Workshop on EnergeticsWorkshop on Energetics--Past and PresentPast and Present77--9 December 20109 December 2010

Hong Kong ChinaHong Kong China

Numerical modeling of Hong Kong, ChinaHong Kong, China

gunderwater explosion by 1-

Dimensional ANSYS AUTODYNDimensional ANSYS-AUTODYN

Huang Hao, Jiao Qing JieState Key Laboratory of Explosion Science and Technology,

Beijing Institute of Technology Beijing ChinaBeijing Institute of Technology, Beijing, China

My research experiencesMy research experiences• Master Degree• 2004-2008; China Ordnance Industry

B t E l i T ti C t N thBooster Explosive Testing Center, North University of China; Supervisor, Prof. Wang Jingyu and Prof. Zhang Jinlin

• Nano crystalline HNS by Prefilming twinNano crystalline HNS by Prefilming twin fluid nozzle precipitation using in EFI, Papers published in PEP, Journal of Hazardous Mat & ICT conferences.

• PHD• 2008 to now, State Key Laboratory of

Explosion Science and Technology, Beijing Institute of Technology;Beijing Institute of Technology; Supervisor, Prof. Jiao Qingjie

• Underwater explosion (former); Thermal decomposition dynamics and mechanism

deco pos t o dy a cs a d ec a sof nano-metallized explosive & propellants

OutlineOutline

• Background and objectives• Typical problem-6 831g TNT under 100m• Typical problem-6.831g TNT under 100m• Mesh and boundary condition• Peak pressure and time constant• The impulse and energy flux density• The first bubble maximum radius and period

Eff t d li f d t l i• Effects on modeling of underwater explosion• Mesh size and cases• Variations of peak pressureVariations of peak pressure• The impulse and energy flux density• The bubble pulse properties

• Summary and Future Endeavors

Background and ObjectivesBackground and Objectives

Air Explosion(AIREX) Water free surface

Surface ship structure Key attributes: Ship’s Anti blast Design & Analysis; Obtainable & Observable.

Shock waveThreats for

Water Field

Pressure

Obtainable & Observable.UNDEX Experiment:Expensive , Dangerous.Analytical solutions: limit to very simple case.Depth of Explosion

Underwater Explosion

Shock wavePeak pressure/Impulse/Energy flux density/Time con.

navy ship

Time

First pulse Second pulse

to very simple case.Numerical simulation:time & cost saving.Code: ALE3D; ABAQUS; LS-DYNA;MSC/DYTRANUnderwater Explosion

(UNDEX) Bubble pulse

Time

Maximum radiusMinimum

LS DYNA;MSC/DYTRAN; DYSMAS; AUTODYN.Problems: Unmatchable. AUTODYN: 1D “wedge”;

Gaseous

Products Propagating detonation wave

Unreacted material

First period Validate the feasibility& accuracy of AUTODYN

for UNDEX modeling

Second period

Unreacted material

Explosive materials/water boundary

for UNDEX modeling

Typical problemTypical problem--6.831g TNT under 100m6.831g TNT under 100m

•• 11--Dimensional wedge modelDimensional wedge model——A simple modelA simple modelTNT was simplified to aTNT was simplified to a spherical charge in the model. The shock wave reflection of free water

•• Mesh and boundary conditionMesh and boundary condition• Maximum radius of models were 20m with the “flow out” boundary

surface was neglected.

• Maximum radius of models were 20m with the flow-out boundary condition and the total mesh number was 18,000.

• Mesh size from center of TNT charge to 1m was 0.2mm.• Mesh size was graded outward gradually for the remnant fluid domainMesh size was graded outward gradually for the remnant fluid domain. • A gauge was located at the gas/water interface to capture the bubble

period and radius (moved). The other gauges were fixed in the water domain range from 100mm to 2000mm to record the pressure time

g phistory (unmoved).

