Efficient implicit algorithm for the equations of 2-D viscous compressible flow: application to shock-boundary layer interaction

A fully implicit algorithm has been developed to time integrate the equations of 2-D compressible viscous flow. The algorithm was constructed so as to optimize computational efficiency. The time-consuming block matrix inversions usually associated with implicit algorithms have been reduced to the trivial non-iterative inversion of four sets of scalar bidiagonal matrices. Thus, the algorithm requires virtually no more computer storage than an explicit algorithm. The efficient structure of the implicit algorithm is reflected in comparative timings which slow that it requires only a factor of two more computer time per point per time step than a typical explicit algorithm. Therefore, the algorithm allows more economical solution of given flows than existing explicit methods and also allows more difficult problems to be attempted using available computer resources. Application of the algorithm to the problem of shock-boundary layer interaction produces results consistent with both experimental measurements and other calculations.     

Creep of thick-walled cylinders subjected to internal pressure and axial load

A creep theory is presented to predict deformations at any specified time for a thick-walled cylinder subjected to internal pressure and axial load. The theory is based on the usual assumptions that the deformations are infinitestimal, that the material is incompressible and that the total strain theory is valid. The stress-strain-time relation for the material is assumed to be represented by an isochronous stress-strain diagram which is approximated by an arc hyperbolic sine function. The experimental part of the investigation included tests of thick-walled cylinders made of high-density poly-ethylene whose ratio of outside to inside radii were either 1.5 or 2.0. The test cylinders were either tested as closed-ented cylinders with internal pressure or subjected to a combination of internal pressure and axial load. Also, the application of the theory for varying load conditions was studied. Good agreement was found between theory and experiment.     

Stabilitätsverhalten und verzweigung stationärer Lösungen der navier-stokesschen gleichungen

Zusammenfassung Am Beispiel der Strömung in einem horizontalen Rohr mit von unten erwärmter Wand wird gezeigt, wie man mit Hilfe der Theorie des topologischen Abbildungsgrades von Leray und Schauder im überkritischen Bereich der Rayleigh-Zahl auf die Existenz einer von der Grundströmung verschiedenen, stationären Strömung (thermische Konvektionsströmung) schließen kann. Unterhalb der kritischen Rayleigh-Zahl existiert genau eine stationäre Lösung der Navier-Stokesschen Bewegungsgleichungen, nämlich die Grundströmung. Beim Überschreiten der kritischen Rayleigh-Zahl verzweigt sich diese stationäre Lösung, wobei die Grundströmung gleichzeitig instabil wird.Die Methode des Abbildungsgrades ist auf ähnliche Strömungsbeispiele mit zellularer Instabilität anwendbar wie z.B. die Strömung zwischen rotierenden Zylindern (Taylor-Wirbel) oder die von unten erwärmte Flüssigkeitsschicht (Benard-Zellen).Diese Arbeit entstand aus dem Institut für Angewandte Mathematik und Mechanik der DVL an der Universität Freiburg i. Br. Über diese Untersuchung wurde bereits auf der GAMM-Tagung in Bonn (24.–28. 4. 1962) berichtet (s. [19]). Vorgelegt von H. Görtler     

Experimental study of large-diameter thin-wall pressure vessels

An experimental stress analysis of three cylindrical pressure vessels with radius/thickness ratios ranging from 100 to 238 and different head closures is described. Brittle coatings and electrical strain gages were employed to determine stress distributions over the entire outer surface of the vessels. Electrical strain gages alone were used to determine stresses on the inside surface of the vessels. Particular emphasis was placed on determining stress concentrations and on nonlinear effects produced by geometric imperfections. An attempt was also made to correlate the failure, which started in the cylindrical portion of the three vessels, with the elastic-stress distribution. It was found that the imperfections in the cylinder were not significant if the vessel was fabricated from a ductile steel. However, if the vessel was constructed from a high-strength but brittle steel, the imperfections significantly lower the bursting strength of the vessel.     

Comparison of Combustion Models and Assessment of Their Applicability to the Simulation of Premixed Turbulent Combustion in IC-Engines

In order to simulate the turbulent combustion process occurring in spark-ignition (IC) engines, it is necessary to provide suitable and numerically economical models, the latter being particularly important in the application to industrial problems. Moreover, these models must deliver sufficiently accurate results for the unsteady operation of spark combustion engines, concerning variable geometries, temperatures, pressures and charge development in different configurations. In this work different turbulent combustion models for premixed hydrocarbon combustion are compared with respect to their ability to accurately predict the propagation of turbulent perfectly premixed flames. As a first configuration a cylinder of constant volume was studied. Transient calculations were used to simulate the propagation of the turbulent flame and to evaluate the resulting turbulent burning velocity. These calculations were performed for a perfect mixture of air and hydrocarbons at stoichiometric mixture and different initial conditions concerning pressure, temperature and turbulence intensity. As a second configuration a stationary turbulent bunsen-type flame with methane fuel was used to validate the turbulent combustion model of [Lindstedt and Vaos, Combust. Flame 116 (1999) 461] at different pressures. Calculated results were then compared to experimental data of [Kobayashi, Tamura, Maruta and Niioka. In: Proceedings of the 26th Symposium on Combustion, 1996, p. 389] and show excellent agreement for the turbulent burning velocity at several pressure levels using only a single set of model parameters.     

