Calculation of aerodynamic heating of the rocket in the compartment. Calculation of aerodynamic coefficients of a cruise missile of the Tomahawk type. Main characteristics of RDTT

2. Equation of thrust as a result of the action of all gas-dynamic forces. Full thrust impulse. Specific impulse and specific thrust. Pressure, fuel combustion temperature, energy and mass perfection
3. Thermodynamic calculation of processes in the chamber. Basic thermodynamic characteristics of fuel, the procedure for their determination.
5. Determination of the gas-dynamic parameters of the flow in the nozzle using gas-dynamic functions.
6. Types of charges and their main characteristics. Requirements for charges. Selection of the required combustion surface. Calculation of the charge of the channel-slot form.
8. The reasons for the deviation of the parameters of the RDTT from the nominal value. Determination of the scatter vbx. Pressure and draft regulation.
8.1 Classification of liquids, areas of application, advantages and disadvantages. Characteristics of the camera and the engine. Loss factors. Characteristics: consumable high-rise. Fuel for liquid
9. The main elements of transformation processes. Purpose and types of nozzles. K.S. heads Nozzle arrangement diagrams. Calculation of the ratio of the cross-section of the chamber.
10. Regulation of railway Starting and stopping the engine. The main tasks of regulation.
11. Cooling liquid. The processes of heat exchange and protection of the walls of the combustion chamber. Features of heat transfer. Cooling methods. Cooling calculation.
13. La control system. Types of trajectories. Determination of flight range. Guidance trajectory. La control systems.
14.Main characteristics of RDTT
15.La layout
16. Layout diagrams of missiles; ways of creating governing forces and moments. The principle of breaking the rocket into stages.
17. The main weight and geometric characteristics of the aircraft
18. Basic design schemes of hybrid, turbojet, rocket-ramjet engines, combined rocket-ramjet engines. Basic nodes and elements.
19.Elliptical trajectory. Integral of areas and energies. Shape and main sections of the trajectory. Optimal throwing angle. Estimation of flight range along elliptical and parobalic trajectories.
21. Motion control systems LA, their purpose and general structural diagram. Flight range control.
3. Control of flight range.
3. Control of flight range. According to Bulbovich:
22. Outraged movement la. Linearization of the equations of perturbed motion. Decomposition of the disturbed motion into longitudinal and lateral. Dynamic coefficients.
25. Classification dynam. Loads acting on the la at various stages of its operation. Transport load. Wind load. Acoustic loading. Pressure pulsation in the rdmt chamber.
29. Problems of dynamic analysis of la. The main tasks of dynamic analysis. Methods for solving dynamic problems. Technical solutions at the stage of dynamic analysis.
33. The main features of the 2-phase flow. Specific impulse losses in the nozzle: their classification, physical processes causing them.
37. Appointment of the tail. Balancing dependence. General approach to the choice of feathers in the initial approximation.
44. Basic models of the stress-strain state, used for firmly attached charges of RDTT. Safety margins as the ratio of breaking and design loads. Safety factor.
45. Mathematical formulation of the MEC. The main stages of solving the problem of microelectronics. Writing the basic relations of the theory of elasticity for a finite element in matrix form.
46. Calculation of plates. Basic equations and hypotheses. Derivation of the basic equations of the theory of thin plates in a Cartesian coordinate system.
47 Bending of plates. Differential equation for the elastic surface of the plate. Methods for solving the differential equation of a plate.
48. Geometry of shells of revolution. Kirchhoff-Lyav's hypotheses and geometric relationships. Basic relations of the general theory of shells.
49. Equations of the momentless theory of shells (bto). Elimination of the axisymmetric problem. Spherical and cylindrical shells under the action of internal pressure.
51. Stability of cylindrical shells. Basic equations of stability of cylindrical shells. Stability of cylindrical shells under axial compression and external pressure.
52. The main forces acting on the hull in flight and the nature of their changes. Determination of the axial forces acting on the aircraft body in flight.
53. Calculation of fuel compartments. Calculation of the RDTT body. Calculation of spherical, elliptical and torispherical heads. Features of the calculation of the strength of the structure of the liquid crystal.
54. Design and calculation of engine nozzle blocks.
55. Design and calculation of shells of combustion chambers of RDTT.
56. Design and calculation of controls
57. Design and technological characteristics of connections.
2.Inseparable
58. Design of pressure test benches for engines
59. Reliability la at the stage of development.
60.La reliability at the stage of serial production.
61. The content of operational tests of RDTT during development.
62. Test of RDTT for service safety.
63. Methods of aiming at the target. Zur control systems.
64. Estimated trajectories - remote-controlled, self-guided, with a combined control system.
65. Classification of cruise missiles. Types of cruise missile trajectories. The dive trajectory of a cruise missile.
66. Features of the design, guidance system and design of aircraft missiles. Anti-satellite aircraft missiles
68. Classification of rocket projectiles
69. Methods for carrying out static strength analysis of a firmly attached charge of RDTT using finite element packages.
70. Technique for modal analysis of a solidly attached charge of RDTT using finite element packages.
71. Methods for the harmonic analysis of a firmly attached charge of RDTT using finite element packages.
72. Methods for the dynamic analysis of a firmly attached charge of RDTT using finite element packages.
73. Methods for determining the vat of a firmly bound charge rdmt under the action of temperature using finite element packages.
74. The method of carrying out the temperature-strength analysis of a firmly attached charge of RDTT using finite element packages.
75. Methodology for calculating the stability of a cylindrical shell using finite element packages.
76. General information about pkm. Basic definitions, structure of materials, phases, purpose of binders and fillers in the composition of materials.
78. Forming products from PCM methods of forming: winding, pressing, autoclave molding, molding modes.
79. Physics and mechanics, thermophysical, etc. Properties of carbon, glass, organo, boroplastics, thermoplastic km.
80. Heat-stressed nodes la and dla from pcm. Calculation of temperature fields, analysis of thicknesses with and without ablation, assessment of heat and thermal resistance.
81. Structural features of the material and their consideration in structures, strength analysis.
82. Chemical resistance of PCM in structures la and dla
83. Technical preparation of production.
84. The type of production and its definition.
85.Dot charts and practical curves of distribution (dispersion) of sizes (errors).
86. Classification of bases. Principles of aligning bases when constructing operations. The principle of the constancy of bases.
87. Errors in processing caused by the installation of blanks.
88. Allowances. Maximum and minimum allowances.
89. The concept of manufacturability. Quantification of manufacturability. Qualitative assessment of manufacturability.
90. Basic principles of construction of technological processes.
91 Principles for the selection of fuel and form of charge for a specific design of a rocket motor
92. Comparative analysis of characteristics of ballistic and mixed solid fuels.
93. Features of the design of the end combustion charge.
94. Factors affecting the burning rate of solid fuel
95. The principle of choosing a booking cover for the charge vt.
96. Types of flammable compositions and design principles of ignitors.
97. Technology for the production of charges from composite solid fuels.
98. Technology of manufacturing charges from ballistic solid propellants.
99. Technology of applying armor (from 3 to 8 mm)
100. Technology of fastening charges of solid fuel in the combustion chamber of RDDT
101. Technology of preparation of RDTT bodies before filling them.
102. Technology of production of pyrotechnic igniting compositions.
109. Appointment and content of the terms of reference.
110 Purpose and content of the technical proposal
111. Purpose and content of draft and technical projects
112. Appointment and content of the program and test methods.
113. Purpose and content of the rules for handling.
14.Main characteristics of RDTT
1. Tsiolkovsky's formula
where W is the effective flow rate of combustion products from the nozzle
Q T - charge weight
q k = Q 0 -Q T - dry weight of the rocket
2

