Wave propagation by the passage of two high-speed trains in a tunnel

A numerical simulation of unsteady compressible flow induced by two high-speed trains in oncoming traffic within a tunnel is presented. The computations were carried out by means of a second-order accurate Harten-Yee type upwind TVD scheme. In order to take the effect of friction into account, a source term is included in the governing flow equations. In the computation, moving boundary configurations were used to simulate the two trains passing through the tunnel. As geometrical configuration, the Einmalberg tunnel, where experimental data are available, was selected. The computational results agree reasonably well with their experimental counter-part. The waves interaction and the waves propagation process at the tunnel entrance and exit as well as within the tunnel are addressed. Finally, the influence on the transmitted waves at the tunnel exit portal and the variation of the negative pressure drop during the passage of the two trains are discussed.     

Pressure wave propagation in a short tunnel caused by passing trains

The aerodynamic behaviour of pressure transients in railway tunnels due to the passage of train are accompanied by the wave reflection between the entrance and exit of the tunnel as well as the tunnel wall and train surface. This study presents a numerical method using the Harten-Yee upwind TVD scheme to simulate compression wave transients and reflection in a railway tunnel. The strength of the compression wave generated by the entrance of a train into a tunnel emerged within the applied calculation procedure, without any special consideration of the boundary condition for the entrance or exit of the tunnel as well as the train nose and tail. Good agreements were obtained when the initial pressure rise at tunnel entrance and the process of pressure variations in a short tunnel, which were calculated by the presented numerical method, were compared with experimental data. The pressure wave reflection at the entrance and exit, the unsteady flow around the train and the transmitted wave at tunnel exit portal were simulated. The transmitted wave at the tunnel exit portal is also discussed. In addition a method to determine the non-reflective boundary condition for multi-dimensional Euler equation is given.     

Pressure wave propagation in a short tunnel caused by passing trains

The aerodynamic behaviour of pressure transients in railway tunnels due to the passage of train are accompanied by the wave reflection between the entrance and exit of the tunnel as well as the tunnel wall and train surface. This study presents a numerical method using the Harten-Yee upwind TVD scheme to simulate compression wave transients and reflection in a railway tunnel. The strength of the compression wave generated by the entrance of a train into a tunnel emerged within the applied calculation procedure, without any special consideration of the boundary condition for the entrance or exit of the tunnel as well as the train nose and tail. Good agreements were obtained when the initial pressure rise at tunnel entrance and the process of pressure variations in a short tunnel, which were calculated by the presented numerical method, were compared with experimental data. The pressure wave reflection at the entrance and exit, the unsteady flow around the train and the transmitted wave at tunnel exit portal were simulated. The transmitted wave at the tunnel exit portal is also discussed. In addition a method to determine the non-reflective boundary condition for multi-dimensional Euler equation is given.

     

Perturbation solutions for blast waves with convective and radiative heat transfer

Summary The non-self-similar point explosion problem is investigated, taking into accont internal heat transfer effects. The conductive heat flux is expressed in terms of Fourier's law and radiation is considered to be of the diffusion type.A co-ordinate expansion based on the reciprocal of the square of the shock Mach number is employed to obtain solutions for the initial stages of blast waves with non-zero counter-pressure for either planar, cyclindrical or spherical symmetry. The first approximation that corresponds to the self-similar problem and the second approximation are discussed. Since both formulations imply a two-point boundary-value problem with a singularity at the centre of symmetry an iterative shooting technique is applied to determine the correct solutions. The comparison of our results with those of other authors is presented.     

Numerical calculation of fully developed turbulent flow in curved channels: An extended algebraic Reynolds-stress model

The primary objective of the paper is to extend an algebraic Reynolds-stress model including a new expression for the turbulent shear stress, in order to describe the negative production of turbulent kinetic energy appearing in curved channel flows in a region between the points of maximum velocity and vanishing shear stress. This so-called energy reversal cannot be captured by the majority of turbulence models with conventional eddy-viscosity formulation. Computations are made for fully developed flows in channels of rectangular cross section and large aspect ratio with mild and strong curvature. The results are compared with different model predictions and experimental data reported in the literature. In the cases considered, the accuracy of present model predictions is comparable to that of a Reynolds-stress model. The latter, however, requires much more computing time and is thus more costly than the model here proposed.     

