Unsteady Simulation of Turbulent Axial Vortex by Means of a Non-Linear k-.EPSILON. Model

Simulations of Unsteady Blade Row Interactions Using Linear and Non-Linear Frequency Domain Methods

Volume 2B: Turbomachinery ◽

10.1115/gt2015-43453 ◽

2015 ◽

Cited By ~ 6

Author(s):

Christian Frey ◽

Graham Ashcroft ◽

Hans-Peter Kersken

Keyword(s):

Frequency Domain ◽

Harmonic Balance ◽

Measurement Data ◽

Harmonic Balance Method ◽

Balance Method ◽

Frequency Domain Methods ◽

Blade Row ◽

Non Linear ◽

Rotor Stator Interaction ◽

Unsteady Simulation

This paper compares various approaches to simulate unsteady blade row interactions in turbomachinery. Unsteady simulations of turbomachinery flows have gained importance over the last years since increasing computing power allows the user to consider 3D unsteady flows for industrially relevant configurations. Furthermore, for turbomachinery flows, the last two decades have seen considerable efforts in developing adequate CFD methods which exploit the rotational symmetries of blade rows and are therefore up to several orders of magnitude more efficient than the standard unsteady approach for full wheel configurations. This paper focusses on the harmonic balance method which has been developed recently by the authors. The system of equations as well as the iterative solver are formulated in the frequency domain. The aim of this paper is to compare the harmonic balance method with the time-linearized as well as the non-linear unsteady approach. For the latter the unsteady flow fields in a fan stage are compared to reference results obtained with a highly resolved unsteady simulation. Moreover the amplitudes of the acoustic modes which are due to the rotor stator interaction are compared to measurement data available for this fan stage. The harmonic balance results for different sets of harmonics in the blade rows are used to explain the minor discrepancies between the time-linearized and unsteady results published by the authors in previous publications. The results show that the differences are primarily due to the neglection of the two-way coupling in the time-linearized simulations.

Download Full-text

An Optimized and Scalable Algorithm for the Fast Convergence of Steady 1-D Open-Channel Flows

Water ◽

10.3390/w12113218 ◽

2020 ◽

Vol 12 (11) ◽

pp. 3218

Author(s):

Louis Goffin ◽

Benjamin Dewals ◽

Sebastien Erpicum ◽

Michel Pirotton ◽

Pierre Archambeau

Keyword(s):

Steady Flow ◽

Open Channel ◽

Initial Conditions ◽

Computation Time ◽

Efficient Computation ◽

Main Interest ◽

Scalable Algorithm ◽

Non Linear ◽

Saint Venant Equations ◽

Unsteady Simulation

Calculating an open-channel steady flow is of main interest in many situations; this includes defining the initial conditions for the unsteady simulation or the computation of the water level for a given discharge. There are several applications that require a very short computation time in order to envisage a large number of runs, for example, uncertainty analysis or optimization. Here, an optimized algorithm was implemented for the fast and efficient computation of a 1-D steady flow. It merges several techniques: a pseudo-time version of the Saint-Venant equations, an evolutionary domain and the use of a non-linear Krylov accelerator. After validation of this new algorithm, we also showed that it performs well in scalability tests. The computation cost evolves linearly with the number of nodes. This was also corroborated when the execution time was compared to that obtained by the non-linear solver, CasADi. A real-world example using a 9.5 km stretch of river confirmed that the computation times were very short compared to a standard time-dependent computation.

Download Full-text

Investigation of Stator Induced Unsteadiness on a Centrifugal Impeller Using a Mach-Independent Non-Linear Harmonic Method

Volume 2C: Turbomachinery ◽

10.1115/gt2015-42042 ◽

2015 ◽

Author(s):

Benoît Tartinville ◽

Charles Hirsch

Keyword(s):

Experimental Data ◽

Computing Time ◽

Computational Effort ◽

Centrifugal Impeller ◽

Flow Solver ◽

Wide Range ◽

Non Linear ◽

Unsteady Simulation ◽

Number Flow ◽

Short Time

The objective of this paper is to numerically investigate the unsteadiness generated by a bladed diffuser on an upstream centrifugal impeller. The Non-Linear Harmonic (NLH for short) time-spectral method has been retained here. The major advantage of such a method is that it requires much less computational effort than a standard unsteady simulation. In order to further reduce the computing time, the NLH method has been extended to low speed flows by using a preconditioning technic. Therefore, the NLH method can be accurately applied to any Mach number flow and even to purely incompressible fluids. This extension of the flow solver has been validated on a wide range of simple test cases at various reduce frequencies. Solutions have been compared to purely unsteady approach and also to experimental data. In a second step, the NLH method has been applied to a centrifugal impeller and its downstream diffuser. Numerical results have been analyzed and compared to the available experimental data showing the significant influence of the downstream diffuser on the impeller pressure load.

Download Full-text

B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

Download Full-text