RU2494394C2 - Method of determining unit pulse of solid fuel - Google Patents

Abstract

FIELD: chemistry.

SUBSTANCE: method involves measuring the reaction force of gasification products when burning a sample of solid fuel, armoured on the side surface, wherein the reaction force and time for complete combustion of the sample of solid fuel placed in a constant volume explosion apparatus are measured, at pressure in the range of (0.5-1.5)MPa, generated by an inert gas, e.g. nitrogen or argon, wherein the volume of the explosion apparatus and the mass of the sample are in a given ratio, and the value of the unit pulse of is determined using a calculation formula.

EFFECT: enabling determination of a unit pulse using small fuel samples in laboratory conditions without using large stand equipment and explosion-proof boxes.

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Description

The invention relates to the field of rocket technology, in particular to methods for measuring the characteristics of solid fuels for rocket engines. The invention can be used to determine a single (specific) impulse of new solid fuel compositions.

A single impulse J ₁ is the main energy characteristic of the fuel. By definition, a single impulse is the ratio of engine thrust to second mass flow of combustion products. The value of a single impulse is determined by the dependence [1]:

$$J_{\mathrm{one}}=u_a+\frac{S_a\left(p_a-p_n\right)}{G},\left(\mathrm{one}\right)$$

where u _a , p _a is the flow rate and pressure of the combustion products in the output section of the nozzle with an area of S _a ;

p _n - environmental pressure (external pressure);

G - mass second consumption of combustion products.

For the "calculated" nozzle (p _a = p _n ) from (1) it follows

$$J_{\mathrm{one}}=u_a=\sqrt{\frac{2kR{T}_{\mathrm{to}}}{k-\mathrm{one}}{\left(\mathrm{one}-\frac{p_a}{p_{\mathrm{to}}}\right)}^{\frac{k-\mathrm{one}}{k}},\left(2\right)}$$

where R = c _p -c _υ , k = c _p / c _υ is the gas constant and the adiabatic exponent of the combustion products;

c _p , c _υ - isobaric and isochoric heat capacity of the combustion products;

p _to - pressure in the combustion chamber of a rocket engine;

T _to - the temperature of the combustion products in the engine chamber (braking temperature) equal to the combustion temperature of the fuel (T _to = T _g ).

A known theoretical calculation method for determining the thermodynamic unit impulse using equations (1, 2) and calculation of T _g , c _p , c _υ , R, k according to the method [1] using, for example, the Astra-4 algorithm [2] . The thermodynamic value of J ₁ is understood as the value of a single impulse in the complete absence of losses and the condition for the completion of chemical transformations. To implement this method, it is necessary to know the component composition of solid fuel or its equivalent chemical formula [1], which in some cases are unknown for new solid fuel compositions.

A known method of determining a single impulse based on measuring the thrust diagrams P (t) and pressure p _k (t) in the combustion chamber of a model rocket engine when burning a test fuel sample. The value of J ₁ is the ratio of the total thrust impulse during the time τ of the engine to the mass of fuel consumed during this time [1]:

$$J_{\mathrm{one}}=\frac{{\displaystyle \underset{0}{\overset{\tau }{\int }}P\left(t\right)dt}}{{\displaystyle \underset{0}{\overset{\tau }{\int }}G\left(t\right)dt}},$$

where G (t) is the mass second consumption of combustion products, determined by the measured dependence of p _to (t) from the equation

$$G\left(t\right)=\frac{\phi p_{\mathrm{to}}\left(t\right)S_{\mathrm{to}p}}{\sqrt{R{T}_{\mathrm{to}}}}\sqrt{k}{\left(\frac{2}{k+\mathrm{one}}\right)}^{\frac{k+\mathrm{one}}{2\left(k-\mathrm{one}\right)}},$$

where φ, S _кp - flow coefficient and the critical section area of the nozzle.

