Modeling and Analysis of Elevated Skid Mounted High Speed Compressor Structure

1
Modeling and Analysis ofElevated Skid Mounted
High Speed Compressor Structure
GT STRUDL Users Group Presentation Atlanta, GA
June 24-26,2009 Jonathan Guan, P.E.
Houston, Texas Jonathan.guan_at_jacobs.com 832-351-68
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Modeling and Analysis ofElevated Skid Mounted
High Speed Compressor Structure

• Topic Outline
• Design Overview
• Preliminary Design
• Dynamic Properties
• Geometry Modeling
• Dynamic Analysis
• Beyond Moores Law

3
Design Overview

• Project Assignment
• To Design a Recycle Compressor with
• Power 10,000 HP
• Speed 7,242 to 11,522 rpm
• Equipment Weight
• Compressor 30.8 Kips
• Steam turbine 54.0 Kips
• Skid 31.3 Kips
• Piping 6.0 Kips
• Total Machine Skid WT 122 Kips

4
Design Overview
Study Design Data
Study Soil Report
Start Preliminary Design
Request for More Geotech./Vendor Info
Generate Dynamic Impedance
Derive Excitation Force
Create Geometry Model
Perform Dynamic Analysis
Check Criteria
Fine Tune Foundation Geometry
No
Yes
Detail Design Foundation
5
Design Overview

• Design Criteria
• The basic goal in the design of a machine
  foundation is to limit its motion to amplitudes
  that neither endanger the satisfactory operation
  of the machine nor disturb people working in the
  immediate vicinity. (Gazetas 1983)

6
Preliminary Design

• Purpose
• To initialize the foundation dimension and
  arrange columns
• To create the finite element model for dynamic
  analysis
• Based on
• Rule of thumbs
• Vendor data
• Soil Report
• Piping layout
• Modeling Tool
• Other Software May Be Used to Create the Model.

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Preliminary Design
FrameWorks Model
Steam Turbine-Compressor Skid.
Steam Condenser
8
Preliminary Design
Using FrameWorks 3D model to obtain the
foundation center of gravity
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Preliminary Design
Concrete Foundation Only
Equipments Foundation
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Dynamic Properties
Dynamic Equilibrium Equation

• In Veletsos Model, the Dynamic Impedance
  Expressed as

11
Dynamic Properties

• The classic single lumped mass machine-foundation-
  soil system with circular foundation on elastic
  half-space summarized by Richart, Woods, Hall
  (1970)

A Frequency Independent Model, Applied for 0 lt a0
lt1.0 a0 Dimensionless frequency.
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Dynamic Properties
Dimensionless frequency, a0
Where ? machine speed equipment R
foundation radius foundation Vs shear
wave speed soil.
13
Dynamic Properties
Dynamic Stiffness
Dynamic Damping
Dynamic Ratio
Critical Damping
(translational)
(rotational)
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Dynamic Properties
Veletsos Model Dynamic Stiffness and Damping
Coefficients
b1 to b4 in expression above are dimensionless
functions of µ. Given by Veletsos for different
type of soils.
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Dynamic Properties

• Veletsos Model, kx cx to Frequency Relation in
  Horizontal Mode
• cx is independent of a0 , or the frequency.
• kx in sandy soil is kind of sensitive to a0 , or
  the frequency.

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Dynamic Properties

• Veletsos Model, k? c? to Frequency Relation in
  Rocking Mode
• c? is independent of a0 , or the frequency.
• k? in clay soil is very sensitive to a0 , or the
  frequency.

17
Dynamic Properties

• Veletsos Model, kz cz to Frequency Relation In
  Vertical Mode
• cz is independent of a0 , or the frequency.
• kz in clay soil is very sensitive to a0 , or the
  frequency.

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Dynamic Properties
Dynamic Stiffness and Damping Coefficients
19
Dynamic Properties
At The Speed f 7242 Hz
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Dynamic Properties
At The Speed f 11522 Hz
Changes less than 0.2
Changes less than 0.2 .
21
Dynamic Properties
Equivalent Foundation Radius
(The Original Veletsos Studies Was on Circular,
Massless Disk)
22
Dynamic Properties
Evaluation of Static Stiffness of Circular
Footing on Inhomogeneous Half-space (Werkle and
Waas)
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Seismic Downhole Survey
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Seismic Downhole Survey
P-Wave
S-Wave
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Seismic Downhole Survey
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Seismic Downhole Survey

• To Determine Soil Moduli from in-situ testing
  data

• For soils that are not close to saturation, µ can
  be obtained

• Empirical Correlations for Vs (Imai 1977)

N, standard penetration number, however, the
reliability of such relations is very low, and
they should only be used, if necessary, for
preliminary when seismic survey is not done.
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Seismic Downhole Survey
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Dynamic Properties
29
Dynamic Properties

• Dynamic Unbalance Forces
• The Dynamic Equilibrium Equation

GTSTRUDL Harmonic Load Command
Where Sf 2.0, service factor for
centrifugal compressor.
The amplitude of a harmonic forcing function of
the Harmonic Loading Condition in GTSTRUDL
(B C 0)
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Dynamic Properties

