Lecture 39: Turbulence Modeling & 3D Flow Prediction in Turbomachinery with Case Studies, Slides of Turbomachinery

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In this lecture...

• Computational Fluid Dynamics for turbomachinery - Turbulence modelling - Prediction of 3D flows: case studies - Computing requirement - Errors and uncertainties

Turbulence Models

• Zero equation or algebraic eddy viscosity model - Use an algebraic form for the turbulent stresses - Valid for simple 2D shear flows - Mild pressure gradient - 3D boundary layers with small cross flows - Not accurate for flows with pressure or turbulence driven secondary flows - Cannot predict shock-induced separated flows

Turbulence Models

• One equation model: Spalart Allmaras
  • Employ an additional PDE for a

turbulence velocity scale

• Usually used in design-iteration type

simulations

• Popular in recent times due to

inherent problems with more refined

models

• Very robust models, rarely produce

completely unphysical results

Turbulence Models

• Near wall treatment
  • On-design flows without large separated regions, wall function model close to the wall
  • Off-design, low Re model, over production of turbulent KE must be checked
• Menter’s SST Κ-ω and Durbin’s v2f
  • Works well for adverse pressure gradients and separating flows

Turbulence Models

• Reynolds stress models
  • Use seven different PDEs for all the

components of the turbulence

stresses.

• Reasonably better in cases where

two-equation models were not

satisfactory

• More realistic physical simulation of

turbulent flows

Case studies

• Types of shear flows
  • Tip leakage flow
  • Scraping vortex
  • Corner separation
  • Passage vortex
  • Secondary flows
  • Shock boundary layer interaction
  • Inflow distortion

Tip leakage flows

• Several papers on simulation of tip leakage flows
• Steady computations reasonably good
• Vortex fluctuations close to compressor stall for eg. not predicted well.
• Case: Hah et al. 2008
  • Full annulus flow simulation
  • LES of Darmstadt transonic rotor
  • 25 million grid points
  • 60 CPU hours on 124 CPU NASA’s Columbia!
  • Results compared with experimental data from TU Darmstadt

Vortex fluctuations close to stall (Hah et al. 2008)

Measured

Computed

Passage vortex

• Strength of secondary flows, passage

vortices depend upon the blade

loading

• Case: Hjarne et al. , 2007

• Secondary flow studies on turbine

OGV cascade

• Different turbulence models

• Realizable Κ-ε, SST Κ-ω and RSM

• Simulations compared with

experimental data

Passage vortex

W-velocity at downstream location of 0.5C of the blade (Hjarne et al. , 2007)

Transonic rotor: shocks, tip flow

unsteadiness

• Tip flow
  • Significant effect on flow stability, pressure rise, and efficiency
  • Self induced unsteadiness related to spike initiated stall?
  • Role of shock wave in the flow physics
  • Experimentally capturing the tip flow dynamics very challenging

Shock positions at two operating points (Du et al , 2008)

Property variation transience during stalled operation (Du et al , 2008)