What do I mean? Issue trees Hypothesis trees Experimental design

Matthew [email protected]

What do I mean?

Issue trees

Hypothesis trees

Experimental design

Hypothesis-driven and Investigative Experimental Design

Dr. Matthew Juniper, CUED


Experiments

Investigative

Hypothesis-driven


What do I mean?


Experiments

Investigative

Hypothesis-driven

Examples

Millikan's oil drop experiment to determine the charge on the electron (1909)


Millikan's oil drop experiment (1909)


Charge on the electron = 1.592 x 10-19 Coulombs




Charge

Year1909




Charge

Year

1.602 x 10-19

1909



Experiments

Investigative

Hypothesis-driven

Examples

Michelson-Morley experiment to determine the speed of the earth through the Aether (1887)



Michelson-Morley experiment (1887)


Speed of the earth through the Aether = .... very small !

Michelson-Morley experiment (1887)


Experiments

Investigative

Hypothesis-driven

Examples

Michelson-Morley experiment to determine the speed of the earth through the Aether (1887)



Experiments

Investigative

Hypothesis-driven

Examples

Michelson-Morley experiment to determine the speed of light in different reference frames


Light travels at the same speed in any frame of reference


What do I mean?

Issue trees

Hypothesis trees

Experimental design


Contents


Issue Tree

Open question

What ? or How ?

Issue 2

Issue 1

Issue 3

Sub-issue 1b

Sub-issue 1a

Sub-issue 1c

Sub-issue 2b

Sub-issue 2a

Sub-issue 2c

Sub-issue 3b

Sub-issue 3a

Sub-issue 3c

Precise issue

Issues are independent

and complete

Precise issues can be tested by

hypothesis

Issue trees


What ? or How ?

What can we do about climate change ?

Issue trees – an example


What influences the re-light and light-round characteristics of an aeroplane engine

the state of the fuel / air mixture in each burner

aero-dynamics

the introduction of energy to the fuel / air mixture in each burner

reactant properties

the design of the network of burners in the engine The order in which

they are turned on

The distance between burners

position of sparktype of spark

Issue Tree applied to an engineering problem

What ? or How ?

energy of sparkduration of spark

timing of spark

burner face

down-stream

compositiontemperaturepressurecompositiontemperaturepressurepilot / main flame configuration

flow shear at injection point

oxidant

fuel

position of cooling airvelocity of cooling air

burners

spark

Axial view of combustion chamber in an aeroplane engine


What do I mean?

Issue trees

Hypothesis trees

Experimental design


Contents


Primary hypothesis

Why?

Secondary hypothesis 2



Tertiary hypothesis 1b

Tertiary hypothesis 1a

Tertiary hypothesis 1c







All the secondary hypotheses must be true for the primary

hypothesis to be true

All hypotheses must be precise

statements

Statement 3c(i)Statement 3c(ii)

or

Hypothesis trees


Why?

I can make money by blackmailing someone.

Hypothesis trees - example


Hypothesis 1 Secondary Hypothesis Analysis

The concepts of Absolute Instability, Convective Instability and Global Instability apply to flames in the same way that they do to non-reacting flows.

Some flames exhibit self-excited periodic global oscillations.

Strong spectral peaks appear in the PSD of velocity, pressure, and/or high-speed imaging (schlieren and/or OH* emission).

The limit-cycle amplitude of globally unstable flames increases in proportion to the deviation of some control parameter – this is characteristic of a Hopf bifurcation. The control parameters may include the Reynolds number, shear layer thickness, confinement, density ratio, and co-flow/counter-flow (i.e. Λ).

A globally unstable flame is first setup. Co-flow is then introduced gradually until the flame becomes stable; we adopt the 50% intermittency criteria (see Maxworthy; JFM (390) 1999) for objectiveness in establishing the critical co-flow velocity. By varying the co-flow velocity around its critical value and plotting the corresponding limit-cycle amplitude1 at the flame’s base, we can detect the onset of a Hopf bifurcation.

We repeat the above procedure at different Reynolds numbers, density ratios, and confinements.1The limit-cycle amplitude can be measured using schlieren imaging (edge-detection), chemiluminescence (OH* heat release proxy), LDV (local velocity), and/or high-speed PIV (whole-field velocities).

