virtual mass webinar2 - msc software · • therefore, virtual mass is calculated for allgrid...

WEBINAR

INTRODUCTION TO VIRTUAL MASS

WEBINAR_VM, OCTOBER 2011

Copyright© 2011 MSC.Software Corporation S1 - 1

Contents

• Introduction– Assumptions & restrictions

– Some legal configurations

– Some illegal configurations

• The User Interface– The MFLUID and ELIST

entries



entries

– Distorted QUAD4 elements

– Remarks

• Examples– VMOPT parameter

– GPWG output

– Sloshing

Introduction

• Virtual mass method added to MSC.NASTRAN in 1978.Funded by Daimler-Benz, For high frequency response of fuel tanks. (Helmholtz method)

• Virtual mass is used to model the hydrodynamic effects of added mass on a structure when it is in contact with inviscid, incompressible fluids

• The fluid domains, which are not explicitly modelled with a fluid mesh (hence the term virtual mass), could be

– Finite (e.g. fuel in a tank)

– Infinite (e.g. a ship in the sea)



– Infinite (e.g. a ship in the sea)

• A list of wet, or submerged, finite elements define where the fluid contacts the finite element structure.

• Structural surfaces may be wet either on one side only, or on both sides (e.g. baffles).

• The entire fluid domain may be composed of several disjoint regions containing different fluids.

Assumptions

• The fluid is incompressible

• No viscosity effects

• The fluid has uniform density, for example, no immiscible layers are allowed

• Internal (finite) fluids must have a free surface

• External fluids may or may not have a free surface

• No surface wave effects



• No surface wave effects

• No gravity effects

• Irrotational flow(no turbulence/no eddy current effects)

• No steady flow

• No nonlinear effects

• No aerodynamic (high steady flow) effects are present

INTRODUCTION

• Virtual fluid volume produces a mass matrix

• Full coupling between accelerations and pressures on the flexible structural interfaces.

• Represents the fluid coupled to a boundary consisting of:– Structural elements

– Free surfaces

– Planes of symmetry

– Bounded fluids



– Bounded fluids

– Infinite fluids

• One or two wetted sides.

• No sloshing effects unless phantom boundaries are used.

• Multiple fluid volumes

• Only CQUAD4/CTRIA3 plate elements may be defined to be in contact with fluid.

Virtual Mass

• Virtual mass provides a method to include the effects of fluid to a structural model

• It adds mass to the mass matrix

• Full coupling between acceleration and pressure on the flexible structural interfaces

• Represents the fluid coupled to a boundary consisting of:– Structural elements

– Free surfaces



– Free surfaces

– Planes of symmetry

– Infinite fluids

• Generates very dense mass matrix

• The structure’s frequency range of interest must be

– above and away from the frequency range of the fluid sloshing modes

– below the lowest acoustic frequency (speed of sound assumption)

• If a free surface is defined, the pressure at the surface is assumed to be zero.

Restrictions



assumed to be zero.

• The interface between fluid and structure (the wetted surface) is comprised solely of CQUAD4 or CTRIA3 elements

– If for example a tank is meshed with solid elements, it will be

necessary to coat the wetted surface with a thin layer of plate elements

Virtual Mass

• Dynamics of incompressible fluid.

• Allowed in all dynamic solutions except cyclic symmetry.

• Fluids coupled directly to structure through the mass matrix.

• Only wetted structural elements are defined to have fluid.

• Fluids on interior or exterior surfaces.



• Infinite exterior fluid allowed.

• Free surfaces allowed.

• Gravity is not included.

• Fuel tanks, nuclear fluid containers, drilling platforms, underwater devices, and ships where fluid dynamics can be ignored.

