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Incompressible laminar boundary layer, vortex and axisymmetric wake/jet flow parabolic equations solution by weighted residuals method, describing use of exponentials
A noise source identification procedure based on a boundary element implementation of the Helmholtz integral equation is presented. This technique makes it possible to identify noise sources in highly reactive fields and to include complex sources and the effects of environmental interaction in the analysis.
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TAWFIVE computer program calculates transonic flow over transport-type wing and fuselage. Combines multigrid acceleration technique in iterative solution of potential equation with use of integral-form boundary-layer equations to provide software tool computationally efficient, yet accurate enough for use in design. Simplifies solution process by breaking problem into loosely coupled set of modified equations. Inviscid-flow method, using standard inviscid-flow equations, valid in "outer" region away from wing, whereas boundary-layer equations valid in thin region near solid surface of wing. Written in FORTRAN 77.
Contents include the following: Characteristic differential equations - initial and boundary conditions. Integration of the second characteristic differential equations. Direct application of Meyer's characteristic hodograph table for construction of two-dimensional potential flows. Prandtl-Busemann method. Development of the pressure variation for small deflection angles. Numerical table: relation between deflection, pressure, velocity, mach number and mach angle for isentropic changes of state according to Prandtl-Meyer for air (k = 1.405). References.
This slide presentation reviews the software framework for the analysis and design of complex electromagnetic systems. The system called Electromagnetic Interactions GenERalized (EIGER) is a hybrid finite element solution for wave equations and deru=ives boundary element solutions for integral equation formulations. Written in Fortran 90 Eiger uses object-oriented design methods to abstract key analysis components. EIGER has been applied to higher order modeling for analysis of antennas to assist in the design of the antennas of a mini-AERCam. EIGER might also be used to model the Ion Cyclotron Resonant heating stage for the VAriable Specific Impulse Magnetoplasma Rocket (VASIMR).
The objective of this study is the development of a numerical technique which can provide three-dimensional, time-accurate, compressible, turbulent flow solutions in a practical and relatively economical way. The approach taken is that of the method of viscous-inviscid interaction. The Euler equations are assumed to govern the outer inviscid portion of the flow, and the viscous layer close to the solid wall is described by a set of integral boundary-layer equations. The viscous solutions are obtained in a direct fashion with a weighted-average phase error scheme. The method of equivalent sources is used for viscous-inviscid coupling. Steady-state and unsteady computations for an AGARD airfoil and a wing show that satisfactory engineering solutions can be obtained for attached, high Reynolds number flows using this method. Quasi-unsteady interactions are shown to produce similar results to those provided by true-unsteady interactions. Considerable computer resources can be saved for some cases by using quasi-unsteady interactions.
Two boundary element formulations of acoustical behavior exist; the Direct Boundary Element Methods (DBEM) based on the Helmholtz Integral Equations and the Indirect Boundary Element Methods (IBEM) based on Huygen's Principle. In this investigation, both methods are implemented utilizing a simple linear superparametric element. In addition the IBEM is studied using a quadratic isoparametric element. The accuracy and relative efficiency of the various techniques are examined. In order to properly model aircraft interior cavities the additional capability to model wall treatments and internal point sources is added to the methods. The procedures are verified for several well-understood cavity problems. The relative merits of each boundary element method and the finite element method are examined.
The motion of the freezing front between a dendritic crystal and a supercooled liquid is studied using an interface evolution equation derived from a boundary integral transformation of the transient convective-diffusion equation. A new steady-state theory is introduced that incorporates the effects of convection in dendritic growth. It is shown that in the absence of capillary effects the shape of the crystal-melt interface is a paraboloid of revolution, similar to that found in situations where diffusion is the sole heat transfer mechanism. A relation between the supercooling, the product of the tip velocity and tip radius, and the strength of the flow is derived which reduces to the well-known Ivantsov theory in the absence of convection. A non-linear interface-tracking algorithm is developed and used to study the temporal and spatial evolution of the dendritic interface. The important role of capillarity and convection on the interface dynamics is established and the response of the interface to finite amplitude disturbances is examined for the first time. Tip splitting is identified as the dominant destabilization mechanism in the limit of zero surface tension. Finite surface tension leads to interface stabilization, irrespective of the magnitude and structure of the external perturbations. Finally, convection significantly decreases the magnitude of the freezing velocity.
Stress-wave propagation in a composite plate due to an impact has been examined using anisotropic elasticity theory. The plate is modelled as a number of identical anisotropic layers whose elastic moduli are given. Mindlin's (1959) approximate theory of plates is then applied to each layer to obtain a set of difference-differential equations of motion by using the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions these equations are solved for an arbitrary number of layers in the plate, and the transient propagation of a stress wave is calculated by means of a fast Fourier transform algorithm.
With the use of Karman's integrated momentum equation for the boundary layer and data on the wall-shearing stress and heat transfer in forced-convection flow, a calculation was carried out for the flow and heat transfer in the turbulent free-convection boundary layer on a vertical flat plate. The calculation is for a fluid with a Prandtl number that is close to 1. A formula was derived for the heat-transfer coefficient that was in good agreement with experimental data in the range of Grashof numbers from 10sup10 to 10sup12. Because of the good agreement between the theoretical formula and the experimental data, the formula may be used to obtain data for high Grashof numbers. The calculation also yielded formulas for the maximum velocity in the boundary layer and for boundary-layer thickness.
Mean square wall pressure fluctuations in turbulent boundary layer using integral equations
Suddenly started laminar flow in circular tube entrance region, obtaining integral momentum equation for boundary layer thickness, entrance length, velocity profile, etc
The fluid mechanics of transpired incompressible turbulent boundary layers under zero and adverse pressure gradient conditions is investigated using an open-ended wind tunnel with a porous floor in the test section and a secondary air system for supply and metering of the transpiration air. All velocity profiles and turbulence profiles are obtained by linearized constant-temperature hot-wire anemometry. The wall shear stress is determined by measuring the shear stress away from the wall and extrapolating to the wall by integrating the boundary layer equations for the shear-stress profile. Equilibrium boundary layers are obtained when the transpiration velocity is varied such that the blowing parameter and the Clauser pressure gradient parameter are held constant. The experimental results obtained are presented in tabular and graphical forms.
This report presents a viscous-inviscid calculation method for the prediction of turbulent incompressible flows in diffusers with small regions of stall. Integral turbulent boundary layer equations (BLE) are used to provide boundary conditions for a finite difference representation of the inviscid core. The BLE are applied at the floating displacement-thickness line, resulting in a simulataneous set of nonlinear block tridiagonal equations which are solved iteratively using a sucessive line-relaxation technique. Results of the method have been applied to calculate the performance of a variety of asymmetric stalled diffusers.
Incompressible three dimensional, turbulent boundary layer (3DTBL) experiments were simulated numerically by integrating the boundary layer equations together with an algebraic eddy viscosity turbulence model. For the flow treated, the downstream portion, where the crossflow was large, was not predicted with the present computational method; the flow was significantly influenced by elliptic flow field effects. Departures from the boundary layer concept are indicated. Calculations agreed reasonably well with the mean flow development up to separation. In one experiment the normal pressure gradients were found to be neligible in regions with large skewing and allowed testing turbulence models using the boundary layer equations. The simulation of this flow compared favorably with the experimental data throughout the flow field and suggested the applicability of algebraic eddy viscosity models for 3DTBLs.
The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.
The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.