Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Prediction of initiation of low and high explosive fillers due to fragment or projectile impact

A methodology is presented which provides predictions for the probability of initiation of explosion in high explosive filled warheads and in propellant filled rocket motor cases given the impact of compact fragments or of small projectiles. Equations of velocities at which 50 percent of the explosive filled cases will initiate either high or low order are developed for compact fragments, and for projectiles. These data are used to establish the standard deviation of the data from the 50 percent initiation line. Standard deviation is used to provide predictions of the probability of initiation given the impact velocity and other pertinent parameters using equations and logic which are established in a computer model. This computer model uses fragment material properties and encounter parameters to predict fragment impact initiation, and projectile and casing material properties and encounter parameters to predict projectile impact initiation.

Zabel, P. H.↗
NASA NTRS1999

Real-Time Simulation of the X-33 Aerospace Engine

This paper discusses the development and performance of the X-33 Aerospike Engine RealTime Model. This model was developed for the purposes of control law development, six degree-of-freedom trajectory analysis, vehicle system integration testing, and hardware-in-the loop controller verification. The Real-Time Model uses time-step marching solution of non-linear differential equations representing the physical processes involved in the operation of a liquid propellant rocket engine, albeit in a simplified form. These processes include heat transfer, fluid dynamics, combustion, and turbomachine performance. Two engine models are typically employed in order to accurately model maneuvering and the powerpack-out condition where the power section of one engine is used to supply propellants to both engines if one engine malfunctions. The X-33 Real-Time Model is compared to actual hot fire test data and is been found to be in good agreement.

Aguilar, Robert↗
NASA NTRS1995

Rocket-Induced Magnetohydrodynamic Ejector: A Single-Stage-to-Orbit Advanced Propulsion Concept

During the atmospheric boost phase of a rocket trajectory, magnetohydrodynamic (MHD) principles can be utilized to augment the thrust by several hundred percent without the input of additional energy. The concept is an MHD implementation of a thermodynamic ejector. Some ejector history is described and some test data showing the impressive thrust augmentation capabilities of thermodynamic ejectors are provided. A momentum and energy balance is used to derive the equations to predict the MHD ejector performance. Results of these equations are compared with the test data and then applied to a specific performance example. The rocket-induced MHD ejector (RIME) engine is described and a status of the technology and availability of the engine components is provided. A top level vehicle sizing analysis is performed by scaling existing MHD designs to the required flight vehicle levels. The vehicle can achieve orbit using conservative technology. Modest improvements are suggested using recently developed technologies, such as superconducting magnets, which can improve predicted performance well beyond those expected for current single-stage-to-orbit (SSTO) designs.

Cole, John↗
NASA NTRS2002

General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows

Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.

Sondak, Douglas L.↗
NASA NTRS1975

Input guide for computer programs to generate thermodynamic data for air and Freon CF4

FORTRAN computer programs were developed to calculate the thermodynamic properties of Freon 14 and air for isentropic expansion from given plenum conditions. Thermodynamic properties for air are calculated with equations derived from the Beattie-Bridgeman nonstandard equation of state and, for Freon 14, with equations derived from the Redlich-Quang nonstandard equation of state. These two gases are used in scale model testing of model rocket nozzle flow fields which requires simulation of the prototype plume shape with a cold flow test approach. Utility of the computer programs for use in analytical prediction of flow fields is enhanced by arranging card or tape output of the data in a format compatible with a method-of-characteristics computer program.

Tevepaugh, J. A.↗
NASA NTRS1979

A nozzle boundary layer model including the subsonic sublayer usable for determining boundary layer effects on plume flowfields

A model for the boundary layer at the exit plane of a rocket nozzle was developed which, unlike most previous models, includes the subsonic sublayer. The equations for the flow near the nozzle exit plane are presented and the method by which the subsonic sublayer transitions to supersonic flow in the plume is described. The resulting model describes the entire boundary layer and can be used to provide a startline for method-of-characteristics calculations of plume flowfields. The model was incorporated into a method of characteristics computer program and comparisons of computed results to experimental data show good agreement. The data used in the comparisons were obtained in tests in which mass fluxes from a 22.2-N (5 lbf) thrust engine were measured at angles off the nozzle centerline of up to 150 deg. Additional comparisons were made with data obtained during tests of a 0.89-N (0.2 lbr) monopropellant thruster and from the OH-64 space shuttle heating tests. The agreement with the data indicates that the model can be used for calculating plume backflow properties.

Cooper, B. P., Jr.↗
NASA NTRS1986

SSME thrust chamber modeling with Navier Stokes equations

The capability of predicting two-dimensional, compressible and reacting flow in the combustion chamber and nozzle of the Space Shuttle Main Engine (SSME) is demonstrated. A nonorthogonal body fitted coordinate system has been used to represent the combustor and nozzle geometry. The Navier-Stokes equations are solved for the entire thrust chamber with the k-epsilon turbulence model accounting for compressibility and large pressure gradients effects. Results of the computational test cases reveal all expected features of the transonic nozzle flows including location of sonic line, internal shock and boundary layer build-up. Calculated performance parameters such as thrust, flow rate, and specific impulse are also in reasonble agreement with available data. The results show promising potential of solving full Navier-Stokes equations with heat transfer and two-phase combustion in truly comprehensive modeling of rocket engines.