Consider an

Some Legal Configurations



Consider an Infinite fluid

Fluid

Empty closed


Void



Empty closed vessel in an infinite fluid

Fluid

Open




Open container in an infinite fluid

Fluid

Consider a


Free Surface



Consider a

Finite fluid

Fluid

Empty closed


Free Surface



Empty closed vessel in a finite fluid

Fluid

Void

Partially filled


Free Surface Free Surface



Partially filled closed vessel in a finite fluid

Fluid

Void

Fluid

Partially filled


Free Surface

Free Surface



Partially filled open vessel in a finite fluid

Fluid

Fluid

Closed vessel


Free Surface



Closed vessel with internal

fluid

Free Surface

Fluid

Consider an

Some Illegal Configurations



Consider an Infinite fluid

Fluid

Completely


Fluid



Completely filled closed vessel in an infinite fluid

Fluid

Open


Void



Open container with a free surface in an infinite

fluid

Fluid

Free Surface

Consider a


Free Surface



Consider a

Finite fluid

Fluid

Completely


Free Surface



Completely filled closed vessel in a finite fluid

Fluid

Fluid

Open vessel


Free Surface



Open vessel with no free surface

Fluid

Completely


Completely



Completely filled closed vessel

Completely filled closed vessel

Fluid

The User Interface



Virtual Mass

Free SurfacesFree Surfaces

• User interface is very simple.

• The sketch below illustrates some of the features



Fluid Volume 1Fluid Volume 1Fluid Volume 2Fluid Volume 2

Structure ElementsStructure Elements Structure elementsStructure elements Structure ElementsStructure Elements

User Interface

• Case Control

MFLUID

• Bulk Data



MFLUID

ELIST

The MFLUID entry

• The MFLUID case control command references the MFLUID

bulk data entry, which defines the fluid properties of an incompressible fluid for the purpose of generating a virtual mass matrix

SOL 103

CEND

DISP=ALL

MFLUID=17

• Only one case control MFLUID entry is allowed, above SUBCASE level

• If there is no MFLUID case



MFLUID=17

SUBCASE 1

METHOD=12

BEGIN BULK

GRID,52,,5.2,3.4,1.22

...

MFLUID,17,,15.,1.225,22,,N,N

...

• There may be one or more bulk data MFLUID entries

• If there is no MFLUID case control entry present, no virtual mass will be calculated

CID and ZFS

1 2 3 4 5 6 7 8 9 10

MFLUID SID CID ZFS RHO ELIST1 ELIST2 PLANE1 PLANE2

RMAX FMEXACT

• The CID in field 3 allows a coordinate system to be defined,

the Z direction of which is used to locate the free surface of the fluid. The value of ZFS in field 4 defines the location of

the plane of the free surface which is parallel to the X-Y plane of the coordinate system defined by .



plane of the coordinate system defined by CID.

• If CID is left blank, the basic coordinate system is used

ZFS

• The orientation of CID and ZFS is arbitrary

FluidFluid

ZFS



• If ZFS is left blank, an infinitely large positive value is assumed

X

Z ZFS

X

Z

ZFS – to wet or not

• An element that has all of its GRID points on or above the free surface is not wet (no virtual mass)

• A tolerance is calculated for each wetted element

– TOL = 0.01 * SQRT(2 * A)

– A = area of the element



– A = area of the element

Area A

x• If X < TOL for a GRID point, it is considered to be on the free surface and no virtual mass will be calculated for it

• RHO in field 5 is the fluid density

• The MFLUID entry ELIST fields reference the

RHO, ELIST1 and ELIST2

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



• The MFLUID entry ELIST fields reference the wetted elements on ELIST bulk data entries

1 2 3 4 5 6 7 8 9 10

ELIST LID E1 E2 E3 E4 E5 E6 E7

E8 E9 E10 etc.

ELIST – candidates to be wet

• Any elements appearing on ELIST entries referenced by an

active MFLUID entry are candidates to be wet by a fluid

• However, only elements below the free surface defined by ZFS



the free surface defined by ZFS

are actually wetted

Partially wetted elements

• Geometrically, elements intersected by the free surface are only partially wetted

• To account for this, the centroids of the wetted areas are established

Centroid of quadrilateral

Centroid of wetted area



• Mass distribution for a partially wetted element is calculated using the same principal as static equilibrium among all GRID points of the element for a concentrated load applied at the centroid of the wetted area

• Therefore, virtual mass is calculated for all GRID points attached to the partially wetted element, even those above the free surface

