Erozif yanmanın katı yakıcı-yakıtlı roket motoru performansına etkisinin incelenmesi

Abstract

ÖZET Bu tez, katı yakıcı-yakıtlı (propellant) bir roket motoru yanma odasında meydana gelen termokimyasal olayların ve performans parametrelerinin bilgisayar yardımıyla simülasyonunu gerçekleştiren bir çalışmadır. Motor yanma odası içerisindeki akış olayı, bir boyutlu, sürekli ve dengeli akış olarak incelenmiştir. Yanma ürünü gazlarının yalnız termal olarak ideal olduğu varsayılmıştır. Geliştirilen teorik model ile bir boyutlu ve şoksuz gaz akımı üzerine alan değişimi, cidar sürtünmesi, ısı transferi, kimyasal reaksiyon, faz değişimi, gaz enjeksiyonu, moleküler ağırlık ve özgül ısı değişimi tesirlerinin incelenmesi imkanı sağlanmış tır. Grain, sonlu farklar tekniği gereği olarak sonlu uzunluktaki elemanlara (dilimlere) ayrılmıştır. Basınç, kütle debisi, Mach sayısı, hız, yanmış doku kalınlığı, sıcaklık, itme kuvveti, transfer edilen ısı miktarı ve akışa ait diğer değerler türetilen diferansiyel denklemleri sonlu farklar yöntemi yardımıyla çözümü sonucu, her bir zaman artışı için, motor eksenel uzunluğu boyunca her noktada bulunmuştur. ideal haldeki ve sözü edilen tesirlerin dikkate alındığı gerçek halde motor performans değerleri hesaplanmıştır. Yanmanın erozif ve erozif olmayan halleri için bulunan sonuçlar mukayese edilmiştir. Muhtelif grain geometrisi ve yanma hızı değerleri için hesaplanan değerler literatürdeki deneysel sonuçlarla karşılaştırılmıştır. Geliştirilen model program ile, optimum tasarım için kararlı motor çalışma şartını sağlayan, balistik ve yapısal dizayn faktörlerinin parametrik olarak denenmesi imkanı elde edilmiştir. - ıx -

