How rocket engine nozzle walls are designed method of. Nov 23, 2018 rocket engine design with matlab and solidworks method of characteristics nozzle tutorial. Rocket engine design with matlab and solidworks method of. Pdf geometrical study of 2d method of characteristics. Design, analysis, and simulation of rocket propulsion system. Design and verification of minimum length nozzles with. Numerous numerical methods have been utilized to simulate fuel spray characteristics, for example, the. The usual presenta tion of their method of characteristics is rather mathematical in nature. Minimum length nozzle wave interactioninteraction underexpanded jet wind tunnel nozzle 4 3 2 3 2 2. The method of characteristics moc approach has been favored by textbook authors 2,3 because it is explicit and thus easy to set up and solve. Dillaway 4 presents a semiempirical method for designing shortened nozzles without considering whether the nozzles obtained are optimum for the specified exit condi tions.
Multidisciplinary approach to aerospike nozzle design. Finally the input variable g specifies the ratio of specific heats to be used in relating prandtl meyer and mach angles. General theory of method of characteristics characteristics. Hence, the method of characteristics is a numerical procedure suitable to solve twodimensional compressible flow field problems. The method of characteristic moc nozzle flowfield solver code is a fortran 9095 1 structured, twodimensional 2d both planar and axisymmetric, isentropic supersonic flow solver for convergingdiverging nozzle problems under choked flow conditions. The method of characteristics is therefore applied to allow the. Introduction to the method of characteristics and the.
Us7278294b2 system and method for determining atomization. Design evaluation was carried out using highfidelity simulations. The present study is aimed at investigating the supersonic flow in conical nozzle. In this paper, a method based on the theory of characteristics is presented for twodimensional, supersonic nozzle design. General discussion aerospike performs an expansionwave analysis from the throat of the thruster nozzle, where mn 1.
This development allows the process for designing rocket nozzles to be automated, fa. A minimum length 2d bell nozzle is designed using moc. The method of characteristics is therefore applied to allow the design of a supersonic nozzle which meets these requirements. The most prominent method for determining nozzle oontours is, perhaps, that of prandt1 and buseman reference a. Due to the multidimensionality of the converging subsonic flow, the sonic line is gently curved. Aerodynamic design of axisymmetric hypersonic windtunnel. In this paper, a method based on the theory of characteristics is presented for two dimensional, supersonic nozzle design. This paper examines the effect of varying the number of characteristic lines on the design of moc nozzle at 10, 20, 50, 100, and 200 numbers of characteristic lines at mach numbers 1. A generic c language computer code is developed for designing a scramjet nozzle contour using the method of characteristics numerical technique. The bellshaped or contour nozzle had a high angle expansion section 20 to 50 right behind the.
Jun 12, 2018 the method of characteristics moc is a popular tool used to design liquid and solid rocket engine nozzles. Minimum length of the supersonic nozzle has been calculated for the optimum mach number at the nozzle exit with uniform flow at the diverging section of the nozzle by developing a matlab program. The contour obtained is compared to theoretical isentropic area ratios for the selected fluid and desired exit mach number. Rocket engine design with matlab and solidworks method of characteristics nozzle tutorial. Introduction pdf rocket nozzles and thrust pdf ideal nozzle fluid mechanics pdf nozzle design. The contour formed allows for a smooth throat, shock free. This thesis presents a program that the user chooses input. Design of a supersonic nozzle using method of characteristics.
A series solution of the nonlinear wave equation was used, only the leading terms in the series being retained in the design proper. A system and method for determining the atomization characteristics of fluids being emitted by a nozzle is disclosed. Automated nozzle design through axissymmetric method of. The nozzle contours are constructed using tile method of characteristics which is detailed in many texts such as reference 2 and are of the wind tunnel or perfect nozzle type. Minimum length nozzle design using method of characteristics. Mod01 lec22 lecture22application of the method of characteristics. In the method of characteristics moc for the supersonic. Characteristic method is the most appropriate method to be used with the supersonic nozzle design.