... Thrust equation
The thrust is the resultant of all gas-dynamic forces acting on the engine, both due to internal ballistic processes in the combustion chamber and external forces.
Ra = Rn - design thrust mode. In engineering practice, along with the direct calculation of thrust, there is a calculation method:
, where R beats = R / G - specific thrust - the main energy characteristic of solid propellants (thrust referred to the unit of mass flow)
3
... Total impulse:
The specific (unit) impulse of the propulsion system is the ratio I  for the total operating time to the total mass of the fuel.
15.La layout
After that, the mass and overall dimensions of the units, loads and equipment blocks placed inside the hull are determined, the next stage is the layout of the aircraft - the choice of external forms and the mutual arrangement of parts, units and loads placed on the aircraft.
The aerodynamic (external) layout of the aircraft is characterized by the relative position of the hull and bearing surfaces that create lift (wings, rudders, stabilizers and destabilizers). Main goal: determination of aerodynamic loads.
Volumetric (internal) layout - placement of all units on board the aircraft (propulsion system, target cargo, control system equipment, onboard energy sources). Conditions must be created for the reliable and efficient operation of all cargo and equipment placed on the aircraft; technical convenience. Providing a high density of the layout, which helps to reduce the volume and weight of the aircraft. The required position of the aircraft center of mass must be ensured.
The structural layout is characterized by the structural-power scheme (CSC) and technological solutions, the choice of which is due to the volumetric layout, aerodynamic design and external loads acting on the aircraft. The structural layout affects: the strength and rigidity of the aircraft structure; the adopted design and technological decisions and methods of manufacturing, testing, assembly and transportation of aircraft; dividing the aircraft structure into units, compartments and assemblies; interchangeability of individual structural elements; the shape of the aircraft and overall restrictions; the choice of the location of the butt joints.
The layout of the propulsion systems: the fuel is a consumable mass, therefore it should be placed near the CM. The requirements for the placement of engines largely depend on their type and the purpose of the aircraft. The chambers of the main rocket engines are usually located in the tail section of the hull. Loads must be transferred to the load-bearing set without deformation of the skin. When installing multi-chamber liquid-propellant rocket engines (multi-nozzle solid propellants), it is necessary to take into account the occurrence of reverse convective heat fluxes - hot gases from the nozzle - which cause additional heating of the tail section of the LA. the most convenient, however, it creates the greatest spread of the center of mass during fuel burnout. The placement of the solid propellant rocket in the middle part of the aircraft body is most favorable from the point of view of aircraft alignment, however, it leads to the need to use side nozzles in solid propellants, which create additional losses in thrust due to the inclination of the nozzles to the aircraft axis, or install a gas duct between the solid propellant rocket chamber and the axial nozzle, the presence of which complicates the layout of equipment in the tail compartments of the aircraft and losses When solid propellant rocket engines are nasally located, gases flowing out of the nose annular nozzle wash over the entire aircraft body, which causes it to heat up, and also disrupts the operation of aerodynamic controls.
Equipment layout: it is necessary to ensure the required conditions in terms of temperature, pressure and humidity, to prevent excessive thermal influences from the propulsion system and aerodynamic heating, harmful electromagnetic interference from adjacent equipment units, to prevent interference with the reception and transmission of control signals, to limit possible fluctuations and deformation of instrument compartments. The equipment is usually completed in blocks, each of which has the same operating conditions, and not its intended purpose. Convenient access to equipment (hatches) should be provided. The control system is usually installed near the central heating system, because there is less impact on geroscopes from structure vibrations. Electronic equipment, sensors, computing units are usually installed in the nose of the aircraft. Antennas for radar homing heads (RLGSN) are covered with a radio-transparent fairing. The actuating elements (steering gears and drives) must be located near the steering wheels and other controls. On-board electrical power supplies are usually installed near major energy consumers. Cables connecting devices with power supplies, as well as various pipelines can be laid inside the aircraft body or in a special harness.

