CN102980970A - Method for obtaining propelling agent combustion speed by utilizing constant-capacity combustor - Google Patents

Abstract

The invention relates to a method for obtaining a propelling agent combustion speed by utilizing a constant-capacity combustor. The method is technically characterized by comprising the following steps of: calculating a gas mol number NPt of a propelling agent testing sample under different pressures and calculating a gas mol number Nit of ignition powder under the different pressures by utilizing a Bricklin method; testing a propelling agent gas temperature-pressure (Tpt-Pt) relation curve by utilizing a method for testing a relation between an actual temperature and time in a combustion process of a constant-capacity combustor method; calculating gas temperatures TPt under the different pressures Pt according to the relation curve; and calculating the mass Wpt of the propelling agent which is combusted at a t moment, the volume Vet of the propelling agent and the combustion speed rt of the propelling agent under the pressures Pt. The method has the beneficial effects that a P-t curve of the propelling agent testing sample in a constant-capacity container is tested through a dynamic pressure collection system; and a combustion speed expression formula is deduced according to a combustion process dynamic combustion model, and the propelling agent combustion speeds under the different pressures are obtained through data processing.

Description

Method for obtaining burning rate of propellant by using constant volume combustor

Technical Field

The invention relates to a method for obtaining the burning rate of a propellant by using a constant volume burner, which can be used for efficiently measuring the burning rate of the propellant in a wide range under high pressure.

Background

The current methods for testing the burning rate of the solid propellant comprise the following steps: a target line method (GJB 770B-2005-706.1), an acoustic emission method (GJB 770B-2005-706.2), and a closed exploder method. The three methods have high test precision and are commonly used methods for testing the burning rate of the propellant, but the methods are all used for testing the average burning rate of the solid propellant under the constant pressure, and the burning rate of the propellant under one pressure point can be tested only by one test, so that the testing of the burning rate of the propellant with a limited point is difficult to truly reflect the burning rate characteristic of the propellant in a wider pressure range when the three methods are used for testing.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides a method for obtaining the burning rate of the propellant by using a constant volume combustor, the burning rate of the propellant at each pressure point is calculated according to a pressure-time curve obtained by testing and related parameters of a propellant test sample, and a propellant burning rate formula of each pressure section can be fitted, so that the burning rate of the propellant in a wide range under high pressure can be efficiently measured.

Technical scheme

A method for obtaining the burning rate of a propellant by using a constant volume burner is characterized by comprising the following steps:

step 1: method for calculating gas mole number N of propellant test sample under different pressures by utilizing Blacklin method_PtAnd calculating the gas mole number N of the ignition charge under different pressure intensities_it；

Step 2: method for measuring relationship between actual temperature and pressure in combustion process by using constant volume burner method to measure temperature-pressure (T) of propellant gas_pt-P_t) A relation curve, according to which different pressures P are calculated_tTime-lapse gas temperature T_Pt；

And step 3: calculating the mass W of the propellant burnt at the moment t_pt：

$W_{\mathrm{pt}}=\frac{(W_i{N}_{\mathrm{it}}+\frac{W_a}{M_a}){\mathrm{RT}}_{\mathrm{pt}}-P_t(V_0-\frac{W_{p0}}{{\mathrm{\ρ}}_p}-W_i{\mathrm{\α}}_i-V_{\mathrm{st}})}{\frac{P_t}{{\mathrm{\ρ}}_p}-P_t{\mathrm{\α}}_P-{\mathrm{RT}}_{\mathrm{pt}}{N}_{\mathrm{pt}}}$

Wherein: r is a universal gas constant; w_iThe ignition charge quality; w_aIs the mass of air in the burner; m_aRelative molecular mass of air; v₀Is the initial free volume of the burner; w_p0The initial mass of the propellant sample; a is_i、a_pRespectively the residual volumes of ignition powder and propellant; v_stA volume of condensed phase combustion products of the propellant consumed for combustion;

and 4, step 4: calculating the volume V of the propellant burnt at the moment t_et：