• Industrial Standard

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Dynamic Properties

• Calculating Amplitude of Harmonic Force

UNIT LBS FEET SEC CYCLE HARMONIC LOADING 2
'FREQUENCY FROM 7,000RPM TO 12,000RPM-IN
PHASE' JOINT LOAD SIN FREQ FROM 120.0 TO 200.0 AT
1.0 1 2 FORCE Y A 0.00024 PHASE 0.0 3 4 FORCE Y
A 0.00060 PHASE 0.0 1 2 FORCE X A 0.00024 PHASE
0.0 3 4 FORCE X A 0.00060 PHASE 0.0 END OF
HARMONIC LOAD
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Geometry Modeling
Tabletop with Skid Finite Element Modeling
Tabletop mass c.g. elevation
Plate elements continuity violation
Compressor skid
How to Set the Elevation?
The dilemma of modeling to accurate mass
elevation or column length?
Model with Plates and Beams
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Geometry Modeling
Why Foundation Modeled as Linear Instead of
Nonlinear Elastic ? For the small strains (less
than about 0.005) usually induced in the soil by
a properly designed machine foundation, shear
deformations are the result of particle
destortion rather than sliding and rolling
between particles, such deformation is almost
linearly elastic.

• STATUS SUPPORT JOINT -
• 1029 TO 1041 BY 2 1042 TO 1054 BY 2 -
• 1085 TO 1097 BY 2 1098 TO 1110 BY 2 -
• 1141 TO 1153 BY 2 1154 TO 1166 BY 2 -
• 1197 TO 1209 BY 2 1210 TO 1222 BY 2 -
• 1253 TO 1265 BY 2 1266 TO 1278 BY 2 -
• 1309 TO 1321 BY 2 1322 TO 1334 BY 2 -
• 1365 TO 1377 BY 2 1378 TO 1390 BY 2 -
• 1421 TO 1433 BY 2 1434 TO 1446 BY 2
• .
• JOINT RELEASES MOMENT X Y Z
• 1029 TO 1041 BY 2 1042 TO 1054 BY 2 -
• 1085 TO 1097 BY 2 1098 TO 1110 BY 2 -
• 1141 TO 1153 BY 2 1154 TO 1166 BY 2 -
• 1197 TO 1209 BY 2 1210 TO 1222 BY 2 -
• 1253 TO 1265 BY 2 1266 TO 1278 BY 2 -
• 1309 TO 1321 BY 2 1322 TO 1334 BY 2 -
• 1365 TO 1377 BY 2 1378 TO 1390 BY 2 -
• 1421 TO 1433 BY 2 1434 TO 1446 BY 2

Physically Similar to Shock Absorber
Maxwell Model For Vibration of Viscoelastic
Foundation
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Geometry Modeling
Dynamic Stiffness and Damping Distribution
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Geometry Modeling

• Convert Skid Beam, W18X97 to a Modulus of
  Elasticity Equivalent Solid Element
• W18X97 Properties
• Ix 1910 in4
• Iy 220 in4 A 28.5 in2
• Equation shall satisfy
• EsIsx EeIex (1)
• (Stiffness in y-y is not critical)

y
x
x
y
Note E of Filled Epoxy Grout can be ignored.
Its only 1/3 of Regular concrete.
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Geometry Modeling
Skid Modeled in Solid Elements
Converted Steel Frame Elements
Filled Grout Elements
Exhaust Opening
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Dynamic Analysis
Mode Shape Mode 56 Freq 146.7 c/sec. As
expected, one of the typical mode shape shows
that the table top remain rigid while large
deflection observed at columns and base slab. The
vibrating energy has been absorbed by the columns
and base slab.
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Dynamic Analysis

• Velocity (in vertical Y) vs Frequency, Out of
  Phase Load Case.
• Machine frequency range 120 cps to 200 cps.
• Max vertical velocity found at joint 101,
  Vy0.032 in/sec, within the Very Good range.

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Dynamic Analysis

• Acceleration (in X dir.) vs Frequency, Out of
  Phase Load Case.
• The criteria to make sure machine parts at
  attachment point not overstressed.
• Max Horizontal Acceleration found at joint 8128,
  ax60.0 in/sec2, lt 0.2g.

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Beyond Moores Law
Multiple Core Processors
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Beyond Moores Law
GTSTRUDL Job Monitoring on a Intel Duo Core CPU
at 1.86Ghz
CPU No. 1 Fully Occupied by GTSTRUDL
CPU No. 2 Not Reached by GTSTRUDL
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Beyond Moores Law

• Finite Element Dimension Limit
• It is usually recommended that the maximum
  dimension of an element should not exceed ?/8 (G.
  Gazetas).
• ?V/f
• 762ft/s/120, 192(c/s)
• 4,6.35
• ?/80.5, 0.8.
• Try Element with Horizontal Dimension 1x1
• Resulting the Tabletop with
• 4373 solid elements
• 7024 joints
• 21,000 DOF.

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Beyond Moores Law

• Dynamic System Solution Implement Comparison
• Dynamic Model Consist of 4373 solid elements and
  7024 joints, about 21,000 degree of freedoms.
• Max. Velocity and Acceleration Calculated with
  the Compressor Speed from 120 200 cycle/sec. at
  1.0 cycle/sec. step.
• GTSTRUDL V29.0 Dynamic Speed Report for the
  Design Example

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Modeling and Analysis ofElevated Skid Mounted
High Speed Compressor Structure

• QUESTIONS?

Jonathan Guan, P.E. Jacobs Engineering Houston,
Texas Jonathan.guan_at_jacobs.com 832-351-6847