"

An air launch (launch from an aircraft) of an ILV with a mass of 103 tons is being considered. The catapult must accelerate it to a speed that ensures the missile leaves the aircraft without shock. The rocket moves on the yokes along the guides, and after one pair of yokes remains on the guides, under the action of gravity it begins to acquire an angular velocity, as a result of which a collision with the aircraft ramp may occur.

This determines the lower limit on the ejection speed: uobc> 12.5 m / s.

Compared to a mortar launch, launching an ILV from an aircraft using a catapult has a number of advantages: there is no force (wave) and thermal effect of hot gases on the aircraft, the rocket can have aerodynamic surfaces, the dimensions of the launch system are reduced, which simplifies its layout in the cargo compartment, it can be removed the missile in the correct orientation (head towards the stream). The latter advantages allow the speed of the aircraft to be used to impart an initial speed to the missile.

A catapult scheme with two pulling cylinders is used. The total mass of the moving parts of the catapult, based on preliminary calculations, was taken equal to 410 kg. Since the operating time of this catapult is much longer than that considered above, a scheme with two GGs operating in series is considered, which allows changing the gas flow in a larger range than in a scheme with one GG. Considering the large distance between the power cylinders (2.5 m) and, therefore, the large length of the connecting pipelines, schemes are considered with two GGs feeding both power cylinders in series, and with two pairs of GGs, each pair feeding its own cylinder. In this case, a connecting pipe with a diameter of 50 mm is used to equalize the pressures between the cylinders. Based on the strength of the rocket and the support nodes (the elements against which the traverse of the catapult rests), the calculations were carried out for the values of the total force created by the catapult: Lcat = 140 t and Lcat = 160 t. Note that the total force acting on the aircraft at the start is less than these values by the magnitude of the friction force in the ILV yokes. This circuit uses a pneumatic braking device. When carrying out the calculations, it was taken into account that at the moment the catapult is triggered, the plane makes a "slide" maneuver. In this case, the pitch angle is 24 °, which additionally contributes to the acceleration of the ILV due to the projection of the force of gravity, and the apparent lateral acceleration of gravity in the cargo compartment is 3 m / s2. A low-temperature ballistic fuel with a combustion temperature at a constant pressure of 2200 K is used. The maximum pressure in the gas generator should not exceed 200-105 Pa.

In variant 1 with a maximum force of 140 tons (scheme with two pairs of gas generators), after a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.45 s, and the diameter of the nozzle hole was 27 mm. The diameter of the channels in the checkers is 4 mm, the initial combustion surface area of the first chamber is 0.096 m2, and the charge mass is 1.37 kg (for each GG). The diameter of the nozzle hole of the second chamber is 53 mm, the diameter of the channels in the checkers is 7.7 mm, the initial area of the combustion surface is 0.365 m2, and the mass of the charge is 4.95 kg. The diameter of the working chamber of the power cylinder is 225 mm, the diameter of the rod is 50 mm, the path of the piston before the start of braking is 5.0 m.