It is named by minimum length nozzle with centered expansion, which gives the minimal length compared to the other existing types. The supersonic nozzle design has been carried out using method of characteristics which can be applied for designing the nozzle for the pwt for given mach numbers 1517. In the present work, design of both thus, helping in developing the supersonic nozzle. For a firstorder pde partial differential equation, the method of characteristics discovers curves called characteristic curves or just characteristics along which the pde becomes an ordinary differential equation ode. Cfd simulation has been carried out for supersonic nozzle flow with exit mach number of 3 1012. Pdf 15773350 nozzle design method of characteristics. To address the actual conditions, the consideration should be made on account of the phenomena due to the viscous effect, pressure difference with respect to the back pressure, heat conduction and so on. The diverging contour was generated using the method of characteristics. We are making it available for beta testing among the nozzle. The turbulence characteristics of incompressible flow through nozzles at reynolds number of approximately 50,000 were investigated in their study.
Numerical simulation of micronozzle and micronozzlearray. Four nozzle configurations were considered in the study. Method of characteristics an overview sciencedirect topics. In this paper we develop a computer code which uses the method of characteristics and the stream function to define the annular nozzle contour for isentropic, inviscid, irrotational supersonic flows of any working fluid for any userdefined exit mach number. This algorithm uses the method of characteristics moc which is a very popular tool to design a. Recent developments in rocket nozzle configurations. Nag32460, design of exhaust nozzle for the rbcc gtx. Inclined manometer or equivalent device two, as described in section 6.
The type s pitot tube assembly shall have a known coefficient, determined as outlined in section 10. Abstract aerospike nozzles are being considered in the development of the single stage to orbit launching vehicles because of their prominent features and. The method allows for the nozzle boundary to be formed through a full method of characteristics solution. Nozzle design optimization by methodofcharacteristics. Aerospike nozzles are rather unique, in that they are somewhat of a reverse version of the standard bell nozzle. This method can be applied to onedim ensional unsteady flow, two and three. It uses the classic method of characteristics moc technique to design a jet nozzle and analzye the internal flow field, the plume, and the external flow near the nozzle exit. A method for the design of a ducted axisymmetric nozzle for high speed, low density flows is described and this work was carried out in the rules of aerodynamics with the aim of. This can be performed by designing the nozzle surface such that mach waves e. It also tends to preserve wave behavior that is very important for fast, brief, transient calculations that are required for pipeline surge calculations. Method of characteristics the method of characteristics ideal gas ref.
Using method of characteristics to design a bell nozzle this approach prescribes the expansion section of the nozzle, and then uses m. Rocket nozzle geometries georgia institute of technology. This approach is efficient and allows direct comparison with existing preliminary aerodynamic analysis and design methods based on the traditional method of characteristics moc. Nozzle geometry variations on the discharge coefficient. Phillip thompson compressive fluid dynamics, mcgraw hill, 1972, ch. Even hybrid rockets use this tool to design a nozzle. The method of characteristics is older and more developed, whereas. Method of characteristics is a standard approach to the calculation of the supersonic region of a convergingdiverging nozzle. This algorithm uses the method of characteristics moc which is. Schematic of supersonic nozzle design above centerline by the method of characteristics. Method of characteristics is a simple and efficient met hod for supersonic nozzle design. The ideal nozzle designed with moc is able to achieved uniform exit flow conditions 3. In one embodiment, a fluid is emitted through a nozzle while simultaneously sensing vibrations occurring within the nozzle.
It is based on the method laid out in references 2 and 3. General theory of method of characteristics characteristics are lines in a supersonic flow. Once the ode is found, it can be solved along the characteristic curves and transformed into a solution for. Minimum length of the supersonic nozzle has been calculated for the. Whitmore mechanical and aerospace engineering department material taken from anderson, chapter 11. Method of characteristics in this section we explore the method of characteristics when applied to linear and nonlinear equations of order one and above. Jan 16, 2009 a solve for the nozzle exit area that produces the max amount of thrust.
Method of characteristics in this section, we describe a general technique for solving. May 1983 perfect bell nozzle parametric and optimization. Cfd analysis of conical nozzle for mach 3 at various. A nozzle design which does not directly employ the mathematical method of characteristics was evolved by friedrichs 1 o 1944. Bintner design engineer delavan hanufacturing company west des moines, iowa 95 the many varieties of herbicides on the market today, make the proper selection of spray nozzles and nozzle materials an increasingly important and difficult task. I dont know a whole lot about it since ive only used it a few times and never actually designed an entire nozzle with it, but that should at least give you a starting point. Introduction to the method of characteristics and the minimum.