•• Effects of quadratic and linear viscosityEffects of quadratic and linear viscosity

•• Peak pressurePeak pressure180

190

200

VQ=1 VQ=0.75 VQ=0.5 VQ=0.25V =0 1 Empirical

28 VQ=1 VQ=0.75 VQ=0.5 VQ=0.25 VQ=0.1 Empirical

130

140

150

160

170

essu

re P

eak

(MP

a)

VQ=0.1 Empirical

22

24

26

ress

ure

Peak

(MPa

)

Q

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22100

110

120

130

Pre

VL

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.2218

20

Pr

VLScaled distance of 0 527

• VQ : 1, 0.75, 0.5, 0.25 , 0.1 ;VL: 0.2, 0.15, 0.1, 0.05 and 0.023.4

3.6

a)

VQ=1 VQ=0.75 VQ=0.5 VQ=0.25 VQ=0.1 Empirical

Scaled distance of 0.527 Scaled distance of 2.108

• Quadratic viscosity almost has no influence on the peak pressure

• The peak pressure increases idl i h h d i f

2.6

2.8

3.0

3.2

Pres

sure

Pea

k (M

Pa

rapidly with the decreasing of value for all scaled distances.0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

2.4

VL

Scaled distance of 10.54

•• Peak pressurePeak pressure

• Exists a value different from each scaled distance, with which the peak pressure equal or near to the empirical

SD(m/kg1/3) 0.527 1.054 1.581 2.108 3.689 5.27 10.54

which the peak pressure equal or near to the empirical value.

SD(m/kg ) 0.527 1.054 1.581 2.108 3.689 5.27 10.54VL 0.2 0.2 0.12 0.08 0.05 0.04 0.02VQ 1 1 1 1 1 1 1

• May be a fixed value for given spans of scaled distance where the predicted peak pressure can agree with the empirical value in the acceptable extent.

•• Time constants (TC)Time constants (TC)

0.012

0.013

0.014

ms) 0.026

0.028

0.030

t(ms)

VQ=1 VQ=0.5 VQ=0.1 Empirical

0.009

0.010

0.011

Tim

e co

nsta

nt(m

VQ=1 VQ=0.5 0.020

0.022

0.024 Ti

me

cons

tan t

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.220.008

VL

Q Q VQ=0.1 Empirical

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.220.018

VLScaled distance of 0.527Scaled distance of 2.108

0 12

0.16

0.20

t(ms)

VQ=1 VQ=0.5 VQ=0.1 Empirical

• Effects of VQ and VL on time constants are similar to the tendency of peak pressure.

0.04

0.08

0.12

Tim

e co

nsta

nt

y p p• Simulation results of time

constant can no be used in the l l ti f I l

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

VL

Scaled distance of 5.27

calculation of Impulse…..

•• Impulse of shock waveImpulse of shock wave

• Poor modeling accuracy of the TC, empirical value of TC was used in the calculation of impulse and energy flux density.

1.02 • The VQ and VL have slight influences on the values of

0.98

1.00

I N/I E

impulse in different scaled distance.Th di t d l

0 94

0.96

• The predicted values are near to the empirical values within 2%.

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.220.94

VL

(VQ=1,SD=0.53) (VQ=0.1,SD=0.53) (VQ=1,SD=2.11) (VQ=0.1,SD=2.11)(V =1 SD=5 27) (V =0 1 SD=5 27)

within 2%.

(VQ 1,SD 5.27) (VQ 0.1,SD 5.27) (VQ=1,SD=10.54) (VQ=0.1,SD=10.54)

•• Energy flux density (EFD) of shock wave Energy flux density (EFD) of shock wave

• Climb for shock wave pressure history, use P=0.1Pm as the start point of integration for impulse and energy flux density. p g p gy y

• VQ also almost no effect on EFD1.10

1.12

• VL influences significantly on the EFD, especially for th l l d di t

1.04

1.06

1.08

E N/E

E

the larger scaled distances.• The simulated values of

EFD are also in acceptable 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

1.00

1.02

pagreement differing by less than 12%.