The maximum ILV acceleration was 16.6 m / s2, the rocket speed at the moment of separation from the traverse was 12.7 m / s (since the length of the guides when using the catapult is, as a rule, greater than the course of the catapult, the speed of the rocket when leaving the guides differs from the speed that the catapult imparts to the rocket). The maximum temperature of the inner wall of the power cylinder is 837 K, the rod is 558 K.

Appendix 3 provides graphs corresponding to this option. The turn-on time of the second HG is selected in such a way that the pressure in the power cylinder remains unchanged. Taking into account the spread of the ignition time of the second GG in real conditions, it starts up somewhat later than the estimated time, therefore, the pressure curve in the power cylinders may have a small dip. If the second HS is started earlier, an unwanted pressure surge will appear on the curve. In fig. A3.1 shows the dependences of the pressures in the gas generator, working cylinders and in the braking chamber on the movement of the moving parts of the catapult. Representation of pressure as a function of the path makes it possible to more clearly assess the efficiency of the catapult's working cycle, since the work performed by it is proportional to the integral of the force (pressure) along the path. As can be seen from the curves, the area of the integrand is close to the maximum possible (taking into account the limitation on the maximum force). The use of a two-stage HG allows for high speed.

For option 2 (a catapult developing an effort of 160 t) the diameter of the power cylinder was increased to 240 mm, the diameter of the rod was increased to 55 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.45 s, and the nozzle hole diameter was 28 mm. The diameter of the channels in the checkers is 4 mm, the initial combustion surface area is 0.112 m2, the mass of the charge is 1.43 kg (for each GG). The diameter of the nozzle opening of the second chamber is 60 mm, the diameter of the channels in the checkers is 7.4 mm, the initial area of the combustion surface is 0.43 m2, and the mass of the charge is 5.8 kg. At the same time, the maximum ILV acceleration was 18.5 m / s2, the missile speed at the moment of separation from the traverse was 13.4 m / s. The maximum temperatures of the inner wall of the power cylinder (850 K), the rod (572 K) practically did not change.

Next, consider a scheme in which both power cylinders operate from the same two successively triggered GGs. To do this, you have to use a sufficiently large manifold (pipeline) connecting the gas generator to the gas cylinders. In this and subsequent versions, we consider that the pipeline is made of steel with increased heat resistance 12МХ, a yield point of 280 MPa at a temperature of 293 K and 170 MPa at a temperature of 873 K, which has a high coefficient of thermal conductivity.

For variant 3 with a force of 140 tons, the diameter of the connecting pipeline is assumed to be 110 mm with a wall thickness of 13 mm. The diameter of the power cylinder, as in version 1, is 220 mm, the diameter of the rod is 50 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.46 s, and the diameter of the nozzle hole was 40 mm. The diameter of the channels in the checkers is 16 mm, the initial combustion surface area is 0.43 m2, and the charge mass is 4.01 kg. The diameter of the nozzle opening of the second chamber is 84 mm, the diameter of the channels in the checkers is 8.0 mm, the initial area of the combustion surface is 0.82 m2, and the mass of the charge is 11.0 kg.

The maximum ILV acceleration was 16.5 m / s2, the missile speed at the moment of separation from the traverse was 12.65 m / s (0.05 m / s less than in option 1). The maximum temperature of the inner wall of the power cylinder is 755 K, the rod is 518 K (decreased by 40-80 K due to heat loss in the pipeline). The maximum temperature of the inner wall of the pipeline is 966 K. This is a rather high, but quite acceptable temperature, given that the thickness of the zone in which the tensile strength of the material significantly decreases due to heating is only 3 mm.

For the variant of the catapult developing a force of 160 tons (variant 4), the diameter of the power cylinder is taken equal to 240 mm, the diameter of the rod is 55 mm, and the diameter of the pipeline is 120 mm. After a series of preliminary calculations, the operating time of the first chamber was chosen equal to 0.46 s, and the diameter of the nozzle hole was 43 mm. The diameter of the channels in the checkers is 16 mm, the initial combustion surface area is 0.515 m2, and the charge mass is 4.12 kg. The diameter of the nozzle opening of the second chamber is 90 mm, the diameter of the channels in the checkers is 7.8 mm, the initial combustion surface area is 0.95 m2, and the charge mass is 12.8 kg. At the same time, the maximum acceleration of the ILV is 18.4 m / s2, the missile speed at the moment of separation from the traverse is 13.39 m / s. The maximum temperatures of the inner wall of the power cylinder are 767 K, the rod is 530 K. The maximum temperature of the inner wall of the pipeline is 965 K. A decrease in the diameter of the pipeline to 95 mm leads to an increase in the temperature of its walls to 1075 K, which is still permissible.

