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The properties of the solutions of the hydrodynamic equations of viscous fluid by "boundary-layer omission" are discussed. A method is indicated for the numerical determination of the solution for a known initial profile u(x(sub o),y) and pressure distribution p(x) within the region.
A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.
In the present work, the boundary element method (BEM) is chosen as the basic analysis tool, principally because the definition of temperature, flux, displacement and traction are very precise on a boundary-based discretization scheme. One fundamental difficulty is, of course, that a BEM formulation requires a considerable amount of analytical work, which is not needed in the other numerical methods. 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 primary thrust of the program to date has been directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state.
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Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
The capability of analyzing a coupled dynamic system of flowing fluid and elastic structure was added to the SPAR computer code. A method, developed and adopted for use in SPAR utilizes the existing assumed stress hybrid plan element in SPAR. An operational mode was incorporated in SPAR which provides the capability for analyzing the flaw of a two dimensional, incompressible, viscous fluid within rigid boundaries. Equations were developed to provide for the eventual analysis of the interaction of such fluids with an elastic solid.
This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.
An analysis is given using finite element techniques which addresses the propagaton of a uniform incident pressure wave through a finite diameter axisymmetric tapered plate immersed in a fluid. The approach utilized in developing a finite element solution to this problem is based upon a technique for axisymmetric fluid structure interaction problems. The problem addressed is that of a 10 inch diameter axisymmetric fixed plate totally immersed in a fluid. The plate increases in thickness from approximately 0.01 inches thick at the center to 0.421 inches thick at a radius of 5 inches. Against each face of the tapered plate a cylindrical fluid volume was represented extending five wavelengths off the plate in the axial direction. The outer boundary of the fluid and plate regions were represented as a rigid encasement cylinder as was nearly the case in the physical problem. The primary objective of the analysis is to determine the form of the transmitted pressure distribution on the downstream side of the plate.
We develop a general method of calculating the linear stability of a fluid with homogeneous layers that is heated from below. The method employs a propagator technique to obtain expressions for the fluid velocity, stress, and temperature. The principal advantage of the method is the ease with which solutions are adapted to a wide variety of boundary conditions and fluid properties. We demonstrate the utility of the method using three examples which quantify the effects of (1) rheological layering, (2) mobile plates at the surface, and (3) multiple phase transitions. Each example is presented in the context of Earth's mantle. In the first example, we predict that convection becomes confined to the upper mantle once the viscosity increase between the upper and lower mantle exceeds a factor of 2000, consistent with the nonlinear calculations of Davies (1977). In the second example we find that the heat flux variations in a convecting fluid with variably sized, surface plates can be attributed, in part, to changes in the critical Rayleigh number. The linear stability of a fluid with multiple phase transitions is significantly affects by the locations of the transitions. We find that phase transitions have their largest effect when they are located at the center of the fluid layer and become much less important when they are located near the exterior boundaries.
A differential equation for the scale tensor in turbulent flow is developed from basic considerations and applied to the flow of a constant-density fluid in the boundary layer on a flat plate. Results from preliminary runs of a computer implementation are discussed.
A computational and experimental study has been undertaken to investigate methods of modeling solid and porous wall boundary conditions in CFD codes. The procedure utilizes experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution is then imposed as a boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the boundary conditions at the wind tunnel walls using only sparse experimental measurements has been investigated. Verification of the approach using computational studies has been carried out using an incompressible flow solver. The current work demonstrates this technique for low speed flows and compares the result with experimental data obtained from a heavily instrumented variable porosity test section. Position and refinement of experimental measurements required to describe porous wall boundary conditions has also been considered for application to other porous wall wind tunnels.
The fluid mechanics of hurricanes strongly depends on boundary layer energetics due to the warm-core nature of the system with peak velocities located at lower levels. One barrier that has inhibited a more complete characterization of energy transfer in the boundary layer is a lack of observations that resolve large, turbulent eddies. In particular, the occurrence and structure of upscale energy transfer (backscatter) in the hurricane boundary layer as well as the effects of backscatter on the vortex intensity are unknown. The analysis presented here of very high-resolution, three-dimensional wind observations from Hurricane Rita (2005) at peak intensity reveals large regions of organized backscatter in the boundary layer associated with coherent, turbulent eddies. Strong forwardscatter is also found next to the backscatter regions due to the interaction between adjacent eddies. Two components of the stress tensor are primarily responsible for this alternating scatter structure, as shown by large correlation coefficients between the fields: the radial–vertical component (τ13) and the azimuthal–vertical component (τ23) with average correlations of 79% and 49 %, respectively. The Leonard, Reynolds and cross-term stress components are also provided. The impact of the sub-filter-scale energy transfer is estimated by computing the kinetic energy budget for the resolved-scale and eddy-scale motions. The results show that the sub-filter-scale energy transfer term is of the same order as the other terms in the eddy-scale budgets, contributing between 16% and 40% to the local time tendency with an average contribution of approximately 30 %. These results indicate that the coherent turbulent eddies can affect the vortex dynamics through wave–wave nonlinear interactions, which can subsequently influence the wave–mean flow interactions. This is the first study to examine the full sub-filter-scale
For many important classes of Mod-Sim problems, even quantum computing will not enable accurate predictions/computation vis-à-vis the real world due to boundary/initial condition shortfalls in terms of both range of parameters and requisite amplitudes/coverage. The Mod-Sim community needs to consider going forward the knowability of initial and boundary conditions.
The present work is an experimental study of the influence of a uniform magnetic field on the structure of a free convection turbulent boundary layer in a conducting fluid. The boundary layer was formed along the heated vertical wall of a cell. The applied magnetic field was normal to the wall. The measured mean temperature profiles, temperature turbulent intensity distributions, and temperature spectra along the wall, indicated that transition from turbulent to laminar flow occurs at a constant value of the ratio (Rayleigh number)/(Hartmann number). The study of the recorded spectra indicated that the presence of the magnetic field enhances the mechanism of turbulent suppression due to the buoyancy forces. Finally, a possible mechanism by which turbulence is suppressed by the presence of a magnetic field is discussed.
The Conservative Supra-Characteristic Method (CSCM) Navier-Stokes solver is applied to ascertain the problems inherent in the design of a nominal Mach 14 nozzle for NASA-Ames' 3.5-ft Hypersonic Wind Tunnel; attention is given to the effects of boundary layer cooling systems on the aerodynamic redesign of the nozzle throat region. Complete nozzle flowfields are calculated with and without slot injection of either hot or cold fluid into the boundary layer just upstream of the throat, as well as with alternatively adiabatic and cold walls. The CSCM method is capable of resolving subtle differences in the flows.
A system and method for reducing skin friction of an object in relative motion to a fluid. A skin forming a boundary between the object and the fluid, the skin having holes through which micro-blowing of air is blown and a transmitting mechanism for transmitting air through the skin. The skin has an inner layer and an outer layer. the inner layer being a low permeable porous sheet, the outer layer being a plate having high aspect ratio high porosity. and small holes. The system may further include a suction apparatus for suctioning air from the outer layer. The method includes the steps of transmitting air through the inner layer and passing the air transmitted through the inner layer to the outer layer. The method may further include the step of bleeding air off the outer layer using the suction apparatus.