Academic literature on the topic 'Rockets (Ordnance) Mathematical models'

The choice of thermal protection of the rocket fairing is approached with special care, because the fairing must protect against aerodynamic heating, radiation, temperature changes. Currents with large Mach numbers are accompanied by gas-dynamic and physicochemical effects. When flowing around the blunt body, a shock wave is formed, which departs from the body, remaining in the vicinity of the frontal point almost equidistant to its surface. Physico-chemical effects are due to rising temperatures caused by the inhibition of gas by the shock wave. At the same time there is a transition of kinetic energy of a stream rushing in thermal, fluctuating degrees of freedoms of gas molecules are excited, its dissociation and even ionization begins. Therefore, among the problems of great theoretical and practical interest is the problem of studying the temperature fields arising in the fairings for missiles in the form of a truncated cone, which rotate around its axis, given the finiteness of the rate of heat propagation. In the article the mathematical model of calculation of temperature fields for a truncated cone is constructed for the first time which approximately models distribution of temperature fields which arise in fairings for rockets, with taking into account the angular velocity and the final speed heat distribution in the form of a boundary value problem of mathematical physics for hyperbolic equation of thermal conduc-tivity with boundary conditions Dirichlet. A new integral transformation for a two-dimensional finite space is constructed, in the application of which the temperature field in the form of a convergent series is found. The solution found can be used to predict the possible value of thermomechanical stresses, to promote the correct choice of technological parameters, objective control, allows to identify ways to improve the thermal protection of fairings for missiles.

Liquid-propellant rocket propulsion systems of the first stages of launch vehicles of medium, heavy, and super-heavy class usually include POGO-suppressors, which are one of the most widely used methods to eliminate launch vehicle longitudinal structural vibrations (POGO phenomena). However, until now, the theoretical studies and analysis of the effect of the POGO-suppressors’ installation in the feedlines of main liquid rocket engines on transient processes in systems during rocket engine starting have not been carried out due to the complexity of such analysis and the lack, first of all, reliable nonlinear models of cavitation phenomena in rocket engine pumps. A mathematical model for the start-up of a clustered rocket propulsion of the Cyclone-4M launch vehicle has been developed that takes into account the low-frequency dynamics of the POGO-suppressors and the asynchronous start-up timeline sequences of the rocket engines. The first stage of the launch vehicle propulsion system includes four RD-870 rocket engines. A nonlinear mathematical model of low-frequency dynamic processes of the POGO-suppressor with bellows separation of liquid and gaseous media is presented. A significant effect of cavitation in the pumps of engines and the POGO-suppressor installation to the LOX feedline on the propulsion system dynamic gains is shown. Based on the developed mathematical model of the clustered rocket propulsion start-up, the studies of the Cyclone-4M main engines’ start-up transients were carried out. The asynchronous start-up timeline sequences of the rocket engine and the places of installation of the POGO-suppressors in the LOX feedline branches to the RD-870 rocket engine – near the general feedline collector as standard placement or directly at the entrance to the engines – were investigated. The analysis of start-up transients in the oxidizer feed system of the considered propulsion (the time dependences of the flowrate and pressure at the engine inlet) showed the following. Firstly, while the synchronous start-up of the engines, the installation of the POGO-suppressors near the feedline collector makes it possible to eliminate all engine inlet overpressures that exist in the rocket propulsion system in case of the absence of the POGO-suppressors. Secondly, the RD-870 engine asynchronous start-up operation affects negatively the time dependences of the propellant flowrate and pressure at the engine inlet if the POGO-suppressors are located near the feedline collector. So, in the propulsion system’s start-up timeline interval 0.95 s - 1.35 s, for some computational variants of the initial moments of the engine operation start, an abnormally large drop in the LOX flow rate and the overpressures at the engine inlet is observed. The asynchronous start-up of the RD-870 engines with the installation of the POGO-suppressors at the engine inlet does not significantly change the start-up transients compared to the synchronous starting of the engines. Thirdly, thus, it is shown that the installation of the POGO-suppressors both at the engine inlet and at the RD-870 branches near the collector has a significant positive effect on the quality of start-up transient processes for the main engines of the 1st stage of the Cyclone-4M launch vehicle. Placing the POGO-suppressors at the engine inlets is not standard and is considered without reference to the propulsion system layout. Nevertheless, the POGO-suppressors installed at the inlet to the engines are an effective means of preventing overshoots and dips in the parameters of the liquid-propellant rocket engine, including the conditions of asynchronous starting of the liquid rocket engines in the clustered propulsion system. The results obtained can be used in mathematical modeling of the start-up of the first stage propulsion system either for multistage sustainer rockets used in parallel with booster rockets or for the clustered multi-engine rocket propulsion system containing POGO-suppressors.

