Computational Modeling of Turbulent Asymmetric Jet Flows Prof. Ed Akin Mechanical Engineering and...
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Transcript of Computational Modeling of Turbulent Asymmetric Jet Flows Prof. Ed Akin Mechanical Engineering and...
Computational Modeling of Turbulent Asymmetric Jet
Flows
Prof. Ed AkinMechanical Engineering and Materials Science
Rice University
Houston, Texas
Jon Bass, Ph. D., P.E.
Computational Mechanics CompanyAustin, Texas
Fifth US-Japan Symposium on Flow Simulation & Modeling
Overview
Asymmetric Nozzle Flow Features Designs for Cleaning and Mixing
» Submerged incompressible jets» Reynold’s Number, 6 E5 < Re < 1.2 E6» Geometry, Parametric studies
New Results, Power imparted to fluid
Conclusions
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
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.
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
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.
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
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
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
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
Sketch of Exit Flows
A. Circular Nozzle
B. Asymmetric Nozzle
VxV z
00
Internal edge vortex
Vx = 0V z = 0
V = Q / A P constant
V * T 0
T perpendicular to V
P varies T varies
New power term s
V * T 0
V varies
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.
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
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 /
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 >1.
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 c=1 c>1
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 < c < 3.
Asymmetric Jet Net Power Increase
(For corrected areas.)
Size (d*32) 7 8 9 10 11 1213
% Increase79 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.
Drilling Nozzle Parametric Studies
Fluted transition exit shapes» Oval (2 lobes @ 180), 3 lobes @ 120,
Cruciform (4 lobes @ 90), 2 lobes @ 60, single flute to offset circular outlet, etc.
Distance to impingement surface Volumetric flow rates
Unique Impingement Pressures
Regions of less than hydrostatic pressure
Locations controlled by asymmetric shape
Peak value 15-20% of stagnation pressure
Example Asymmetric Jet Flows
Pressures Velocity Fields Turbulence Power levels Related Lab and Field Results