In conclusion, let us consider the influence of the number of GGs on the reliability of the catapult. One single-stage GG will provide maximum reliability at minimum rocket ejection speed. In case of non-start of the GH, the accident does not occur. The emission rate can be increased by increasing the fuel burning rate, the indicator in the combustion law, the pressure at the end of the GG operation to 60-80 MPa (the pressure in the power cylinders and the pipeline remains unchanged), the diameter of the pipeline (initial volume).

The general two-stage GG has less reliability, but provides an increase in the rocket ejection speed. In the case of non-launch of the second stage, one of the following options occurs: the rocket is ejected at a low speed, excluding its further use, the rocket touches the aircraft with insignificant consequences (the inability to completely close the ramp,

the impossibility of subsequent pressurization of the cargo compartment), distortion or impact of the missile on the aircraft, leading to breakdowns or fire and, ultimately, to the death of the aircraft. To increase the reliability for this case, the following measures can be taken to prevent the worse development of events, duplication of the second stage main generator launch systems, and an increase in the first stage main generator operation time (due to which the rocket exit speed when only the first stage main generator is operating will increase so much that the consequences of non-launching will not be so dangerous) , a change in the design of the aircraft, excluding its accident when the rocket exits at a lower speed. It should be noted that in the variants under consideration, when only the first GG is triggered, the missile exit speed will decrease by 3-4 m / s.

In flight to OUT, the rocket body structure experiences aerodynamic heating. The shells of the fuel compartments are additionally heated with gas generator boost, the heating temperature can reach 250-300 ° C. When calculating the safety margins and stability, the mechanical characteristics of the material (ultimate strength and elastic modulus) are taken taking into account the heating of the structure.

Figure 1.3 shows a schematic diagram of the loading of the fuel compartment. Axial forces are applied to the support shells (adapters); lateral forces and bending moments; the bottoms and cylindrical shells of the tanks are affected by the internal overpressure pн and the hydrostatic pressure determined by the height of the liquid column H and the value of the axial overload nx1. Figure 1.3 also depicts a diagram of axial forces occurring in the cross-sections of the fuel compartment. Here, the effect of a bending moment is reduced to an additional axial compressive force Δ N, which is calculated from the maximum value of normal stresses in a compressed panel:

Here W = pR2h is the moment of resistance cross section cylindrical shell of the fuel tank. With Fsec = pDh, the equivalent axial force is DN = 4M / D.

The force of the axial thrust from the action of the boost pressure gives its component of the longitudinal force. In this case, in the upper tank, the resulting force NS has a positive value (Figure 1.3), i.e. the cylindrical shell of this tank will experience tension in the axial (meridian) direction (from the boost pressure). This casing should only be checked for strength.

Figure 1.3 - Schematic diagram of loading the fuel compartment.

At the bottom tank, the cylindrical shell works for longitudinal compression, therefore, in addition to checking the strength, it must be checked for stability. The bearing capacity of this shell will be determined by the sum of the critical load and the axial thrust force

, (1.4)

and taking into account the component from bending

(1.5)

Determination of the critical stress value included in this expression is the most important task when checking the stability of a longitudinally compressed thin-walled cylindrical shell of a fuel tank

The theoretical basis for the development of methods for assessing the carrying capacity of thin-walled structures of liquid-propellant rocket bodies is the theory of stability of elastic shells.

The first solutions to this problem date back to the beginning of the century. In 1908-1914. independently of each other R. Lorenz and S.P. Timoshenko obtained a fundamental formula for determining the critical stresses of a longitudinally compressed elastic cylindrical shell:

(1.6)

This formula determines the upper limit of the critical stresses of smooth (isotropic) cylindrical shells ideal in shape. If Poisson's ratio is taken m = 0, З, then formula (1.6) will take the form:

(1.7)

The formulas presented are obtained under strict assumptions of the ideality of the shape and the momentlessness of the subcritical state of an elastic cylindrical shell, which are characteristic of the classical formulation of stability problems. They make it possible to estimate the upper limit of the bearing capacity of longitudinally compressed thin-walled cylindrical shells of medium length. Since the above assumptions are not implemented in practice, the actual critical stresses observed during axial compression tests of cylindrical shells are significantly lower (2 times or more) than the upper values. Attempts to resolve this contradiction led to the creation of a nonlinear theory of shell stability (the theory of large deflections).

The first solutions of the problem under consideration in a nonlinear formulation gave encouraging results. Formulas were obtained that determine the so-called lower boundary of stability. One of these formulas:

(1.8)

has been used for practical calculations for a long time.

