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

Effect on PDC Rate of Penetration

(by changing to asymmetric fluted jets)

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.