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.

L L

Re 



 





  L 

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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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.

inputs

The basic model of an organ or process is

Organ/Process

outputs

(variables) 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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Example of model: Organs linked to a flat solar thermal collector 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.

TUBES

FINS

Material

GLAZING Ready to use

Cutting

Material

Soldering

Cutting

Gluing

INSULATION

CASING

Material

Material

Cutting

Gluing

Cutting

Soldering

Solar thermal flat panel (some simplifications have been made for the sake of brevity)

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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 Ex materials

Organe/Process

Ex supply

Cv

Ex product Ex bi-product Ex env standard Ex env mixing Ex recycling Exlost(δEx)

Practically applied to an organ:

Ex materials = 80*106 kJ Ex supply = 190 kJ

Casing

Ex product = 76*106 kJ Ex bi-product = 2*106 kJ Ex env standard = 8*105 kJ Ex env mixing = 38 kJ Ex recycling = 1.4 *106 kJ

Exlost(δEx) = 0J

Galina Medyna – 12/11/2010

Three environmental aspects are represented through dimensionless parameters Both 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).

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

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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 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: Exmaterial Exsupply Cmaterial Csupply

Organ/Process

Exproduct Cproduct Gproduct

Exsystem Csystem Gsystem

System

Practically applied to an organ this gives: Exmaterial = 80*106 kJ Exsupply = 190 kJ Cmaterial = 164 € Csupply = 0.121€

Casing

Exproduct = 76*106 kJ Cproduct = 132 € Gproduct = 10

Exsystem = 77*106 kJ Csystem = 1125€ Gsystem = 100

System

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Three economic dimensionless parameters to represent resource management and allocation 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 Galina Medyna – 12/11/2010

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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.

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.

0.14 0.12 0.1 0.08 ΠECD

0.06

ΠGCD

0.04 0.02 0

ΠGCD Glazing

Tubes

Fins

ΠECD Insulation

Casing

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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) Ifailure- probability that the failure will result in the requirement not being met

Ifunction– impact on the working status of the product due to the loss of a function

Iecon = economic costs due to mitigation and function loss This aspect of the tool is still under heavy work and remodelling.

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There are multiple relationships within the variables and their evolution can be observed through the dimensionless parameters Environmental evaluation Material lost

Emissions and impacts

Final product

Unused material in product

Material input

Economic evaluation

Organ cost System cost Function failure impact

Gain

Mitigation cost

Risk evaluation

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.

Galina Medyna – 12/11/2010

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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