（海军航空大学，山东烟台，264001）  (Naval Aviation University, Yantai, Shandong, 264001)

主题词：固体发动机；点火；火焰传播  SUBJECT TERMS: solid engines; ignition; flame propagation
中图分类号：V435 文献标识符：A  Classification number: V435 Literature identifier: A

（Naval Aeronautical University，Yantai，Shandong，264001）
(Naval Aeronautical University, Yantai, Shandong, 264001)

Key word：solid rocket motor，ignition，Flame－spreading
Key word: solid rocket motor, ignition, Flame-spreading

固体火箭发动机火焰传播阶段是指从推进剂产生的第一个火焰开始，到推进剂表面完全点燃的这段时间。对于固体火箭发动机来说，火焰传播过程对瞬变压力影响很大，最早期的研究工作是作为点火过程的一部进行的 ${}^{[1-4]}$${}^{[1-4]}$^([1-4]){ }^{[1-4]} ，将火焰传播建立在连续点燃的前提上，并以推进剂表面达到一个临界温度为点火判据。联合技术中心的研究者 ${}^{[5]}$${}^{[5]}$^([5]){ }^{[5]} 提出了沿复合推进剂表面火焰扩张的详细模型，该模型包括了向固体推进剂传热的所有模式，同时考虑传热速率随时间和沿轴向两个方面变化并导出两条相似律，而Reizberg ${}^{[6]}$${}^{[6]}$^([6]){ }^{[6]} 提出一个分析方法，并给出了可以确定火焰传播速率随时间变化的近似解释解；在点火试验研究过程中，主要是通过采用压力传感器记录压力，激光多普勒速度场测试 ${}^{[7]}$${}^{[7]}$^([7]){ }^{[7]} ，高速摄影 ${}^{[8]}$${}^{[8]}$^([8]){ }^{[8]} 和热电偶 ${}^{[9]}$${}^{[9]}$^([9]){ }^{[9]} 等采集实验数据，
The flame propagation phase of a solid rocket motor is the time from the first flame produced by the propellant to the complete ignition of the propellant surface. For solid rocket motors, the flame propagation process has a significant impact on transient pressure, and the earliest research efforts were conducted as part of the ignition process ${}^{[1-4]}$${}^{[1-4]}$^([1-4]){ }^{[1-4]} , basing the flame propagation on the premise of continuous ignition and taking the propellant surface reaching a critical temperature as the ignition criterion. JTC researchers ${}^{[5]}$${}^{[5]}$^([5]){ }^{[5]} proposed a detailed model for flame spread along a composite propellant surface that includes all modes of heat transfer to a solid propellant, considers the rate of heat transfer with respect to both time and axial direction, and derives two similarity laws, while Reizberg ${}^{[6]}$${}^{[6]}$^([6]){ }^{[6]} proposed an analytical method and gave an approximation for determining the rate of flame spread with respect to time. An approximate explanatory solution to determine the variation of flame propagation rate with time is given. During the ignition test study, the experimental data are collected mainly by using pressure sensors to record the pressure, laser Doppler velocity field test ${}^{[7]}$${}^{[7]}$^([7]){ }^{[7]} , high-speed photography ${}^{[8]}$${}^{[8]}$^([8]){ }^{[8]} and thermocouples ${}^{[9]}$${}^{[9]}$^([9]){ }^{[9]} .

Conover G H 利用纹影仪观测发动机头部翼槽部分的燃烧情况 ${}^{[10]}$${}^{[10]}$^([10]){ }^{[10]} ，，Moore J D 等人采用高速摄影和近红外探测器测量方法对发动机翼槽内火焰传播过程进行了实验研究 ${}^{[11]}$${}^{[11]}$^([11]){ }^{[11]} ，李逢春，张富升等人开展复合推进剂实际点火过程试验研究 ${}^{[12]}$${}^{[12]}$^([12]){ }^{[12]} ，王慧等人利用缩比模拟发动机研
Conover G H observed the combustion in the wing channel portion of the engine head using a ripple shader ${}^{[10]}$${}^{[10]}$^([10]){ }^{[10]} , Moore J D et al. conducted an experimental study on the flame propagation process in the wing channel of the engine using high-speed photography and near-infrared detector measurements ${}^{[11]}$${}^{[11]}$^([11]){ }^{[11]} , Li Fengchun, Zhang Fusheng et al. carried out an experimental study on the actual ignition process of composite propellants ${}^{[12]}$${}^{[12]}$^([12]){ }^{[12]} , Wang Hui et al. used a scaled-down simulation of engine research to study the combustion process in the wing channel of the engine. b2>, Wang Hui et al. used the scaled-down simulation engine to study the flame propagation process in the wing groove of a composite propellant.

