Use of the Kernel function in a three-dimensional flutter analysis with application to a flutter-tested delta-wing model
Explore the source record for details and available documents.
Woolston, Donald S↗
SEARCH · Search NASA
Results for “Dimensional analysis”
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.
Three Dimensional Aerodynamic Analysis of a High-Lift Transport Configuration
Two computational methods, a surface panel method and an Euler method employing unstructured grid methodology, were used to analyze a subsonic transport aircraft in cruise and high-lift conditions. The computational results were compared with two separate sets of flight data obtained for the cruise and high-lift configurations. For the cruise configuration, the surface pressures obtained by the panel method and the Euler method agreed fairly well with results from flight test. However, for the high-lift configuration considerable differences were observed when the computational surface pressures were compared with the results from high-lift flight test. On the lower surface of all the elements with the exception of the slat, both the panel and Euler methods predicted pressures which were in good agreement with flight data. On the upper surface of all the elements the panel method predicted slightly higher suction compared to the Euler method. On the upper surface of the slat, pressure coefficients obtained by both the Euler and panel methods did not agree with the results of the flight tests. A sensitivity study of the upward deflection of the slat from the 40 deg. flap setting suggested that the differences in the slat deflection between the computational model and the flight configuration could be one of the sources of this discrepancy. The computation time for the implicit version of the Euler code was about 1/3 the time taken by the explicit version though the implicit code required 3 times the memory taken by the explicit version.
Dodbele, Simha S.↗
Three-Dimensional Postbuckling Analysis of Curved Beams
Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.
Pai, P. Frank↗
Diversity in Terrestrial worlds: analysis ofmulti dimensional factors that shape their evolution
No abstract provided
Estrela, Raissa Freitas↗
A Modified Wall Matching Treatment to Account for Local Solid to Fluid Thermal Coupling
The wall-matching methodology of Wilcox is modified to include a solid-wall, thermal-conduction model. This coupled fluid-thermal-structure model is derived assuming that the wall thermal-structure behavior is locally one-dimensional and that structural deformations, due to thermally induced stresses, are not significant. The one-dimensional coupled fluid-thermal-structure model is derived such that the wall temperature is removed as an independent boundary condition variable. The one-dimensional coupled fluid-thermal-structure model is also derived for the general case of an arbitrary mixture of thermally prefect gases and a wall of arbitrary thickness and conductivity by using a compressible, streamwise-pressure-gradient-corrected, wall-matching function and Fourier's law of heat conduction. The resulting model was implemented in the VULCAN CFD code as a new boundary condition type. VULCAN was then used to simulate a two-dimensional Mach 6 wind tunnel facility nozzle flow to demonstrate/validate the one-dimensional coupled fluid-thermal-structure model. The nozzle internal-wall surface temperature and heat transfer distributions computed using the one-dimensional coupled fluid-thermal-structure model are compared to wall temperature and heat transfer distributions from an iterative multi-dimensional analysis obtained by coupling the VULCAN CFD code and the MSC/NASTRAN-thermal code. The one-dimensional coupled fluid-thermal-structure model analysis is shown to be very robust and in excellent agreement with the multi-dimensional iteratively coupled analysis. It is also shown that the one-dimensional analysis can be used as an initial guess for the multi-dimensional iteratively coupled analysis.
White, Jeffery A.↗
A Modified Wall Matching Treatment to Account for Local Solid to Fluid Thermal Coupling
The wall-matching methodology of Wilcox is modified to include a solid-wall, thermal-conduction model. This coupled fluid-thermal-structure model is derived assuming that the wall thermal-structure behavior is locally one-dimensional and that structural deformations, due to thermally induced stresses, are not significant. The one-dimensional coupled fluid-thermal-structure model is derived such that the wall temperature is removed as an independent boundary condition variable. The one-dimensional coupled fluid-thermal-structure model is also derived for the general case of an arbitrary mixture of thermally prefect gases and a wall of arbitrary thickness and conductivity by using a compressible, streamwise-pressure-gradient-corrected, wall-matching function and Fourier's law of heat conduction. The resulting model was implemented in the VULCAN CFD code as a new boundary condition type. VULCAN was then used to simulate a two-dimensional Mach 6 wind tunnel facility nozzle flow to demonstrate/validate the one-dimensional coupled fluid-thermal-structure model. The nozzle internal-wall surface temperature and heat transfer distributions computed using the one-dimensional coupled fluid-thermal-structure model are compared to wall temperature and heat transfer distributions from an iterative multi-dimensional analysis obtained by coupling the VULCAN CFD code and the MSC/NASTRAN-thermal code. The one-dimensional coupled fluid-thermal-structure model analysis is shown to be very robust and in excellent agreement with the multi-dimensional iteratively coupled analysis. It is also shown that the one-dimensional analysis can be used as an initial guess for the multi-dimensional iteratively coupled analysis.