A STUDY OF EFFECT OF EROSIVE BURNING TO SOLID PROPELLANT ROCKET MOTOR PERFORMANCE SUMMARY In this study, thermochemical phenomena in the combustion chamber of a solid propellant rocket motor and calculation of its performance parameters have been examined by using computer-aided simulation programme. The flow process in the motor has been examined as one-dimensional and steady. The combus tion product gases have been assumed semi-perfect and had a specific heat which, varies only with tempera ture and composition. In theorical model developed, the effects on the one-dimensional and shock-free flow have been examined as follows: -. Area change, - Wall friction, - Heat transfer, - Chemical reaction, - Change of phase, - Gas injection, - Molecular weight and specific heat change. Grain has been divided in slice of finite length as necessary for technique of finite-differences. Pressure, mass flow rate, Mach number, burnt web thick ness, temperature, impulse force, heat transferred and other properties of flow have been found for every moment in every sections of motor axial length. In ideal and real condition, which was stated above, motor performance parameters have been calcula ted and results have been compared with the experimen tal results in literature. By using computer programme developed, the possi bility of parametric trying of balistic and structural design factors and steady motor operation have been obtained. The results of erosive and non-erosive conditions of the solid propellant burning have been compared. Among the aims of the modern technology the most important subjects are reducing the costs and time of the design, manufacture, research and development. Simulation process has been realized for ideal and real motor operation conditions. The analysis of ideal rocket is one in which the - x -following assumptions are valid: - The working substance (propellant products) is homogeneous and invariant in composition throughout the rocket chamber and nozzle. - The working substance obeys the perfect gas laws. - There is no friction. - There is no heat transfer across the rocket walls; therefore, the flow is adiabatic. - The propellant flow is steady and constant. The expansion of the working fluid takes place a uniform and steady manner without shock, vibration, or discontinuities. - All the exhaust gases leaving the rocket nozzle have an axially directed velocity. - The gas velocity, pressure, temperature, or density is uniform across any section normal to the nozzle axis. - Chemical equilibrium is established within the rocket chamber and does not shift in the nozzle. - All the species of the working fluid are gase ous. Because the chamber temperatures are high, the gases are well above their respective saturation and follow the perfect gas laws very closely. Postulating no friction and a steady flow without heat transfer to the wall allows the use of isentropic expansion rela tions in the rocket nozzle, thereby permitting the assumption of a maximum conversion of heat energy into the kinetic energy of the jet. This implies that the nozzle flow is thermodynamically reversible. In the study, homogen type (double-base) solid propellant has been selected as a sample. Heat of combustion of solid propellant is 3 594 800 J/Kg. In the thermochemical calculations, the combustion products selected as C02, CO, H2O, H2, H, 02, 0, OH, N2, N, NO, NO2» N2O, Pb and PbO. Enthalpy, specific heat and Gibbs energy-temperature relations of the combustion products has been expressed as fifth degree polinoms. In the chemical equilibrium condition, in the determing of combustion products composition, the met hod of minimizing the Gibbs energy has been used. Little selecting of slice length increases the precission of calculation. In the real solid rocket motor simulation programme, length of slice has been - xi -selected as 0.005 m. and the time period 0.001. second. The lower values extend the computer operation time but not insrease the precision. The propellant formulation and propellant manu facturing process, burning rate in a full-scale motor is influenced by the following: - Combustion chamber pressure, - Initial temperature of the propellant, - Combustion gas temperature, - Velocity of the gas flow parallel to the burning surface, - Motor motion. The burning rate of propellant in a motor is a function of many parameters, and at any instant governs the mass flow rate of hot gas generated and flowing from the motor. With many propellant it is possible to approxi mate the burning rates as a function of chamber pres sure, at least over a limited range of chamber pressures. In many production-type propellants, whether double base, composite, or composite double base, this empirical equation is r = a + b pn Where f, the burning rate, is usually cm. per second, and the chamber pressure p is atm., a and b are empi rical constant influenced by ambient grain temperature and n is known as the burning rate pressure exponent The burning rates are determined empirically and often cannot be expressed accurately by a simple mathematical relation over a wide range of pressures. For this reason empirical data are often used in design computations instead of simplified burning-rate relations. In the computer program developed, pressure and thrust histories are calculated considering the effect of mass addition, port area change, and burn rate variation under quasi-steady state flow conditions. The governing gas dynamic differential equations are solved by a finite difference technique. The resulting thrust, pressure, amount of propellant burned and delivered specific impulse are determined for each time increment. Eight independent relations between the differential parameters have been forth. As there are fourteen differential variables, six may be chosen as independent variables and eight as dependent variables. For the - xii -independent variables we choose those most easily controlled in practice, as indicated below. Independent Dependent dA/A dM2/M2 (dQ-dWx dH)/CpT dV/V 4fdx/D da/a dw/w d p/ p dW/W dp/p dk/k dF/F dT/T ds`/C0 The usual methods for solving a system of simultaneous, linear, algebraic equations may be employed for obtaining each dependent variable in terms of the six independent parameters. The overall design considerations for the internal ballistic design of a rocket motor include the physical constraints on the motor, the total impulse requirement and the environmental limits which must be met. These requirements are all ultimately defined by the mission requirements. Physical constraints on the motor include length, diameter, total volume, weight and center of gravity location. Most motors must be designed for a nearly constant center of gravity location. Since motors are always designed as part of a missile or vehicle, there are typically physical constraints in the form of critical interface dimensions which must be maintained. Once the propellant has been selected, the overall design of the propellant grain begins. A first conside ration is the basic grain geometry. The primary purpose of the features just mentioned is to obtain a nearly neutral relationship between burning surface area and burn distance as the propellant grain burns. In the absence of the other geometric features, the circular cylindrical bore or port of the motor would rapidly increase in area y in other words, it would have a highly progressive ` burning characteristic. ?I In order to achieve a high volumetric loading in the motor, the designer must therefore incorporate some initial burning surface in the motor in the early stages of the grain burnback while reducing the net burning - xiii -surface later in the burnback. The burning rate exponent n must be less than unity for stable combustion, as may be demonstrated by the above simple argument. Neglecting the relatively small gas storage terms, nozzle flow rate and gas generation rate must be equal. Nozzle gas flow rate is directly proportional to p. Consider a small decrease from the operating point pressure. It can be seen that for n<l the resultant gas generation rate will than exceed the nozzle flow rate, and thus the chamber pressure will return toward the original value. For n>l, any small decrease in chamber pressure means that nozzle flow rate will exceed gas -generation rate and the pressure will drop even further. Thus for n>l, small disturbances are amplified and the combustion cannot be stable. Hence for stable combustion n must be less than unity. Erosive burning occurs in the central port, near nozzle and in the place in which the gas volecity is high. Erosion term is showen as below ; r e = r° Here, r is the burning rate at the condition of non- erosive and r is the burning rate at the condition ero sive. In this study, G r = 1+ k G* relation which was given by Green, has been used. The sub-programs are suitable to change to the different conditions. Solid propellant rocket motor simulation program is useful for the correctness and time saving of designing studies. On the other hand simulation program is appropriate to being adapted for use condition of rocket motors. - xxv -