VL

(VQ=1,SD=0.53) (VQ=0.1,SD=0.53) (VQ=1,SD=2.11) (VQ=0.1,SD=2.11) (VQ=1,SD=5.27) (VQ=0.1,SD=5.27) (VQ=1,SD=10.54) (VQ=0.1,SD=10.54)

•• The first bubble maximum radius &periodThe first bubble maximum radius &period

140

142

VQ=1 VQ=0.75 VQ=0.5 VQ=0.25 VQ=0.1 Empirical

8.5

8.6

VQ=1 VQ=0.75 VQ=0.5 VQ=0.25VQ=0.1 Empirical

136

138

adiu

s(m

m)

Q

8.2

8.3

8.4

104.53% 104.61% 104.76% 104.89% 105.03%

Perio

d(m

s)

Q p

132

134

95.21% 95.28% 95.42% 95.52% 95.64%

Ra

7.9

8.0

8.1

P

• Agree well with the empirical values by less than 5%• Radius & period grow slightly with the increasing of VL

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

VL

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

VL

L• Comparable to the results of 2D axisymmetric AUTODYN

Euler model considering pressure gradient and gravitational acceleration in the water field1.

1. Abe A. and Katayama M.. 2007, Numerical simulation on underwater explosions and following bubble pulses. Symposium on Shock Waves (In Japanese). pp.319-322

Effects study for underwater explosionEffects study for underwater explosion

•• IntroductionIntroduction• VL has vital effect on peak pressure modeling of TNT UNDEX. VQ

h l i flhas almost no influence. • Existing appropriate VL (0.02 to 0.2) for some ranges of scaled

distances in given grid sizes that key attributes are in acceptable agreements.

• Find this appropriate value using in UNDEX numerical simulation.• Even though obtaining the value for typical problem it is also• Even though obtaining the value for typical problem, it is also

doubtable that this value is applicable and feasible for different charge weights, charge depths and different explosives.

fi i f h lidi f h l d f• Confirmation of the validity of the selected VL for TNT, H-6, Pentolite and PETN with variable charge weight detonated in different water depth (with the empirical values).

•• Mesh size and casesMesh size and cases

• 1D “wedge” model and flow-out boundary condition • Combination of computation time and comparable of results, different

reasonable mesh sizes were used for various ranges of charge weightsreasonable mesh sizes were used for various ranges of charge weights.

Charge weight (kg) Mesh size for charge & water domains (mm)Numerical mesh size for different charge weights

0.001 0.01 0.05 0.5 (300m depth)0.05 0.5 2.5 1.5 (300m depth)2.5 25 125 4.5 (300m depth)2.5 25 125 4.5 (300m depth)125 1250 5000 14.5 (300m depth)

W i ht (k ) D th ( )Cases for effect of charge weight and depth on bubble pulse

Weight (kg) Depth (m)0.01 0.5 25 1250 100 200 500 1000

• Refinement: VL for SD from 3 to 10 was 0.34, from 1.5 to 3 was 0.68, for

L , ,SD smaller than 1.5, take the default value. VQ take the default value.

•• Variations of peak pressure (SD 3Variations of peak pressure (SD 3--10)10)

1.04

1.06

1.08

1.10

1.12

1gTNT 10gTNT 50gTNT 1gPentolite 10gPentolite 50gPentolite

1 04

1.08

1.12 1gPETN 10gPETN 50gPETN 1gH-6 10gH-6 50gH-6

1-50g explosive charge

0.94

0.96

0.98

1.00

1.02

P N/P

E

0.96

1.00

1.04

P N/P

E

g p g

3 4 5 6 7 8 9 10 11

0.90

0.92

R/W1/3(m/kg1/3)2 3 4 5 6 7 8 9 10 11

0.92

R/W1/3(m/kg1/3)

50gTNT 500gTNT 1 12 50gPETN 500gPETN

1.05

1.10

E

50gTNT 500gTNT 2.5kgTNT 50gPentolite 500gPentolite 2.5kgPentolite

1.04

1.08

1.12

E

50gPETN 500gPETN 2.5kgPETN 50gH-6 500gH-6 2.5kgH-6

50 2 5k l i h

0.95

1.00P N/P

E

0.96

1.00P N

/PE50g-2.5kg explosive charge

2 3 4 5 6 7 8 9 10 11

0.90

R/W1/3(m/kg1/3)2 3 4 5 6 7 8 9 10 11

0.92

R/W1/3(m/kg1/3)

