2024 | Book

# Rocket Propulsion Primer

Authors: Subramaniam Krishnan, Jeenu Raghavan

Publisher: Springer Nature Singapore

2024 | Book

Authors: Subramaniam Krishnan, Jeenu Raghavan

Publisher: Springer Nature Singapore

This textbook covers fundamentals of rocket propulsion such as history, classification, qualitative design, quantitative design of internal ballistics and rocket vehicle optimization. It is intended to be used as a textbook by the undergraduate/advanced undergraduate students of aerospace engineering. It further describes the classification of aerospace propulsion, two-phase flows, nozzle contour design, advanced nozzle concepts (plug and expansion deflection nozzles) and materials. It also deals with the optimization of multistage rocket vehicles and their trajectories with reference to the currently operational orbital launch vehicles. This textbook contains numerous end-of-chapter problems to aid in self-learning of the students. It will be highly useful for the aerospace and mechanical engineering students. This can also be used as a reference guide by the scientists and engineers working in the areas of aerospace engineering.

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Abstract

Tracking the spread of rocket technology from China to America over six centuries; and drawing the biographical sketches of rocket pioneers form the subject matter of this chapter. \(\bullet \) The demonstrations of action–reaction principle in the first century B.C. by the Greek philosopher Archytas through his toy pigeon and by the Greek mathematician Hero of Alexandria through his aeolipile are presented. The rocket-technology route evolved through battles: from Chinese to Mongols (battle of Kai-fung-fu in 1232), from Mongols to Arabs, from Arabs to European Countries, and as a closure from Europe to America at the battle of Bladensburg in 1814. \(\bullet \) With undaunted determination and dedicated perseverance, three eminent rocket pioneers Tsiolkovsky, Goddard, and Oberth independently worked tirelessly against many odds such as delayed recognition, acute shortage of funding, rebuke, criticism, and ill health. Biographical sketches of these great men are drawn. \(\bullet \) The use of Tsiolkovsky equation for velocity increments of space vehicles is described along with problems with answers at the chapter end.

Abstract

Classification and operating principles of air-breathing engines (variants of gas turbines and ramjets) and non-air-breathing engines (chemical-, electric-, and nuclear-rockets) are discussed in this chapter. \(\bullet \) How the suitability of air-breathing engines for different flight ranges—subsonic to hypersonic—changes from turboshaft to scramjet is addressed. \(\bullet \) Merits and demerits of solid-, liquid-, and hybrid-rockets are discussed. Compared to solid rockets, liquid engines find wider applications. \(\bullet \) Most electric rockets, contrary to chemical ones, are of unlimited energy but limited by power. And, this makes them suitable for interplanetary travel and beyond. Working principles of resistojets, arcjets, ion engines, and Hall-, pulsed-plasma-, magneto-plasmadynamic-, and pulsed-inductive-thrusters are explained. Features of flight-proven electric thrusters are tabled. \(\bullet \) For interplanetary travel and beyond by humans, a relatively large power with unlimited energy through nuclear propulsion is the requirement. \(\bullet \) Number of concept questions and numerical problems with answers are included at the chapter end.

Abstract

Internal ballistics, performance, and construction of rocket engines are considered in this chapter. \(\bullet \) Under- and over-expansion, and adaption; nozzle-divergence loss; and effects of propellant density and \(I_{sp}\) on stage mass are all discussed. Nozzle-flow equations for mass-flow rate, velocity, and area ratio are derived. Nozzle-flow separation, maximum thrust, thrust controls, wider altitude operations, and side loads are all considered. Characteristic velocity, thrust coefficient, and \(I_{sp}\), and their experimental and theoretical values towards engine development are discussed. Frozen and equilibrium flow are introduced. \(\bullet \) A two-phase flow model is included. \(\bullet \) Considering real flow effects and turn-back angles, the optimum nozzle contours are discussed. Rao’s charts for optimum nozzle contours are presented. \(\bullet \) Characteristics of plug and ED nozzles are discussed. \(\bullet \) Polymeric materials, composites, and structural as well as high-temperature alloys, and their applications in the construction of solid and liquid rockets are considered. \(\bullet \) Under the sections worked examples and at the end a large number of concept questions and numerical problems with answers are included.

*The pedagogy of the energy minimization technique to calculate equilibrium composition and rocket internal ballistics is the purpose of this chapter.* \(\bullet \) Classification and composition selection are discussed for propellants. Data on proven LOX/LH2 and LOX/Kerosene engines are presented. Thermodynamic data of many propellant ingredients and additives are tabled. And, to evaluate the species’ properties \(\overline{c}_{p,j}^0\), \(\overline{h}_j^0\), and \(\overline{s}_j^0\), the fourth-order polynomials are introduced along with the coefficients’ values. \(\bullet \) The chemical potential \(\mu _j\) is the unit molar Gibbs energy of species *j*. Hence, the equilibrium is reached when \(\sum \mu _j\) reaches a minimum along with the conservation of elements. Following this and adopting Lagrange multipliers, the governing equations are obtained. Next, to simplify calculations, reduced Gibbs correction equations are derived. Using the calculated compositions, the three key derivatives \((\partial v/\partial T)_p\), \((\partial v/\partial p)_T\), and \(c_p\) are evaluated. Adopting all these, rocket performance parameters \(c^*\), \(C_F\), and \(I_{sp}\) under equilibrium or frozen flows are quantitatively evaluated. Detailed design analyses of internal ballistics and engine envelope for a proven engine are presented. \(\bullet \) Under the Sections worked examples and at the end, a large number of concept questions and engine design problems with answers are included.

Abstract

The stage optimization of serially staged rocket vehicles is discussed in this chapter. \(\bullet \) The tabled data of orbital launch vehicles and stage structural coefficients \(\varepsilon \)’s indicate that LOX/Kerosene and LOX/LH2 vehicles are preferred for large payloads. And, solid propellant stages are of high \(\varepsilon \)’s. \(\bullet \) The gravity- and drag-free optimization along with its two variants, marked-up terminal velocity and scaled-up stage mass, are discussed using Lagrange multipliers. \(\bullet \) The different layers of the Earth’s atmosphere up to 10,000 km are detailed. The equation for density estimation in the homosphere \(0 \le h \le 120\,\textrm{km}\) is derived. The atmospheric continuum, Knudsen number, and gravity variation with altitude are explained. \(\bullet \) Considering drag and gravity, the equations of motion in polar coordinates are drawn for serially staged rocket vehicles. To enable trajectory optimization, the equations for vertical climb, constant pitch angle maneuver, gravity turn, bilinear and linear tangent steering, and coasting are drawn. \(\bullet \) The ascent of sounding rockets is analyzed considering burnout-velocity and -altitude, and coasting height. \(\bullet \) Under the sections worked examples and at the end, a large number of concept questions and numerical problems with answers are included.