Storage Tank Dike Design - Purdue University
Storage Tank Dike DesignGeorge HarriottComputational Modeling CenterAir ProductsP2SAC Spring MeetingPurdue UniversityMay 3, 2017
Tank Rupture Consequences Molasses tank, Boston MA, 1919, 2.5x106 gallons, 21 fatalities Water tank, Juarez, MX, 1986, 7.5 x105 gallons, 4 fatalities Oil tank, Floreffe PA, 1988, 3.8x106gallons Molasses tank, Loveland CO, 1990, 6.2 x105 gallons HCl tank, McDonald, PA, 2002,104 gallons
Floreffe Aftermath
Regulatory Requirements Secondary containment volume must besufficient to hold the contents of the tank(EPA/OSHA). Fire code constraints Dynamics not considered!
Design Considerations Dike height Dike diameter Dike shape Complete tank rupture Small hole in tank wall
Rupture Flow Scales Height: H 10 m Distance: L 10 m Velocity: (gH) 10 m/s Time: L/(gH) 1 s Reynolds number: Re 10Initial ConditionH1/21/2L8
Shallow-Water Theory Depth-averaged inviscid equations of motion Exact mass balance Hydrostatic pressure Analogous to compressible gas dynamics h (hu) 0 u u u h 0uh
Shock Conditions Multi-valued SWT solutions Supplemental jump equations(u()2 )() λ h u λ h 0()2u λ h u λ h ()1 2(h ) (h )2 02 λ(-)( )
Numerical Pitfalls Diffusive Errors Dispersive Errors
Computational Methods Method of Characteristics Explicit Finite-Difference (Lax, FCT, WENO) Implicit Finite Element (DG, SUPG) Projection Methods (POD)
Method of Characteristics h φ φφ Ai Bi ψ 0 t x u Eigenvalue: λ (ξ iA ) ξ iB φ φξiAi λ( ) ξ iψ 0 x t(ξ iA )idφdx ξ iψ 0 : λdtdt
Simple Planar WaveWavespeed : c hdhdu c 0dtdt:dx u cdtxSplashc 0u 0c c 1u 02 1 x α 3 3 t t: u 2 32 x α 3 t
Lax FD Methodti, j 1i - 1, ji, ji 1, jx h q 0 : q uh t x hi, j 1 1 Δt hi 1, j hi 1, j q qi 1, j 2Δx i 1, j2()()
Planar Rupture Splash
Complete RuptureSymmetric Planar FlowComplete Rupture: Planar Flow1.0Dike all Position0.81.0
Polar Rupture Splash
Complete RuptureSymmetric Polar FlowComplete Rupture: Polar Flow1.0Dike ank Radius0.81.0
Similarity Solution0 r R(t ) α 4t22α2 r2 h(r,t ) 2 2 1 2 R R u(r,t ) Polar Paraboloid Wave2.0t 0.01.5t 0.2h 1.0t 0.40.50.00.00.20.40.6r0.81.04rtR2
Polar Parabaloid SplashPolar Paraboloid Splash1.00.80.6H0.40.20.00.00.20.40.6Tank Radius0.81.0
Rupture Flow Experiments Greenspan & Young (1978)(a) planar flow, validated SWT(b) sloped dikes particularly ineffective(c) initial splash exceeds tank height Greenspan & Johansson (1981)(a) polar flow(b) dike shape study(c) proposed trip rings, deflectors
Summary Low (equilibrium) dikes do not contain rupture flow Shallow Water Theory can be applied to address:(a) small hole splash(b) dike overflow(c) multiple dike interaction Small-scale experiments are representative
Storage Tank Dike Design George Harriott Computational Modeling Center Air Products P2SAC Spring Meeting Purdue University May 3, 2017. Tank Rupture Consequences Molasses tank, Boston MA, 1919, 2.5x106 gallons, 21 fatalities Water tank, Juarez, MX, 1986, 7.5 x105 gallons, 4 fatalities
Dike Cross Section Nicomen Slough (river side) Pump Station Floodbox pipe Floodbox pipe: 1m diameter concrete pipe in 4 foot lengths Internal inspection revealed deflection under dike crest and open joints Dike fill (silts and sands) piped (migrated) over time into flood box and washed away. Highway 7 and Dike Crest Sink hole
3- Differential surge tank: an orifice tank having a riser is called differential tank. 4- One- way surge tank: in a one way surge tank the liquid flows from the tank into the pipeline only when the pressure in the pipeline drops below the liquid level in the surge tank. 5- Closed surge tank: if the top of the tank is closed and there is
tank, this work was designed the refill sauce storage tank connection to the normal sauce storage tank to control level sauce in tank. m Fig.7. two liquid storage tank systems The purpose of this study is to control level in normal sauce tank. The apparatus, shows in Fig.7, consisting of normal sauce tank and one more refill sauce tank.
dike designation with model spur dike was measured in a laboratory flume with 180 degree bend under clear-water. Experiments were conducted for different locations with various Froude number. In this study, the time development of the scour hole around the spur dike plates was studied. The results of the model study indicated that the maximum
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DIKE DIOR EON EPDT FD FGN Fix FLT FT FV GAB GBNR GC GD GR GRDR GRGN GRG5 GRP GRPH GRWY HGAB HZBG IBZ IF IGN IT IV LC LGAB LGBNR LST MD M DIA MGAB MGN MIG MNZ MNZD MS MT MTX MV MYLN . Dike Diorite End of Hole Epidote j Felsic Dyke Felsic Gneiss problems to be fixed Fault Felsic Tuff Felsic Voteanfc Gabbro Gabbronorite Ground Core Granitic Dike .
2. Map showing the location of tunnels in relation to rift (dike complex) and marginal dike zones._ 4 3. Photograph of Waihee tunnel, February 10, 1955, heading at 12-foot dike; water gushing from drill hole through dike_ 7 4. Map of Waihee Valley showing location of Cited by: 2Publish Year: 1971Author: George Tokusuke Hirashima
ELSEVIER Artificial Intelligence 82 ( 1996) 369-380 Book Review Stuart Russell and Peter Norvig, Artificial Intelligence Artijcial Intelligence: A Modem Approach * Nils J. Nilsson Robotics Laboratory, Department of Computer Science, Stanford University, Stanford, CA 94305, USA 1. Introductory remarks I am obliged to begin this review by confessing a conflict of interest: I founding director .