At the design of intakes of fuel tanks of launch vehicles in engineering practice, empirical and semi-empirical dependences are used for the determination of main parameters of the movement of liquid. However, the received from skilled data, empirical dependencies are applicable for a limited circle of tasks in which conditions (initial and boundary) are similar to for what these dependencies were received. Therefore, the calculated parameters of intakes it has to be validated by the results of experimental working off. Experimental working off intakes at hydrodynamic stands is, as a rule, carried out on natural tanks and their large-scale models (skilled designs) in terrestrial conditions. For confirmation of similarity of hydrodynamic processes, experimental working off the large-scale models is carried out on several skilled designs of different scales and several model liquids. Now, with the development of computer facilities and numerical methods of the solution of the differential equations of the movement of liquid, there was an opportunity to replace almost universal use of empirical dependences with more exact computing experiment. It, in some cases, allows reducing the quantity of the used skilled designs, terms of carrying out experimental working off, and, as a result, material expenses. The article presents results of the experimental definition of the static hydraulic rest of a component of fuel in skilled designs of a tank of the first step of carrier rockets with the central selection of a component and numerical modeling on mathematical 3D and 2D models of skilled designs (similar scale) are considered. The authors developed the calculated and experimental method of verification of results of numerical modeling allowing them to conduct necessary researches with the demanded accuracy. The offered approach allows improving the existing traditional method of experimental working off of intakes, already at the initial stage of development to optimize their parameters, to reduce the volume of necessary experimental working off and to lower time and material expenditure on its carrying out.

The purpose of this work is to develop a method for determining the types of acoustic sources of radiation and their acoustic fields during the space rockets launch in the first seconds based on the wave parameter values. The main noise source during the space rocket launch is its propulsion system (PS). The cross-section of the nozzle is taken as the oscillation source. The theory of siren sound emission is based on the acoustic power calculation of a jet as a volume sound radiator or a radiator with a space velocity. In the model of a volumetric spherical radiator, the front of a spherical wave is a spherical surface, and the sound rays, according to the definition of the wave front, coincide with the radii of the sphere. As a result of the divergence of waves, the sound intensity decreases with distance from the source. The present work has a prospective character for clarifying the nature of the acoustic fields and for calculating the noise levels from the space rocket launch when designing the cosmodromes. In the requirements for the construction of such structures, the noise impact on the environment of infrasound radiation upon launching launch vehicles is identified. A method for determining the types of acoustic radiation sources during the space rocket launch and their acoustic fields has been developed. The method makes it possible to develop physical models of acoustic fields and apply known mathematical models to calculating their characteristics. The method is applicable for the study of acoustic emissions in the first seconds of the space rocket launch based on the determination of the wave parameter kR and allows us to provide valid data on the levels of sound pressure, intensity and acoustic power at specific points of airspace around the PS in the first seconds of the launch. The character of the acoustic wave radiation from a hole in a specific size gas flue has been studied. To calculate the acoustic characteristics, an algorithm and a program on Java programming language have been developed. Two models of acoustic field generation in the environment are described during the work of a rocket as a plane radiator and spherical waves, depending on the value of the wave parameter kR. A technique for calculating the noise of a remote control in the range for the first 1.5-4 seconds of the space rocket start time is developed