•• Variations of peak pressure (SD 3Variations of peak pressure (SD 3--10)10)

1.06

1.08

1.10

1.12 2.5kgTNT 25kgTNT 125kgTNT 2.5kgPentolite 25kgPentlolite 125kgPentolite

1.08

1.10

1.12

1.14

1.16

2.5kgPETN 25kgPETN 125kgPETN 2.5kgH-6 25kgH-6 125kgH-6

• Charge weight from 0.001 to 1250kg, the peak pressure values of TNT, H-6, Pentolite, and PETN at the scaled distances range from 3 to 10 agree with the empirical values within ±12%. With th i i f h i ht th ti t SD f 3 t 10

0.96

0.98

1.00

1.02

1.04

P N/P

E

0 96

0.98

1.00

1.02

1.04

1.06

P N/P

E2.5kg-125kg explosive charge• With the increasing of charge weight, the ratio at SD from 3 to 10

becomes larger whereas it will not exceed the tolerance. • The ratio lowers gradually with decreasing of scaled distance. • VL 0.34 with the given grid structure can simulate the peak pressure in

2 3 4 5 6 7 8 9 10 11

0.92

0.94

0.96

R/W1/3(m/kg1/3)

2 3 4 5 6 7 8 9 10 11

0.92

0.94

0.96

R/W1/3(m/kg1/3)1.16

VL 0.34 with the given grid structure can simulate the peak pressure in an acceptable result for SD (3-10) of charge weight less than 5000kg.

1.04

1.08

1.12 125kgTNT 1250kgTNT 5000kgTNT 125kgPentolite 1250kgPentolite 5000kgPentolite

1.08

1.12

125kgPETN 1250kgPETN 5000kgPETN 125kgH-6 1250kgH-6 5000kgH-6

125 5000k l i h

0.96

1.00P N/P

E

0.96

1.00

1.04P N

/PE125-5000kg explosive charge

3 4 5 6 7 8 9 10 11

0.92

R/W1/3(m/kg1/3)2 3 4 5 6 7 8 9 10 11

0.92

R/W1/3(m/kg1/3)

•• Variations of peak pressure (SD 1.5Variations of peak pressure (SD 1.5--3)3)

1.10

1.15

1.20

1gTNT 50gTNT 1gH-6 50gH-6 1gPentolite 50gPentolite 1gPETN 50gPETN 1.10

1.15 50gTNT 2.5kgTNT 50gH-6 2.5kgH-6 50gPentolite 50gPentolite 50gPETN 2.5kgPETN

0 95

1.00

1.05

P N/P

E

0 95

1.00

1.05

P N/P

E

1-50g 50g to 2.5kg

1.5 2.0 2.5 3.0

0.90

0.95

R/W1/3(m/kg1/3)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.90

0.95

R/W1/3(m/kg1/3)1.20 1.20

125k TNT 5000k TNT

1.10

1.15

2.5kgTNT 125kgTNT 2.5kgH-6 125kgH-6 2.5kgPentolite 125kgPentolite 2.5kgPETN 125kgPETN

1.08

1.12

1.16

125kgTNT 5000kgTNT 125kgH-6 5000kgH-6 125kgPentolite 5000kgPentolite 125kgPETN 5000kgPETN

2.5kg to 125kg 125kg to 5000kg• The predicted results for the range of 1.5 to 3 agree to the

empirical values within 12% for these four kinds of explosive.

