Mining Turbulence Data

Ivan Marusic

Department of Aerospace Engineering and MechanicsUniversity of Minnesota

Collaborators: Victoria Interrante, George Karypis, Vipin Kumar Graham Candler, Ellen Longmire, Sean Garrick

Acknowledgement: National Science Foundation

Mathematical Challenges in Scientific Data MiningIPAM 14-18 January, 2002

Flow direction

Solid surface

Turbulent Boundary Layer(Flow visualization using Al flakes in water channel)

Outline

• Turbulent boundary layers: introduction and background Need for both simulation and experimental datasets

• Visualization and feature extraction What are the important features? What is to be “data mined”?

• Difficulties with present analysis approach

• New analysis strategy to investigate causal relationships

• Data mining issues and challenges

Flow direction

Solid surface

Turbulent Boundary Layer

Responsible for heat transfer, skin friction (drag), mixing of scalars

Issues in wall turbulence

• Described by Navier-Stokes equations (non-linear PDEs)

• Direct numerical simulation is restricted to low Re (Reynolds number) Re = ratio of inertia to viscous forces (U) No. of simulation grid points ~ (Re)9/4 , Cost ~ (Re)3 Present simulation: Re = O(103), Require Re = O(106)

• Also need experimental datasets to investigate high Re flows

• Better understanding of physics/causal relationships would lead to more accurate modeled simulation tools (CFD) and analytical scaling laws

What features do we extract?

• Flow field information involves in (x,y,z,t) : Velocity u, Pressure p, Temperature , etc

• Good candidate = Coherent vortex structures

Vortex identification using velocity gradient tensor

Flow topology classification

Isosurfaces of:

Decreasing threshold levels

Enstrophy

Discriminant

Volume rendered visualizations( DNS data Re = 700)

Discriminant

Cross-section of “blue” vortex

EXPERIMENTAL WIND TUNNEL FACILITY

PIV SETUP

Kodak Megaplus Cameras

1024 x 1024 pixels

Pulsed Lasers

Nd:YAG

= 15

In-plane Vorticity

In-plane Swirl

Difficulties with present analysis approach

Typical Turbulent Boundary Layer Simulation

• O(108) grid points

• Generates >10 Terabytes per day (every day)

• Write to disk every 1/1000 time steps (99.9% discarded)

• Final database ~1 Terabyte

• All analysis is done after final database is obtained

Present approach

New analysis approach

Some important trigger eventsassociated with drag

• “Bursting”

• High values of Reynolds shear stress (-uw) (associated with momentum transport)

Example of bursting events

N.B. High –uw region

Swirl (|ci|) Reynolds shear stress

Vorticity Wall-normal velocity

20Apr_06 zone1

Consistent with “packets of vortices” (together with other evidence):

SIMPLE SEARCH ALGORITHM

Dual threshold search routine

Define connected region only if 8 neighboring points

To search for ‘Packets of hairpin vortices’, define a region if Positive Vorticity in the bottom and Negative Vorticity in the top..

Additional search for (a) Low streamwise velocity (Low momentum) (b) High Reynolds shear stress

in the adjoining region of patches of vorticity

z+ = 92

All quantities non-dimensionalized usingU and

VORTICITY MOMENTUM

SWIRL STRENGTH

VORTICITY u’w’

z+ = 92

All quantities non-dimensionalized usingU and

VORTICITY u’w’

MOMENTUM

Adrian, Meinhart & Tomkins (2000)

Modeling Data With Graphs Beyond Transactions

Graphs are suitable for capturing arbitrary relations between the various objects.

VertexObject

Object’s Attributes

Relation Between Two Objects

Type Of Relation

Vertex Label

Edge Label

Edge

Data Instance Graph Instance

Frequent Subgraph DiscoveryDiscovery(FSG – Karypis & Kuramochi 2001)

Interesting Patterns Frequent Subgraphs

Discovering interesting patterns

Finding frequent, recurrent subgraphs

Efficient algorithms must be developed that operate and take advantage of the new representation.

Finding Frequent Subgraphs:Input and Output

Problem setting: similar to finding frequent itemsets for association rule discovery

Input Database of graph transactions

Undirected simple graph (no loops, no multiples edges) Each graph transaction has labeled edges/vertices. Transactions may not be connected

Minimum support threshold σ Output

Frequent subgraphs that satisfy the support threshold

Each frequent subgraph is connected.

Finding Frequent Subgraphs:Input and Output

Support = 100%

Support = 66%

Support = 66%

Input: Graph Transactions Output: Frequent Connected Subgraphs

Example

Example of datasets (Database type-B) for investigation using a Frequent Subgraph Discovery scheme:

- PIV data : In-plane swirl S(x,y) for multiple timesteps (with and without trigger signal)

- Full 3D data from simulation

Further Challenges

• Temporally and Spatially evolving structures (objects change)

• Interactions of vortex structures

C

BA

D