. . . . . .

. . . . . .

EHTC 2011

.Simulation of nasal flow

.. .

. ..

.

.

Development of a process for estimating the pressure drop

W.Liu, U.JanoskeLehrstuhl Stromungsmechanik, Bergische Universitat Wuppertal

B.Schmalenbeck, S.Langenberg, KWG EichhornHals-Nasen-Ohrenheilkunde/Chirurgie, Bonn

S.WenischInstitut fur Veterinar-Anatomie, Histologie und Embryologie, Giessen

November 7, 2011, Bonn

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Layout

...1 Motivation

...2 Experiment

...3 Geometry modification

...4 Grid generation

...5 Simulation in OpenFOAM

...6 Results analysis

...7 Conclusion

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Motivation

The Rhinomanometry is a preoperative investigation in orderto test the patency of the patient’s nose.

Project idea: develop methods to determine pressure drop inAnalytical solution and CFD simulation.

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Motivation

The Rhinomanometry is a preoperative investigation in orderto test the patency of the patient’s nose.

Project idea: develop methods to determine pressure drop inAnalytical solution and CFD simulation.

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Motivation

Figure: Project scheme

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Experiment-Rhinomanometry

Figure: Rhinomanometry

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Figure: Flow channel partitioning

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Figure: Process of analytical solution

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

The cross section planes are located by given points andnormal directions.

These sections have different lengths, bending angles, in-,andoutlet areas.

Figure: Parameters of sections

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Assumptions

Incompressible,isothermal flow ⇒ air density, viscosity andtemperature constant;

Average velocity of a section⇒ va = (vin + vout)/2;

Average hydraulic diameter⇒ da = (din + dout)/2;

Figure: Simplified model of the nose

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

.The pressure drop of one section of the nose is calculated by:..

.

. ..

.

.

∆p = λl

d

ρ

2c2 + ξ

ρ

2c2 + ξb

ρ

2c2

Pressure drop due to friction;

Change of the geometry sections;

Change of the curvature.

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Parameters of the equation

P—wetted perimeter of cross section,

d—hydraulic diameter, calculated by

d =4A

P

The section length l , perimeter of cross section P , and thecross sectional area A can be directly measured.

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solutionParallel channels

Figure: Parallel channels

Q1 = Q(1− 1

1 +√

λ2λ1(d1d2 )

5)

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Implementation in ExcelThe total pressure drop is the summation of all sections.

∆ptotal =i=n∑i=1

∆pi

Therefore an Excel sheet is implemented regarding each section:

Figure: Excel sheet

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Results: Pressure drop with increasing volume flowThe curve of pressure over volume flow can be plotted based on

the results of the excel sheet.

Figure: Pressure drop/Volume flow diagram

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Analytical solution

Results: Pressure drops in each section

Figure: Division of the flow channel Figure: Histogram of pressure drop

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

CFD process

Figure: CFD process

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Geometry modification

Figure: HyperMesh

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Geometry modification

Figure: Original STL model Figure: Modified model with a mask

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Grid generation

3-D mesh generation

The snappyHexMesh utility generates 3-dimensional meshescontaining hexahedra cells.

Figure: 3-D mesh, 1.5M cells

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Simulation Model

Figure: Simple boundary conditions

Assumptions:

steady state

isothermal

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Simulation in OpenFOAM

Results:Pressure drop with increasing volume flowIn CFD simulation also show that the pressure drop increases

monotonically with volume flow.

Figure: Pressure drop/Volume flow diagram

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Simulation in OpenFOAM

Visualization application: ParaView

The CFD simulation result are visualized in ParaView:

Figure: Pressure distribution (0.927 l/s, left side)

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Result analysis

The different results are as follows:

Left side Right side

Volume flow [l/s] For all cases 0.982 0.927

Pressure [Pa]Experimental results 150 150Analytical results 1800 393

CFD simulation results 1585 229

Table: Comparison of different results

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Result analysis

The analytical results differ from the experimental results mighthave the following reasons:

simplified model ⇐⇒ complex original geometry

low accuracy when setting assumptions and determinecoefficients

As to the CFD simulation results,Patched up model differ from the original geometry:

all holes closed ⇐⇒ leakage in experiment

unnecessary parts cut ⇐⇒ air might flow into these partsduring experiment

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

ConclusionThis study presents the attempt in analytical method andCFD solution against experiment. Possible further studywould be to get a complete model and make less modification.

snappyHexMesh and HyperMesh are both able to generatemeshes for complex geometries with small effort.

The simulation results depend on the boundary conditions,mesh quality etc.

Further models should be tested, work is still under progress,further projects are planned.

EHTC 2011 Simulation of nasal flow

. . . . . .

. . . . . .

Thanks for your attention!

Questions?

EHTC 2011 Simulation of nasal flow