Modeling and Analysis of Elevated Skid Mounted High Speed Compressor Structure

Modeling and Analysis ofElevated Skid Mounted High Speed Compressor Structure

GT STRUDL User’s Group Presentation

Atlanta, GA June 24-26,2009

Jonathan Guan, P.E.

Houston, Texas

[email protected] 832-351-6847


Topic Outline

Design Overview Preliminary Design Dynamic Properties Geometry Modeling Dynamic Analysis Beyond Moore’s Law

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

Design Overview

Study Soil Report

Start Preliminary Design

GenerateDynamic Impedance

DeriveExcitation Force

Create Geometry Model

Perform Dynamic Analysis

Check CriteriaFine Tune

Foundation Geometry

Request for MoreGeotech./Vendor Info

No

Yes

Detail DesignFoundation

Study Design Data

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)

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.

Preliminary Design

Steam Turbine-Compressor Skid.

FrameWorks Model:

Steam Condenser

Preliminary Design

Using FrameWorks 3D model to obtain the foundation center of gravity:

Preliminary Design

Equipments + Foundation Concrete Foundation Only

Dynamic Properties

In Veletsos Model, the Dynamic Impedance Expressed as:

)()( 000 aciaakKI dds

Dynamic Equilibrium Equation:

)(tFXKXCXM

Mode Vertical Horizontal Rocking Torsion

Static Spring Constants

Dynamic Impedance

1

4 vvv

RGK

2

8 hhh

RGK

13

8 3rr

r

RGK

3

16 3tt

t

RGK

vvv ciakK 0 hhh ciakK 0 rrr ciakK 0 ttt ciakK 0

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 < a0 <1.0

a0: Dimensionless frequency.

Motion Spring Constant Reference

Vertical Timoshenko & Goodier (1951)

Horizontal Bycroft (1956)

Rocking Borowicka (1943)

Torsion Reissner & Sagoci (1944)

1

4 RGK y

87

)1(32

RG

K x

13

8 3RGKrz

3

3

16RGK ry

Dynamic Properties

sV

Ra

0

Dimensionless frequency, a0

Where:

ω: machine speed – equipment;

R: foundation radius – foundation;

Vs: shear wave speed – soil.

Dynamic Properties

Dynamic Stiffness:

)( 0akkK ds

Dynamic Damping:

00 )( aackC ds

Dynamic Ratio:

cr

dscr C

aackCC 00/

Critical Damping:

MKCcr 2 (translational) IKCcr 2 (rotational)

Dynamic Properties

b1 to b4 in expression above are dimensionless functions of μ. Given by Veletsos for different type of soils.

Veletsos’ Model – Dynamic Stiffness and Damping Coefficients:

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.

Dynamic Properties

Veletsos Model, kθ & cθ to Frequency Relation in Rocking Mode:

cθ is independent of a0 ,

or the frequency.

kθ in clay soil is very sensitive to a0 , or the frequency.

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.

Dynamic Properties

Dynamic Stiffness and Damping Coefficients:

Dynamic Properties

At The Speed: f = 7242 Hz:

Dynamic Properties

At The Speed: f = 11522 Hz:

Changes less than 0.2% .

Changes less than 0.2%

Dynamic Properties

Equivalent Foundation Radius:

(The Original Veletsos’ Studies Was on Circular, Massless Disk)

Dynamic Properties

Evaluation of Static Stiffness of Circular Footing on Inhomogeneous Half-space (Werkle and Waas):

Seismic Downhole Survey


P-Wave: S-Wave:



To Determine Soil Moduli from in-situ testing data:

gVG s /2

1/2

2/2

2

sp

sp

VV

VV

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

Empirical Correlations for Vs (Imai 1977):

337.091NVs

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.


