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At least 235 records · Page 13

Time-Accurate Computational Fluid Dynamics Simulation of a Pair of Moving Solid Rocket Boosters

Since the Columbia accident, the threat to the Shuttle launch vehicle from debris during the liftoff timeframe has been assessed by the Liftoff Debris Team at NASA/MSFC. In addition to engineering methods of analysis, CFD-generated flow fields during the liftoff timeframe have been used in conjunction with 3-DOF debris transport methods to predict the motion of liftoff debris. Early models made use of a quasi-steady flow field approximation with the vehicle positioned at a fixed location relative to the ground; however, a moving overset mesh capability has recently been developed for the Loci/CHEM CFD software which enables higher-fidelity simulation of the Shuttle transient plume startup and liftoff environment. The present work details the simulation of the launch pad and mobile launch platform (MLP) with truncated solid rocket boosters (SRBs) moving in a prescribed liftoff trajectory derived from Shuttle flight measurements. Using Loci/CHEM, time-accurate RANS and hybrid RANS/LES simulations were performed for the timeframe T0+0 to T0+3.5 seconds, which consists of SRB startup to a vehicle altitude of approximately 90 feet above the MLP. Analysis of the transient flowfield focuses on the evolution of the SRB plumes in the MLP plume holes and the flame trench, impingement on the flame deflector, and especially impingment on the MLP deck resulting in upward flow which is a transport mechanism for debris. The results show excellent qualitative agreement with the visual record from past Shuttle flights, and comparisons to pressure measurements in the flame trench and on the MLP provide confidence in these simulation capabilities.

Strutzenberg, Louise L.↗

Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of Differential Dynamic Programming (DDP) with the Optimal Reciprocal Collision Avoidance (ORCA) algorithm as the basis for a new algorithm, titled Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance DDP (COBRA-DDP), for trajectory replanning and collision avoidance for Urban Air Mobility (UAM) vehicles. State-constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm start the state constrained DDP algorithms to decrease computation time. Its benefits and effectiveness of the algorithm are demonstrated on a UAM Vertical Takeoff and Landing (VTOL) vehicle simulation with highly nonlinear dynamics.

Optimal Reciprocal Collision Avoidance↗

Comparison of beam and shell theories for the vibrations of thin turbomachinery blades

Vibration analysis of turbomachinery blades has traditionally been carried out by means of beam theory. In recent years two-dimensional methods of blade vibration analysis have been developed, most of which utilize finite elements and tend to require considerable computation time. More recently a two-dimensional method of blade analysis has evolved which does not require finite elements and is based upon shell equations. The present investigation has the primary objective to demonstrate the accuracy and limitations of blade vibration analyses which utilize one-dimensional, beam theories. It is found that beam theory is generally inadequate to determine the free vibration frequencies and mode shapes of moderate to low aspect ratio turbomachinery blades. The shallow shell theory, by contrast, is capable of representing all the vibration modes accurately. However, the one-dimensional beam theory has an important advantage over the two-dimensional shell theory for blades and vibration modes. It uses fewer degrees of freedom, thus requiring less computer time.

Leissa, A. W.↗

Multi-Zone Liquid Thrust Chamber Performance Code with Domain Decomposition for Parallel Processing

Computational Fluid Dynamics (CFD) has considerably evolved in the last decade. There are many computer programs that can perform computations on viscous internal or external flows with chemical reactions. CFD has become a commonly used tool in the design and analysis of gas turbines, ramjet combustors, turbo-machinery, inlet ducts, rocket engines, jet interaction, missile, and ramjet nozzles. One of the problems of interest to NASA has always been the performance prediction for rocket and air-breathing engines. Due to the complexity of flow in these engines it is necessary to resolve the flowfield into a fine mesh to capture quantities like turbulence and heat transfer. However, calculation on a high-resolution grid is associated with a prohibitively increasing computational time that can downgrade the value of the CFD for practical engineering calculations. The Liquid Thrust Chamber Performance (LTCP) code was developed for NASA/MSFC (Marshall Space Flight Center) to perform liquid rocket engine performance calculations. This code is a 2D/axisymmetric full Navier-Stokes (NS) solver with fully coupled finite rate chemistry and Eulerian treatment of liquid fuel and/or oxidizer droplets. One of the advantages of this code has been the resemblance of its input file to the JANNAF (Joint Army Navy NASA Air Force Interagency Propulsion Committee) standard TDK code, and its automatic grid generation for JANNAF defined combustion chamber wall geometry. These options minimize the learning effort for TDK users, and make the code a good candidate for performing engineering calculations. Although the LTCP code was developed for liquid rocket engines, it is a general-purpose code and has been used for solving many engineering problems. However, the single zone formulation of the LTCP has limited the code to be applicable to problems with complex geometry. Furthermore, the computational time becomes prohibitively large for high-resolution problems with chemistry, two-equation turbulence model, and two-phase flow. To overcome these limitations, the LTCP code is rewritten to include the multi-zone capability with domain decomposition that makes it suitable for parallel processing, i.e., enabling the code to run every zone or sub-domain on a separate processor. This can reduce the run time by a factor of 6 to 8, depending on the problem.

Homayun K. Navaz↗

Inviscid surface streamline program for use in predicting shuttle heating rates

A number of methods are currently under development for computing the exact three-dimensional flow field about real configurations. However, even when these methods are available, they will require large computational times on present generation computers. Thus, there is still a need to develop approximate methods to solve three-dimensional flow problems. An inviscid-surface-streamline program (for predicting shuttle heating rates) which uses approximate methods to obtain a solution is described.

Hamilton, H. Harris↗

Baseline mathematics and geodetics for tracking operations

Various geodetic and mapping algorithms are analyzed as they apply to radar tracking systems and tested in extended BASIC computer language for real time computer applications. Closed-form approaches to the solution of converting Earth centered coordinates to latitude, longitude, and altitude are compared with classical approximations. A simplified approach to atmospheric refractivity called gradient refraction is compared with conventional ray tracing processes. An extremely detailed set of documentation which provides the theory, derivations, and application of algorithms used in the programs is included. Validation methods are also presented for testing the accuracy of the algorithms.

James, R.↗

An implicit marching procedure for the treatment of supersonic flow fields using the conservative full potential equation

A new aerodynamic prediction technique based on the conservative full potential equation is developed for the treatment of supersonic flow fields. This new technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar phi. The method produces results that compare well with Euler solvers and requires an order of magnitude less computer time and significantly less computer memory over existing nonlinear codes. The scalar phi formulation can be extended to handle subsonic pockets in the marching direction and also is suitable for developing inverse procedures where the shape corresponding to a prescribed loading is sought.

Shankar, V.↗

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

The treatment of convected vortices in compressible potential flow

A method is described for incorporating line vortices into the three dimensional compressible potential flow equation. A modified Biot-Savart law is used to compute a vortical velocity field, which is added to the gradient of the potential to form a total velocity. A rapidly converging approximate factorization (AFZ) scheme is then used to compute a potential such that the modified potential flow equation as well as the appropriate boundary conditions, based on total velocity, are satisfied. As part of a coupled iteration procedure, the positions of the line vortices are computed so that they convect with the total flow. The method is used to compute the field due to a single line vortex convecting past a wing. This represents an approximation of the effect of a canard or other lifting surface ahead of the wing, which sheds a tip vortex. It is seen that the flow field is substantially modified by the passage of the vortex. Unlike Euler equation schemes, which are also used to compute these flows, the solutions exhibit no numerical diffusion: The convected vortices retain their initial upstream width. Euler solutions, on the other hand, involve a vorticity which is numerically convected in an Eulerian frame and, unless extensive adaptive grid refinement is used they result in vortices with spread as they convect. Also, the potential flow method requires approximately two orders of magnitude less computing time and much less computer storage than the Euler methods.

Steinhoff, J.↗

Elimination sequence optimization for SPAR

SPAR is a large-scale computer program for finite element structural analysis. The program allows user specification of the order in which the joints of a structure are to be eliminated since this order can have significant influence over solution performance, in terms of both storage requirements and computer time. An efficient elimination sequence can improve performance by over 50% for some problems. Obtaining such sequences, however, requires the expertise of an experienced user and can take hours of tedious effort to affect. Thus, an automatic elimination sequence optimizer would enhance productivity by reducing the analysts' problem definition time and by lowering computer costs. Two possible methods for automating the elimination sequence specifications were examined. Several algorithms based on the graph theory representations of sparse matrices were studied with mixed results. Significant improvement in the program performance was achieved, but sequencing by an experienced user still yields substantially better results. The initial results provide encouraging evidence that the potential benefits of such an automatic sequencer would be well worth the effort.

Hogan, Harry A.↗

Real-time computer-generated hologram by means of liquid-crystal television spatial light modulator

The usefulness of an inexpensive liquid-crystal television) (LCTV) as a spatial light modulator for coherent-optical processing in the writing and reconstruction of a single computer-generated hologram has been demonstrated. The thickness nonuniformities of the LCTV screen were examined in a Mach-Zehnder interferometer, and the phase distortions were successfully removed using a technique in which the LCTV screen was submerged in a liquid gate filled with an index-matching nonconductive mineral oil with refractive index of about 1.45.

Mok, Fai↗

A numerical method for predicting hypersonic flowfields

The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.

Maccormack, Robert W.↗

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.

Melson, N. Duane↗

A multigrid algorithm for the cell-centered finite difference scheme

In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.

Ewing, Richard E.↗