究了大后翼与主流的相互作用 ${}^{[13]}$${}^{[13]}$^([13]){ }^{[13]} ，余贞勇等人开展了尾翼槽内火焰传播过程对固体火箭发动机整个点火升压过程的影响研究 ${}^{[14]}$${}^{[14]}$^([14]){ }^{[14]} ，肖波等人通过在推进剂表而嵌入热电偶丝的类靶线法及光电探测法开展了后向台阶型装药的高能推进剂火焰传播实验 ${}^{[15]}$${}^{[15]}$^([15]){ }^{[15]} ；除了试验研究之外，大量学者利用数值模拟的方法对点火火焰传播过程进行研究，唐金兰 ${}^{[16]}$${}^{[16]}$^([16]){ }^{[16]} 等人以＂大力神 4 ＂运载火箭助推发动机PQM－1 为例，通过建立纯气相流动和气固两相流动模型，分析了SRM点火瞬态凝相粒子对火焰传播过程的影响，王健儒等 ${}^{[77]}$${}^{[77]}$^([77]){ }^{[77]} 通过质量流率入口模拟初期小火箭式点火装置的火焰喷射方式对整个的点火过程进行数值研究，丁鸿铭等 ${}^{[18]}$${}^{[18]}$^([18]){ }^{[18]} 采用颗粒轨道模型对某型固体火箭发动机点火瞬态点火药颗粒在燃烧室内的流动与燃烧特性进行数值研究，官典 ${}^{[19-20]}$${}^{[19-20]}$^([19-20]){ }^{[19-20]}等人建立塊合颗粒惯性过载场，颗粒碰撞推进剂增强传热，推进剂侵蚀／过载耦合燃烧，流场惯性过载场效应的综合点火模型，对横向过载下气一粒两相流对固体火箭发动机点火过程影响进行了研究。本文在分析总结国内外研究的基础上，通过不定常理论推导了火焰传播规律，并设计研制了模拟试验发动机，研究了在不同点火药量的点火燃气以不同的角度喷射到推进剂表面情况下的火焰传播速率。
, Yu Zhenyong et al. carried out a study on the influence of flame propagation process in the tail groove on the whole ignition boosting process of solid rocket motor ${}^{[14]}$${}^{[14]}$^([14]){ }^{[14]} , Xiao Bo et al. carried out an experiment on the flame propagation of high-energy propellant of backward stepped charge ${}^{[15]}$${}^{[15]}$^([15]){ }^{[15]} by embedding a thermocouple filament in the surface of the propellant with the target-like line method and photoelectric detection method; besides the experimental study, a large number of scholars used numerical simulation to study the ignition flame propagation process. b2>; In addition to experimental research, a large number of scholars use numerical simulation to study the ignition flame propagation process, Tang Jinlan ${}^{[16]}$${}^{[16]}$^([16]){ }^{[16]} et al. take the "Hercules 4" launch vehicle booster engine PQM-1 as an example, and analyze the SRM ignition flame propagation process by establishing the pure gas-phase flow and gas-solid two-phase flow model, and analyze the SRM ignition flame propagation process by establishing the pure gas-phase flow and gas-solid two-phase flow model. By establishing pure gas-phase flow and gas-solid two-phase flow models, they analyzed the influence of SRM ignition transient condensed-phase particles on the flame propagation process. The flow and combustion characteristics of a solid rocket motor ignition transient ignition drug particles in the combustion chamber for numerical study, Guan Dian ${}^{[19-20]}$${}^{[19-20]}$^([19-20]){ }^{[19-20]} et al. to establish a block of particles inertial overload field, particles collision propellant to enhance heat transfer, propellant erosion / overload coupled combustion, the flow field of inertial overload field effect of the integrated ignition model, the transverse overload of the two-phase flow of the gas under the gas a particle on the ignition process of solid rocket motors for research. In this paper, based on the analysis and summary of domestic and foreign research, the flame propagation law is deduced by the uncertainty theory, and a simulation test engine is designed and developed to study the flame propagation rate under the condition that the ignition gas with different ignition charge is sprayed onto the propellant surface at different angles.