Partially wetted elements

• Virtual mass added above the free surfaceis mitigated by two effects

• Appropriate element mesh density

– If the finite element mesh in the region of the free

surface is not too coarse, virtual mass added above

the free surface can be minimised



the free surface can be minimised

• Free surface pressure

– The pressure at the free surface is zero. It is therefore immediately

obvious that pressures near the free surface are low resulting in lower

relative values of mass for the virtual mass effects from elements near the

free surface – any value of mass added to a GRID point above the free

surface will therefore be of a correspondingly low value

ELIST1 and ELIST2

• If elements are to be wet on one side only, they are added to an ELIST entry referenced by the ELIST1 field

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT

MFLUID=1

...

BEGIN BULK



Baffle

Fluid

BEGIN BULK

...

MFLUID,1,,20.,1.,11,,N,N

...

ELIST,11,27,43,46

...

ENDDATA

ELIST1 and ELIST2

• If elements are to be wet on both sides by the same fluid (e.g. a baffle), they are added to an ELIST entry referenced by the ELIST2 field

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT

MFLUID=1

...

BEGIN BULK



Baffle

Fluid

BEGIN BULK

...

MFLUID,1,,20.,1.,,12,N,N

...

ELIST,12,62,88,82

...

ENDDATA

ELIST - which side is wet?

• The right hand rule is used to determine which side of the elements on an ELIST entry, referenced by the ELIST1

field, is wet!

• The GRID point order gives the positive normal direction for the element



1

2

3

4

• If the id on the ELIST entry is positive, the element is wet on its positive normal side

• If the id on the ELIST entry is negative, the element is wet on the side opposite the positive normal side

ELIST

• A fluid may be represented by a single MFLUID bulk data entry only if a fish can swim from one region of the fluid to another



• If a fish cannot swim from one region to another, multiple MFLUID entries are needed (no jumping fish allowed!)

ELIST

• If elements form a barrier between unconnected fluids, they may appear on two ELIST entries each referenced by different MFLUID entries

MFLUID=1

...

BEGIN BULK

...



Fluid

Fluid20.015.0

...

MFLUID,1,,20.,1.,11,,N,N

ELIST,11,27,43,46,-58,-59,...

...

MFLUID,1,,15.,1.,12,,N,N

ELIST,12,62,88,82,58,59,...

...

ENDDATA

MFLUID=1

...

BEGIN BULK

...

ELIST

ELIST1 forELIST 11

ELIST1 forELIST 12



...

MFLUID,1,,20.,1.,11,,N,N

ELIST,11,27,43,46,-58,-59,...

...

MFLUID,1,,15.,1.,12,,N,N

ELIST,12,62,88,82,58,59,...

...

ENDDATA

These elements appearon 2 ELIST entries

PLANE1 and PLANE2

• Symmetry and anti-symmetry planes may be defined to reduce model size.

• Symmetry planes are planes of zero displacement.

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



• Symmetry planes are planes of zero displacement.

• Anti-symmetry planes are planes of zero pressure.

• The free surface is treated exactly like a plane of anti-symmetry.

PLANE1 and PLANE2

• PLANE1 refers to the X-Z plane of the coordinate system defined by CID

• PLANE2 refers to the Y-Z plane of the coordinate system defined by CID

• PLANE1 and PLANE2 may be defined as S, A or N

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



• PLANE1 and PLANE2 may be defined as S, A or N

• S means the plane will be treated with a symmetry condition

• A means the plane will be treated with an anti-symmetry condition

• N means no symmetry treatment is defined

RMAX

• RMAX may be used to limit the distance among elements for which interactions are calculated.

• If the elements are further away from each other than

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



• If the elements are further away from each other than RMAX, then no interaction virtual mass terms will be calculated for these elements. This can speed up the calculation of the virtual mass matrix and reduced the density of the final mass matrix.

• The default value is 1.0E+10

FMEXACT

• FMEXACT may be used to limit the elements for which virtual mass terms are calculated using exact integration.

• Exact integration takes around 5 times longer than centre

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



• Exact integration takes around 5 times longer than centre point integration to calculate the virtual mass terms, but the pay-off is better accuracy.

