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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Pulsed Ejector Wave Propogation Test Program

The development of, and initial test data from, a nondetonating Pulse Detonation Engine (PDE) simulator tested in the NASA Glenn 1 x 1 foot Supersonic Wind Tunnel (SWT) is presented in this paper. The concept is a pulsed ejector driven by the simulated exhaust of a PDE. This pro- gram is applicable to a PDE entombed in a ramjet flowpath, i.e., a PDE combined-cycle propulsion system. The ejector primary flow is a pulsed, uiiderexpanded, supersonic nozzle simulating the supersonic waves ema- nating from a PDE, while the ejector secondary flow is the 1 x 1 foot SWT test section operated at subsonic Mach numbers. The objective is not to study the detonation details, but the wave physics including t,he start- ing vortices, the extent of propagation of the wave front, the reflection of the wave from the secondary flowpath walls, and the timing of these events of a pulsed ejector, and correlate these with Computational Fluid Dynamics (CFD) code predictions. Pulsed ejectors have been shown to result in a 3 to 1 improvement in LID (length-to-diameter) and a near 2 to 1 improvement in thrust augmentation over a steady ejector. This program will also explore the extent of upstream interactions between an inlet and large, periodically applied, backpressures to the inlet as would be present due to combustion tube detonations in a PDE. These interactions could result in inlet unstart or buzz for a supersonic mixed compression inlet. The design of the present experiment entailed the use of an 2-t diagram characteristics code to study the nozzle filling and purging timescales as well as a series of CFD analyses conducted using the WIND code. The WIND code is a general purpose CFD code for solution of the Reynolds averaged Navier-Stokes equations and can be applied to both steady state and time-accurate calculations. The first, proof-of-concept, test entry (spring 2001) pressure distributions shown here indicate the simulation concept was successful and therefore the experimental approach is sound.

Fernandez, Rene↗
NASA NTRS1993

A semi-Lagrangian approach to the shallow water equation

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

Bates, J. R.↗
NASA NTRS2002

Innovative Airbreathing Propulsion Concepts for High-speed Applications

The current cost to launch payloads to low earth orbit (LEO) is approximately loo00 U.S. dollars ($) per pound ($22000 per kilogram). This high cost limits our ability to pursue space science and hinders the development of new markets and a productive space enterprise. This enterprise includes NASA's space launch needs and those of industry, universities, the military, and other U.S. government agencies. NASA's Advanced Space Transportation Program (ASTP) proposes a vision of the future where space travel is as routine as in today's commercial air transportation systems. Dramatically lower launch costs will be required to make this vision a reality. In order to provide more affordable access to space, NASA has established new goals in its Aeronautics and Space Transportation plan. These goals target a reduction in the cost of launching payloads to LEO to $lo00 per pound ($2200 per kilogram) by 2007 and to $100'~ per pound by 2025 while increasing safety by orders of magnitude. Several programs within NASA are addressing innovative propulsion systems that offer potential for reducing launch costs. Various air-breathing propulsion systems currently are being investigated under these programs. The NASA Aerospace Propulsion and Power Base Research and Technology Program supports long-term fundamental research and is managed at GLenn Research Center. Currently funded areas relevant to space transportation include hybrid hyperspeed propulsion (HHP) and pulse detonation engine (PDE) research. The HHP Program currently is addressing rocket-based combined cycle and turbine-based combined cycle systems. The PDE research program has the goal of demonstrating the feasibility of PDE-based hybrid-cycle and combined cycle propulsion systems that meet NASA's aviation and access-to-space goals. The ASTP also is part of the Base Research and Technology Program and is managed at the Marshall Space Flight Center. As technologies developed under the Aerospace Propulsion and Power Base Research and Technology Program mature, they are incorporated into ASTP. One example of this is rocket-based combined cycle systems that are being considered as part of ASTP. The NASA Ultra Efficient Engine Technology (UEET) Program has the goal of developing propulsion system component technology that is relevant to a wide range of vehicle missions. In addition to subsonic and supersonic speed regimes, it includes the hypersonic speed regime. More specifically, component technologies for turbine-based combined cycle engines are being developed as part of UEET.

Whitlow, Woodrow, Jr.↗
NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗
NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗
NASA NTRS1972

Optical properties of materials at low temperature and their application to optical detection

A lumped model to represent the photodielectric effect is developed. An analog simulation for a sample in a microwave cavity with a static magnetic field is developed. A system to measure continuously the PDE is analyzed. A performance factor to compared PD detectors versus ac photoconductors is computed. The operating conditions are defined for the appropriate noise conditions. The detectivity of the detector is found to be limited by the semiconductor sample noise.

Hartwig, W. H.↗
NASA NTRS1995

The estimation of material and patch parameters in a PDE-based circular plate model

The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions form the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio, and Kelvin-Voigt damping for the system as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically-derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics.

Banks, H. T.↗
NASA NTRS1994

A PDE-based methodology for modeling, parameter estimation and feedback control in structural and structural acoustic systems

A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn lead to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.

Banks, H. T.↗
NASA NTRS2005

Thrust Augmentation Measurements for a Pulse Detonation Engine Driven Ejector

Thrust augmentation results of an ongoing study of pulse detonation engine driven ejectors are presented and discussed. The experiments were conducted using a pulse detonation engine (PDE) setup with various ejector configurations. The PDE used in these experiments utilizes ethylene (C2H4) as the fuel, and an equi-molar mixture of oxygen and nitrogen as the oxidizer at an equivalence ratio of one. High fidelity thrust measurements were made using an integrated spring damper system. The baseline thrust of the PDE engine was first measured and agrees with experimental and modeling results found in the literature. Thrust augmentation measurements were then made for constant diameter ejectors. The parameter space for the study included ejector length, PDE tube exit to ejector tube inlet overlap distance, and straight versus rounded ejector inlets. The relationship between the thrust augmentation results and various physical phenomena is described. To further understand the flow dynamics, shadow graph images of the exiting shock wave front from the PDE were also made. For the studied parameter space, the results showed a maximum augmentation of 40%. Further increase in augmentation is possible if the geometry of the ejector is tailored, a topic currently studied by numerous groups in the field.

