Computational Modeling of Turbulent Asymmetric Jet Flows

1
Computational Modeling of Turbulent Asymmetric
Jet Flows

• Prof. Ed Akin
• Mechanical Engineering and Materials Science
• Rice University
• Houston, Texas
• Jon Bass, Ph. D., P.E.
• Computational Mechanics Company
• Austin, Texas
• Fifth US-Japan Symposium on Flow Simulation
  Modeling

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Overview

• Asymmetric Nozzle Flow Features
• Designs for Cleaning and Mixing
• Submerged incompressible jets
• Reynolds Number, 6 E5 lt Re lt 1.2 E6
• Geometry, Parametric studies
• New Results, Power imparted to fluid
• Conclusions

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Asymmetric Jet Flow Features

• Wide variety found in the literature
• Flat plate orifices, smooth interior nozzles
• Incompressible, Compressible transonic
• Mainly experimental studies
• Simplified non-circular vortex ring studies
• Very few CFD studies

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Typical Asymmetric Jet Flows

• Eccentric vortex ring axes switch positions
  (called vortex induction).
• Increase entrainment and mixing.
• Shear layers asymmetric and change downstream.
• Turbulence asymmetric and changes downstream.

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Designs for Cleaning and Mixing

• Submerged jets, Impinging jets
• Specialized interior fluted transition
• Application to Subterranean Drilling and
  Environmental Cleaning
• Example Jets for fixed cutter PDC
  (Polycrystalline Diamond Compact) drill bits with
  3 to 8 nozzles

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CFD Considerations

• High levels of recirculation and mixing require a
  good turbulence model.
• Interior nozzle geometry is important.
• Large length scale differences between flows
  internal and external to the jet suggest adaptive
  solutions.
• Hp-adaptive methods are most efficient.

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ProPhlex CFD Software

• Three-dimensional Navier-Stokes Eqs
• Turbulent K - ? closure
• Adaptive - hp finite element system
• Automatic mesh refinement / de-refinement
• Automatic degree enrichments (1- 8 degree)
• Ainsworth-Oden N-S error estimator
• Specialized kernel for auxiliary calculations

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Fluted Nozzle Geometries

• Non-circular interior cross-sections
• Sharp interior edges parallel to flow direction
• Terminate with sharp transverse edges at outlet
  area
• Controlled area changes to enhance shear stresses
  at the outlet

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Fluted Nozzle Hydraulics

• Less than hydrostatic face pressures on
  impingement surface
• Increases local re-circulation
• Increases mass entrainment
• Increases hydraulic power
• Changes location of peak turbulence

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Exit Flow Differences

• Velocity varies in magnitude and direction over
  outlet area
• Velocity has additional components
• Pressure varies over area
• Shear stresses vary over area
• Shear stresses contribute to power

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Sketch of Exit Flows
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Power Imparted to Fluid

• Power per unit area The product of the velocity
  vector and force per unit area.
• Fluid Power Integral of this product over the
  nozzle inflow and outflow areas.
• Circular Jet reduces to the product of the
  pressure drop and flow rate.
• Significantly increases in asymmetric jets, by a
  factor of 2 to 3.

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Primary Variables

• Velocity vector Vj
• Stress tensor ?kj
• Pressure and shear stress tensors
• pkj p ?kj, ?kj pkj ?kj
• Area normal vector nk
• Surface force vector Fj ?kj nk
• Power per unit area P Vj Fj
• Volumetric flow rate Q

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Stress Tensors

• ?kj p ?kj ?kj stress tensor
• ?kj µt(Vk,j Vj,k) shear stresses
• Vk is the velocity vector
• Turbulent viscosity, µt, changes significantly
  with location, µt ? ?K2 / ?

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Integrals Over Exit Area

• Net Flow rate, Q Q ?A Vk nk dA
• Net Power, P P ?A Vk Fk dA
• Circular Vk, nk, Fk are parallel vectors
• Asymmetric Vk, nk, Fk are not parallel, more
  terms appear in Fk ?jk nj
• Asymmetric jet power is higher for same A, Q,
  ?p. Correlates to P c Q ?p, c gt1.

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Engineering Design Differences

• Exit Flow Description Cir Asy
• Velocity, Vk, parallel to axis, nk yes no
• Velocity constant over the area yes no
• Pressure, p, constant over area yes no
• Rapid change in shear stress, Tkj no yes
• Surface force, Fk, parallel to nk yes no
• Product of Vk its gradient is 0 yes no
• Power c Q ?p c1 cgt1

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Power Calculations via CFD

• CFD post-processing was modified to numerically
  integrate the power contributions over the nozzle
  inlet and outlet surfaces.
• Applying to a 3-D model of an axisymmetric jet
  gave P 0.98 Q ?p where 1-D result is P Q ?p.
• Applying to a 3-D model of an asymmetric jet gave
  P c Q ?p where 2 lt c lt 3.

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Asymmetric Jet Net Power Increase(For corrected
areas.)

• Size (d32) 7 8 9 10 11 12 13
• Increase 79 84 88 91 95 98 100
• Size 14 15 16 17 18 19 20
• Increase 101 103 105 107 108 109 109
• Asymmetric jets impart more power to the
  fluid
• for the same flow rate and pressure
  drop.

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Drilling Nozzle Parametric Studies

• Fluted transition exit shapes
• Oval (2 lobes _at_ 180), 3 lobes _at_ 120, Cruciform (4
  lobes _at_ 90), 2 lobes _at_ 60, single flute to offset
  circular outlet, etc.
• Distance to impingement surface
• Volumetric flow rates

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Unique Impingement Pressures

• Regions of less than hydrostatic pressure
• Locations controlled by asymmetric shape
• Peak value 15-20 of stagnation pressure

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Example Asymmetric Jet Flows

• Pressures
• Velocity Fields
• Turbulence
• Power levels
• Related Lab and Field Results

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Effect on PDC Rate of Penetration(by changing to
asymmetric fluted jets)
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Conclusions

• Asymmetric jets give higher entrainment, mixing
  and turbulence levels.
• They impart more power to the fluid and have
  unusual pressure distributions.
• CFD is necessary to understand them.
• A number of industrial flow applications are
  apparent and merit study.