0.95

1.00

1.05

P N/P

E

0.96

1.00

1.04P N

/PE

p p

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.90

R/W1/3(m/kg1/3)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.92

R/W1/3(m/kg1/3)

•• Variations of peak pressureVariations of peak pressure

1.08

1.12

1.08

1.12

1.00

1.04

P N/P

E

0 96

1.00

1.04

P N/P

E

2 3 4 5 6 7 8 9 10 110.92

0.96

R/W1/3(m/kg1/3)1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.92

0.96

R/W1/3( /k 1/3)

the ratio of

/N EP P

R/W (m/kg )

50gH-6(0.5mm) 50gH-6(1.5mm) 2.5kgTNT(1.5mm) 2.5kgTNT(4.5mm) 125kgPentolite(4.5mm) 125kgPentolite(14.5mm) 125kgPETN(4.5mm) 125kgPETN(14.5mm)

R/W1/3(m/kg1/3) 125kgTNT(4.5mm) 125kgTNT(14.5mm) 125kgH-6(4.5mm) 125kgH-6(14.5mm) 50gPentolite(0.5mm) 50gPentolite(1.5mm) 2.5kgPETN(1.5mm) 2.5kgPETN(4.5mm)

• The PN/PE decreases with the increase of the mesh size at the scaled distance 1.5 to 10 for TNT, H-6, Pentolite and PETN, whilst it is still in an acceptable range .

•• ImpulseImpulse1 08

1.05

1.06

1.07

1.08

1.09

1.02

1.03

1.04

I N/I E

1.08

I N/I E

3 4 5 6 7 8 9 10

Scaled Distance(m/kg1/3) 1g TNT 50gTNT(0.5mm) 50gTNT(1.5mm) 2.5kgTNT(1.5mm) 2.5kgTNT(4.5mm) 125kgTNT(4.5mm) 125kgTNT(14.5mm) 5000kgTNT(14.5mm)

2 3 4 5 6 7 8 9 10 11

Scaled Distance(m/kg1/3)

1g H-6 50gH-6(0.5mm) 50gH-6(1.5mm) 2.5kgH-6(1.5mm) 2.5kgH-6(4.5mm) 125kgH-6(4.5mm) 125kgH-6(14.5mm) 5000kgH-6(14.5mm)

• The IN/IE increase with the enlarging of the charge weight in the same grid size1 08

1.09

1.10

1.11

E the same grid size • For a fixed charge weight, IN/IE for

TNT increase gradually with the increase of scaled distance, for H-6 and Pentolite the ratio decreases2 3 4 5 6 7 8 9 10 11

1.05

1.06

1.07

1.08

I N/I E

and Pentolite, the ratio decreases .2 3 4 5 6 7 8 9 10 11

Scaled Distance(m/kg1/3)

1g Pentolite 50gPentolite(0.5mm) 50gPentolite(1.5mm) 2.5kgPentolite(1.5mm) 2.5kgPentolite(4.5mm) 125kgPentolite(4.5mm) 125kgPentolite(14.5mm) 5000kgPentolite(14.5mm)

•• Energy flux densityEnergy flux density

1.12

1.14

1.16

/EE

1.00

1.01

1.02

2 3 4 5 6 7 8 9 10 11

1.06

1.08

1.10E N/

0 96

0.97

0.98

0.99

E N/E

E

Scaled Distance(m/kg1/3)

1g TNT 50gTNT(0.5mm) 50gTNT(1.5mm) 2.5kgTNT(1.5mm) 2.5kgTNT(4.5mm) 125kgTNT(4.5mm) 125kgTNT(14.5mm) 5000kgTNT(14.5mm)

2 3 4 5 6 7 8 9 10 11

0.96

Scaled Distance(m/kg1/3)

1g H-6 50gH-6(0.5mm) 50gH-6(1.5mm) 2.5kgH-6(1.5mm) 2.5kgH-6(4.5mm) 125kgH-6(4.5mm)125kgH-6(14 5mm) 5000kgH-6(14 5mm)

1.12

• The EN/EE have similar tendency with the IN/IE.