When forced periodically at frequencies different from its natural mode, a globally unstable flame locks-in only above a critical forcing amplitude, which is proportional to │ff

− f0│.

Low-amplitude fixed-frequency sinusoidal forcing is applied to the inner and/or outer flow of a globally unstable flame. The global mode should be more sensitive to outer forcing because the high viscosity, low density layer at the flame shields perturbations in the inner flow from the outer buoyant plume, from which global instability arises. As the forcing amplitude increases, the flame eventually locks-in to the forcing, as indicated by a complete suppression of the natural mode in the PSD of OH* emission, edge-detection (schlieren), and/or local velocity (LDV). If we plot the critical forcing amplitude against the forcing frequency, a V-shaped plot is expected centred around the natural global mode.

We repeat the above procedure for flames with different degrees of global instability, and should observe a change in the slopes of the V in the plots.

A convectively unstable – but globally stable – flame remains stationary unless forced, in which case it responds at the forcing frequency.

A globally stable – almost everywhere convectively unstable, but no self-excited mode – flame is setup. When fixed-frequency variable-amplitude forcing is applied to either the inner or outer flow, the flame’s response amplitude should be proportional to the forcing amplitude, provided the latter is small (i.e. within the linear regime).

We repeat the above procedure for a range of forcing frequencies, enabling the construction of transfer functions (scaled flame response vs. forcing frequency).



The concepts of Absolute Instability, Convective Instability and Global Instability apply to flames in the same way that they do to non-reacting flows.

Some flames exhibit self-excited periodic global oscillations.

Strong spectral peaks appear in the PSD of velocity, pressure, and/or high-speed imaging (schlieren and/or OH* emission).

The limit-cycle amplitude of globally unstable flames increases in proportion to the deviation of some control parameter – this is characteristic of a Hopf bifurcation. The control parameters may include the Reynolds number, shear layer thickness, confinement, density ratio, and co-flow/counter-flow (i.e. Λ).

A globally unstable flame is first setup. Co-flow is then introduced gradually until the flame becomes stable; we adopt the 50% intermittency criteria (see Maxworthy; JFM (390) 1999) for objectiveness in establishing the critical co-flow velocity. By varying the co-flow velocity around its critical value and plotting the corresponding limit-cycle amplitude1 at the flame’s base, we can detect the onset of a Hopf bifurcation.

We repeat the above procedure at different Reynolds numbers, density ratios, and confinements.1The limit-cycle amplitude can be measured using schlieren imaging (edge-detection), chemiluminescence (OH* heat release proxy), LDV (local velocity), and/or high-speed PIV (whole-field velocities).


− f0│.

Low-amplitude fixed-frequency sinusoidal forcing is applied to the inner and/or outer flow of a globally unstable flame. The global mode should be more sensitive to outer forcing because the high viscosity, low density layer at the flame shields perturbations in the inner flow from the outer buoyant plume, from which global instability arises. As the forcing amplitude increases, the flame eventually locks-in to the forcing, as indicated by a complete suppression of the natural mode in the PSD of OH* emission, edge-detection (schlieren), and/or local velocity (LDV). If we plot the critical forcing amplitude against the forcing frequency, a V-shaped plot is expected centred around the natural global mode.

We repeat the above procedure for flames with different degrees of global instability, and should observe a change in the slopes of the V in the plots.

A convectively unstable – but globally stable – flame remains stationary unless forced, in which case it responds at the forcing frequency.

A globally stable – almost everywhere convectively unstable, but no self-excited mode – flame is setup. When fixed-frequency variable-amplitude forcing is applied to either the inner or outer flow, the flame’s response amplitude should be proportional to the forcing amplitude, provided the latter is small (i.e. within the linear regime).

We repeat the above procedure for a range of forcing frequencies, enabling the construction of transfer functions (scaled flame response vs. forcing frequency).


amplitude of forcing signalampl

itud\

e of

resp

onse


Hypothesis 1.4

Conv. Unst. flame


itud\

e of

resp

onse Abs. Unst. flame



itud\

e of

resp

onse


Hypothesis 1.4

Conv. Unst. flame


itud\

e of

resp

onse Abs. Unst. flame

Experimental results


Hypothesis 2 Secondary Hypothesis Tertiary Hypothesis

We can predict the conditions under which a flame exhibits self-excited global oscillations.