White, Jeffery A.↗
Turbofan forced mixer lobe flow modeling. 2: Three-dimensional inviscid mixer analysis (FLOMIX)
A three-dimensional potential analysis (FLOMIX) was formulated and applied to the inviscid flow over a turbofan foced mixer. The method uses a small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a high penetration symmetric mixer in a planar duct. In addition, calculations showing pressure distributions and induced secondary vorticity fields are presented for practical trubofan mixer configurations, and where possible, comparison was made with available experimental data. A detailed description of the required data input and coordinate definition is presented along with a sample data set for a practical forced mixer configuration. A brief description of the program structure and subroutines is also provided.
Barber, T.↗
Out of plane analysis for composite structures
Simple two dimensional analysis techniques were developed to aid in the design of strong joints for integrally stiffened/bonded composite structures subjected to out of plane loads. It was found that most out of plane failures were due to induced stresses arising from rapid changes in load path direction or geometry, induced stresses due to changes in geometry caused by buckling, or direct stresses produced by fuel pressure or bearing loads. While the analysis techniques were developed to address a great variety of out of plane loading conditions, they were primarily derived to address the conditions described above. The methods were developed and verified using existing element test data. The methods were demonstrated using the data from a test failure of a high strain wingbox that was designed, built, and tested under a previous program. Subsequently, a set of design guidelines were assembled to assist in the design of safe, strong integral composite structures using the analysis techniques developed.
Paul, P. C.↗
A variable-order laminated plate theory based on the variational-asymptotical method
The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.
Lee, Bok W.↗
Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics
Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.
Fischbach, S. R.↗
Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics
Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.
Fischbach, Sean R.↗
Numerical analysis of the scramjet-inlet flow field by using two-dimensional Navier-Stokes equations
A computer code was developed to solve the full two dimensional Navier-Stokes equations in a supersonic combustion ramjet (scramjet) inlet. In order to be able to consider a general inlet geometry with embedded bodies, a numerical coordinate transformation is used which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with no strut, one strut, or multiple struts in the flow field. The application of the two dimensional analysis in the preliminary parametric design studies of a scramjet inlet is discussed. Detailed results are presented for one model problem and for several actual scramjet-inlet configurations.
Kumar, A.↗
Validation of the NCC Code for Staged Transverse Injection and Computations for a RBCC Combustor
The NCC code was validated for a case involving staged transverse injection into Mach 2 flow behind a rearward facing step. Comparisons with experimental data and with solutions from the FPVortex code was then used to perform computations to study fuel-air mixing for the combustor of a candidate rocket based combined cycle engine geometry. Comparisons with a one-dimensional analysis and a three-dimensional code (VULCAN) were performed to assess the qualitative and quantitative performance of the NCC solver.
Ajmani, Kumud↗
Analysis of MPD arcs with nonequilibrium ionization
One dimensional analysis of magnetoplasm dynamic arcs with nonequilibrium ionization
Hassan, H. A.↗
Simulation and experimental-techniques. Part I - Simulation of liquid sloshing
Dimensional analysis applied to simulation of liquid sloshing
LIQUID SLOSHING↗
Changes in muscle protein composition induced by disuse atrophy - Analysis by two-dimensional electrophoresis
Using 320 g rats, a two-dimensional electrophoretic analysis of muscle proteins in the soleus and EDL muscles from hindlimbs maintained load-free for 10 days is performed. Statistical analysis of the two-dimensional patterns of control and suspended groups reveals more protein alteration in the soleus muscle, with 25 protein differences, than the EDL muscle, with 9 protein differences, as a result of atrophy. Most of the soleus differences reside in minor components. It is suggested that the EDL may also show alteration in its two-dimensional protein map, even though no significant atrophy occurred in muscle wet weight. It is cautioned that strict interpretation of data must take into account possible endocrine perturbations.
Ellis, S.↗
Analysis of Regen Cooling in Rocket Combustors
The use of detailed CFD modeling for the description of cooling in rocket chambers is discussed. The overall analysis includes a complete three-dimensional analysis of the flow in the regenerative cooling passages, conjugate heat transfer in the combustor walls, and the effects of film cooling on the inside chamber. The results in the present paper omit the effects of film cooling and include only regen cooling and the companion conjugate heat transfer. The hot combustion gases are replaced by a constant temperature wall boundary condition. Load balancing for parallel cluster computations is ensured by using single-block unstructured grids for both fluids and solids, and by using a 'multiple physical zones' to account for differences in the number of equations. Validation of the method is achieved by comparing simple two-dimensional solutions with analytical results. Representative results for cooling passages are presents showing the effects of heat conduction in the copper walls with tube aspect ratios of 1.5:l.
Harper, Brent↗
Theory of thermal similitude with applications to spacecraft - A survey.
Mathematical theory of dimensional analysis and similitude, application to spacecraft thermal design and experimental results
MATRIX ALGEBRA↗