为便于分析，进行了如下的假设：  For the purpose of this analysis, the following assumptions were made:
（1）推进剂最先被点燃的部位出现在头部，即火焰只向下游传播。
(1) The first part of the propellant to ignite occurs at the head, i.e., the flame propagates only downstream.
（2）在点火瞬态期间，燃烧室容积 $V$$V$VV 为常数，即为初始容积。
(2) During the ignition transient, the combustion chamber volume $V$$V$VV is constant, i.e., the initial volume.
（3）药柱中热传导是二维瞬变的；  (3) Heat transfer in the pillars is two-dimensional and transient;
（3）燃烧室压强仅随时间变化而不随空间位置变化。
(3) The combustion chamber pressure varies only with time and not with spatial position.
（4）忽略侵蚀燃烧的影响。同样，由于装药通道的气流速度较低，可以忽略气流速度对燃速的影响。
(4) Neglect the effect of erosive combustion. Similarly, the effect of airflow velocity on the burning rate can be ignored due to the low airflow velocity in the charging channel.
（5）忽略两相流的影响，燃烧气体服从理想气体方程。
(5) Neglecting the effect of two-phase flow, the combustion gas obeys the ideal gas equation.

理论模型的基本观点是认为药柱未燃部分既接受燃气流的对流换热，又接受已燃部分固相传导热流，直至表面达到点火温度发生点火，可用二维偏微分方程（1）描述。未燃部分固相热传导所选用坐标系如图1。
The basic idea of the theoretical model is that the unignited portion of the column receives both convective heat transfer from the gas stream and solid-phase heat transfer from the ignited portion of the column until the surface reaches the ignition temperature at which ignition occurs, which can be described by the two-dimensional partial differential equation (1). The coordinate system chosen for the solid-phase heat transfer in the unburned part is shown in Fig. 1.

图1药柱坐标系图  Fig. 1 Coordinate system of pillars
Fig． 1 Propellant coordinate
Fig. 1 Propellant coordinate

式中 $a---x,y$$a---x,y$a---x,ya---x, ~ y 方向热扩散系数。各向同性的物质，其 $x,y$$x,y$x,yx, ~ y 方向热扩散系数相等。初始条件：
Where $a---x,y$$a---x,y$a---x,ya---x, ~ y Directional heat diffusion coefficient. Isotropic substances have equal $x,y$$x,y$x,yx, ~ y directional heat diffusion coefficients. Initial conditions:

边界条件：  Boundary conditions:

式中：$\delta$$\delta$delta\delta－药柱 y 方向厚度；$L-$$L-$L-L- 药柱 x 方向长度；$\sigma (t)$$\sigma (t)$sigma(t)\sigma(t)－时间 t 秒时，已燃药柱表面的轴向长度，即火焰位置；$T_g-$$T_g-$T_(g)-T_{g}- 燃气流温度；$h(x,t)$$h(x,t)$h(x,t)h(x, t)－传热系数，是 $x,t$$x,t$x,tx, t 的函数。
Where: $\delta$$\delta$delta\delta - thickness of the column in the y-direction; $L-$$L-$L-L- length of the column in the x-direction; $\sigma (t)$$\sigma (t)$sigma(t)\sigma(t) - axial length of the surface of the ignited column, i.e., the position of the flame, at time t seconds; $T_g-$$T_g-$T_(g)-T_{g}- gas stream temperature; $h(x,t)$$h(x,t)$h(x,t)h(x, t) - heat transfer coefficient, as a function of $x,t$$x,t$x,tx, t ; and -heat transfer coefficient as a function of $x,t$$x,t$x,tx, t .

本文在确定实际传热系数时，不考虑采热粒子的热辐射作用以及可能撞击未燃表面的情况，采用反映实际传热效果的半经验公式（6），即：
In this paper, in determining the actual heat transfer coefficient, the semi-empirical equation (6) reflecting the actual heat transfer effect is used without considering the thermal radiation effect of the heat harvesting particles and the possibility of impacting the unburned surface, i.e:

式中：$a,b,c---$$a,b,c---$a,b,c---a, b, c--- 常数 $(b<1)$$(b<1)$(b < 1)(b<1) 。 $a$$a$aa 是不等于 1 的常数，反映出辐射传热与粒子撞击表面对药柱表面的热传递的影响，可作为调整参数。
Where $a,b,c---$$a,b,c---$a,b,c---a, b, c--- is the constant $(b<1)$$(b<1)$(b < 1)(b<1) . $a$$a$aa is a constant not equal to 1, reflecting the effect of radiative heat transfer and heat transfer from the particle impact surface to the surface of the pillars, and can be used as a tuning parameter.