Currently, the prevailing opinion is that when assessing the stability of real structures, one should focus on the critical load, determined taking into account the influence of initial irregularities in the shape using a nonlinear theory. However, in this case, only approximate values of critical loads can be obtained, since the influence of unaccounted for factors (uneven loading, scatter of mechanical characteristics of materials, etc.), random in nature, introduces a noticeable error for thin-walled structures. Under these conditions, when assessing the bearing capacity of the developed missile structures in design organizations prefer to focus on results experimental research.

The first mass experiments to study the stability of longitudinally compressed thin-walled cylindrical shells date back to 1928-1934. Since then, considerable material has been accumulated, which has been repeatedly discussed in order to obtain recommendations for the normalization of the critical load parameter, empirical dependences proposed by various authors for the assignment of the parameter are discussed ... In particular, a formula obtained by American scientists (Weingarten, Morgan, Seid) on the basis of statistical processing of the results of experimental studies published in foreign literature before 1965 is recommended for carefully manufactured casings.

(1.9)

The purpose of checking the stability of the fuel tank of a liquid rocket is to determine the operability of the tank body under the action of external loads that cause longitudinal compression of the cylindrical shell of the tank. In accordance with the strength standards, the reliability of the structure will be ensured if its bearing capacity, taking into account the effect of heating on the critical stresses scr, is equal to or greater than the calculated value of the reduced axial load, i.e. the condition that determines the stability margin for the bearing capacity will be satisfied

, (1.10)

The design bearing capacity N p is determined taking into account the safety factors f: according to expression (1.5),

The calculation of the stability margin of the cylindrical shell of the fuel tank can be performed by comparing the stresses

(1.12)

where s 1р is the calculated value of the longitudinal (meridional) compressive stresses

Aerodynamic heating of the rocket structure

Heating of the surface of a rocket during its movement in dense layers of the atmosphere at high speed. A.N. - the result of the fact that air molecules impinging on the rocket are decelerated near its body. In this case, the transition of the kinetic energy of the relative motion of air particles to thermal energy occurs.

If the flight is made from supersonic speed, braking occurs primarily in the shock wave arising in front of the rocket nose cone. Further deceleration of air molecules occurs directly at the very surface of the rocket, incl. boundary layer. When air molecules are decelerated, their thermal energy increases, i.e. the temperature of the gas near the surface rises. The maximum temperature to which the gas in the boundary layer of a moving rocket can be heated is close to the so-called. braking temperature: T0 = Тн + v2 / 2cp, where Тн - the temperature of the incoming air; v is the flight speed of the rocket; cp - specific heat capacity of air at constant pressure.

From areas of gas with an elevated temperature, heat is transferred to a moving rocket, its A.N. There are two forms of A. n. - convective and radiation. Convective heating is a consequence of the transfer of heat from the outer, "hot" part of the boundary layer to the rocket body. Quantitatively, the specific convective heat flux is determined from the ratio: qk =? (Te - Tw), where Te is the equilibrium temperature (the recovery temperature is the limiting temperature to which the rocket surface could heat up if there was no energy removal); Tw is the real surface temperature; ? - the coefficient of heat transfer of convective heat transfer, depending on the speed and altitude of flight, the shape and size of the rocket, as well as on other factors.

The equilibrium temperature is close to the stagnation temperature. The type of coefficient dependence? from the listed parameters is determined by the flow regime in the boundary layer (laminar or turbulent). In the case of a turbulent flow, convective heating becomes more intense. This is due to the fact that, in addition to molecular thermal conductivity, turbulent velocity fluctuations in the boundary layer begin to play an essential role in energy transfer.

With an increase in the flight speed, the air temperature behind the shock wave and in the boundary layer increases, as a result of which the dissociation and ionization of molecules occurs. The resulting atoms, ions and electrons diffuse into a colder region - to the surface of the body. There, a reverse reaction (recombination) occurs, which also occurs with the release of heat. This gives an additional contribution to the convective.

When a flight speed of about 5 km / s is reached, the temperature behind the shock wave reaches values at which the air begins to radiate. Due to the radiant transfer of energy from areas with elevated temperatures to the surface of the rocket, its radiation heating occurs. In this case, the greatest role is played by radiation in the visible and ultraviolet regions of the spectrum. When flying in the Earth's atmosphere at speeds lower than the first cosmic speed (8.1 km / sec), the radiation heating is small compared to convective heating. At the second cosmic speed (11.2 km / s), their values become close, and at flight speeds of 13-15 km / s and higher, corresponding to the return to Earth, the main contribution is made by radiation heating, its intensity is determined by the specific radiation (radiant) heat flow: ql =? ? 0 Te4, where? - the degree of blackness of the rocket body; ? 0 = 5.67.10-8 W / (m2.K4) - the emissivity of an absolutely black body.

In a particular case, A.N. is the heating of a rocket moving in the upper atmosphere, where the flow regime is free molecular, that is, the free path of air molecules is commensurate with or even exceeds the size of the rocket.