Neuere Methode zur Berechnung der ebenen Unterschallströmung an dünnen Profilen bei kleinen Anstellwinkeln

Zusammenfassung Es wird eine Methode beschrieben, welche in einfacher Weise die Berechnung der Druckverteilung an der Oberfläche eines dünnen, mäßig gewölbten Profils in wenig angestellter kompressibler Unterschallströmung bis zur zweiten Ordnung gestattet. Die Arbeit gibt die vollständige Herleitung der Theorie einschließlich einer Untersuchung der Strömung an einer abgerundeten Profilvorderkante. Den Ausgangspunkt für die theoretische Behandlung bildet—ähnlich wie bei der Integralgleichungsmethode für die schallnahe Strömung vonOswatitsch undZierep — dieGreensche Formel. Mit Hilfe von Integraltransformationen und der Anwendung des Faltungssatzes vonTricomi gelingt es, das Problem auf die Berechnung einfacher Integrale zurückzuführen. Die hergeleiteten Formeln eignen sich besonders für die praktische Anwendung, da hierfür nur die Kenntnis der Profilordinaten erforderlich ist. Die Geschwindigkeitsverteilung an der Profilkontur, wie sie aus der Reihenentwicklung folgt, wird in Nähe der Profilnase durch das Anbringen einfacher Korrekturen gleichmäßig gültig gemacht [vgl. Gl. (VII. 7a)].

---

Summary A method is described which permits in a simple way the calculation of pressure distribution on the surface of a thin, cambered aerofoil, at moderate incidence, in compressible subsonic flow, up to the second order. This paper gives a complete derivation of the theory including an investigation of the flow near a rounded leading edge. Starting-point for the theoretical treatment isGreen's formula-similar to that in the method of integral equation for calculating transonic flow proposed byOswatitsch andZierep. By means of integral transforms and application ofTricomi's convolution theorem the problem is reduced to the calculation of simple integrals. The derived formulas are particulary suitable for practical applications, since knowledge of the profile-ordinates only is required. The velocity on the aerofoil surface, as given on a straight forward second approximation is rendered uniformly valid near the leading edge by adding a few simple corrections [see equation (VII. 7a)].

---

---

Mit 3 Textabbildungen

---

Ungekürzte Fassung der gleichnamigen, der Technischen Hochschule Graz vorgelegten Habilitationsschrift. Die Arbeit entstand am Institut für Theoretische Gasdynamik der Deutschen Versuchsanstalt für Luft- und Raumfahrt in Aachen. Dem Leiter des Instituts, Herrn Professor Dr.K. Oswatitsch, Ordinarius für Strömungslehre an der Technischen Hochschule Wien, verdankt der Verfasser die Anregung zu dieser Arbeit sowie viele wertvolle Ratschläge bei ihrer Durchführung. An dieser Stelle möchte der Verfasser auch Herrn Professor Dr.H. Winter von der Technischen Hochschule Graz für das Interesse an dieser Arbeit aufrichtigen Dank sagen.     

Similarity analysis of strong converging spherical shock waves in radiating gas

Summary In this paper the influence of radiation upon the classical adiabatic self-similar solution of a converging spherical shock wave is investigated. The medium is assumed to be an optically thick, inviscid and ideal gas with a constant ratio of specific heats. In front of the shock wave it is considered to be uniform and at rest, and its counter pressure is neglected. The presented paper restricts itself to presenting those similarity solutions which show the least possible deviation from the classical adiabatic solution. Their eigenvalues are determined numerically and listed. The flow profiles of nonadiabatic similarity solutions are shown and compared with the flow profiles of the adiabatic similarity solution.     

Numerische Simulation der Strömung in Anlaufstrecken von Grenzschichtwindkanälen für bauwerksaerodynamische Untersuchungen

Zusammenfassung In der vorliegenden Arbeit wird die dreidimensionale turbulente Str?mung in Anlaufstrecken von Grenzschichtwindkan?len mit rechteckigem Querschnitt unter Berücksichtigung der Sekund?rstr?mung zweiter Art berechnet. Die Brauchbarkeit des Verfahrens wird durch Vergleich mit Messungen und Berechnungsergebnissen anderer Autoren für Str?mungen in Kan?len mit glatten und rauhen W?nden gezeigt, und anschlie?end werden die Ergebnisse für einen Grenzschichtwindkanal besprochen.     

Numerical simulation of a two-dimensional turbulent wall jet in an external stream

Turbulent wall jets possess a region with negative production of turbulent kinetic energy between the points of maximum velocity and vanishing shear stress. This characteristic feature cannot be shown with many turbulence models. The use of an extended expression for the primary turbulent shear stress together with a k–? or an algebraic Reynolds stress model results in a model which can show this physical property. Computed results obtained with this concept are compared with measurements and results obtained with the standard k–? model and a full Reynolds stress closure. It is shown that the computed results with the present and the Reynolds stress model are of similar quality. However, the Reynolds stress solution is more costly in computing time.