• By default a large value is defined (1.0E+15), which essentially means all terms are calculated using exact integration.

FMEXACT

• As the distance between elements increases relative to the cross sectional area of the elements, the relative magnitude of the virtual mass terms drops off rapidly. This means the virtual mass terms for distant elements are comparatively small, and errors in the virtual mass calculation become decreasingly

1 2 3 4 5 6 7 8 9 10


RMAX FMEXACT



errors in the virtual mass calculation become decreasingly important.

• Studies suggest that if the distance between elements is greater than 2 times the square root of the element with the largest area, errors will be lower than 5%. This corresponds to an FMEXACT value of 2.0, but its use is left to the discretion of the user.

Warped QUAD4 elements

• If any QUAD4 elements are warped, the element is first projected onto a mid-plane which is then used for the



projected onto a mid-plane which is then used for the virtual mass calculation

• This is a standard procedure for the QUAD4 element

QUAD4 Aspect Ratio

• The aspect ratio of QUAD4 elements should be kept below 2:1 to

1:1 5:1 10:1



• The aspect ratio of QUAD4 elements should be kept below 2:1 to reduce errors in the virtual mass calculation

• The following graph compares the values of virtual mass in the X,Y & Z directions with the value obtained from a model using elements with only aspect ratios of 1.0

QUAD4 Aspect Ratio

Virtual Mass

15

20

25

30

35

40

Percentage error

X mass



-15

-10

-5

0

5

10

15

0 2 4 6 8 10

Aspect Ratio

Percentage error

X mass

Y mass

Z mass

MFLUID remarks

• Several MFLUID entries, each corresponding to a different

fluid volume, may be used simultaneously.

• If there is an ELIST present, and there is no free surface

(ZFS is blank) nor planes of anti-symmetry (PLANE1 & PLANE2 are either S or N), a special external fluid is assumed.



assumed.

• For the special external fluid case, the origin of the coordinate system on the MFLUID entry must be close to

the centre of the enclosed volume.

VMOPT Parameter

• The VMOPT parameter is a method to include or exclude the virtual mass effects during the normal mode calculation for the modal dynamic solutions (i.e., SOLs 103, 110, 108,109,111 and 112)

• However, for large models, if one is doing frequency response or transient response, its advisable to use the “direct method” (sol 108/109), since it bypasses the more time consuming normal modes calculation, due to dense and coupled mass matrix!



• Three ways to perform virtual mass analysis:

– PARAM,VMOPT,0 (default)

– PARAM,VMOPT,1

– PARAM,VMOPT,2

Option for Virtual Mass� Param,vmopt,0 (default)

• VM is added before eigenvalue calculation

– Similar to vmopt,1 when component modes are not requested

• Option to perform component modes by specifying qset points on structure and VM is added afterwards to perform 2nd eigenvaluecalculation

– Similar to vmopt,2 when component modes are requested

– Autoqset is not supported

– Must request more modes than desired. Higher modes are not accurate



accurate

• GPWG output doesn’t contain any evidence of Fluid mass!

� Param,vmopt,1

• VM is added before eigenvalue calculation

• This is the most expensive and accurate option! (only useful in testing academic problems)

• Not feasible for any decent size model

• GPWG output does contain the virtual fluid mass in mass output.

VMOPT contd…

� Param,vmopt,2

• Less expensive, implemented to Improve efficiency

• Calculate modes of structure without VM or fluid effects(dry modes)

• Use these modes to form generalized coordinates

• A modal reduction is performed on the structure and the fluid, then combined.

• 2nd eigenvalue calculation with the VM added (wet modes)

• Both eigenvalue tables are printed, allowing comparison of the dry and wet modes.



wet modes.

• Only practical method with high VM density (more than several hundred fluid elements)

• Must request more modes than desired. A general rule-of-thumb is to double the frequency range of interest. Higher modes are not accurate.

• GPWG output doesn’t contain the virtual fluid mass, but the virtual mass of the fluid is printed in a separate table.