The especially important role of A.N. plays during the return to the Earth's atmosphere of spacecraft and combat equipment of guided ballistic missiles. To combat A.N. spacecraft and elements of combat equipment are supplied with special thermal protection systems.

Lit .: Lvov A.I. Design, strength and calculation of missile systems. Tutorial... - M .: Military Academy. F.E. Dzerzhinsky, 1980; Fundamentals of Heat Transfer in Aviation and Rocket Engineering. - M., 1960; Dorrens W.H., Hypersonic Viscous Gas Flows. Per. from English - M., 1966; Zel'dovich Ya.B., Raizer Yu.P., Physics of shock waves and high-temperature hydrodynamic phenomena, 2nd ed. - M., 1966.

Norenko A.Yu.

Encyclopedia of Strategic Missile Forces. 2013 .

AERODYNAMIC HEATING- heating of bodies moving at high speed in air or other gas. A. n. inextricably linked with aerodynamic resistance, a cut test bodies when flying in the atmosphere. The energy spent on overcoming resistance is partially transferred to the body in the form of A. n. Consideration of physical. of the processes that determine A. n., it is convenient to carry out from the point of view of an observer who is on a moving body. In this case, it can be seen that the gas incident on the body is decelerated near the body's surface. First, braking occurs in shock wave formed in front of the body if the flight occurs at supersonic speed. Further deceleration of the gas occurs, as in the case of subsonic flight speeds, directly at the very surface of the body, where it is caused by the forces of viscosity, forcing the molecules to "stick" to the surface with the formation boundary layer.

When decelerating the gas flow, its kinetic. energy decreases, which, in accordance with the law of conservation of energy, leads to an increase in int. energy of gas and its temperature. Max. heat content ( enthalpy) of the gas when it is decelerated near the surface of the body is close to the enthalpy of deceleration:, where is the enthalpy of the incident flow, and is the flight speed. If the flight speed is not too high (1000 m / s), then beats. heat capacity at constant. pressure with p can be considered constant and the corresponding gas deceleration temp-pa can be determined from the expression

where T e- equilibrium temp-pa (limiting temperature, up to a cut the surface of the body could heat up if there was no energy removal), - koef. convective heat transfer, the index marks the parameters on the surface. T e is close to the braking temperature and can be determined from the expression

where r-coeff. temperature recovery (for laminar, for turbulent), T 1 and M 1 - temp-pa and Mach number to ext. border of the boundary layer, - the ratio of beats. heat capacities of gas at constant. pressure and volume, Pr is the Prandtl number.

The value depends on the speed and altitude of the flight, the shape and size of the body, as well as on some other factors. Similarities theory allows you to represent the laws of heat transfer in the form of ratios between the main dimensionless criteria - Nusselt number , Reynolds number , Prandtl number and temperature factor taking into account the variability of thermal physics. gas properties across the boundary layer. Here and - and the gas velocity, and - coeff. viscosity and thermal conductivity, L- typical body size. Naib. influence on convective A. n. renders the Reynolds number. In the simplest case of a longitudinal flow around a flat plate, the law of convective heat transfer for a laminar boundary layer has the form

where and are calculated at temperature a for a turbulent boundary layer

On the nose of the body with dull spherical. form laminar heat transfer is described by the ratio:

where r e and m е are calculated at temperature T e... These f-ly can be generalized to the case of calculating heat transfer in a continuous flow around bodies of a more complex shape with an arbitrary pressure distribution. With a turbulent flow in the boundary layer, an intensification of convective A. n. Occurs, associated with the fact that, in addition to molecular heat conduction, there is. turbulent pulsations begin to play a role in the transfer of the energy of the heated gas to the surface of the body.

With theoretical. calculation A. n. a spacecraft flying in dense layers of the atmosphere, the flow near the body can be divided into two regions - inviscid and viscous (boundary layer). From the calculation of the flow of inviscid gas in the ext. area is determined by the distribution of pressure over the surface of the body. The flow in a viscous region with a known pressure distribution along the body can be found by numerically integrating the equations of the boundary layer or for calculating the A. n. can be used decomp. approximate methods.

A. n. plays creatures. role in supersonic flow gas in the channels, primarily in the nozzles of rocket engines. In the boundary layer on the nozzle walls, the gas temperature can be close to the temperature in the rocket engine combustion chamber (up to 4000 K). In this case, the same mechanisms of energy transfer to the wall operate as in the boundary layer on a flying body, as a result of which A. n. walls of the nozzle of rocket engines.

To obtain data on A. n., Especially for bodies of complex shape, including bodies, streamlined with the formation of separation regions, an experiment is carried out. studies on small-scale, geometrically similar models in wind tunnels with reproduction of the defining dimensionless parameters (numbers M, Re and temperature factor).