Problem statement. The concept of solving problems of identification and technical diagnostics of spacecraft (SC), launch vehicles (LV), upper stages (RB) under conditions of imperfect models and methods of their identification with a priori uncertainty of statistical relationships of controlled parameters is proposed. Goal. Increasing the reliability of technical diagnostics of spacecraft, launch vehicles and missile launchers under conditions of imperfect models and methods of their identification under destructive influences. Results. A commutative diagram of extended technical diagnostics of complex objects of rocket and space technology (SFBT), as well as a model of augmented identification and technical diagnosis of SFBT as a set of interrelated mathematical models of systems of an object and an object as a whole, control of their technical state, search for the location and causes of malfunctions, assuming the detection of signs of erroneous decisions of typical technical diagnostics and increasing its reliability in case of malfunctions. Practical significance. The idea of RCBT augmented identification and technical diagnostics of the RCBT with the function of recognizing errors of standard solutions is proposed as a basis for creating special software and mathematical support for standard and promising automated test complexes for the preparation of spacecraft, launch vehicles, RB during factory tests, tests at technical and launch complexes, as well as means spacecraft flight control centers during flight design tests and routine control.

AbstractA computational tool able to perform a fast analysis of hybrid rocket engines is presented, describing briefly the mathematical and physical models used. Validation of the code is also shown: 16 different static firing tests available in the open literature are used to compare measured operational parameters such as chamber pressure, thrust, and specific impulse with the code’s output. The purpose of the program is to perform rapid evaluation and assessment on a possible first design of hybrid rockets, without relying on computationally expensive simulations or onerous experimental tests. The validated program considers as benchmark and study case the design of a liquid-oxygen/paraffin hybrid rocket engine to be used as the upper stage of a small launcher derived from VEGA building blocks. A full-factorial parametric analysis is performed for both pressure-fed and pump-fed systems to find a configuration that delivers the equivalent total impulse of a VEGA-like launcher third and fourth stage as a first evaluation. This parametric analysis is also useful to highlight how the oxidizer injection system, the fuel grain design, and the nozzle features affect the performance of the rocket.

A fundamental diagram of a control system for missiles of various classes is investigated. A functional diagram of a control system with an intelligent component for long-range aerodynamic rockets returning to the atmosphere is developed. It is proposed to use in the control loop an ensemble of a priori missile models and models of external influences. It is proposed to improve the accuracy of control systems with an intelligent component by increasing the degree of controllability of the state variables for a priori models. The most convenient numerical criterion of controllability degree for of the state variables of the models is presented. The results of mathematical modeling showed a slight increase in the efficiency of missile control with an increase in the degree of controllability of the pitch angle by changing the coefficients of the control matrix. Keywords rocket; control system; intelligent component; an action acceptor; a priori model; controllability; degree of controllability; management efficiency

The clearance of underwater ordnance is one of the most complex tasks entrusted to appropriately trained and equipped soldiers. State-of-the-art knowledge in this area is rarely published and is most often possessed by a narrow group of navy specialists. The aim of this paper was to find a link between the existing mathematical models for the peak pressure of underwater explosion with measurements of small charge detonations for long ranges to the observation point in real life scenarios. We have shown the results of the research in which the underwater explosion tests were presented for different TNT equivalents and standoff distances and thus distance ratios. The curves of pressure versus time of ignition were reported. The measurements were confronted with empirical formulas. The comparison showed large, but expected, differences, since the empirical formulas are advised for smaller distance ratios. Based on the conclusions from the study, the new methodology to identify the loading from underwater explosions based on a database collected was postulated. By creating a survey methodology for ships crew for recording explosion parameters, a large number of events can be registered without a strict setup of the test area. The database obtained can be used by military commanders to identify the explosive hazard in the Baltic Sea region.