Example 1

• Tank with fluid and interested in 1st 10 modes

StructureStructure

FluidFluid



StructureStructure

Example 1SOL 103

CEND

TITLE = tank with virtual mass - vmopt=0 - no qset

SPC = 1

DISPLACEMENT=ALL

$

subcase 2

method=10

mfluid=5

$

BEGIN BULK

param,vmopt,0

PARAM POST 0

$

Fluid Fluid DensityDensity

Free Free SurfaceSurface



$

cord2r,1,, 5.0,3.5,0, 5.0,3.5,1.0,+

+, 6.0,3.5,0.0

$

mfluid, 5, 1, 4.0, 9.35e-5, 11,, n, n

elist,11, -33,thru,-102, 103,thru,306

$

eigrl,10,,,10

$

SPC1 1 123456 4 8 12 16

$

include 'tank.bdf'

$

ENDDATA

DensityDensity

Example 1

• Element Normal (isometric view)



Negative ELEM IDs on the ELIST

Example 1

• Element Normal (top view)



Example 1

• Example is run 7 different ways1. Without fluid – request 10 modes

2. With fluid and using vmopt,1 – request 10 modes

3. With fluid and using default vmopt,0 – request 10

modes





modes and component modes





Example 1

1. Without fluid – request 10 modes




Example 1


modes





Example 1





Example 1

• Vmopt=2 is the recommended (and only practical option) method for any decent size model

• Note than when using vmopt=2, more modes must be requested to obtain accurate lower modes



• Note that when using vmopt=0, more modes must be requested to obtain accurate lower modes if component modes are requested

Model Size restrictions

• VM is accurate for small sized models. Maximum wetted element size is around ~5000!

• The problem is that within a MFLUID enclosure, the mass matrix is 100% dense which creates efficiency issues for the solver

• PARAM,VMOPT,2 may get as high as 20,000 for an overnight run on today's computers if you run on a 8gb computer.

• So what are people supposed to do when the model sizes are 1 million grids?



grids?

� Make a maximum number of wetted element (Wmax) test on an easily

scalable model.

� Then make a coarse loads model, with no greater than Wmax, for the

loads analysis

� For detailed effects I would do local analyses, again with Wmax, using

loads from the coarse model..

GPWG OUTPUT

• Firstly, The GPWG output is never used in any subsequent calculation, it is strictly used for information purposes

• The mass are different in different direction for the MFLUID.

• The mass differences in the three component directions of the fluid coordinate system is a realistic effect.

• Take example of a flat plate immersed completely in a fluid. The associated fluid mass is zero for any motion in the plane of the plate. But fluid mass is effective for any motion normal to the plate.



effective for any motion normal to the plate.

• However, Usually the longer dimension, would lead to the least amount of mass. It is fully effective in say z-direction, but it is only partially effective in the other 2 directions. Think of it as coffee cup. If you move the cup up and down, the full fluid is fully effective. However, if you move it sideway, it's not fully effective. It is a function of the geometry.

Can we output virtual mass and structural mass separately?

• Yes, we do have an alter that prints

– VIRTUAL MASS GPWG OUTPUT

– TOTAL MASS GPWG OUTPUT

– STRUCTURAL MASS GPWG OUTPUT

– STANDARD GPWG OUTPUT



ALTER TO BE USED IN EXECUTIVE CONTROL



Gpwg output – virtual mass



GPWG output – Structural Mass



GPWG output – Total Mass = Standard GPWG output!



SLOSHING WITH VIRTUAL MASS

• Produce normal modes due to a fluid using virtual mass in a tank on a simulated structure.




• Since virtual mass is a linear phenomenon, using it to model sloshing is a gross

approximation due to sloshing's nonlinear nature!

• The desired tool to do this analysis is really Dytran. Validate using Dytran!

• 'virtual mass' capability, can help represent the modes of a fluid contained in a structure

• NOT ACCOUNTED FOR:

– The effect of these gravity waves on the walls due to change in height

– Other fluid volume changes

– Viscoelastic or shear effects



– Viscoelastic or shear effects

– Momentum effects due to volume changes

– assumes an incompressible fluid.

• Only phantom boundary modes with half of the deformations above the original surface and

half below the original surface may be valid. The first phantom boundary breathing mode

where the deformation is all in the same direction may not represent a valid shape.