Przekwas, A. J.↗
NASA NTRS1991

Nonlinear analysis of longitudinal-mode liquid propellant rocket combustion instability

A computational technique for the nonlinear analysis of longitudinal-mode liquid propellant rocket combustion instability is examined based on the unsteady, quasi-one-dimensional Euler equations with appropriate source terms introduced to account for interphase transport coupling with the spray. The method is first assessed for unsteady, nonreacting, isentropic duct flow with specified admittances at the outflow and inflow boundaries. For small amplitude disturbances, numerical results based on a sufficient number of grid points compare favorably with predictions from a small-disturbance linearized analysis.

Jeng, San-Mou↗
NASA NTRS1993

Computation of incompressible viscous flows through turbopump components

Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. the equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use a one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. In the fuel pump impeller, the effect of downstream boundary conditions is investigated. Flow analyses at 80 percent, 100 percent, and 120 percent of design conditions are presented.

Kiris, Cetin↗
NASA NTRS1993

Incompressible Navier-Stokes computations of rotating flows

Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high-pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. Flow analyses at 80-, 100-, and 120-percent of design conditions are presented.

Kiris, Cetin↗
NASA NTRS1993

Development of a droplet breakup model considering aerodynamic and droplet collision effects

A model is currently under development to predict the occurrence and outcome of spray droplet breakup induced by aerodynamic forces and droplet collisions. It is speculated that these phenomena may be significant in determining the droplet size distribution in a spray subjected to acoustic velocity fluctuations. The goal is to integrate this breakup model into a larger spray model in order to examine the effects of combustion instabilities on liquid rocket motor fuel sprays. The model is composed of three fundamental components: a dynamic equation governing the deformation of the droplet, a criterion for breakage based on the amount of deformation energy stored in the droplet and an energy balance based equation to predict the Sauter mean diameter of the fragments resulting from breakup. Comparison with published data for aerodynamic breakup indicates good agreement in terms of predicting the occurrence of breakup. However, the model significantly over predicts the size of the resulting fragments. This portion of the model is still under development.

Wert, K. L.↗
NASA NTRS1994

Progress In Incompressible Pump Flow Calculations

Steady and unsteady flows for propulsion systems are efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard kappa - epsilon model equations. The resulting computer code is applied to the flow analysis inside an advanced rocket pump impeller in steadily rotating reference frames. Numerical results are compared with experimental measurements. The effects of exit and shroud cavities with the leak-age flow are investigated. Time-accurate incompressible Navier-Stokes formulation with the overlapped grid scheme capability was evaluated by using MIT flapping foil experiment. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗
NASA NTRS2015

Skylon Aerodynamics and SABRE Plumes

An independent partial assessment is provided of the technical viability of the Skylon aerospace plane concept, developed by Reaction Engines Limited (REL). The objectives are to verify REL's engineering estimates of airframe aerodynamics during powered flight and to assess the impact of Synergetic Air-Breathing Rocket Engine (SABRE) plumes on the aft fuselage. Pressure lift and drag coefficients derived from simulations conducted with Euler equations for unpowered flight compare very well with those REL computed with engineering methods. The REL coefficients for powered flight are increasingly less acceptable as the freestream Mach number is increased beyond 8.5, because the engineering estimates did not account for the increasing favorable (in terms of drag and lift coefficients) effect of underexpanded rocket engine plumes on the aft fuselage. At Mach numbers greater than 8.5, the thermal environment around the aft fuselage is a known unknown−a potential design and/or performance risk issue. The adverse effects of shock waves on the aft fuselage and plumeinduced flow separation are other potential risks. The development of an operational reusable launcher from the Skylon concept necessitates the judicious use of a combination of engineering methods, advanced methods based on required physics or analytical fidelity, test data, and independent assessments.

Mehta, Unmeel↗
NASA NTRS1993

A generic efficient adaptive grid scheme for rocket propulsion modeling

The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.

Mo, J. D.↗
NASA NTRS1991

Examination of various turbulence models for application in liquid rocket thrust chambers

There is a large variety of turbulence models available. These models include direct numerical simulation, large eddy simulation, Reynolds stress/flux model, zero equation model, one equation model, two equation k-epsilon model, multiple-scale model, etc. Each turbulence model contains different physical assumptions and requirements. The natures of turbulence are randomness, irregularity, diffusivity and dissipation. The capabilities of the turbulence models, including physical strength, weakness, limitations, as well as numerical and computational considerations, are reviewed. Recommendations are made for the potential application of a turbulence model in thrust chamber and performance prediction programs. The full Reynolds stress model is recommended. In a workshop, specifically called for the assessment of turbulence models for applications in liquid rocket thrust chambers, most of the experts present were also in favor of the recommendation of the Reynolds stress model.

Hung, R. J.↗
NASA NTRS1971

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Levine, J. N.↗
NASA NTRS1974

Design and calibration of a rocket-borne electron spectrometer for investigation of particle ionization in the nighttime midlatitude E region

An explanation was developed for the formation, near midnight at midlatitudes, of a broad electron density layer extending approximately from 120 to 180 km and usually referred to as the intermediate E layer. The responsible mechanism is believed to be the converging vertical ion drifts resulting from winds of the solar semidiurnal tide. Numerical solutions of the continuity equation appropriate to the intermediate layer is described for particular models of ion drift, diffusion coefficents, and ionization production. Analysis of rocket observations of the layer show that the ionization rate is highly correlated with the planetary geomagnetic index, K sub p. Particle flux measurements support the idea that energetic electrons are the principal source of this ionization. A semiconductor spectrometer experiment for investigation of the particle flux, spectrum, and angular properties was designed and successfully flown on a Nike Apache rocket. A detailed description of the theory, design, and calibration of the experiment and some preliminary results presented.

Voss, H. D.↗