There is also a method of measuring a single impulse using a ballistic pendulum, which is an "absolute" device [3-5]. The momentum of the force acting on the pendulum when burning fuel in the engine is proportional to the length of the chord of deviation of the center of mass of the pendulum (counting from the equilibrium position).

To measure a single pulse in [3], a “pulse meter-counter” was proposed, which is an equal-arm beam with small friction rotating around a vertical axis. A model rocket engine is installed at one end of the beam, and an inert load of equivalent mass is at the other. With a known moment of inertia of the system, the magnitude of the reactive force impulse is determined by the measured angular velocity of rotation of the beam.

The closest in technical essence is the method proposed in [6]. This method is based on measuring the reactive force F flowing from the surface of the fuel combustion gasification products. The value of F is associated with the energy characteristics of the fuel (in particular, with its mass burning rate).

The disadvantages of these methods is the need to use model engines with a charge of solid fuel of at least (0.2 ÷ 0.5) kg and special bench equipment located in explosion-proof boxes.

The technical result of the present invention is the development of a method for determining a single momentum of solid fuel in a wide pressure range, based on direct measurement of the complex of its thermodynamic characteristics when laboratory samples of fuel are burned weighing (0.5 ÷ 10) g.

The technical result of the invention is achieved by the fact that a method for determining a single pulse of solid fuel is developed, which includes measuring the reactive strength of gasification products when burning a sample of solid fuel, armored on the side surface, and the time of its complete combustion in a constant volume bomb at a pressure in the range (0.5 ÷ 15) MPa generated by an inert gas, such as nitrogen or argon.

The volume of the bomb V is determined from the ratio

$$V\ge \mathrm{one\; hundred}\frac{R_0{T}_n{m}_m}{M{p}_{\min }},\left(3\right)$$

and the value of a single impulse is determined by the formula

$$J_{\mathrm{one}}=\frac{\tau }{{\rho }_m{h}_m}\sqrt{\frac{F{p}_{\mathrm{to}}}{S_m}\frac{2k}{k-\mathrm{one}}{\left(\mathrm{one}-\frac{p_n}{p_{\mathrm{to}}}\right)}^{\frac{k-\mathrm{one}}{k}}},\left(\mathrm{four}\right)$$

Where

R ₀ = 8.31441 J / (mol · K) is the universal gas constant;

T _n - ambient temperature;

m _m , ρ _m , h _m , S _m - mass, density, height and end surface area of the combustion of the fuel sample;

M is the molecular mass of an inert gas;

p _min is the minimum pressure from the studied range;

τ is the combustion time of the sample;

F is the reactive force of the effluent combustion products;

p _to - pressure in a constant volume bomb.

The obtained positive effect of the invention is achieved by the fact that when burning small-sized samples weighing (0.5 ÷ 10) g in a constant volume bomb at a given pressure p _k , the reactive force of gasification products flowing from the end surface of the burning sample is measured [6, 7]. According to Newton’s third law, this force is

$$F={\rho }_{\mathrm{to}}{u}^2{S}_m,\left(5\right)$$

where ρ _k , u is the density and swelling rate of gasification products.

From the law of conservation of mass follows

$${\rho }_m{u}_m={\rho }_{\mathrm{to}}u,\left(6\right)$$

where u _m is the linear burning rate of the fuel.

From (5) and (6) and the equation of state for an ideal gas

$$p_{\mathrm{to}}={\rho }_{\mathrm{to}}R{T}_g\left(7\right)$$

you can get an expression for reactive force in the form

$$F=\frac{{\left({\rho }_m{u}_m\right)}^2}{p_{\mathrm{to}}}R{T}_g{S}_m,\left(8\right)$$

where R is the gas constant of the combustion products.