• What virtual mass sloshing is intended to do is grossly approximate fluid gravity wave

modes and the loads they impart to the sides of a fluid tank. Hopefully this is more accurate

than modeling it with masses on springs


• Sloshing using virtual mass is done by putting a non-structural set of QUAD elements at the fluid free surface (phantom surface) and attaching ELAS elements to ground in the direction of gravity. The stiffness value of the ELAS elements use the following formula to simulate the pull of gravity on the mass projected on the phantom surface from the virtual mass

Ki = Ai * ρ ρ ρ ρ * g

where,



where,

Ki = stiffness of one of the ELAS elements

Ai = area associated with a grid point with

CELAS

rho = density of the liquid

g = acceleration of gravity

Steps involved for sloshing analysis• Note that the phantom surface is a smaller area

(~90%) of the total area of the free surface of the fluid. This is to avoid the singularity that occurs with virtual mass when the fluid volume is totally enclosed with structure. Hopefully the error introduce with this area approximation is slight compared with other errors due to other approximations.

• The phantom surface plate thickness is very small in order to minimize the stiffness added to the system and have no mass



• To calculate the stiffness of the CELAS elements that represent the fluid in gravity, a second static analysis is run that calculates these values for arbitrarily shaped phantom elements. A pressure representing the gravity and density is applied to the phantom surface equal to:

pressure = ρρρρ * g

• Apply this pressure on phantom surface, constrain suitably to stabilize it (Z direction)and run static analysis and the SPCFORCES that result are equal to the value of the CELASs! (-vesign)

Steps (contd)

• Use the positive value of SPCFORCE to create CELAS2

• The ends of the simulated structure are fixed and the phantom surface is only allowed to move in the Z direction.

• complete the structure with MFLUID, ELIST clearly defined

• Note: There is a rule that MFLUID boundary elements may not lie on or above a free surface of the fluid. So,Nastran simply discards any element found on an ELIST that is on or above the surface. There is a tolerance to decide if an element is 'on' the free surface. It is based upon the element's



decide if an element is 'on' the free surface. It is based upon the element's area. SMALL = .01 * SQRT(2. * AREA)

If all grid points of an element are at a distance less then SMALL from the free surface, that element is discarded.

• Ask for MPRES=ALL to get the pressure output on wetted elements.

• Run Normal Modes to get the sloshing effect.

Results



RESULTS

Tank Only - No

Fluid (remove

both Phantom

surface and

MFLUID)

Fluid Only Sloshing - No

Tank (Remove all

structure, keep

Phantom with MFLUID)

Fluid in a Tank - No

Sloshing (Just

Remove PHANTOM

SURFACE)

Sloshing in Tank Filled with

Liquid (Keep Phantom n

MFLUID both)

Mode Tank Fluid Slosh Tank+Fluid Tank Slosh

1 19.00 hz 2.15 hz 4.72 hz 1.37 hz

2 21.62 hz 2.73 hz 6.52 hz 2.37 hz

3 31.28 hz 3.04 hz 6.69 hz 2.67 hz



• The results above indicate that the lower modes are all slosh modes which have been slightly stiffened by the structure. With the exception of the first mode, the eigenvectors show that the structure moves slightly compared to the phantom surface.

3 31.28 hz 3.04 hz 6.69 hz 2.67 hz

4 37.18 hz 3.37 hz 8.56 hz 3.14 hz

5 49.99 hz 3.38 hz 9.17 hz 3.17 hz

6 50.49 hz 3.88 hz 9.89 hz 3.71 hz

7 57.60 hz 4.07 hz 13.84 hz 3.80 hz

8 65.55 hz 4.12 hz 14.65 hz 4.00 hz

9 66.64 hz 4.33 hz 18.57 hz 4.18 hz

10 67.28 hz 4.56 hz 20.63 hz 4.45 hz

ACKNOWLEDGEMENT

• Greatly indebted to Mark Robinson and John Lee from MSC for all their help!! –Ananth Joisa



virtual mass webinar2 - msc software · • therefore, virtual mass is calculated for allgrid...

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