Global instability is caused by large regions of AI upstream.

Strong experimental evidence accumulated over the past three decades.

Pier’s analysis.

Regions of AI in a flame can be predicted from the velocity and density profiles.

The velocity and density profiles can be obtained theoretically (e.g. based on equilibrium chemistry), numerically (e.g. FLUENT® simulations), and/or experimentally (e.g. LDV, PIV, and thermocouple measurements).

Reliable tools are available to map regions of AI/CI based on input from velocity and density profiles (i.e. theoretical techniques developed by MPJ and SJR).

Global instability can be confirmed in an experimental flame.


− f0│ (see analysis in Hypothesis 1).

AND/OR...

The limit-cycle amplitude of globally unstable flames increases in proportion to the deviation of some control parameter – this is characteristic of a Hopf bifurcation (see analysis in Hypothesis 1).



Presence of global instability in a flame can reduce its ability to couple with surrounding acoustic modes.

The concepts of AI, CI and global instability can be applied to flames. Refer to analysis in Hypothesis 1.

For a given forcing amplitude, the heat released at the forcing frequency is lower for a globally unstable flame than it is for a convectively unstable flame.

Fixed-amplitude forcing: We compare, between globally unstable and convectively unstable flames, the areas under the PSD of OH* emission at a common forcing frequency.

Simulated “self-excited” forcing: The signal from a photomultiplier tube (PMT) aimed at the flame body drives the amplitude of loudspeaker forcing (either in the inner or outer flow). The forcing frequency, meanwhile, can be varied around the natural global mode. We again compare, between globally unstable and convectively unstable flames, the areas under the PSD of OH* emission at a common forcing frequency.

A physical resonance pipe cannot be used to force the flow because it would have to be impractically long to excite frequencies on the order of the flame flicker (~10 Hz for a jet diffusion flame).

We expect the convectively unstable flame to be sensitive to nearly all simulated “natural acoustic frequencies”. We expect the globally unstable flame to respond significantly only to simulated forcing that is at a frequency near the natural global shear mode. Such a distinction is illustrated in the transfer functions below.



A globally unstable flame mixes more quickly than a convectively unstable flame.

At equivalent fuel flow rates, a globally unstable flame releases more heat near the nozzle than a convectively unstable flame.

Without varying the fuel stream’s composition or flow rate, we generate in turn two flames: a globally unstable flame and a convectively unstable flame. High-speed OH* emission imaging provides the spatial distribution of heat released by each flame. Hence, by plotting the section-averaged OH* intensity as a function of downstream distance, we should see that the globally unstable flame releases more heat near the nozzle than the convectively unstable flame.

1) We produce a marginally globally stable flame, without co-flow, by diluting CH4 , H2 , C3H8 and/or their mixtures with inert gas(es) in order to shift the flame closer to the shear layer (i.e. towards the centreline). We then apply low-amplitude forcing to the flame in order to trigger a global mode. Because the fuel input into the two flames is equal, the total heat output should also be roughly equal, thus justifying our use of heat release (OH* proxy) as an indicator of mixing performance.

2) We produce a globally unstable flame (no co-flow or forcing) – a relatively straightforward task. We then apply air co-flow to suppress the global instability and thus produce a convectively unstable flame. What about the increase in molecular diffusion due to the fresh co-flow air? Also, what about the reduced entrainment due to the reduced relative velocity at the jet/surrounding interface?


What do I mean?

Issue trees

Hypothesis trees

Experimental design


Contents


What ? or How ?

Application to experimental design

1. Start with an issue tree (ask 'what?' or 'how?') e.g. • What questions do I have?• What do I want to show?• What is my PhD about?

2. For each sub-issue, think of an investigative experiment. Then ask 'so what?' – does this tie in with a theory?

3. For each relevant sub-issue, develop a hypothesis tree (ask 'why?' or 'what has to be true for this hypothesis to be true?') Develop the analysis to test the sub-hypotheses.

Why?

So what ?

Documents

What do I mean? Issue trees Hypothesis trees Experimental design