From equation (8), it is possible to determine the complex (RT _g ) - the "power of the powder" [1], which is included in the equation for calculating a single impulse (2):

$$R{T}_g=\frac{F{p}_{\mathrm{to}}}{S_m{\left({\rho }_m{u}_m\right)}^2}.\left(9\right)$$

All values included in (9) are directly measured in the experiment (F, p _k , S _m , ρ _m ). The linear burning rate is also determined experimentally from the combustion time τ of the sample of a given height h _m

$$u_m=h_m/\tau .\left(10\right)$$

Substituting (9), (10) into (2), we obtain the formula for determining J ₁ (4).

The value of the adiabatic exponent k is taken from a thermodynamic calculation or its average value is selected for fuels with a similar composition. This value changes only slightly with a wide variation in the initial fuel composition.

The choice of the pressure range p _k = (0.5 ÷ 15) MPa, for which a single impulse of fuel is determined, corresponds to the actual conditions for the use of fuel in engines [1, 3].

The volume of the bomb in which the solid fuel sample is burned is selected from the condition p _k = const. The increase in pressure in the constant volume bomb due to the gas intake from the combustion of the fuel sample should be negligible. Using the equation of state (7) and assuming that the pressure increase does not exceed 1%, we can obtain the ratio for determining the required volume of the bomb (3).

The invention is illustrated by drawings:

Figure 1 - diagram of an experimental setup for determining a single pulse of solid fuel.

Figure 2 - experimental (points) and calculated (solid line) values of a single pulse depending on pressure.

A diagram of the experimental laboratory setup is shown in Fig. 1 A cylindrical sample of the solid fuel 1 being studied, booked along the side surface 2 with a quartz (or carbon) beaker, placed in a constant volume bomb 3. On the basis of 4 bombs 3, a capacitive sensor 5 for measuring reactive forces flowing from the burning end surface of the sample 1 combustion products. The electrical signal from the reactive force sensor 5 through the electronic sensor signal to voltage converter 6 and the analog-to-digital voltage converter to digital code 7 is supplied to the recording computer 8. Before the experiment, the bomb 3 is filled with inert gas (nitrogen) from the battery of cylinders 9 to a predetermined pressure, which is recorded by an exemplary pressure gauge 10. The release of the combustion products of the sample after the experiment is carried out through the valve 11.

Before the experiment, the sample is weighed on an analytical balance with an accuracy of ± 0.01 g and its height h _m and diameter d _m are measured. According to these data, the density of the fuel mouth and the surface area of the surface S _m At a given pressure p _{k, the} sample is ignited using a heated spiral and during its combustion the reactive force F is measured using a sensor 5 and the combustion time of the sample τ according to pressure diagrams p _k (t) measured using a strain gauge pressure sensor type LH-412 (spiral and the pressure sensor in the diagram is not shown).

A single pulse was measured for the model composition of a mixed solid fuel containing 81 wt.% Finely divided ammonium perchlorate, 14 wt.% Fuel-binding agent NTRV, 1.5 wt.% ALEX aluminum nanopowder [7], 1.5 wt.% Fe ₂ O ₃ and 2 wt.% technological additives. We studied fuel samples with a diameter of d _m = 10 mm and a height of h _m = 20 mm, the mass of each sample (without reservation) was 2.5 g, and the density of the fuel was ρ _m = 1.60 g / cm ³ .

The results of determining a single impulse for three values of p _k averaged over five duplicate experiments are presented in Figure 2. Here are the results of thermodynamic calculation of J ₁ using the Astra-4 program (solid line).

The analysis of the obtained data shows that the calculated values of J _{1 are} (10 ÷ 15)% higher than the measured ones. This is apparently due to the fact that the calculated data correspond to completely completed chemical reactions. During the experiment, the response time of gas-phase products in the armor tube is limited, which is closer to the conditions of fuel combustion in the combustion chamber of a rocket engine than in thermodynamic calculations.

Thus, it is experimentally shown that when implementing the proposed method, the achieved positive effect is as follows.

1. The method allows to determine a single momentum of fuels containing new components with unexplored properties. For such compositions, a complete thermodynamic calculation does not provide acceptable accuracy. In addition, when implementing the proposed method, reactions in the gas phase occur during a finite period of time (as opposed to thermodynamic calculation), which corresponds to the residence time of the gaseous products of fuel combustion in the engine.

