2010.11.11 - crecos - medyna

Dimensional analysis for multi-criteria

assessment during the early stages of design

Galina Medyna – 11/11/2010

CRECOS


Why are proper representations needed during the

early stages of design?

Engineering projects cover multiple disciplines and the early phases are key as they

influence a large portion of the final structure and costs.

Although many design aid and assessment tools are available for designers they are

rarely efficiently used. They present shortcomings such as only considering one aspect

or discipline or necessitating data which is not readily available during the early stages.

This is especially true for environmental assessment tools.

Environmental awareness is now required in many products and the best time to take

the environmental impact into account is during the early stages of design.

The proposed dimensional analysis (DA) approach currently has been applied to two

disciplines. Its bases can be applied to further disciplines to widen the scope.

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Dimensional analysis – who? when? where? what? how?

Dimensional analysis is a powerful tool which can be used to describe a

system through base dimensions (e.g. time, length). It has been and still is

used in multiple fields such as fluid dynamics (Reynolds number) and

mathematics (Golden ratio).

Buckingham’s theorem is considered as a basis for DA. Its application and the

creation of pertinent dimensionless numbers (parameters) have been the

subject of many publications. The application of DA outside of the scope of

fields with clear physical dimensions has been slow but there are examples of

meaningful applications. The study of the application of DA to different fields

has also lead to the definition of Reverse Dimensional Analysis for the cases

where the dimensions of a variable is not easily defined.

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Dimensionless numbers hold interesting

properties for an assessment tool

A dimensionless number describes and provides information about a system. The

principle of similitude can be applied to two systems by making and keeping the

dimensionless parameters equal.

Keeping the overall system intact while varying the values of the variables used is

facilitated by keeping the dimensionless parameters constant. This aspect helps corner

the repercussions of the variations of variables and find optimal combinations.

For example, a glance at Reynolds number gives the possible evolutions of variables

without multiple experiments.

Moreover if a system is described with multiple dimensionless parameters containing

common variables, the interactions between the dimensionless parameters can be

studied. This is especially useful is the number of variables is important and to easily

visualise the evolution of the different dimensionless parameters.

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LRe

L L


Dimensionless numbers are everywhere and are

used to describe many aspects of our lives

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Dimensional analysis in different fields

In fields such as physics or chemistry DA uses well known and

defined base dimensions (length, mass, time, etc.) and sometimes

set combinations of these base dimensions (force in Newtons) to

facilitate calculations.

In economy, DA is often used to represent and interpret ratios

(debt/GDP, etc.) but these ratios are not dimensionless. The most

common dimension for DA results is T-1 (years-1).

Risk is only rarely explicitly associated to DA although it is

expressed through ratios such as . The definition of risk

considered in this work (“possibility that a requirement is not met”)

can be simplified, at first, to be limited to two aspects, probabilities

and physics.

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Before the method can be applied, a system needs to

be modeled

In this work we consider a bottom-up approach where each system is composed of organs

and processes. Each of these organs and processes can be described by laws, which, as

enounced by Buckingham, can be written as a combination of dimensionless parameters.

The basic model of an organ or process is

Where the inputs, outputs and variables needed for a full description depend on the field of

study. The definition of the organs and processes depends on the depth of the study.

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Organ/Process

(variables)

outputsinputs


Solar thermal flat panel

Example of model: Organs linked to a flat solar

thermal collector

(some simplifications have been made for the sake of brevity)

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CASING

SolderingCutting

Material

GLAZING

Ready to use

Each organ either comes as a “ready to use” part or needs to be made from provided materials and

processes, as indicated in each bubble.

FINS

Material

Cutting Gluing

TUBES

SolderingCutting

Material

INSULATION

GluingCutting

Material


Environmental assessment through exergy

Exergy – useful work (J – ML2T-2)[the maximum amount of energy which a system of flow can produce when coming while reaching

equilibrium with the environment]

The data needed to fully describe an organ or process is as follows

Practically applied to an organ:

Ex materials

Ex supply

Ex product

Ex bi-product

Ex env mixing

Ex env standard

Ex recycling

Exlost(δEx)

Organe/Process

Cv

Ex supply = 190 kJ

Ex materials = 80*106 kJ

Ex product = 76*106 kJEx bi-product = 2*106 kJ

Ex env mixing = 38 kJ

Ex env standard = 8*105 kJ

Ex recycling = 1.4 *106 kJ

Exlost(δEx) = 0J

Casing


Three environmental aspects are represented

through dimensionless parametersBoth the inputs and outputs in the model proposed measure exergetical data making it possible to

represent ratios easily. The three aspects are the overall exergy conversion efficiency, the efficiency

of material and resource consumption and the environmental impact calculated through the exergy of

mixing (see related publications for full calculations).

