Studies of the equatorial ionosphere using rocket techniques
Equatorial ionospheric propagation studies using rocket sounding techniques
MAGNETIC EQUATOR↗
SEARCH · Engineering Papers
Results for “rocket equation”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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On the dynamic characteristics of a variable- mass slender elastic body under high accelerations.
Dynamic characteristics of variable mass slender elastic body, solving vector differential equations
SOLID PROPELLANT ROCKET ENGINE↗
Stable limit cycles and triggering limits of the first radial model in unstable liquid rockets
Stable limit cycles and triggering limits of first radial mode in nonlinearly unstable liquid propellant rocket motors, using wave equation and Galerkin method
Powell, E. A.↗
Numerical analysis of bipropellant combustion in liquid thrust chambers by an Eulerian-Eulerian approach
The liquid thrust chambers performance (LTCP) code is used for parametric studies of flow and combustion in liquid rocket engines. Multiphase flow equations are solved in an Eulerian-Eulerian framework, and multistep finite rate chemistry is incorporated. The discretization scheme is fully implicit and is based on the total variation diminishing (TVD) scheme, which is accurate, robust, very efficient and capable of handling steep gradients and stiff chemistry. Effects of injection velocity and chamber size have been considered, and the effect of group combustion on the evaporation rate has been studied for a dense spray.
Dang, A. L.↗
Pressure Oscillations and Structural Vibrations in Space Shuttle RSRM and ETM-3 Motors
The complex interactions between internal motor pressure oscillations resulting from vortex shedding, the motor's internal acoustic modes, and the motor's structural vibration modes were assessed for the Space Shuttle four-segment booster Reusable Solid Rocket Motor and for the five-segment engineering test motor ETM-3. Two approaches were applied 1) a predictive procedure based on numerically solving modal representations of a solid rocket motor s acoustic equations of motion and 2) a computational fluid dynamics two-dimensional axi-symmetric large eddy simulation at discrete motor burn times.
Mason, D. R.↗
Expendable Launch Vehicles Briefing and Basic Rocketry Physics
This slide presentation is composed of two parts. The first part shows pictures of launch vehicles and lift offs or in the case of the Pegasus launch vehicle separations. The second part discusses the basic physics of rocketry, starting with Newton's three physical laws that form the basis for classical mechanics. It includes a review of the basic equations that define the physics of rocket science, such as total impulse, specific impulse, effective exhaust velocity, mass ratio, propellant mass fraction, and the equations that combine to arrive at the thrust of the rocket. The effect of atmospheric pressure is reviewed, as is the effect of propellant mix on specific impulse.
Delgado, Luis G.↗
Dynamics of variable mass systems with application to the star 48 solid rocket motor
Existing methods for the derivation of equations of motion of variable mass systems are reviewed and compared, the end product being a system of general dynamical equations for variable mass systems. These equations are used to study the lateral stability problem associated with the Star 48 solid rocket engine. It is shown that the shape of the combustion chamber could have a significant effect on the lateral stability of the rocket; specifically, a short and wide combustion chamber is destabilizing, while a long and narrow chamber is stabilizing.
Eke, F. O.↗
Approximate optimal guidance for the advanced launch system
A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.
Feeley, T. S.↗
Note on the semi-annual wind variation in the equatorial stratosphere.
Semiannual wind variation in equatorial stratosphere analyzed for origin from rocket sounding data
STRATOSPHERE↗
A study of the steady state spray equation.
A constant cross-sectional area rocket motor was used to study the combustion of a spray of ethanol in gaseous oxygen. The variables of the combustion gas and the flux of liquid ethanol versus the distance from the injector, were determined by an experimental-analytical method which did not require any assumption about the distribution, drag, and vaporization of the fuel drops (static pressure measurements were used instead). The steady-state spray equation is solved, for various drag and vaporization models, and the local flux of liquid ethanol thus calculated is compared with the experimentally determined one for the purpose of selecting a proper spray combustion model.
Bracco, F. V.↗
A real-time approximate optimal guidance law for flight in a plane
A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.
Feeley, Timothy S.↗
Numerical study of nozzle wall cooling for nuclear thermal rockets
The flowfields and performance of nuclear thermal rockets, which utilize radiation and film-cooling to cool the nozzle extension, are studied by solving the Navier-Stokes equations and species equations. The thrust level of the rocket for the present study is about 75,000 lb(f) for a chamber pressure of 68 atm(l,000 psi) and a chamber temperature of 2700 K. The throat radius of the nozzle is 0.0936 m and the area ratios of the nozzles are 300 and 500. It is assumed that the flow is chemically frozen and the turbulence is simulated by the modified Baldwin-Lomax turbulence model. The calculated results for various area ratios and film mass-flow rates are presented as Mach number contours, variations of nozzle wall temperature, exit profiles, and vacuum specific impulses. The present study shows that by selecting the flow rate of the film-cooling hydrogen and area ratio of the nozzle correctly, high area ratio nozzle extensions can be cooled effectively with radiation and film-cooling without significant penalty in performance.