2. The determination of a single impulse is carried out in laboratory tests using the minimum mass of the fuel sample (0.5 ÷ 10 g), which is especially important when studying the components of the fuel available in a limited amount (new synthesized substances).

3. Unlike the known methods of experimental measurement of J ₁ , this method does not require expensive bulky equipment and special explosion-proof stands for testing model rocket engines weighing (0.2 ÷ 0.5) kg or more.

LITERATURE

1. Sorkin R.E. Gas thermodynamics of solid propellant rocket engines. - M .: Nauka, 1967 .-- 368 p.

2. Sinyarev G.B., Vatolin N.A., Trusov B.G., Miseev G.K. The use of computers for thermodynamic calculations of metallurgical processes. - M .: Nauka, 1982.- 263 p.

3. Zeldovich Ya. B., Rivin M.A., Frank-Kamenetsky D.A. Impulse of reactive power of powder rockets. - M .: Oborongiz, 1963 .-- 191 p.

4. Rogulin V.V., Gergel V.G., Lyakh Yu.A., Oglih V.V. On methods for determining the total impulse of thrust of a solid propellant rocket engine of a special purpose of a pulsed type // Space technology. Missile Weapons: Collection of scientific and technical articles. - Dnepropetrovsk: State Enterprise "Design Bureau" Yuzhnoye ", 2009, Issue 2. - S.80-91.

5. Beskrovnyi IB, Rogulin VV, Mikulyak MV, Lyakh Yu.A., Flaxen V.N. The choice of bench devices for testing pulsed solid propellant rocket motors // Space technology. Missile Weapons: Collection of scientific and technical articles. - Dnepropetrovsk: SE "Design Bureau" South ", 2010. - S.63-70.

6. Simonenko V.N., Zarko V.E. Reactive force of combustion products as a measure of the unsteady burning speed of gunpowder // Combustion and Explosion Physics. 1981. T. 17, No. 3. - S.129-132.

7. Arkhipov V.A., Bondarchuk S.S., Korotkikh A.G., Lerner M.I. The technology of production and dispersed characteristics of aluminum nanopowders // Mountain Journal. Specialist. release. Non-ferrous metals. 2006, No. 4. - S. 58-64.

Claims (1)

A method for determining a single pulse of solid fuel, including measuring the reactive strength of gasification products when burning a sample of solid fuel armored on the side surface, characterized in that the reactive force and time of complete combustion of a sample of solid fuel placed in a constant volume bomb are measured at a pressure in the range ( 0.5 ÷ 15) MPa created by an inert gas, such as nitrogen or argon, and the volume of the bomb and the mass of the sample are in the ratio
$$V\ge \mathrm{one\; hundred}\frac{R_0{T}_n{m}_m}{M{p}_{\min }},$$

and the value of a single impulse is determined by the formula
$$J_{\mathrm{one}}=\frac{\tau }{{\rho }_m{h}_m}\sqrt{\frac{F{p}_{\mathrm{to}}}{S_m}\frac{2k}{k-\mathrm{one}}{\left(\mathrm{one}-\frac{p_n}{p_{\mathrm{to}}}\right)}^{\frac{k-\mathrm{one}}{k}}},$$

where V is the volume of the bomb;
R ₀ = 8.31441 J / (mol · K) is the universal gas constant;
T _n - ambient temperature;
m _m , ρ _m , h _m , S _m - mass, density, height and end surface area of the combustion of the fuel sample;
M is the molecular mass of an inert gas;
p _min is the minimum pressure from the studied range;
J ₁ - a single pulse of solid fuel;
τ is the combustion time of the sample;
F - reactive force of effluent combustion products;
p _to - pressure in a constant volume bomb;
k is the adiabatic exponent of the fuel combustion products;
p _n - external (atmospheric) pressure.

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