With an increase in the flight speed, the gas temp-pa behind the shock wave and in the boundary layer increases, as a result of which the dissociation of the molecules of the incident gas occurs. The resulting atoms, ions and electrons diffuse into a colder region - to the surface of the body. There is a reverse chemical. reaction - recombination proceeding with the release of heat. This gives the complement. contribution to convective A. n. In the case of dissociation and ionization, it is convenient to go from temperature to enthalpies:

where -equilibrium enthalpy, and - enthalpy and gas velocity at ext. boundary layer boundary, and is the enthalpy of the incident gas at the surface temperature. In this case, the same critical can be used to determine. ratio as at relatively low flight speeds.

When flying at high altitudes, the nonequilibrium physicochemical effect can affect convective heating. transformations. This phenomenon becomes significant when the characteristic times of dissociation, ionization, etc. chem. reactions become equal (in order of magnitude) to the residence time of gas particles in a region with an increased temperature near the body. The influence of physical and chemical. nonequilibrium on A. n. manifests itself in the fact that the products of dissociation and ionization, formed behind the shock wave and in the high-temperature part of the boundary layer, do not have time to recombine in the near-wall, relatively cold part of the boundary layer, the heat of the recombination reaction is not released and A. n. decreases. In this case, catalytic plays an important role. material properties of the body surface. Using materials or coatings with low catalytic. activity in relation to recombination reactions (for example, silicon dioxide), it is possible to significantly reduce the value of convective A. n.

If through the permeable surface of the body there is a supply ("blowing") of a gaseous coolant into the boundary layer, then the intensity of the convective A. n. decreases. This happens ch. arr. as a result, add. heat consumption for heating gases blown into the boundary layer. The effect of reducing the convective heat flux upon injection of foreign gases is the stronger, the lower their molecular weight, since this increases the beats. heat capacity of the injected gas. In the case of a laminar flow in the boundary layer, the blowing effect is more pronounced than in a turbulent one. With moderate beats. the flow rate of the gas injected, the decrease in the convective heat flux can be determined by the formula

where is the convective heat flux to the equivalent impermeable surface, G - beats. mass flow rate of injected gas through the surface, and - coefficient. injection, depending on the flow regime in the boundary layer, as well as the properties of the incoming and injected gases. Radiation heating occurs due to the transfer of radiant energy from areas with an increased temperature to the surface of the body. In this case, it plays the greatest role in the UV and visible regions of the spectrum. For theoretical. calculation of radiation heating it is necessary to solve the system of integro-differential equations of radiation. gas, taking into account own. emission of gas, absorption of radiation by the medium and transfer of radiant energy in all directions in the high-temperature region of the flow surrounding the body. Spectrum-integral radiation flow q P0 to the body surface can be calculated using Stefan-Boltzmann's law of radiation:

where T 2 - temp-pa gas between the shock wave and the body, = 5.67 * 10 -8 W / (m 2 * K 4) - Stefan's constant, - eff. the degree of emissivity of the radiating volume of gas, which in the first approximation can be considered as a flat isotherm. layer. The value of e is determined by a set of elementary processes that cause emission of gases at high temperature pax. It depends on the speed and altitude of flight, as well as on the distance between the shock wave and the body.

If it does. value of radiation A. n. great then creatures. the role of radiation begins to play. gas cooling behind the shock wave, associated with the transfer of energy from the radiating volume to environment and lowering its temperature. In this case, when calculating the radiation. A. n. an amendment must be introduced, the value of which is determined by the highlighting parameter:

where is the flight speed, is the density of the atmosphere. When flying in the Earth's atmosphere at speeds below the first cosmic radiation. A. n. small compared to convective. With the second cosm. speed they are compared in order of magnitude, and at flight speeds of 13-15 km / s, corresponding to the return to Earth after flight to other planets, main. the contribution is made by radiation A. n.

A special case of A. n. Is the heating of bodies moving upward. layers of the atmosphere, where the flow regime is free-molecular, that is, gas molecules are commensurate with or even exceed the dimensions of the body. In this case, the formation of a shock wave does not occur even at high flight speeds (of the order of the first cosmic one) for calculating the A. n. simple f-la can be used

where is the angle between the normal to the surface of the body and the velocity vector of the incident flow, a- coeff. accommodation, to-ry depends on the properties of the incident gas and surface material and, as a rule, is close to unity.

With A. n. related to the problem of the "thermal barrier" arising in the creation of supersonic aircraft and launch vehicles. Important role A. n. plays when the cosmic returns. spacecraft into the Earth's atmosphere, as well as when planets enter the atmosphere with velocities of the order of the second space velocity and higher. To combat A. n. specials are applied. systems thermal protection.

Lit .: Radiation properties of gases at high temperatures, M., 1971; Foundations of the theory of spacecraft flight, M., 1972; Fundamentals of heat transfer in aviation and rocket-space technology, M., 1975. I. A. Anfimov.

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