And 5: calculating the thickness e of propellant burning meat at the time t_t. Assuming that the propellant test sample has n pieces with respective radii R_iHeight is respectively H_iCalculating e by iterative method_t：

$-2n\·e_t^3+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({4R}_i+H_i)\·e_t^2-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({2R}_i^2+{2R}_i{H}_i)\·e_t+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(R_i^2\·H_i)-\frac{V_{P0}-V_{\mathrm{et}}}{\mathrm{\π}}=0;$

Step 6: calculating the pressure at the time t as P_tBurning rate r of propellant_t：

The method for measuring the relation between the actual temperature and the pressure in the combustion process by using the constant volume burner method comprises the following steps: dividing a main test sample into equal parts according to the mass n, designing a corresponding test simulation auxiliary sample aiming at each mass equal part, wherein the corresponding equal parts of the auxiliary sample and the main sample start combustion and end combustion to be the same; the method comprises the following specific steps:

step a: dividing a test main sample into equal parts according to the mass n, wherein the number of the test main sample is 1,2 and 3 … n from outside to inside; n is a radical of₁A layer equally divided by reference numeral 1; n is a radical of₂One layer composed of the reference numerals 1 and 2; n is a radical of₃One layer composed of the reference numerals 1,2 and 3; by analogy, N_nA layer consisting of the reference numerals 1,2, 3 … n;

step b: for any layer N of the test master sample_iI ═ 1,2, … n, the corresponding test simulation subsamples were designed: the mass of the auxiliary sample is equal to N_iThe mass is divided equally, and the thickness of an auxiliary sample is N_iEqually dividing the thickness by 2 times, and making the initial combustion surface of the auxiliary sample equal to N_iEqually dividing the initial combustion surface;

step c: carrying out constant volume burner test on each auxiliary sample, and measuring the maximum pressure P after the combustion of each auxiliary sample is finished_iCalculating to obtain the gas temperature T after sintering of each auxiliary sample_ptThe temperature is equal to the gas temperature of the main sample after the corresponding partial combustion sintering;

step d: the pressure P of each auxiliary sample_iAnd corresponding temperature T_ptFitting polynomial using least squares $T_{\mathrm{pt}}=a+b(P_{\mathrm{tn}}-\stackrel{\‾}{P})+c{(P_{\mathrm{tn}}-\stackrel{\‾}{P})}^2+d{(P_{\mathrm{tn}}-\stackrel{\‾}{P})}^3,$ Wherein,

the average value of each pressure point is.

Said different pressure P_tTime-lapse gas temperature T_PtIs obtained by adopting a Blackberlin method.

Calculating the burning rate r of the propellant for each pressure point P, and fitting a burning rate formula r ═ a.P for the selected pressure section by using a least square methodⁿ。

Advantageous effects

The invention provides a method for obtaining the burning rate of a propellant by using a constant volume burner, which is a method for indirectly measuring the burning rate of a solid propellant by using a constant volume burner method.

Drawings

FIG. 1: burning rate-pressure curve of propellant

Detailed Description

The invention will now be further described with reference to the accompanying drawings in which:

testing the burning rate characteristic of a certain solid propellant under 15 MPa-60 MPa.

The test specimens are two cylinders with a diameter D =20.0mm and a height H =12.0mm and a density of 1.734g/cm³。

(1) Constructing a data processing basic equation of a constant volume combustor method

Propellant test specimens of known size and density were burned in a volumetric burner and the pressure-time (P-t) curve was recorded. According to the gas state equation, P corresponding to any time t on the P-t curve_tAt the moment of burning out the propellant quantity W_ptCan be expressed as the following relation:

$P_t{V}_t=(W_{\mathrm{pt}}+N_{\mathrm{pt}}+W_i{N}_{\mathrm{it}}+\frac{W_a}{M_a}){\mathrm{RT}}_{\mathrm{Pt}}---\left(1\right)$

in the formula: t is_PtIs the actual temperature of the gas in the burner. N is a radical of_PtThe number of moles of fuel gas for combustion of the propellant; n is a radical of_itThe number of moles of the ignition powder combustion gas; r is a universal gas constant; w_iThe ignition charge quality; w_aIs the mass of air in the burner; m_aRelative molecular mass of air; v_tIs the free volume in the burner at time t.

the free volume in the burner at time t is calculated as follows:

$V_t=V_0-\frac{W_{p0}}{{\mathrm{\ρ}}_p}+\frac{W_{\mathrm{pt}}}{{\mathrm{\ρ}}_p}-(W_i{\mathrm{\α}}_i+W_{\mathrm{pt}}{\mathrm{\α}}_p)-V_{\mathrm{st}}---\left(2\right)$

in the formula, V₀For initial free volume of burnerAccumulating; w_p0The initial mass of the propellant sample; alpha is alpha_i、α_pRespectively the residual volumes of ignition powder and propellant; v_stVolume of propellant condensed phase combustion products consumed for combustion. Substituting the formula (2) into the formula (1) to obtain the mass of the propellant burnt at the moment t:

$W_{\mathrm{pt}}=\frac{(W_i{N}_{\mathrm{it}}+\frac{W_a}{M_a}){\mathrm{RT}}_{\mathrm{pt}}-P_t(V_0-\frac{W_{p0}}{{\mathrm{\ρ}}_p}-W_i{\mathrm{\α}}_i-V_{\mathrm{st}})}{\frac{P_t}{{\mathrm{\ρ}}_p}-P_t{\mathrm{\α}}_P-{\mathrm{RT}}_{\mathrm{pt}}{N}_{\mathrm{pt}}}---\left(3\right)$

for equation (3), V₀、ρ_p、M_a、W_p0、W_i、α_i、α_pAll can be determined in advance; w_aMay be determined based on combustor volume; p_tThe pressure value obtained for the experiment; v_stCan be composed of N_ptCalculating to obtain; therefore, only has T_Pt、N_Pt、N_itThree parameters are unknown.

(2) Calculating the gas mole number of the propellant test sample and the ignition powder under different pressures

Method for calculating gas mole number N of propellant test sample under different pressures by utilizing Blacklin method_PtAnd synthesizing N by least square fitting_pt-a P-curve.

Calculating the gas mole number N of the ignition charge under different pressures by utilizing a Blacklin method_itAnd synthesizing N by least square fitting_it-a P-curve.

When given P_tThen, N can be calculated according to the fitting curve_Pt、N_itTwo parameters.

Propellant powder is selected as the ignition powder, namely the ignition powder is the same as the propellant, and the number of moles of the propellant under different pressures can be calculated. The results of the thermal calculations are shown in Table 2

TABLE 2 gas mole number as a function of pressure

Pressure intensity/MPa	Molar number/mol/Kg of fuel gas
		20	37.92
30	37.88
		40	37.85
50	37.83
		60	37.81
70	37.80
		80	37.78

(3) Measuring the gas temperature-pressure (T) of a test sample by using an experimental simulation method_pt-P_t) Relation curve

Method for measuring relationship between actual temperature and time in combustion process by using constant volume burner method to measure temperature-pressure (T) of propellant gas_pt-P_t) Closing deviceIs a curve.