如果知道公式（6）中的气流速度 $u$$u$uu ，则可以通过数值方法计算公式（1），并得出 $T(x,y,t)$$T(x,y,t)$T(x,y,t)T(x, y, t)的结果，通过点火判断准则确定药柱是否点燃，若达到点火温度则有燃气加入燃烧室。
If the air velocity $u$$u$uu in equation (6) is known, equation (1) can be calculated numerically and the result of $T(x,y,t)$$T(x,y,t)$T(x,y,t)T(x, y, t) can be obtained, and the ignition judgment criterion can be used to determine whether or not the pill column is ignited, and if it reaches the ignition temperature, then gas is added to the combustion chamber.

在固体发动机点火瞬态过程中，加入燃烧室装药通道的燃气流质量有二个来源：一个是点火器提供的点火燃气质量；另一个是主装药燃烧所提供的燃气质量。未燃的装药表面不提供燃气质量，采用简化的分析方法，见图 2，根据质量守恒方程可导出气流速度的数学表达式，假设压力，温度仅随时间变化而不随空间位置变化。
In the solid engine ignition transient process, the gas flow mass added to the combustion chamber charge channel has two sources: one is the ignition gas mass provided by the igniter; the other is the gas mass provided by the main charge combustion. The unburned charge surface does not provide gas mass. Using a simplified analytical method, see Fig. 2, a mathematical expression for the gas flow velocity can be derived from the mass conservation equation, assuming that the pressure and temperature vary only with time and not with spatial position.

图2发动机模型  Fig. 2 Engine model
Fig． 2 Model of motor
Fig. 2 Model of motor
图2中 x 处的质量守恒方程写为：  The equation for conservation of mass at x in Fig. 2 is written as:

式中：${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} —点火器气体质量生成速率；${\dot{m}}_g$${\dot{m}}_g$m^(˙)_(g)\dot{m}_{g} —点燃的推进剂的气体质量生成速率；${\dot{m}}_x$${\dot{m}}_x$m^(˙)_(x)\dot{m}_{x} － x 截面流出的气体质量速率；${\dot{m}}_c$${\dot{m}}_c$m^(˙)_(c)\dot{m}_{c} —头部距 x 截面容积内的气体质量生成速率。
Where: ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} - igniter gas mass production rate; ${\dot{m}}_g$${\dot{m}}_g$m^(˙)_(g)\dot{m}_{g} - gas mass production rate of ignited propellant; ${\dot{m}}_x$${\dot{m}}_x$m^(˙)_(x)\dot{m}_{x} - gas mass rate of x-section outflow; ${\dot{m}}_c$${\dot{m}}_c$m^(˙)_(c)\dot{m}_{c} ${\dot{m}}_c$${\dot{m}}_c$m^(˙)_(c)\dot{m}_{c} - the rate of gas mass production in the volume of the head from the x-section.

点燃推进剂的气体生成率 ${\dot{m}}_g$${\dot{m}}_g$m^(˙)_(g)\dot{m}_{g} 为：  The gas generation rate for ignition of propellant ${\dot{m}}_g$${\dot{m}}_g$m^(˙)_(g)\dot{m}_{g} is:

式中：${\rho }_P$${\rho }_P$rho_(P)\rho_{P} —推进剂密度；$A_b$$A_b$A_(b)A_{b} —燃面面积；$S$$S$SS —燃烧周长；$a$$a$aa —燃速系数；$n$$n$nn 一压力指数。
Where: ${\rho }_P$${\rho }_P$rho_(P)\rho_{P} - propellant density; $A_b$$A_b$A_(b)A_{b} - burning surface area; $S$$S$SS - combustion perimeter; $a$$a$aa - burning velocity coefficient; $n$$n$nn a pressure index.
x 截面流出的气体质量速率为：  The rate of gas mass flowing out of the x-section is:

