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Experimental and Modeling
Skills
Prof. Sarit K. Das
Department of Mechanical Engineering
Indian Institute of Technology Madras
Can/should research methodology /
experimental skills be taught by giving
lectures?
No, because
 These are arts and experiences.
 They are diverse.
Yes, because
 Even art has a grammar.
 There are commonalities.
 It serves as a guidance to the research scholar.
Jokes about Experiments
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“When you do not know what you are doing, do
it neatly.”
“Team work is essential. It always allows you to
blame someone else.”
“If reproducibility may be a problem, conduct
the test only once.”
“If a straight line fit is required, obtain only two
data points.”
“If an experiment works, something has gone
wrong.”
“If enough data is collected, anything may be
proven by statistical methods.”
Why should we do experiments at all?
• To know the truth.
• To get insight into the physics.
• To determine the unknown factors responsible.
• To test a theory.
• To facilitate simulation/modeling work.
(eg. use of experimentally determined unknown
constants in turbulence modeling)
Planning
• Defining aim/objective of the experiments
(but remain flexible)
• Scope of the work
(research is infinite but requirement of a
research degree is limited – Dr. Sahoo)
• Defining the parameters you are looking at.
• Broadly decide the approach
(e.g., theoretical, experimental, both, numerical)
Design
• Working out the best possible design with all the
constraints you have got.
• Inputs from literature and suggestions from the
technicians.
• Changing design at a later stage may be very
costly in terms of time and money.
• In case of a new design, trial and error method
is the only option.
(eg. Heater-thermocouple design.)
Fabrication
• Making thorough enquiries to find a potential
fabricator/supplier with good expertise in the
relevant area.
• Following proper order in steps/stages involved
in fabrication with parallel efforts so as to
minimize the time.
• Maintaining the healthy relationship with the
fabricator to get the best out of him. Respect
the technicians, you can learn from them what
you cannot learn from your Professor.
Points to remember in instrumentation
While choosing the instruments, attention has to
be paid to:
• Accuracy
• Precision
• Range
• Response time
• Least count
• Cost
Calibration and error analysis
• Principles of transducers.
• Calibration of the equipment with a standard
device.
• Systematic errors and random errors (Lord
Rayleigh).
• Number of variables and error estimation
principle statistically.
• A realistic approach towards accuracy.
Validation of the experimental set-up and results with
benchmark results from literature.
Running the experiments
• Before running the experiments, make sure that all the
components/ connections/loops/circuits are proper.
• Make a measurement protocol with date and specific
conditions. Do not forget to specify atmospheric
conditions if they are important.
• Carry out the experiments according to the laid-out
procedure.
• Monitor all the components and devices for possible
fluctuations/deviations from the set values while
experiment is in progress.
• After few experiments try to explain your results and
then proceed further.
Safety measures
Do not compromise on safety aspect. All the possible precautions are
to be taken. Some of them are:
• Goggles/Masks/Helmets/Gloves/Apron while doing experiments with
poisonous/ hazardous chemicals, applying silicone sealants, dealing
with extremely fine powder.
• Safety valves/ safety meshes while doing high pressure glass vessel
experiments. (Prof. RN)
• Sound guards in case of wind tunnel experiments. (Prof at ME).
• Utmost care (shock-proof gloves and shoes) while doing high
voltage experiments.
• Fire extinguisher a must for all experiments.
• Care and ethical issues in handling biological samples and living
animals.
Analysis of the experimental results
• Sufficient number of data points.
“ Between three data points, any curved profile
can be fit”
• Consistency and repeatability (precision).
• Accuracy
• Look at the results in unbiased way or with out
any prejudice. (eg. Nano-boiling)
….contd.
• Keen observation of the data.
(eg. Becquerel) …. experiments with frogs
(Galvany) etc….
• Honesty- Don’t ‘MOVE’ your experimental points
so as to match with theory. Leave them as they
are. An explanation may be there.( Positron at
Saha Institute,Fynmann)
• Changing the course of the experiments
depending on the results.