Experimental measurements and computational modeling of the flow field in an idealized human oropharynx

The velocity field in the central sagittal plane of an idealized representation of the human oropharynx (HOP) during steady inspiration, simulating oral inhalation through an inhaler mouthpiece, was measured experimentally using endoscopic particle image velocimetry (PIV). Measurements were made at three flow rates: 15, 30, and 90 L/min, which correspond to a wide range of physiological conditions. Extensive tests were performed to verify the veracity of the PIV data. The flow was also modeled computationally using Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) methods. The PIV data clearly indicate the complex nature of HOP flow, with three-dimensionality and several regions of separation and recirculation evident. Comparison of the experimental and computational results shows that, although the RANS CFD reproduces the basic features of the flow, it does not adequately capture the increased viscous effects at lower Reynolds numbers. The results demonstrate the need for more development and validation of CFD modeling, in particular RANS methods, in these flows.     

Experimental study of the Kolmogorov refined similarity variable

Recently Thoroddsen and Van Atta (1992, Phys. Fluids A4, 2592) showed that Kolmogorov's refined similarity hypothesis (1962, J. Fluid Mech. 13, 77; 82) is supported by experimental data from a wind-tunnel study of a cylinder wake, at Re_λ of 550. We show here that the probability density of the Kolmogorov similarity variable approaches a Gaussian distribution. The data also suggest that it may obey an even more demanding conditional similarity, which leads to important conclusions regarding the scaling exponents.     

Relation between steady shear flow and dynamic rheology

Summary The relationships between steady shear flow and dynamic rheology are investigated at relatively high shear rates and frequencies. A useful empirical relationship in this region predicts that the magnitude of the complex dynamic viscosity | ^*| should be compared with the shear viscosity at equal values of frequency and shear rate (Cox-Merz-rule). Polystyrenes (PS) and Polyacrylamides (PAAm) have been investigated over a wide range of concentration and molecular weight. Only in case of PAAm/H₂O solutions we have found that the results do not coincide with Cox-Merz-rule. As far as we know this is the first time that deviations from Cox-Merz-rule were observed in a homogeneous system. A molecular interpretation is given.

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Zusammenfassung Die Beziehung zwischen der Scherviskosität und der komplexen (dynamischen) Viskosität bei relativ hohen Schergeschwindigkeiten und Frequenzen wurde untersucht. Eine geeignete empirische Beziehung in diesem Bereich sagt aus, daß der Betrag der komplexen Viskosität | ^*| mit der Scherviskosität bei gleichen Werten von Frequenz und Schergeschwindigkeit vergleichbar ist (Cox-Merz-Regel). Polystyrole (PS) and Polyacrylamide (PAAm) wurden über einen weiten Bereich der Konzentration und des Molekulargewichts untersucht. Nur im Fall der PAAm/H₂O-Lösungen wurden Abweichungen von der Cox-Merz-Regel gefunden. Soweit uns bekannt, ist es das erste Mal, daß Abweichungen von der Cox-Merz-Regel in einem homogenen System gefunden wurden. Eine molekulare Erklärung wird gegeben.

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Presented at the IUPAC 26^th International Symposium on Macromolecules, Mainz, September 17–21, 1979.

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With 4 figures and 1 table     

Basic equations for the microscopic theory of plasticity of polycrystalline materials with given texture

An expression for the yield stress of anisotropic materials is applied to the anisotropic strength of hard rolled copper foils whose crystallographic texture is known. We assume that this crystallographic texture is the only cause of the anisotropic plastic behaviour of the material. The model used for the yield stress is also used to deduce:

1. Stress-strain relations for isotropic polycrystalline materials;
2. A formula for the fully plastic strain tensor, applied to anisotropic hard rolled copper foils.

For the anisotropic copper foils considered the calculated curves of the yield stress and of the strain tensor as a function of the angle x between rolling and tensile direction agree qualitatively with the measured values. However, the theory is not complete, since the yield stress and the plastic strain tensor are both a function of a parameter Q, the fraction of the number of available crystallographic slip planes on which the maximum shear stress has reached the critical value τ_a. We assume that for “fully” plastic deformation a certain critical fraction Q _e of the total number of slip planes has to be active. The fraction Q _e is called the critical active quantity. With the parameter Q _e we adjust the calculated curves to the measured ones. The dependence of Q _e on the properties of the material (e.g. the crystallographic texture) is discussed in Appendix I.     

Boundary layer development in an MHD duct

This study presents a method of calculation for two-dimensional, steady-state, laminar flow in the entrance region of an MHD duct. The electrically conducting fluid in the free stream is compressible whereas the medium in the boundary layer itself is taken to be incompressible. Thus, the density is variable in the axial direction of the duct only, and the momentum and energy equations for the boundary layer are uncoupled. These equations are solved using an extended Von Kármán-Pohlhausen method as described by U. P. Hwang for a compressible MHD flow with zero electric field. In this study, however, the electric field is essentially not zero and the MHD duct can work as a generator. The equations of the insulator boundary layer are solved in the assumption that the displacement thickness of the electrode boundary layer equals that of the insulator boundary layer, so the total influence of the varying effective crossection on the free stream is taken into account. In this way a quick method of calculating the MHD flow in the entrance region of a duct is obtained.