式中：$\rho$$\rho$rho\rho —推进剂密度；$A$$A$AA —通道截面面积；$u$$u$uu —流速；
Where: $\rho$$\rho$rho\rho - propellant density; $A$$A$AA - channel cross-sectional area; $u$$u$uu - flow velocity;
头部距 x 截面容积内的气体质量生成速率为：  The rate of gas mass generation in the head distance x cross-sectional volume is:

根据理想气体状态方程：  According to the ideal gas equation of state:

将式（8）－－－式（11）代入式（7）得：  Substituting Eq. (8) - Eq. (11) into Eq. (7) gives:

移项得：  Shift the term to get:

从该式中可以看出，流速 $u$$u$uu 是 $x,t$$x,t$x,tx, t 的函数。另外根据通道截面面积不变的假设，可得：
From this equation it can be seen that the flow rate $u$$u$uu is a function of $x,t$$x,t$x,tx, t . Also based on the assumption that the cross sectional area of the channel is constant:

在火焰传播期间，在 $0\le \sigma \le x$$0\le \sigma \le x$0 <= sigma <= x0 \leq \sigma \leq x 范围内，$A_b$$A_b$A_(b)A_{b} 随 $x$$x$xx 线性变化；在 $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L 范围内，$A_b$$A_b$A_(b)A_{b} 是常数。而在 $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L 范围内的气流速度直接影响火焰传播速度，因此只对 $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L 范围内的气流速度进行分析。
During flame propagation, $A_b$$A_b$A_(b)A_{b} varies linearly with $x$$x$xx in the $0\le \sigma \le x$$0\le \sigma \le x$0 <= sigma <= x0 \leq \sigma \leq x range, and $A_b$$A_b$A_(b)A_{b} is constant in the $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L range. The air velocity in the $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L range directly affects the flame propagation velocity, so only the air velocity in the $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L range is analyzed.

在 $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L 范围内，$A_b(x)=A_b(\sigma ),V(x)=Ax$$A_b(x)=A_b(\sigma ),V(x)=Ax$A_(b)(x)=A_(b)(sigma),V(x)=AxA_{b}(x)=A_{b}(\sigma), V(x)=A x ，代入到（12）式得：
In the range $x\le \sigma \le L$$x\le \sigma \le L$x <= sigma <= Lx \leq \sigma \leq L , $A_b(x)=A_b(\sigma ),V(x)=Ax$$A_b(x)=A_b(\sigma ),V(x)=Ax$A_(b)(x)=A_(b)(sigma),V(x)=AxA_{b}(x)=A_{b}(\sigma), V(x)=A x , substituting into equation (12) yields:

式（14）为燃烧室通道内的气流速度，由于只能通过数值计算求解 $T(x,y,t)$$T(x,y,t)$T(x,y,t)T(x, y, t) ，在此可以通过对流换热系数的变化规律分析火焰锋传播速度变化规律。
Type (14) for the combustion chamber channel air velocity, because only by numerical calculation solution $T(x,y,t)$$T(x,y,t)$T(x,y,t)T(x, y, t) , here can be through the change rule of convection heat transfer coefficient to analyze the change rule of flame front propagation speed.

将式（14）代入反映实际传热效果的半经验公式（6）中可得：
This can be obtained by substituting Eq. (14) into the semi-empirical Eq. (6) which reflects the actual heat transfer effect:

对于距离燃烧室头部为 $x$$x$xx 的某一截面，该位置的对流换热系数越高，则被点燃所需时间越短，即火焰锋传播速度越快。在压强仅随时间变化而不随空间位置变化的假设下，对流换热系数主要受时间 $t$$t$tt 和点火器气体质量生成速率 ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} 的影响，也可以说火焰锋通过该截面的速度主要受时间 $t$$t$tt 和点火器气体质量生成速率 ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} 的影响。
For a section $x$$x$xx from the head of the combustion chamber, the higher the convective heat transfer coefficient at that location, the shorter the time required to ignite, i.e., the faster the flame front propagates. Under the assumption that the pressure varies only with time and not with spatial position, the convective heat transfer coefficient is mainly affected by time $t$$t$tt and the igniter gas mass generation rate ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} , and it can also be said that the speed of the flame front passing through the cross-section is mainly affected by time $t$$t$tt and the igniter gas mass generation rate ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} .