We start by looking at the case when u is a function of only two variables as. Matrix solution cramercramer ss rule v y dv u x dy dx u a v a uv a 0 0. Pdf design of a supersonic nozzle using method of characteristics. These perfect bell nozzles are twodimensional axisymmetric i. The nozzle is to be used in a compact, highmach number wind tunnel for the purpose of material characterization. The nozzle designs created are based on a perfect gas, inviscid nozzle solution algorithm. The method involves the determination of special curves, called characteristics curves, along which the pde becomes a family of. Preliminary numerical simulation using a direct simulation monte carlo dsmc method was conducted to elucidate internal flowfield characteristics of microsinglenozzles and micro nozzle arrays with typical sizes of each rectangular nozzle element of 0. Microsoft powerpoint topic 20 the method of characteristics students author. C to design turning section to achieve wave cancellation at wall. Method of characteristics pdf effects of particles in nozzle flow pdf. Calculation and design of supersonic nozzles for cold gas dynamic spraying using matlab and ansys fluent jeanbaptiste mulumba mbuyamba a dissertation submitted to the faculty of engineering and the built environment, university of the witwatersrand, johannesburg, in ful lment of the requirements for the degree of master of science in engineering.
Such a nozzle is generally known as the ideal nozzle for expanding the gases from the chamber pressure p c to ambient pressure p a. Whitmore mechanical and aerospace engineering department material taken from anderson, chapter 11, pp. This report outlines the pertinent theory and methods for supersonic nozzle design using the method of characteristics. The method of characteristics is a technique for solving hyperbolic partial di. Introduction to the method of characteristics and the minimum length nozzle.
Then, for the external ramp aerospike performs a series of prandtlmeyer expansions from the lip of the cowl, where rre, to the entire length of the. Design, supersonic, scd nozzle, minimum length, method of characteristics. Instead of using a shroud to contain the exit flow. Method of characteristics moc inviscid assumption can use hybrid approach. Design of a pulsefacility nozzle using the rotational method of characteristics richard l. The reflection of a single expansion wave can be analyzed using the method of characteristics. It can then determinine the interactions between these three flow fields. The method of characteristics moc is a numerical procedure appropriate for solving twodimensional compressible flow problems. Characteristics of firstorder partial differential equation. Supersonic nozzles find application in the field of rocket propulsion. The thrust of a nozzle can be shown to reach a maximum when the nozzle is designed for parallel uniform exit flow, with exit plane pressure equal to ambient pressure.
Method of characteristic moc nozzle flowfield solver users. Feb 20, 2017 design mach number, number of expansion waves, ratio of specific heat are supplied by user. A generalized method for the design of optimum rocket nozzles. Then, for the external ramp aerospike performs a series of prandtlmeyer expansions from the lip of the cowl, where rre, to the entire length of the external ramp of the aerospike nozzle. We begin with linear equations and work our way through the semilinear, quasilinear, and fully nonlinear cases. Rocket engine design with matlab and solidworks method. Numerical solution is established for the two dimensional, steady, in viscid. Pdf in this paper, a method based on the theory of characteristics is presented for twodimensional, supersonic nozzle design. Furthermore, this paperstudied the changes in geometry by varying the stagnation temperature and exit. Examples of the method of characteristics in this section, we present several examples of the method of characteristics for solving an ivp initial value problem, without boundary conditions, which is also known as a cauchy problem. The design is done using method of characteristics moc.
The contour formed allows for a smooth throat, shock free nozzle. For simplicity, it is assumed that the sonic line is straight line. One method of finding the most efficient bell contour is the method of characteristics. A e r o s p i k e performs an expansionwave analysis from the throat of the thruster nozzle, where mn 1. Does anybody have any good resources on bell nozzle design. Initially a nozzle contour is designed for parallel flow at the exit. We are making it available for beta testing among the nozzle team members. Method of characteristics mach number compressible.
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