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ΠPECE ΠMRCE ΠEIE

Glazing 1 1 0

Tubes 0.93 0.98 ~10-2

Fins 0.90 1 (0.9998) ~10-5

Insulation 0.89 0.99 ~10-3

Casing 0.97 1 (0.999998) ~10-7


Advantages and disadvantages of the proposed

method for environmental evaluation

The exergetical data is more comprehensible than the data available in software

(SimaPro, Gabi, etc.) databases and easily stored. The method does not impose weights

to the calculations thus giving full reign to the user. For the moment, all the calculations

are done by entering the data linked to the raw materials and processes into specific

cells on an spreadsheet thus showing the lightweightness of the calculations.

Unlike for existing large software databases, all the organs and processes have to be

broken down to the chemical compounds. At this point it is the step that takes the most

time as often it is difficult to obtain accurate chemical data. Nevertheless, this approach

has been proven effective to provide orders of magnitude of data that is useful for

comparisons.

The example shown previously was calculated for the components of the solar thermal

flat panel at a certain point of its life cycle. The main differences between the organs and

processes were the amount of material rejected (partly recycled) as well as the

processes through which they are transformed.

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Economic assessment through links to exergy

and cost drivers

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The proposed approach both assesses the performance of a single organ or process

and the whole system through three dimensionless parameters.

The data needed to fully describe the organ/process and system are:

Practically applied to an organ this gives:

Exproduct

Cproduct

Gproduct

Exmaterial

Exsupply

Cmaterial

Csupply

Organ/Process

System

Exsystem

Csystem

Gsystem

Exproduct = 76*106 kJ

Cproduct = 132 €

Gproduct = 10

Exmaterial = 80*106 kJ

Exsupply = 190 kJ

Cmaterial = 164 €

Csupply = 0.121€

Casing

System

Exsystem = 77*106 kJ

Csystem = 1125€

Gsystem = 100


Three economic dimensionless parameters to

represent resource management and allocation

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The first dimenionsionless parameter takes into account both how the material and resources are used

to make the product and how much is invested in them. The closest the parameter is to 1, the less

losses can be expected from the product.

The two other dimensionless numbers both study cost drivers (section of a project which benefits from

high investments, generally justified by the high functional important of the section). One approach is

through raw material and one is through the gain expected to come from the organ/process. These

ratios should, ideally, be in the same magnitude order which is not the case with the data found for the

flat solar thermal panels.

ΠExC ΠECD ΠGCD

Glazing 1 ~10-5 ~10-1

Tubes 0.78 ~10-6 ~10-1

Fins 0.72 ~10-4 ~10-2

Insulation 0.74 ~10-7 ~10-3

Casing 0.75 ~10-1 ~10-2


Advantages and disadvantages of the proposed

method for economic assessment

The economic approach presented allows us to connect the data from environmental

study and basic economic data for each organ. The ratios provide information on the

repartition of costs in the project.

The cost data necessary for the calculations can be easily found at a company level, it is

more complicated for strictly academic studies. The expected gain from each organ has

been estimated based on experience, showing that the method still relies heavily on the

background of the users.

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GlazingTubes

FinsInsulation

Casing

ΠECD

ΠGCD0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

ΠECD

ΠGCD

The two cost driver parameters are

intended to be compared. As shown in the

graph on the right, they extend over quite

a large range for this analysis.


Risk assessment through probabilities and physics

Risk – « possibility that a requirement is not met».This vision of risk is one of many but it suits design projects. A review of the linked

literature has shown that multiple aspects should be considered such as loss of funtions,

mitigation, etc.

The definition of the variables linked to risk (and the other aspects mentioned previously)

is not complete yet. The general appearance of the risk representation through

mitigation appears to mainly rely on the following parameters:

Imitigation = f(Iecon, Ifailure, Ifucntion)

This aspect of the tool is still under heavy work and remodelling.

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Ifunction– impact on the

working status of the product

due to the loss of a function

Ifailure- probability that the failure will

result in the requirement not being

met

Iecon = economic costs due to mitigation

and function loss


Environmental evaluation

Economic evaluation

There are multiple relationships within the variables and

their evolution can be observed through the dimensionless

parameters

Material input

Final product

Material lost

Unused material in product

Emissions and impacts

Risk evaluation

System cost

Organ cost

Gain

Mitigation costFunction failure

impact

The evolution of one variable brings on

changes in other variables. Observing

their behavior through the dimensionless

parameters can help predict the changes

and indicate further actions.


The main aim of the work is to propose a tool which

integrates multiple aspects of engineering projects thanks

to dimensional analysis

For the moment the framework has been applied to two aspects with the environmental

evaluation being in the center. Through the bases of dimensional analysis and given the

current explorations in the application of dimensional analysis to different domains, the

expansion of the tool is a goal for the future.

The main limiting factor as of today is the data necessary, once it is collected the

calculations are quick and the results can be easily compared.

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2010.11.11 - crecos - medyna

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