Pal, S.↗
NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗
NASA NTRS1989

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗
NASA NTRS1995

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗
NASA NTRS2004

Effect of Detonation through a Turbine Stage

Pulse detonation engines (PDE) have been investigated as a more efficient means of propulsion due to its constant volume combustion rather than the more often used constant pressure combustion of other propulsion systems. It has been proposed that a hybrid PDE-gas turbine engine would be a feasible means of improving the efficiency of the typical constant pressure combustion gas turbine cycle. In this proposed system, multiple pulse detonation tubes would replace the conventional combustor. Also, some of the compressor stages may be removed due to the pressure rise gained across the detonation wave. The benefits of higher thermal efficiency and reduced compressor size may come at a cost. The first question that arises is the unsteadiness in the flow created by the pulse detonation tubes. A constant pressure combustor has the advantage of supplying a steady and large mass flow rate. The use of the pulse detonation tubes will create an unsteady mass flow which will have currently unknown effects on the turbine located downstream of the combustor. Using multiple pulse detonation tubes will hopefully improve the unsteadiness. The interaction between the turbine and the shock waves exiting the tubes will also have an unknown effect. Noise levels are also a concern with this hybrid system. These unknown effects are being investigated using TURBO, an unsteady turbomachinery flow simulation code developed at Mississippi State University. A baseline case corresponding to a system using a constant pressure combustor with the same mass flow rate achieved with the pulse detonation hybrid system will be investigated first.

Ellis, Matthew T.↗
NASA NTRSDate not supplied

Laminar-Turbulent Transition in High Mach-Number Flows

Accurate prediction of laminar-turbulent transition is critical for the design and characterization of high-speed flight systems. Presently, laminar-turbulent transition prediction in computational fluid dynamics (CFD) is accomplished using PDE-based models coupled to the governing equations of the flow system. Current industrial models suffer significant performance issues when analyzing high-speed systems because they were developed for lower speed flows. Current research focuses on multiple solutions to this problem. The coupling of physics-based stability analysis tools which produce quality transition predictions for high-speed flows to NASA’s OVERFLOW CFD solver is being pursued, as well as the implementation and improvement of emerging models developed specifically for high-speed flow.

High-Speed Flow↗
NASA NTRS1989

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Tzes, Anthony P.↗
NASA NTRS2000

PDE Nozzle Optimization Using a Genetic Algorithm

Genetic algorithms, which simulate evolution in natural systems, have been used to find solutions to optimization problems that seem intractable to standard approaches. In this study, the feasibility of using a GA to find an optimum, fixed profile nozzle for a pulse detonation engine (PDE) is demonstrated. The objective was to maximize impulse during the detonation wave passage and blow-down phases of operation. Impulse of each profile variant was obtained by using the CFD code Mozart/2.0 to simulate the transient flow. After 7 generations, the method has identified a nozzle profile that certainly is a candidate for optimum solution. The constraints on the generality of this possible solution remain to be clarified.

Billings, Dana↗
NASA NTRS2002

Progress in the Development of a Nozzle Design Methodology for Pulsed Detonation Engines

The Johns Hopkins University Applied Physics Laboratory (JHU/APL), in support of the NASA Glenn Research Center (NASA GRC), is investigating performance methodologies and system integration issues related to Pulsed Detonation Engine (PDE) nozzles. The primary goal of this ongoing effort is to develop design and performance assessment methodologies applicable to PDE exit nozzle(s). APL is currently focusing its efforts on a common plenum chamber design that collects the exhaust products from multiple PDE tubes prior to expansion in a single converging-diverging exit nozzle. To accomplish this goal, a time-dependent, quasi-one-dimensional analysis for determining the flow properties in and through a single plenum and exhaust nozzle is underway. In support of these design activities, parallel modeling efforts using commercial Computational Fluid Dynamics (CFD) software are on-going. These efforts include both two and three-dimensional as well as steady and time-dependent computations to assess the flow in and through these devices. This paper discusses the progress in developing this nozzle design methodology.

Leary, B. A.↗
NASA NTRS2002

Oxidation- and Creep-Enhanced Fatigue of Haynes 188 Alloy-Oxide Scale System Under Simulated Pulse Detonation Engine Conditions

The development of the pulse detonation engine (PDE) requires robust design of the engine components that are capable of enduring harsh detonation environments. In this study, a high cycle thermal fatigue test rig was developed for evaluating candidate PDE combustor materials using a CO2 laser. The high cycle thermal fatigue behavior of Haynes 188 alloy was investigated under an enhanced pulsed laser test condition of 30 Hz cycle frequency (33 ms pulse period, and 10 ms pulse width including 0.2 ms pulse spike). The temperature swings generated by the laser pulses near the specimen surface were characterized by using one-dimensional finite difference modeling combined with experimental measurements. The temperature swings resulted in significant thermal cyclic stresses in the oxide scale/alloy system, and induced extensive surface cracking. Striations of various sizes were observed at the cracked surfaces and oxide/alloy interfaces under the cyclic stresses. The test results indicated that oxidation and creep-enhanced fatigue at the oxide scale/alloy interface was an important mechanism for the surface crack initiation and propagation under the simulated PDE condition.

Zhu, Dongming↗