A hybrid viscous body force model for low-speed centrifugal compressors

The flow in centrifugal compressors is viscous and unsteady. Flow separation off the blades challenges the accuracy of simulations. A viscous body force model is expected to speed up numerical convergence and reduce the computational costs of unsteady simulations. In this paper, both stability and accuracy of the viscous body force model are investigated based on the case of a low-speed centrifugal compressor. First, two formulations of the viscous body forces are obtained from the expression of the viscous flux. Then, the numerical stability of two body force models is found to be related to drag coefficient and flow angle. For large negative drag coefficients, the viscous body forces would lead to divergences. Since unsteady Reynolds-averaged Navier–Stokes simulations show that two formulas have considerable accuracy, stability is considered as the main factor for modeling. With the findings, a hybrid viscous body force method is proposed. To assess the applicability of the hybrid model, two test cases are compared against the results obtained by unsteady Reynolds-averaged Navier–Stokes simulations. The first case is the capability evaluation of unsteady characteristics capture for low-speed centrifugal compressors. The simulation results show that the hybrid viscous body force model can capture main unsteady viscous characters, including wake vortexes and tip leakage flow. The other is the case in which the inlet total pressure is disturbed. It is found that fluctuations of pressure, temperature, and velocity predicted by the viscous body force method are close to unsteady Reynolds-averaged Navier–Stokes results. In addition, the time-accurate overall performance of the compressor with disturbance is also predicted satisfactorily. With the advantage in lowering computer resource requirement, the viscous body force model is a promising method for long length scale unsteady cases.

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Performance of Unsteady Reynolds-Averaged Navier-Stokes and Hybrid Scale-Resolving Simulation Approaches in Simulating a Low-Speed Axial Compressor Rotor

10.1115/gt2021-59028 ◽

2021 ◽

Author(s):

Xiangyi Chen ◽

Björn Koppe ◽

Martin Lange ◽

Wuli Chu ◽

Ronald Mailach

Keyword(s):

Experimental Data ◽

Turbulence Modeling ◽

Navier Stokes ◽

Tip Leakage Flow ◽

Low Speed ◽

Turbulent Characteristics ◽

Sst Model ◽

Reynolds Averaged Navier Stokes ◽

Sas Model ◽

Les Model

Abstract Aerodynamics phenomena in compressors are highly unsteady and turbulent. Selecting a proper turbulence-modeling method is significant to reveal the complex flow mechanism in turbomachines. In the current paper, the shear stress transport (SST) model as an unsteady Reynolds-averaged Navier-Stokes (RANS) method, the scale-adaptive simulation (SAS) model, and the zonal wall-modeled large eddy simulation (zonal-LES) as two hybrid scale-resolving simulation approaches have been compared. These turbulence-modeling methods were employed to simulate a single rotor of a low-speed research compressor featuring a tip clearance of 1.3% of chord length. Comparisons were made between the simulation results and the experimental data at three operating points, and the flow fields at the design point have been specifically discussed in detail. The results show that the advantage of the zonal-LES model becomes obvious as the compressor throttles. The zonal-LES model brings a significant improvement over both the SST model and the SAS model in capturing the experimental data, especially the velocity distribution in the low-span region, as well as the loss near the endwalls. The SAS model as a scale-resolving method presents no benefits in predicting the relevant flow compared with the SST model, as the activation of the SAS source term is limited for this test case. For the loss prediction, the variation in the upper half-span region is mainly due to the different results in modeling turbulent characteristics of the tip leakage flow, whereas the mechanism behind the higher loss at the lower half-span predicted by the zonal-LES model is a consequence of the complex topology of the corner separation and the intensive mixing.

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The solution of the dynamic field of the Haskell fault model reconsidered

Bulletin of the Seismological Society of America ◽

10.1785/bssa0720041069 ◽

1982 ◽

Vol 72 (4) ◽

pp. 1069-1083

Author(s):

R. D. List

Keyword(s):

Half Space ◽

Displacement Field ◽

Body Force ◽

Fault Model ◽

Earthquake Source ◽

Infinite Space ◽

Force Method ◽

Body Force Method ◽

Rupture Speed ◽

Seismic Dislocations

abstract A method of obtaining the displacement field of the Haskell model of an earthquake source, based on the well-known equivalence of seismic dislocations and body force, is described. It is shown that the solution of Madariaga (1978) can be generalized and that the two methods are equivalent for the problem of a rectangular dislocation expanding on a plane in an infinite space with a variable rupture speed and variable slip in the direction of rupture. One of the advantages of the equivalent body force method is that it can be used to readily obtain the transformed solution to the Haskell model in a half-space for a rectangular dislocation, expanding with variable rupture speed and variable slip.

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Accurate Solutions of Stress Intensity Factors of Standard Fracture Test Specimens

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.452-453.405 ◽

2010 ◽

Vol 452-453 ◽

pp. 405-408 ◽

Cited By ~ 1

Author(s):

Akihide Saimoto ◽

Fumitaka Motomura ◽

Hironobu Nisitani

Keyword(s):

Stress Intensity ◽

Body Force ◽

General Purpose ◽

Two Dimensional ◽

Fracture Test ◽

Intensity Factors ◽

Force Method ◽

Body Force Method ◽

Standard Specimens ◽

Significant Figures

Practically exact solutions of stress intensity factor for several two-dimensional standard specimens were calculated and shown in numeric tables. The solutions were confirmed to converge until 6 significant figures through a systematical computation of discretization analysis. The convergence analyses were carried out by using a general purpose program based on a body force method.

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Assessment Procedure for Multiple Volumetric Flaws in p-M Diagram

Journal of Pressure Vessel Technology ◽

10.1115/1.3110036 ◽

2009 ◽

Vol 131 (3) ◽

Cited By ~ 3

Author(s):

Shinji Konosu

Keyword(s):

Body Force ◽

Pressure Vessels ◽

The Body ◽

Assessment Procedure ◽

Force Method ◽

Reference Stress ◽

Body Force Method ◽

Common Problems ◽

Shielding Effects

Assessment of multiple volumetric flaws is one of the most common problems relating to pressure vessels and piping components. Under the current fitness for service rules, such as ASME, BS, and so on, multiple volumetric flaws are usually recharacterized as an enveloping volumetric flaw (defined as a single larger volumetric flaw) as well as multiple cracklike flaws, following their assessment rules. However, the rules proposed in their codes will not often agree and their justification is unknown. Furthermore, they can provide unrealistic assessment in some cases. In this paper, the interaction between two differently sized nonaligned volumetric flaws such as local thin areas is clarified by applying the body force method. Unlike multiple cracklike flaws, the effect of biaxial stresses on the interaction is evident. Based on the interaction that indicates the magnification and shielding effects and reference stress solutions, a new procedure for multiple volumetric flaws is proposed for assessing the flaws in the p-M (pressure-moment) diagram, which is a simple assessment procedure for vessels with volumetric flaws.

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