Documentation/communication of the
results
• All the results are to be documented
irrespective of the nature/use as these may be
of use later. (eg. Pressure drop -Prabhakar).
• Communicating the results to
journals/conferences is not just for publication,
but also to get comments/ suggestions/reviews
from international community which will be of
much help in your research.
Mental Frame
• Pride and modesty
• Avoid frustration have patience and perseverance.
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Never give up (Edison).
Be relaxed and appreciate difficulties (Heater).
Stay focused (Arjuna).
Be flexible in approach (Frank and me- temp.
measurement).
Be honest (Fermi / IISc. Scholar).
Always have a mental picture of your experiments
going right (even in dream or toilet).
Avoid postponement.
……some more
• Discipline, sincerity, punctuality but freedom and
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informality promotes creativity.
Interaction with your friends – Help each other
without jealousy/envy.
Be fully prepared for the unforeseen problems.
Requires few months to few years of preparation
to get results in no time.
It is in journey or in efforts that true
satisfaction/happiness lies, not in reaching goal.
Besides helping you in getting
publications, degree, and a job, what do
experiments teach you in life?
 Skill of planning.
 Hope.
 Patience.
 Art of management.
 Broad outlook.
 Pleasure of getting to a truth
Mathematical Modeling
Why mathematical modeling?
• To understand the behaviour of systems
• To obtain optimal designs/ operational
conditions
• To analyse critical or failure scenarios where
experiments are not possible (Nuclear / Rockets
etc.,)
• To obtain variation of parameters in details like
the complete field (flow /thermal/electric)
Modeling Methods
• Order-of-magnitude & Dimensional analysis
• Overall system level models (Steady/ transient)
Lumped/Assembly (Fuel cells)
• Simplified 1-D/ 2-D models
• Fully comprehensive transient, 3-D models
• Heuristic /statistical models
Types of Solutions
• Closed form analytical solutions
• Asymptotic solutions (perturbation solutions)
• Numerical solutions
• Heuristic solutions
Example- understanding phenomena
• Failure of Takoma bridge
• The vortex shedding frequency of wind flow
matched with the natural frequency of the
suspension bridge
• Failure occurred by torsional vibrations -
resonance with vortex shedding
• It is possible to carry out a detailed dynamic
anaylsis of the bridge structure using FEM and the
natural frequencies can be predicted
Example- Optimisation
•Consider a projectile with initial velocity
Vo and projected angle ‘a’
•Vertical distance travelled
y = (Vo sina)t - ½ gt2
• Horizontal distance x = (Vo cosa)t
• When projectile hits the ground, y = 0. In other words, tmax
= (2Vo sina)/g
• The maximum horizontal distance travelled
= xmax = (Vo2 sin2a)/g
For given Vo the range is maximum for a = 45o
Order of Magnitude Analysis
• Consider a water drop of 1 mm
diameter falling in air. We want to get
the terminal velocity of the drop
Drag force = CD.(½ rair V2). pd2/4
• At terminal velocity,
drag on drop = weight of the drop
• Drag force = CD.(½ rair V2). pd2/4
• Weight
= rwater.(pd3/6).g
• Taking rair= 1 kg/m3, rwater = 1000
kg/m3 , g = 10 m/s2 and CD= 0.5, we
get V = 2.58 m/s. This is a typical
velocity for a falling droplet
Weight
= rwater.(pd3/6).g
Order of Magnitude Analysis
• If we want to see whether a falling drop of 1 mm
will be distorted, the analysis can be done as
follows.
• Inertial force ~ drag force ~ (½ rair V2). pd2/4
• Surface tension force ~ (4s/d). Pd2
• The non-dimensional number called Weber
number We = (rair V2d/s) = (inertia/ surface
tension) determines whether a drop will be
distorted from spherical shape or not.
Dimensional Analysis
• This helps in constructing laboratory scale models
which can simulate the situation of the actual
prototype
• By testing an aircraft model at the same Reynolds
number and Mach number as the actual
prototype, wind tunnel studies can give valuable
data for the actual aircraft
• Reynolds number = (inertial force/ viscous force)
• Mach number = (fluid velocity/ velocity of sound).