Kim, Suk C.↗
Modeling of Non-Spherical Droplet Dynamics
A two-dimensional time-dependent computer code based on the modified Arbitrary Lagrangian Eulerian (ALE) technique, has been developed to simulate non-spherical droplet dynamics and evaporation under convective flows at real rocket combustion chamber conditions. The equations of mass, momentum, energy and species are simultaneously solved for both liquid and gas phases with an accurate dynamic interface tracking. The jump boundary conditions across the deforming droplet surface are obtained by applying the integral forms of conservation of mass, momentum, and energy. At each time step, the interface geometry and flow properties at the droplet surface are implicitly solved by satisfying the interface boundary conditions. A Lagrangian technique was developed to track the arbitrarily moving interface between the liquid droplet and the external gas. An elliptic grid generator is adopted to dynamically reconstruct grids both inside and outside the droplet surface. This code has been used to study droplet oscillation, droplet deformation/breakup, nonspherical droplet evaporation in both low and high pressure convective flows. This presentation briefly describes the numerical algorithm for modeling of the nonspherical droplet dynamics and demonstrates the representative simulation results of nonspherical droplet evaporation at low and high pressure convective flows. Potential applications of this code to rocket combustor design and performance predictions are discussed.
Deng, Zheng-Tao↗
A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle
A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.
Orr, Jeb S.↗
Ignition transient analysis of solid rocket motor
To predict pressure-time and thrust-time behavior of solid rocket motors, a one-dimensional numerical model is developed. The ignition phase of solid rocket motors (time less than 0.4 sec) depends critically on complex interactions among many elements, such as rocket geometry, heat and mass transfer, flow development, and chemical reactions. The present model solves the mass, momentum, and energy equations governing the transfer processes in the rocket chamber as well as the attached converging-diverging nozzle. A qualitative agreement with the SRM test data in terms of head-end pressure gradient and the total thrust build-up is obtained. Numerical results show that the burning rate in the star-segmented head-end section and the erosive burning are two important parameters in the ignition transient of the solid rocket motor (SRM).
Han, Samuel S.↗
Predictions of launch-induced, near-field acoustics of clustered rocket engines using a scaling approach
A scaling technique is proposed for the prediction of clustered rocket engine, near-field acoustics. Scaling equations predict the mean square pressures and power spectral density (PSD) of an unknown vehicle, using near-field measurements from a similar vehicle. Separation of nonhomogeneous Shuttle acoustics into Space Shuttle Main Engine (SSME) and Solid Rocket Booster (SRB) component acoustics forms the basis for verification of the proposed scaling equations. Three separate models, based on the total Shuttle PSD, a three-SSME vehicle PSD, and a two-SRB vehicle PSD, are recommended for the Advanced Launch System (ALS) near-field predictions. Acoustic efficiency, equivalent diameter of closely/widely spaced clustered engines, and the use of a distance-dependent spectra for scaling ALS vehicle near-field acoustics are briefly addressed.
Sepcenko, Valentin↗
Development of Erosive Burning Models for CFD Predictions of Solid Rocket Motor Internal Environments
Four erosive burning models, equations (11) to (14). are developed in this work by using a power law relationship to correlate (1) the erosive burning ratio and the local velocity gradient at propellant surfaces; (2) the erosive burning ratio and the velocity gradient divided by centerline velocity; (3) the erosive burning difference and the local velocity gradient at propellant surfaces; and (4) the erosive burning difference and the velocity gradient divided by centerline velocity. These models depend on the local velocity gradient at the propellant surface (or the velocity gradient divided by centerline velocity) only and, unlike other empirical models, are independent of the motor size. It was argued that, since the erosive burning is a local phenomenon occurring near the surface of the solid propellant, the erosive burning ratio should be independent of the bore diameter if it is correlated with some local flow parameters such as the velocity gradient at the propellant surface. This seems to be true considering the good results obtained by applying these models, which are developed from the small size 5 inch CP tandem motor testing, to CFD simulations of much bigger motors.
Wang, Qun-Zhen↗
Computational fluid dynamic analysis of hybrid rocket combustor flowfields
Computational fluid dynamic analyses of the Navier-Stokes equations coupled with solid-phase pyrolysis, gas-phase combustion, turbulence and radiation are performed to study hybrid rocket combustor flowfields. The computational study is closely co-ordinated with a companion experimental program using a planar slab burner configuration with HTPB as fuel and gaseous oxygen. Computational predictions agree reasonably well with measurement data of fuel regression rates and surface temperatures. Additionally, most of the parametric trends predicted by the model are in general agreement with experimental trends. The computational model is applied to extend the results from the lab-scale to a full-scale axisymmetric configuration. The numerical predictions indicate that the full-scale configuration burns at a slower rate than the lab-scale combustor under identical specific flow rate conditions. The results demonstrate that detailed CFD analyses can play a useful role in the design of hybrid combustors.
Venkateswaran, S.↗