In order to obtain T in the whole combustion process_PtAnd pressure P_tThe relation between the main samples and the auxiliary samples is that for the main samples with given geometric shapes and geometric sizes subject to instantaneous complete combustion, n-1 auxiliary samples are designed. The geometric dimension between the auxiliary sample and the main sample meets the following requirements: the initial burning surfaces of all samples are equal; secondly, if the mother sample is burnt, e is pushed towards the interior of the sample according to the rule of parallel layers_tWhen the distance (thickness) is over, the primary sample is burnt out, and the first auxiliary sample is pushed towards the interior of the sample according to the rule of the parallel layer e₁When the distance is within the range of (thickness), the sample is burnt out, and the first auxiliary sample mass and the mother sample are burnt out₁Equal mass at distance (thickness); the second auxiliary sample pushes the sample inwards according to the rule of parallel layers₂When the distance (thickness) is over, the second auxiliary sample is burnt out₂Equal mass at distance (thickness), … … up to the (n-1) th subpel moving in parallel layers towards the interior of the sample e_(n-1)And (3) burning off the sample at the (thickness) distance, wherein the mass of the (n-1) th auxiliary sample is equal to the mass of the main sample at the (n-1) e (thickness) burning-off distance.

Burning the first sub-sample in a constant volume burner, recording the P-t curve of the burning process, and obtaining a P of the main sample according to the mass of the sample_t1Corresponding to T_t1. The same experiment and treatment are carried out on the second auxiliary sample to the nth auxiliary sample in sequence (the nth sample is the mother sample), and n different P of the mother sample can be obtained in total_tnT corresponding thereto_tn. T of a sample with given geometric shape and geometric dimension when the sample is burnt in a constant volume burner is obtained through polynomial fitting_PtAnd pressure P_tThe relationship between them.

The pressure P of each auxiliary sample_tAnd corresponding temperature T_ptFitting polynomial using least squares $T_{\mathrm{pt}}=a+b(P_{\mathrm{tn}}-\stackrel{\‾}{P})+c{(P_{\mathrm{tn}}-\stackrel{\‾}{P})}^2+d{(P_{\mathrm{tn}}-\stackrel{\‾}{P})}^3,$ Wherein,

the average value of each pressure point is.

When given P_tThen, T can be calculated according to the fitting curve_ptThe results are shown in Table 1.

TABLE 1 variation of gas temperature with pressure

Pressure intensity/MPa	Temperature of gas/K
		31.389516	3183.779765
40.272030	3335.579033
		58.131432	3408.325390
75.104404	3466.800819
		96.805232	3543.803698

(4) Calculating time t (corresponding pressure P)_t) Burning rate of propellant

The mass W of the propellant burnt at time t is determined by the formula (3)_ptThe corresponding propellant combustion volume V can then be determined_et，

$V_{\mathrm{et}}=\frac{W_{\mathrm{pt}}}{{\mathrm{\ρ}}_P}---\left(4\right)$

According to V_etCan determine the thickness e of the burned meat_t. Assuming that the propellant test sample has n pieces with respective radii R_iHeight is respectively H_iThen e_tThe expression of (a) is as follows:

$-2n\·e_t^3+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({4R}_i+H_i)\·e_t^2-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({2R}_i^2+{2R}_i{H}_i)\·e_t+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(R_i^2\·H_i)-\frac{V_{P0}-V_{\mathrm{et}}}{\mathrm{\π}}=0---\left(5\right)$

according to e_tFind the time t (pressure P)_t) The burning speed of the propellant is as follows:

$r_t=\frac{{\mathrm{de}}_t}{\mathrm{dt}}---\left(6\right)$

(5) method for fitting combustion speed formula of propellant in certain pressure section by using least square method

For each pressure point P_tCalculating the burning rate r of the propellant_tThe burning rate-pressure (r) of the propellant can be obtained_t-P_t) Curve line. For any one pressure section, fitting a combustion rate formula r ═ a · P by using a least square methodⁿ。

The propellant combustion rate results at different pressures are shown in Table 3 and FIG. 1

TABLE 3 propellant burning Rate characteristics

Pressure intensity range (MPa)	Burning rate formula (cm/s)
		15～25	4.9656·P0.3557
25～40	4.4966·P 0.3877
		40～60	2.2159·P 0.5786
60～73	1.1353·P0.7419

The combustion speed of the propellant at each pressure point under 15-60 MPa can be measured by one-time test of a constant volume combustor method, and the test range of the combustion speed is 6-300 mm/s. The constant volume burner method has the advantages of simple and reliable equipment, no pipeline valve, convenient use and maintenance, good safety and the like, and is an ideal method for testing the combustion rate of the propellant under high pressure.