Dynamic Properties

Dynamic Properties

Dynamic Unbalance Forces: The Dynamic Equilibrium Equation:

)(tFKYYCYM

)()( tSinSaMtF f

)(2

tSinSe

g

Wf

)(2

tSinSe

g

Wf

)(2 tSinA

CBAf 2

The amplitude of a harmonic forcing function of the Harmonic Loading Condition in GTSTRUDL:

(B = C = 0)2Af

Where:

Sf = 2.0, service factor for centrifugal compressor.

GTSTRUDL Harmonic Load Command:

Dynamic Properties

ISO 1940 G2.5

for Turbo-Compressor

API 617 for

Centrifugal Compressor

e = 0.1/ω

= 0.1/(2πx200)

= 8.0x10-5(in)

e = 0.25/f0

= 0.25/(12,000 rpm)

=2.0x10-5(in)

For Compressor Foundation Design

For New Equipment Testing

(For Equipment Vendor)

)/(1.0 sine )/(25.00 minfe

Industrial Standard:

Dynamic Properties

Calculating Amplitude of Harmonic Force:

Equipment Rotor Weight

Compressor 2922 lbm

Steam-Turbine 1175 lbm

UNIT LBS FEET SEC CYCLEHARMONIC 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 0.03 4 FORCE Y A 0.00060 PHASE 0.0$1 2 FORCE X A 0.00024 PHASE 0.03 4 FORCE X A 0.00060 PHASE 0.0END OF HARMONIC LOAD$

f

r Seg

WA

35

102.10.212

100.8

0.32

2922

45

108.40.212

100.8

0.32

1175

Geometry Modeling

Tabletop with Skid Finite Element Modeling:

Plate elements continuity violation

How to Set the Elevation?

Model with Plates and Beams

The dilemma of modeling to accurate mass elevation or column length?

Tabletop mass c.g. elevation

Compressor skid

Geometry Modeling

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 –………………………………………FORCE X Z KFY 720 DAMPING 0.70$ JOINT RELEASES MOMENT X Y Z 3102 TO 3112 BY 2 3115 TO 3127 BY 2 - FORCE X Y KFZ 12960 DAMPING 0.4$ JOINT RELEASES MOMENT X Y Z 2020 TO 2568 BY 56 2652 TO 3100 BY 56 - FORCE Y Z KFX 10080 DAMPING 0.40

Maxwell Model For Vibration of Viscoelastic Foundation

Physically Similar to Shock Absorber

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.

Geometry Modeling

Dynamic Stiffness and Damping Distribution:

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:

Es·Isx = Ee·Iex (1)

(Stiffness in y-y is not critical)

ksi

I

IEE

ex

sxse 500,9

12/1812

1910000,293

Note:

E of Filled Epoxy Grout can be ignored. It’s only 1/3 of Regular concrete.

xx

y

y

Geometry Modeling

Skid Modeled in Solid Elements:

Converted Steel Frame Elements

Filled Grout Elements

Exhaust Opening

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.

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, Vy=0.032 in/sec, within the “Very Good” range.

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, ax=60.0 in/sec2, < 0.2g.

Beyond Moore’s Law

Multiple Core Processors


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


Finite Element Dimension Limit:

It is usually recommended that the maximum dimension of an element should not exceed λ/8 (G. Gazetas).

λ=V/f

=762ft/s/[120, 192](c/s)

=[4’,6.35’]

λ/8=[0.5’, 0.8’].

Try: Element with Horizontal Dimension: 1’x1’

Resulting the Tabletop with

• 4373 solid elements;

• 7024 joints;

• 21,000 DOF.


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

Large Problem Size GTSELANCZOSTime to Solve Eigenproblem

Total CPU Time

X X 11 Min. 8 Sec. 26 Min. 8 Sec.

√ X 2 Min. 13 sec. 6 Min. 14 Sec.

√ √ 43.8 Sec. 4 Min. 25 Sec.


QUESTIONS?

Jonathan Guan, P.E.

Jacobs Engineering

Houston, Texas

[email protected] 832-351-6847

Documents

Modeling and Analysis of Elevated Skid Mounted High Speed Compressor Structure