1）时间 $t$$t$tt 对火焰传播速率的影响
1) Effect of time $t$$t$tt on flame propagation rate
通过式（15）可以分析，随着 $t$$t$tt 的增大，燃面面积 $A_b(\sigma )$$A_b(\sigma )$A_(b)(sigma)A_{b}(\sigma) 增大，燃烧室内的压强 $P$$P$PP 相应的增大，由于压力指数 $n<1$$n<1$n < 1n<1 ，故 $P^{1-n}<P$$P^{1-n}<P$P^(1-n) < PP^{1-n}<P ，因此 $\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$$\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$(arho_(p)RT)/(MAP^(1-n))A_(b)(sigma)-(x)/(P)(dp)/(dt)\frac{a \rho_{p} R T}{M A P^{1-n}} A_{b}(\sigma)-\frac{x}{P} \frac{d p}{d t} 随着 $t$$t$tt 的增大而增大，即 $x$$x$xx 截面的传热系数 $h(x,t)$$h(x,t)$h(x,t)h(x, t) 随着 $t$$t$tt 的增大而增大，而传热系数的增大直接导致了推进剂药条达到着火温度时间的缩短，故火焰传播速率随着时间的增大而增大。
It can be analyzed through equation (15) that with the increase of $t$$t$tt , the area of combustion surface $A_b(\sigma )$$A_b(\sigma )$A_(b)(sigma)A_{b}(\sigma) increases, and the pressure inside the combustion chamber $P$$P$PP increases accordingly, and because of the pressure exponent $n<1$$n<1$n < 1n<1 , it is $P^{1-n}<P$$P^{1-n}<P$P^(1-n) < PP^{1-n}<P so that the $\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$$\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$(arho_(p)RT)/(MAP^(1-n))A_(b)(sigma)-(x)/(P)(dp)/(dt)\frac{a \rho_{p} R T}{M A P^{1-n}} A_{b}(\sigma)-\frac{x}{P} \frac{d p}{d t} increases with the increase of $t$$t$tt , i.e., the heat transfer coefficient $x$$x$xx of the > cross section increases, and the increase of heat transfer coefficient directly leads to the increase of time for the propellant strip to reach the ignition temperature. > The heat transfer coefficient of the cross-section $h(x,t)$$h(x,t)$h(x,t)h(x, t) increases with the increase of $t$$t$tt , and the increase of the heat transfer coefficient directly leads to the shortening of the time for the propellant strips to reach the ignition temperature, so the flame propagation rate increases with the increase of time.

2）点火器气体质量生成速率 ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} 对火焰传播速率影响
2) Igniter gas mass generation rate ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} on flame propagation rate
通过式（15）显而易见，当 ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} 增大时，燃烧室内压强 $P$$P$PP 相应的增大，由于压力指数 $n<1$$n<1$n < 1n<1 ，故 $P^{1-n}<P$$P^{1-n}<P$P^(1-n) < PP^{1-n}<P ，因此 $\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$$\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$(arho_(p)RT)/(MAP^(1-n))A_(b)(sigma)-(x)/(P)(dp)/(dt)\frac{a \rho_{p} R T}{M A P^{1-n}} A_{b}(\sigma)-\frac{x}{P} \frac{d p}{d t} 增大，传热系数 $h(x,t)$$h(x,t)$h(x,t)h(x, t) 相应增大，即同一时刻 $t$$t$tt同一截面 $x$$x$xx 火焰传播速率增大。
Through equation (15), it is obvious that when ${\dot{m}}_i$${\dot{m}}_i$m^(˙)_(i)\dot{m}_{i} increases, the pressure inside the combustion chamber $P$$P$PP increases accordingly, and since the pressure exponent $n<1$$n<1$n < 1n<1 is $P^{1-n}<P$$P^{1-n}<P$P^(1-n) < PP^{1-n}<P , the heat transfer coefficient $h(x,t)$$h(x,t)$h(x,t)h(x, t) increases because of the increase in $\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$$\frac{a{\rho }_{p}RT}{MA{P}^{1-n}}{A}_b(\sigma )-\frac{x}{P}\frac{dp}{dt}$(arho_(p)RT)/(MAP^(1-n))A_(b)(sigma)-(x)/(P)(dp)/(dt)\frac{a \rho_{p} R T}{M A P^{1-n}} A_{b}(\sigma)-\frac{x}{P} \frac{d p}{d t} , i.e., the flame propagation rate increases in the same cross section at the same moment $t$$t$tt . b7> The rate of flame propagation increases.