SPE Members Abstract This paper details a study made of the analytical (diagnostic) and numerical (predictive) models commonly used today in the analysis and design of sucker rod pumping systems. The results should help the user of this technology in selecting appropriate values for the several parameters used in applying the models. Introduction The walking beam sucker rod pumping system is one of the oldest mechanical systems known to man, having been used by the Chinese at least 3000 years ago. The standard analysis and design procedure for these systems used by the industry for the past 20 to 25 years was completed by the Midwest Research Institute in 1962. The Institute, under contract to Sucker Rod Pumping Research, Inc., developed a method for computing forces and displacements using an analog computer simulation. This method, called the API RP11L method, has been a powerful engineering tool but has several limitations. These limitations include a simplified pumping unit geometry and polished rod motion, low slip prime movers and full pump fillage. Pioneering work by Gibbs in the 1960s resulted in the development of two mathematical models which form the basis for most of the technology today. These two models, which include solutions to the damped wave equation. are a diagnostic analytical model and a predictive finite difference model. The diagnostic analytical model is a classical Fourier Series solution of the damped wave equation. Stated simply, the input to this model is the surface dynamometer card, and the output is the pump dynamometer card. The primary use of this model is to diagnose downhole pump problems. The predictive finite difference model is a solution to the same equation but with a different statement of the boundary conditions. The input to this model is the surface polished rod motion and load at the pump, and the output is load at the surface and motion at the pump. The primary use of this model, when used together with the kinematic description of the surface unit and characteristics of the prime mover, is to predict loads at any point in the system so that the suitability of a particular design may be verified. The purpose of this paper is to present a discussion of the effect of the various parameters on the solution of the problem by these two methods. This should aid the user in selecting appropriate values of these parameters for use in both models. THE ROD PUMPING SYSTEM The sucker rod pumping system, represented mathematically as a boundary value problem, can be divided into three sections for analysis: the surface equipment, the rod string and the pump. Complete analysis involves a study of the interaction of these three sections. The motion described by the surface unit has been analyzed by Gray and more recently by Svinos. In this study, the method described by Svinos was used to solve the four-bar linkage problem. Gibbs and others have considered the effect to prime mover speed variations on the problem; we only considered constant prime mover speed in this study. P. 405^

A promising alternative to modern swirl combustors for gas turbines are high momentum jet stabilized combustors. This gas turbine burner concept consists of circular arranged jet nozzles through which partially premixed high momentum jets enter the combustion chamber in axial direction. Furthermore, it features fuel flexibility, load flexibility and low pollutant emissions. The investigated generic combustor consists of an eccentric single nozzle in a square chamber. This nozzle represents a full-scale segment of a concentrically arranged multi-nozzle configuration. All measurements were carried out at the high pressure combustion test rig (HBK-S) at the German Aerospace Center (DLR) in Stuttgart. The generic single nozzle model combustor has been operated in a high-pressure test rig with large optical access in order to gain a detailed understanding of fuel distribution, droplet distribution, fuel air mixing and high temperature regions through various sections of the combustion chamber. For this purpose, different laser based measurement techniques have been applied simultaneously under gas turbine relevant conditions on liquid fuels (oil and oil/water). Other measurements in this combustor on gaseous fuels were presented in preceding (parts A and B) and current publications (part C). Mie scattering was used to visualize the liquid phase of oil and water downstream of the nozzle. In order to gain knowledge about the droplet velocity, a Nd:YAG double pulse laser at 532 nm was used for Particle Image Velocimetry (PIV). Additionally the gaseous and liquid phases of oil have been visualized through Planar Laser Induced Fluorescence (PLIF) by excitation of poly-cyclic aromatic hydrocarbons (PAHs) with a laser wavelength of 266 nm. To observe high temperature regions, OH and PAH PLIF was also performed with a low bandwidth at 283 nm from a Nd:YAG pumped dye laser. It was possible to separate the low-intensity OH signal of the hot gas regions from the PAH signal by collecting the different LIF signals simultaneously through a dual camera setup. Instantaneous PAH LIF images of the liquid and gaseous phase were compared with Mie scattering images for a qualitative impression of the evaporation. For this a structural comparison between the liquid phases of both images has been carried out. Results indicate, that the evaporation of most of the liquid fuel takes place near the hot gas region, as a large proportion of droplets are carried far downstream of the nozzle by the high momentum jet.

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It is known that the dynamic aeroelastic stability of T-tails is dependent on the steady aerodynamic forces at aircraft trim condition. Accounting for this dependency in the flutter solution process involves correction methods for doublet lattice method (DLM) unsteady aerodynamics, enhanced DLM algorithms, unsteady vortex lattice methods (UVLM), or the use of CFD. However, the aerodynamic improvements along with a commonly applied modal approach with linear displacements results in spurious stiffness terms, which distort the flutter velocity prediction. Hence, a higher order structural approach with quadratic mode shape components is required for accurate flutter velocity prediction of T-tails. For the study of the effects of quadratic mode shape components on T-tail flutter, a generic tail configuration without sweep and taper is used. Euler based CFD simulations are applied involving a linearized frequency domain (LFD) approach to determine the generalized aerodynamic forces. These forces are obtained based on steady CFD computations at varying horizontal tail plane (HTP) incidence angles. The quadratic mode shape components of the fundamental structural modes for the vertical tail plane (VTP), i.e., out-of-plane bending and torsion, are received from nonlinear as well as linear finite element analyses. Modal coupling resulting solely from the extended modal representation of the structure and its influence on T-tail flutter is studied. The g-method is applied to solve for the flutter velocities and corresponding flutter mode shapes. The impact of the quadratic mode shape components is visualized in terms of flutter velocities in dependency of the HTP incidence angle and the static aerodynamic HTP loading.

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