Claims (4)

1. A method for obtaining the burning rate of a propellant by using a constant volume burner is characterized by comprising the following steps:

step 1: method for calculating gas mole number N of propellant test sample under different pressures by utilizing Blacklin method_PtAnd calculating the gas mole number N of the ignition charge under different pressure intensities_it；

Step 2: method for measuring relationship between actual temperature and pressure in combustion process by using constant volume burner method to measure temperature-pressure (T) of propellant gas_pt-P_t) A relation curve according to which the difference is calculatedPressure P_tTime-lapse gas temperature T_Pt；

And step 3: calculating the mass W of the propellant burnt at the moment t_pt：

Wherein: r is a universal gas constant; w_iThe ignition charge quality; w_aIs the mass of air in the burner; m_aRelative molecular mass of air; v₀Is the initial free volume of the burner; w_p0The initial mass of the propellant sample; alpha is alpha_i、α_pRespectively the residual volumes of ignition powder and propellant; v_stA volume of condensed phase combustion products of the propellant consumed for combustion;

and 4, step 4: calculating the volume V of the propellant burnt at the moment t_et：

And 5: calculating the thickness e of propellant burning meat at the time t_t. Assuming that the propellant test sample has n pieces with respective radii R_iHeight is respectively H_iCalculating e by iterative method_t：

Step 6: calculating the pressure at the time t as P_tBurning rate r of propellant_t：

。

2. The method for obtaining the burning rate of the propellant by using the constant volume burner as claimed in claim 1, wherein the method comprises the following steps: the method for measuring the relation between the actual temperature and the pressure in the combustion process by using the constant volume burner method comprises the following steps: dividing a main test sample into equal parts according to the mass n, designing a corresponding test simulation auxiliary sample aiming at each mass equal part, wherein the corresponding equal parts of the auxiliary sample and the main sample start combustion and end combustion to be the same; the method comprises the following specific steps:

step a: dividing a test main sample into equal parts according to the mass n, wherein the number of the test main sample is 1,2 and 3 … n from outside to inside; n is a radical of₁A layer equally divided by reference numeral 1; n is a radical of₂One layer composed of the reference numerals 1 and 2; n is a radical of₃One layer composed of the reference numerals 1,2 and 3; by analogy, N_nA layer consisting of the reference numerals 1,2, 3 … n;

step b: for any layer N of the test master sample_iI ═ 1,2, … n, the corresponding test simulation subsamples were designed: the mass of the auxiliary sample is equal to N_iThe mass is divided equally, and the thickness of an auxiliary sample is N_iEqually dividing the thickness by 2 times, and making the initial combustion surface of the auxiliary sample equal to N_iEqually dividing the initial combustion surface;

step c: carrying out constant volume burner test on each auxiliary sample, and measuring the maximum pressure P after the combustion of each auxiliary sample is finished_iCalculating to obtain the gas temperature T after sintering of each auxiliary sample_ptThe temperature is equal to the gas temperature of the main sample after the corresponding partial combustion sintering;

step d: the pressure P of each auxiliary sample_iAnd corresponding temperature T_ptFitting polynomial using least squaresWherein,

the average value of each pressure point is.

3. The method for obtaining the burning rate of the propellant by using the constant volume burner as claimed in claim 1, wherein the method comprises the following steps: said different pressure P_tTime-lapse gas temperature T_PtIs obtained by adopting a Blackberlin method.

4. The method for obtaining the burning rate of the propellant by using the constant volume burner as claimed in claim 1 or 2, wherein: to pairCalculating the burning rate r of the propellant at each pressure point P, and fitting a burning rate formula r ═ a.P for the selected pressure section by using a least square methodⁿ。

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