Einfluß der Geometrie auf die Wärmeleitung in Kühlkanälen einer Flüssigkeits-Rakete

Gas Turbines: Internal Flow Systems Modeling

Abstract: This long-awaited, physics-first and design-oriented text describes and explains the underlying flow and heat transfer theory of secondary air systems. An applications-oriented focus throughout the book provides the reader with robust solution techniques, state-of-the-art three-dimensional computational fluid dynamics (CFD) methodologies, and examples of compressible flow network modeling. It clearly explains elusive concepts of windage, non-isentropic generalized vortex, Ekman boundary layer, rotor disk pumping, and centrifugally-driven buoyant convection associated with gas turbine secondary flow systems featuring rotation. The book employs physics-based, design-oriented methodology to compute windage and swirl distributions in a complex rotor cavity formed by surfaces with arbitrary rotation, counter-rotation, and no rotation. This text will be a valuable tool for aircraft engine and industrial gas turbine design engineers as well as graduate students enrolled in advanced special topics courses.

Numerical methods for solving linear least squares problems

Abstract: A common problem in a Computer Laboratory is that of finding linear least squares solutions. These problems arise in a variety of areas and in a variety of contexts. Linear least squares problems are particularly difficult to solve because they frequently involve large quantities of data, and they are ill-conditioned by their very nature. In this paper, we shall consider stable numerical methods for handling these problems. Our basic tool is a matrix decomposition based on orthogonal Householder transformations.

Linear least squares solutions by householder transformations

Abstract: Let A be a given m×n real matrix with m≧n and of rank n and b a given vector. We wish to determine a vector x such that $$\parallel b - A\hat x\parallel = \min .$$ where ∥ … ∥ indicates the euclidean norm. Since the euclidean norm is unitarily invariant $$\parallel b - Ax\parallel = \parallel c - QAx\parallel $$ where c=Q b and Q T Q = I. We choose Q so that $$QA = R = {\left( {_{\dddot 0}^{\tilde R}} \right)_{\} (m - n) \times n}}$$ (1) and R is an upper triangular matrix. Clearly, $$\hat x = {\tilde R^{ - 1}}\tilde c$$ where c denotes the first n components of c.

Laminar flow friction and forced convection heat transfer in ducts of arbitrary geometry

Abstract: A least-squares-matching technique is presented to analyze fully developed laminar fluid flow and heat transfer in ducts of arbitrary cross-section. Forced convection heat transfer is considered under constant axial heat-transfer rate with arbitrary peripheral thermal boundary conditions. As an application of the method, flow and heat-transfer results are presented for the duct geometries of isosceles triangular, rounded corner equilateral triangular, sine, rhombic and trapezoidal cross-sections. These numerical results are discussed from a heat exchanger designer's viewpoint.

Pressure Drop and Heat Transfer in a Duct With Triangular Cross Section

Abstract: Friction factors were measured for a duct whose cross section has the shape of an isosceles triangle witb a side ratio 5 to 1 in the fully developed now region ior laminar, transitional, and tarbulent conditions. In addition. local and average heat-transfer coefficients and the temperatare field in the duct wall have been determined for the condition of constant heat generation per unit volume of the duct walls. Friction factors in laminar flow agreed well with analytical predictions. In the turbulent flow range they were by 20 per cent lower than values calculated from relations for a round tube with the use of the "hydraulic diameter." Heat-transfer coefficients averaged over the circumference of the duct were only half as large as values calculated from round tube relations in the Reynolds number range from 4300 to 24,000. The measurements also revealed that thermal starting lengths were in excess of 100 diameters. In round tubes a length of 10 to 20 diame ters has been found sufficient to develop the temperature field. (auth)

Numerical Analysis: Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations

Abstract: An implementation of Stiefel's exchange algorithm for determining a Chebyshev solution to an overdetermined system of linear equations is presented, that uses Gaussian LU decomposition with row interchanges. The implementation is computationally more stable than those usually given in the literature. A generalization of Stiefel's algorithm is developed which permits the occasional exchange of two equations simultaneously.