• The impulse agrees with the empirical

125kgH-6(14.5mm) 5000kgH-6(14.5mm)

1.04

1.08

E N/E

E e pu se ag ees w e e p cavalues with in 12%

• The energy flux density agrees slightly poor than the impulse within 14% especially for H-6 and Pentolite2 3 4 5 6 7 8 9 10 11

0.96

1.00

E

1/3

14%, especially for H-6 and Pentolite. Scaled Distance(m/kg1/3) 1g Pentolite 50gPentolite(0.5mm) 50gPentolite(1.5mm) 2.5kgPentolite(1.5mm) 2.5kgPentolite(4.5mm) 125kgPentolite(4.5mm) 125kgPentolite(14.5mm) 5000kgPentolite(14.5mm)

•• Bubble pulse properties vs. charge weightBubble pulse properties vs. charge weight

0.91

1 05

1.06

1.07

0.89

0.90

R N/R

E

1.02

1.03

1.04

1.05

T N/T

E

0 86

0.87

0.88

0.99

1.00

1.01

0 200 400 600 800 1000 1200 14000.86

Charge weight (kg) TNT(300m charge depth) H-6(300m charge depth) Pentolite(300m charge depth)

0 200 400 600 800 1000 1200 1400

Charge weight(kg)

TNT(charge depth 300m) H-6(charge depth 300m) Pentolite(charge depth 300m)

• The radius and period decrease with the increase of the charge weight, but the increasing extent is very slowly within 1%.

PETN(charge depth 300m)

•• Bubble pulse properties vs. charge depthBubble pulse properties vs. charge depth

0.93

0.96 0.5kgTNT 0.01kgH-6 25kgPentolite

1 07

1.08

1.09

1.10

0.5kgTNT 0.01kgH-6 25kgPentolite 1250kgPETN

0.87

0.90

R N/R

E

1 03

1.04

1.05

1.06

1.07

T N/T

E

0.81

0.84

0 200 400 600 800 1000

1.00

1.01

1.02

1.03

• The increase of the charge depth reduces the accuracy of the radius significantly about 12%

0 100 200 300 400 500 600 700 800 900 1000 1100

Charge depth(m)

0 200 400 600 800 1000

Charge depth(m)

significantly, about 12%. • For period, it also decreases with the increase of the charge depth and is

moderately within 2%. • The prediction of the period is more accurate and steady than the radius for

p p yall charge depths.

•• Bubble pulse properties vs. mesh sizeBubble pulse properties vs. mesh size

1.05

1.10

0.95

1.00 RN/RE of 0.05kg TNT in 700m RN/RE of 2.5kg H-6 in 700mR /R of 125kg Pentolite in 700mio

0.90

RN/RE of 125kg Pentolite in 700m PN/PE of 0.05kg TNT in 700m PN/PE of 2.5kg H-6 in 700m PN/PE of 125kg Pentolite in 700m

Rat

i

0 2 4 6 8 10 12 14 160.80

0.85

Mesh size(mm)

• The ratios increase with the increase of mesh size.• Tthe first bubble maximum radius and period of TNT explosive are

more sensitive to the mesh size than other explosives

Mesh size(mm)

more sensitive to the mesh size than other explosives.

Conclusions and Future EndeavorsConclusions and Future Endeavors

• Fixed values of quadratic and linear viscosity exist for the UNDEX model with a settled mesh structure in ANSYS-AUTODYN simulation processwith a settled mesh structure in ANSYS AUTODYN simulation process.

• VQ and VL, 1 and 0.034, 1 and 0.068 were applicable for the scaled distances range from 3 to 10 and 1.5 to 3, respectively.

• System based on given mesh size and viscosities was constructed for y gAUTODYN simulation of UNDEX key attributes for various kinds of explosives, wide range of scaled distances, charge depths and charge weights.

id f d l h d f d li f d l i b• Provide fundamental method for modeling of underwater explosion by simple 1-D AUTODYN.

• The modeling results of key attributes by AUTODYN were in acceptable agreementagreement.

• Future work: Determination of EOS for aluminized explosive formulation• Future work: Evaluation underwater explosion performance of

formulations

formulations.

Acknowledgements Acknowledgements

• Sponsor: Beijing Institute of Technology of InnovationSponsor: Beijing Institute of Technology of Innovation Fund of Graduate Students (No. 3020012240907)

• Fund of State Key Laboratory of Explosion Science andFund of State Key Laboratory of Explosion Science and Technology