The Mach number characterizes the effects due
to compressibility in a flow.
Dimensional Analysis
• With the help of non- dimensional parameters, a
large number of experimental data can be
reduced and correlated in terms of the
dimensionless numbers
• For example, the drag coefficient CD = f(Re) for
any low speed flow over an object of given
shape
Dimensional Analysis
Renowned British scientist G.I. Taylor was told by the British
government about the development of the atomic bomb and was asked
to think about the mechanical effect produced by such an explosion.
Taylor using dimensional analysis gave the radius of the shock wave at
any time t as
1/5
E
R  C 

t 2/5
System Level Simulation
• For a mass-spring- damper system, the governing
equation is
mx  Bx  kx  F (t )
• Similarly, for an electrical system (inductor L,
resistance R and capacitor C)
1
Lq  Rq  q  E (t )
C
System Level Simulation
• The governing equations can be solved
exactly for simple linear systems and the
dynamic behaviour of the system can be
predicted
• The frequency of oscillations for the system
and the possibility of resonance leading to
system instability can be predicted
Computational Modeling
• Computers and numerical techniques have
witnessed phenomenal growth
• Compared to experimental analysis which
may
be
expensive,
computational
simulation has become an economic
alternative
Applications of
computational modeling
• Aerospace vehicles
• Automobiles
• Power generation
• Manufacturing technology
• Structural designs
• Environmental pollution
Steps involved in modeling
• Creation of the geometry
• Division of the geometry into a computational
mesh
• Application of mass balance, force balance and
energy balance principles to small computational
cells
• Solution of variables such as velocity, pressure,
density, temperature, stresses, displacements
etc. At various points in the geometry
Steps involved in modeling
• Pre-processing (creation geometry & mesh and
application of boundary conditions)
• Analysis (solution of governing equations)
• Post-processing (estimation of desired
quantities- say, heat transfer from prediction of
temperature, etc.)
Aircraft Model
Launch vehicle
Modeling Methods
• Finite Difference Method
• Finite Volume Method
• Finite Element Method
• Boundary Element Method
• Spectral Method
Artificial Intelligence Tools
• Many non-deterministic search methods are
available for the development of expert
systems and artificial intelligence tools
• These search methods have great utility for the
solution of practical engineering problems
which are difficult to solve because of the
enormity, complexity, non- linearity and
uncertainty involved. They provide quite useful
solutions with very little effort.
Non-deterministic search methods
• Fuzzy sets and Fuzzy logic
• Artificial Neural Networks
• Genetic Algorithms
• Simulated Annealing
Illustrations
Modeling of biological heat transfer
Thermal profile of tumor (laser ablation):
experimental and model
Photothermal Tumor Destruction
Thermal profile of tumor
(magnetic ablation) : model
Thermal history of tumor : experimental
and model
Modeling of Two-Phase Flow
Rayleigh -Taylor Instability
Transient Evolution of Film
Liquid Falling Film on an Inclined Surface
Non dimensional film thickness,
β0 = 1.26
β=
Local film thickness
Fully developed film thickness
β0 = 2.63
Before you begin modeling…..
• Understand the limitations – “as the model so are the
solutions”. Model can simulate only the physics that you
have considered through mathematical equations
(channel vs micro-channel and surface tension).
• Beware of your assumptions and boundary conditions
(continuum / no-slip / constant property etc.,)
• Cannot replace experiments fully. Can only reduce the
number of experiments.
• Always look for proper validation and accuracy
What is important in research?
• Whether you are doing experiment or modeling
your aim is to reveal THE TRUTH not some
degree or publication. Those you get incidentally.
• The method is not more important than the
problem unless you are developing the method
itself.
• Always look for novelty in research. Analysis is
important to prove an idea but the idea is more
important than that. Hence spend more time at
your table than computer terminal or laboratory.
Thank You
Prof. Sarit Kumar Das
Professor, Mechanical Engineering
[email protected]
: +91-9500072602