In this thesis, a simple moving boundary technique has been suggested, implemented and verified. The technique may be considered as a generalization of the well-known "ghost" cell approach for boundary condition implementation. According to the proposed idea, the moving body does not appear on the computational grid and is allowed to move over the grid. The impermeable wall boundary condition is enforced by assigning proper gasdynamic values at the grid nodes located inside the moving body close to its boundaries (ghost nodes). The reflection principle taking into account the velocity of the boundaries assigns values at the ghost nodes. The new method does not impose any particular restrictions on the geometry, deformation and law of motion of the moving body.
The developed technique is rather general and can be used with virtually any finite-volume or finite-difference scheme, since the modifications of the schemes themselves are not required. In the present study the proposed technique has been incorporated into a one-dimensional non-adaptive Euler code and a two-dimensional locally adaptive unstructured Euler code.
It is shown that the new approach is conservative with the order of approximation near the moving boundaries. To reduce the conservation error, it is beneficial to use the method in conjunction with local grid adaptation.
The technique is verified for a number of one and two dimensional test cases with analytical solutions. It is applied to the problem of supersonic inlet starting via variable geometry approach. At first, a classical starting technique of changing exit area by a moving wedge is numerically simulated. Then, the feasibility of some novel ideas such as a collapsing frontal body and "tractor-rocket" are explored.

The present research is an experimental and numerical study of aeroacoustic phenomena occurring in large solid rocket motors (SRM) as the Ariane 5 boosters. The emphasis is given to aeroacoustic instabilities that may lead to pressure and thrust oscillations which reduce the rocket motor performance and could damage the payload. The study is carried out within the framework of a CNES (Centre National d'Etudes Spatiales) research program.

Large SRM are composed of a submerged nozzle and segmented propellant grains separated by inhibitors. During propellant combustion, a cavity appears around the nozzle. Vortical flow structures may be formed from the inhibitor (Obstacle Vortex Shedding OVS) or from natural instability of the radial flow resulting from the propellant combustion (Surface Vortex Shedding SVS). Such hydrodynamic manifestations drive pressure oscillations in the confined flow established in the motor. When the vortex shedding frequency synchronizes acoustic modes of the motor chamber, resonance may occur and sound pressure can be amplified by vortex nozzle interaction.

Original analytical models, in particular based on vortex sound theory, point out the parameters controlling the flow-acoustic coupling and the effect of the nozzle design on sound production. They allow the appropriate definition of experimental tests.

The experiments are conducted on axisymmetric cold flow models respecting the Mach number similarity with the Ariane 5 SRM. The test section includes only one inhibitor and a submerged nozzle. The flow is either created by an axial air injection at the forward end or by a radial injection uniformly distributed along chamber porous walls. The internal Mach number can be varied continuously by means of a movable needle placed in the nozzle throat. Acoustic pressure measurements are taken by means of PCB piezoelectric transducers. A particle image velocimetry technique (PIV) is used to analyse the effect of the acoustic resonance on the mean flow field and vortex properties. An active control loop is exploited to obtain resonant and non resonant conditions for the same operating point.

Finally, numerical simulations are performed using a time dependent Navier Stokes solver. The analysis of the unsteady simulations provides pressure spectra, sequence of vorticity fields and average flow field. Comparison to experimental data is conducted.

The OVS and SVS instabilities are identified. The inhibitor parameters, the chamber Mach number and length, and the nozzle geometry are varied to analyse their effect on the flow acoustic coupling.

The conclusions state that flow acoustic coupling is mainly observed for nozzles including cavity. The nozzle geometry has an effect on the pressure oscillations through a coupling between the acoustic fluctuations induced by the cavity volume and the vortices travelling in front of the cavity entrance. When resonance occurs, the sound pressure level increases linearly with the chamber Mach number, the frequency and the cavity volume. In absence of cavity, the pressure fluctuations are damped.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished