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Some recent work on adaptive FEMs for solving transient Euler equations in two-dimensional domains is summarized. The formulation of an FEM model of the Euler equations is shown, and the application of the adaptive strategies to data management schemes is addressed. Sample numerical results from the application of the model and strategies to the flow over a step and to transient cases are given.
Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engines is to decompose a CFD-generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non-harmonic excitation sources that become present in complex flows. A substantial effort has been made to account for this denser spatial Fourier content in frequency response analysis (described in another paper by the author), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements. Six loading cases were generated by varying a baseline harmonic excitation in different ways based upon cold-flow testing from Heritage Fuel Air Turbine Test. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. It was hypothesized that enforcing periodicity in the CFD (inherent in the frequency response technique) would overestimate the response. The results instead showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists. Because the bulk of resonance problems are due to the "clean" excitations, a 10% underprediction is not necessarily a problem, especially since the average response in the transient is similar to the frequency response result, and so in a realistic finite life calculation, the life would be same. However, in the rare cases when the "messy" excitations harmonics are identified as the source of potential resonance concerns, this research does indicate that frequency response analysis is inadequate for accurate characterization of blade structural capability.
The dynamic behavior of the vapor flow in heat pipes is investigated at startup and during operational transients. The vapor is modeled as two-dimensional, compressible viscous flow in an enclosure with inflow and outflow boundary conditions. For steady-state and operating transients, the SIMPLER method is used. In this method a control volume approach is employed on a staggered grid which makes the scheme very stable. It is shown that for relatively low input heat fluxes the compressibility of the vapor flow is low and the SIMPLER scheme is suitable for the study of transient vapor dynamics. When the input heat flux is high or the process under a startup operation starts at very low pressures and temperatures, the vapor is highly compressible and a shock wave is created in the evaporator. It is shown that for a wide range of input heat fluxes, the standard methods, including the SIMPLER scheme, are not suitable. A nonlinear filtering technique, along with the centered difference scheme, are then used for shock capturing as well as for the solution of the cell Reynolds-number problem. For high heat flux, the startup transient phase involves multiple shock reflections in the evaporator region. Each shock reflection causes a significant increase in the local pressure and a large pressure drop along the heat pipe. Furthermore, shock reflections cause flow reversal in the evaporation region and flow circulations in the adiabatic region. The maximum and maximum-averaged pressure drops in different sections of the heat pipe oscillate periodically with time because of multiple shock reflections. The pressure drop converges to a constant value at steady state. However, it is significantly higher than its steady-state value at the initiation of the startup transient. The time for the vapor core to reach steady-state condition depends on the input heat flux, the heat pipe geometry, the working fluid, and the condenser conditions. However, the vapor transient time, for an Na-filled heat pipe is on the order of seconds. Depending on the time constant for the overall system, the vapor transient time may be very short. Therefore, the vapor core may be assumed to be quasi-steady in the transient analysis of a heat pipe operation.
A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.
The development of a comprehensive fluid-structure interaction capability within a boundary element computer code is described. This new capability is implemented in a completely general manner, so that quite arbitrary geometry, material properties and boundary conditions may be specified. Thus, a single analysis code can be used to run structures-only problems, fluids-only problems, or the combined fluid-structure problem. In all three cases, steady or transient conditions can be selected, with or without thermal effects. Nonlinear analyses can be solved via direct iteration or by employing a modified Newton-Raphson approach. A number of detailed numerical examples are included at the end of these two sections to validate the formulations and to emphasize both the accuracy and generality of the computer code. A brief review of the recent applicable boundary element literature is included for completeness. The fluid-structure interaction facility is discussed. Once again, several examples are provided to highlight this unique capability. A collection of potential boundary element applications that have been uncovered as a result of work related to the present grant is given. For most of those problems, satisfactory analysis techniques do not currently exist.
In a three-part series of papers, a generalized finite element methodology is formulated to handle traveling load problems involving large deformation fields in structure composed of viscoelastic media. The main thrust of this paper is to develop an overall finite element methodology and associated solution algorithms to handle the transient aspects of moving problems involving contact impact type loading fields. Based on the methodology and algorithms formulated, several numerical experiments are considered. These include the rolling/sliding impact of tires with road obstructions.
A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.
In 2014 NASA published the outcome of the 2030 CFD Vision study: “CFD Vision 2030: A path to Revolutionary Computational Aerosciences” (Slotnick et al., 2014). The study provided a comprehensive review of the state of the art of CFD in 2014 for aerospace applications including, but not limited to, numerical algorithms, physics models, MDAO and HPC hardware. The study also proposed four conceptual ideas of Grand Challenge problems that would benefit from advances outlined in the roadmap including “off-design turbofan engine transient simulation”. The proposed challenges served as a starting point for more detailed problem descriptions that would benefit from advances in simulation. The objective of this paper is to build upon the NASA 2030 CFD Vision study and provide a detailed overview of what needs to take place to enable accurate and efficient simulation of flow through an aircraft engine at off-design condition for transient operation . Execution of the proposed roadmap would significantly advance aircraft engine development by reducing program cost, reducing program development timelines and enabling design objectives associated with Specific Fuel Consumption (SFC), noise, weight and durability.
Computer program solves transient or steady-state heat flow problems through the concept of lumped parameters expressed as the electrical analog of the heat transfer problem using finite differences techniques.
Analysis of viscoelastic materials under transient thermal conditions related to solid rocket propellants
Computer program for solving both transient and steady-state heat transfer problems is presented. Specific applications of computer program are described. Formulation for individual nodes of solid medium for heat balance is presented. Diffusion equation is solved for all nodes simultaneously at finite increments of time.
The time-dependent response of the upper atmosphere to transient heat sources is considered. The basic problem is that of heating a compressible, heat-conducting fluid, which is described in the one-dimensional case by an analytic solution. Comparisons with satellite drag data of such first-order solutions are shown to be useful in determining energy requirements and in determining some constraints on the spatial distribution of the heating. Recent OGO-6 mass spectrometer and interferometric temperature measurements show that atmospheric disturbances during geomagnetic storms are much more prominent in the auroral zones. These results suggest that joule dissipation of auroral currents are important contributors to orbital perturbations of satellites.
Since for maximum range a supersonic transport must cruise near its maximum Mach number, accurate flight control is needed, especially when severe atmospheric transients are encountered. This paper describes atmospheric transients that have been encountered by the XB-70, YF-12, and Concorde aircraft during supersonic flights and the ensuing responses of the aircraft propulsion and flight control systems. It was found that atmospheric conditions affected these supersonic cruise vehicles in much the same way, with minor differences according to the type of propulsion and flight control system. Onboard sensors are sufficiently accurate to provide data on the atmosphere, including turbulence over the route, that are accurate enough for entry in the climatic record and for use as inputs to the control systems. Nominal atmospheric transients can be satisfactorily controlled, but some problems remain for extreme cases.
The formulation of the problem of finite elastic-viscoplastic deformation of thin beams is described. The finite element analysis of a representative problem is presented and various solution methods are surveyed.
Eigenspace assignment is explored as a control-law synthesis approach for 'shaping' the transient response of an elastic aircraft. A direct technique is utilized for synthesizing a full-state- as well as a reduced-order-output-feedback control law and the selection of the desired eigenspace is discussed. Robustness issues and results are evaluated and robustness recovery with full state estimation is demonstrated. Also, an appropriate implementation of state estimation to preserve the desired transient response (or desired eigenspace) is presented. Problems regarding actuator bandwidth and unmodeled modes are noted.
The problem of buckling of shallow arches under transient thermomechanical loads is investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all non-isothermal, elasto-viscoplastic characteristics. The solution scheme is capable of predicting response which includes pre and postbuckling with creep and plastic effects. The solution procedure is demonstrated through several examples which include both creep and snap-through behavior.
The Eleven Node Thermal Model (GEM) of the Get Away Special (GAS) container was originally developed based on the results of thermal tests of the GAS container. The model was then used in the thermal analysis and design of several NASA/GSFC GAS experiments, including the Flight Verification Payload, the Ultraviolet Experiment, and the Capillary Pumped Loop. The model description details the five cu ft container both with and without an insulated end cap. Mass specific heat values are also given so that transient analyses can be performed. A sample problem for each configuration is included as well so that GEM users can verify their computations. The model can be run on most personal computers with a thermal analyzer solution routine.
The progress made toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-Orbit engine hot section components is reported. The convective viscous integral formulation was derived and implemented in the general purpose computer program GP-BEST. The new convective kernel functions, in turn, necessitated the development of refined integration techniques. As a result, however, since the physics of the problem is embedded in these kernels, boundary element solutions can now be obtained at very high Reynolds number. Flow around obstacles can be solved approximately with an efficient linearized boundary-only analysis or, more exactly, by including all of the nonlinearities present in the neighborhood of the obstacle. The other major accomplishment was the development of a comprehensive fluid-structure interaction capability within GP-BEST. This new facility is implemented in a completely general manner, so that quite arbitrary geometry, material properties and boundary conditions may be specified. Thus, a single analysis code (GP-BEST) can be used to run structures-only problems, fluids-only problems, or the combined fluid-structure problem. In all three cases, steady or transient conditions can be selected, with or without thermal effects. Nonlinear analyses can be solved via direct iteration or by employing a modified Newton-Raphson approach.