The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1991 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodolgy. The fully three dimensional, compressible, Reynolds averaged Navier-Stokes equations with k-ε turbulence modelling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1992 ◽  
Vol 114 (3) ◽  
pp. 528-537 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier–Stokes equations with k–ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

IGV-Rotor Interaction Analysis in a Transonic Compressor Using the Navier-Stokes Equations

1996 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Inlet Guide Vane ◽  
Operating Characteristics ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Mass Flow Rates

A recently developed, time-accurate multigrid viscous solver has been extended to handle quasi-three-dimensional effects and applied to the first stage of a modern transonic compressor. Interest is focused on the inlet guide vane (IGV):rotor interaction where strong sources of unsteadiness are to be expected. Several calculations have been performed to predict the stage operating characteristics. Flow structures at various mass flow rates, from choke to near stall, are presented and discussed. Comparisons between unsteady and steady pitch-averaged results are also included in order to obtain indications about the capabilities of steady, multi-row analyses.

scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

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