor under fast cook-off and slow cook-off.The temperature of the motor shell rises rapidly at fast heating condition.The temperature difference between the shell and propellant is great.The heat is always transferred from the outside,which causes the temperature of the ignition region to reach the ignition temperature very quickly as shown in Fig.9(a).And then the propellant reacts quickly to release heat.The heat is not enough to transmit to other places of the motor in time,and then ignites in the region.The ignition temperature is higher.The temperature of the motor rises slowly and the heat is still transferred from the outside in the slow cook-off early process,but the temperature difference between the shell and the propellant is smaller.As shown in Fig.8(b),the gradual temperature rise of the propellant makes the AP decomposition reaction rate small.And the decomposition reaction is basically completed in the later period.The amount of heat released by the final product is greater than the heat absorbed by the decomposition reaction.The heat accumulation in the shoulder of the propellant is accumulated and the high temperature zone appears.At this time,the heat is transmitted from the high temperature zone to the adjacent Insulation and the propellant,which makes the ignition temperature slightly lower than that of the fast cook-off condition.

Table 6 Ignition temperature,delay and position of different heating rates.

In the above numerical simulation results of two sets, six different heating rate conditions, the ignition positions appear in the shoulder of the AP/HTPB propellant, but the definitions of the ignition position is different, under three kinds of fast heating rates, the position of the ignition point is close to the boundary between the propellant and the thermal insulation layer.It can be inferred that there is a critical heating rate between the two sets of heating rates,so that the ignition position no longer moves with the heating rate.

4.Conclusions

(1)The ignition occurred in the same position of AP/HTPB propellant under fast heating rates of 1.45 K/s,1.95K/s,and 2.45K/s.And coordinate is(889.1,149.6)mm,in the annular area near the annular region of the propellant.The ignition temperatures corresponding to the three heating rates are 531.87 K,529.44K,and 532.54 K,and the ignition delays are 649.0 s,600.3 s and 539.5 s.The heating rate is currently under a definite influence on the ignition delay period,the ignition delays period shortens as the heating rate increases.

(2)Under the slow heat rates of 0.001K/s,0.002K/s,and 0.003K/s,the initial cook-off response locations of AP/HTPB propellants all occurs in the annular region of the outer wall of the propellant near the nozzle,while the center positions are(880,148)mm,(886,148)mm and(886.5,149)mm respectively.The ignition delay time is158927s,102613s and 81829s,with the corresponding ignition temperature of 528.16K,523.03K and 534.20K.The ignition center position of the propellant shifts along the axial direction toward the right end face of the propellant with an increase in the heating rate.

(3)The center of the ignition stay the same position with the fast heating rate increasing,while the center of the ignition shifts along the axial to the right end face of propellant with an increase in the heating rate.It indicates that there is a critical heating rate between 0.003 K/s and 1.45K/s so that the ignition points remain the same.