D.Ing. / The aim of this thesis is to research the use of Computational Fluid Dynamics (CFD) as design tool to predict fluid flow across stationary and moving bluff bodies. The principle of moving meshes is introduced to move the body vertically with respect to time. The moving mesh idea is first tested on a square body with a coarse discretized flow domain for transient conditions. The results can be animated to see how the flow pattern and mesh change with time. The idea is then implemented on a cylinder with a very fine mesh to capture the build-up and dispersion of vortices being shed from the cylinder as it moves cyclically for transient conditions. With this first approach a bluff body is forced to move cyclically with respect to time in cross flow. Many possibilities now exist to apply this idea further for other applications where forced vibration is important.The next approach is to use CFD to simulate flow-induced vibrations of bluff bodies. The pressure force on the bluff body is considered as a first approach to solve this problem. The inertia mass of the body balancing the effect of the pressure force on the body is first used, but the results indicate that damping and stiffness also have to be considered to obtain more realistic results. The effect of the pressure force on the body shows generally a downwards movement of the body for the first period of simulation and in the case of the square, after six time steps of the period of simulation the .pressure force switches to a positive value with resulting upwards movement of the body. The effect of the total force (shear + pressure) on a bluff body is not presented in this thesis. CFD as design tool is researched for various bundle configurations of cylinders. A new concept of split cylinders is researched and the best configuration obtained for various horizontal and vertical spacings of downstream- and upstream cylinders and cylinder halves. Experimental results on cylinders in a - small scale wind tunnel are used to compare the numerical results with the obtained pressure distribution around a stationary cylinder and the concept of velocity distribution over and between a split cylinder. Further development of the numerical flow model is necessary to include elasticity and longer three dimensional spanwise lengths of the object to obtain predictions of real flow-induced vibrations of bluff bodies. This first approach of numerical predictions of flow across stationary and moving bluff bodies creates many possibilities of complementing experimental results and comparing the obtained results with each other.

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The focus of this research is to numerically predict an infrared image of a jet engine exhaust plume, given field variables such as temperature, pressure, and exhaust plume constituents as a function of spatial position within the plume, and to compare this predicted image directly with measured data. This work is motivated by the need to validate Computational Fluid Dynamic (CFD) codes through infrared imaging. The technique of reducing the three-dimensional field variable domain to a two-dimensional infrared image invokes the use of an inverse Monte-Carlo ray trace algorithm and an infrared band model for exhaust gases. This dissertation describes an experiment in which the above-mentioned field variables were carefully measured. Results from this experiment, namely tables of measured temperature and pressure data, as well as measured infrared images, are given. The inverse Monte-Carlo ray trace technique is described. Finally, experimentally obtained infrared images are directly compared to infrared images predicted from the measured field variables. / Ph. D.

Call number: LD2668 .T4 1964 H99 / Master of Science

Suppose C(x,t) is the concentration at position x in Rᵈ and time t > 0 of a solute which is diffusing in some medium. If on a local scale the dispersion of the solute is governed by a constant dispersion matrix, 1/2(δ²), and a random velocity field, V(x), then C satisfies a convection-diffusion equation with random coefficients, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) (1). Usually V(x) is taken to be μ + εU(x) where μ ε Rᵈ, U(x) is a given stationary random field with mean zero, and ε > 0 is a dimensionless parameter which measures the variability of V(x). Hydrological experiments suggest that on a regional scale the diffusion is classically Fickian with effective diffusion matrix D(ε) and drift velocity α(ε). Thus for large scales (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) (2) is satisfied by the solute concentration. Here τ and χ are respectively time and space measured on large scales. It is natural to investigate the relation of the large scale coefficients D and α to the statistical properties of V(x). To relate (1) to (2)--and thus to approximate D(ε) and α(ε)--it is necessary to rescale t and x and average over the distribution of V. It can then be shown that the transition form (1) to (2) is equivalent to (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) (3) where A = (∇•δ²∇)/2 + √nμ• ∇ and B(U) = √nU(√nx) • ∇. By expanding each side of (3) estimates of D(ε) and α(ε) can be obtained. The estimates have the form (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) (4). Both D₂ and α₂ depend on the power spectrum of U. Analysis shows that in at least the case of incompressible fluids D₂ is positive definite. In one dimensional transport α₂ < 0, hence α(k) < μ(k) through second order.

Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.

A Petrov-Galerkin method for the solution of the compressible Euler and Navier-Stokes equations is presented. The method is based on the introduction of an anisotropic balancing diffusion in the local direction of the propogation of the scalar variables. The direction in which the diffusion is added and its magnitude are automatically calculated locally using a criterion that is optimal for one-dimensional transport equations. Algorithms are developed using bilinear quadrilateral and linear triangular elements. The triangular elements are used in conjunction with an adaptive scheme using unstructured meshes. Several applications are presented that show the exceptional stability and accuracy of the method, including the ram accelerator concept for the acceleration of projectiles to ultrahigh velocities. Both two-dimensional and axisymmetric models are employed to evaluate multiple projectile configurations and flow conditions.

The unsteady two-dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analyzed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The center-to-center distance between adjacent cylinders is a constant. The Biot-Savart law of induced velocities is used to determine the velocity field due to the free vorticity in the surrounding fluid and the bound vorticity distributed on the surface of each cylinder. The bound vorticity is needed to enforce the no-penetration condition and to account for the production of free vorticity in the solid surfaces. It is governed by a Fredholm integral equation of the second kind. This equation is solved by numerical techniques. The transport of free vorticity in the flow field is governed by the vorticity transport equation. This equation is discretized for a control volume and is solved numerically. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder, but necessitates use of a non-orthogonal grid. In order to test the numerical techniques, the simpler case of unsteady flow over a single circular cylinder at various Reynolds numbers if first considered. Results compare favorably with previous experimental and numerical data. Three cases for Reynolds numbers of 10², 10³, and 10⁴ are presented for the array of cylinders. The center-to-center distance is fixed at three diameters. The time development of constant vorticity contours as well as drag, lift, and moment coefficients are shown for each Reynolds number. The motion of stagnation and separation points with time is also given. It is found that the drag for a cylinder in the array may be as low as five percent of that for flow over a single cylinder at the same Reynolds number.

The water level in an open well tapping a confined formation is influenced by natural forces including the solid Earth tide (SET) and atmospheric pressure variation (APV). The spectral method is used to derive an analytical solution for well response to both the random and the periodic components of the combined SET and APV (CSA) forcings. Previously posed models for the individual SET and APV forcings are subsets of this more general model. An inverse theory and an algorithm are developed in order to provide improved results when using such models to estimate the hydraulic parameters associated with a given formation. A complex vector estimation criterion is used in developing a nonlinear, Gauss-Marquardt estimation algorithm. When compared to previous methods of fitting modulus and phase, the complex vector estimation methodology has less bias and variance, and is more robust. An examination of the response surface of the estimation criterion reveals that storativity (S) is relatively non-unique, and thus is not considered in the context of the parameter estimation problem. However, since there is little correlation between transmissivity (T) and S estimators, a good estimate for T is still possible independent of having knowledge of S. An estimate of T is possible only if the data contain sufficient information so that the analysis occurs within an identifiability window, which is defined with respect to the dimensionless transmissivity of the system. The CSA estimation methodology is compared to individual SET and APV schemes. The CSA scheme gives the greatest probability that sufficient information is contained in a data record so that T is identifiable. The results of applications to synthetic data indicate that the OEA scheme gives a T estimate with the most precision, and also that it requires collecting fewer observations.